STRUCTUREOFACIDCASEINGELS
Astudyofgelsformedafteracidificationinthecold
CENTRALELANDBOUWCATALOGUS
000001463088
Promotor:
Co-promotor:
dr.A.Prins,
hoogleraar in de fysica ende fysische chemievan
levensmiddelen, met bijzondere aandacht voor de
zuivel
dr.ir.T.vanVliet,
wetenschappelijk hoofdmedewerker
?OMO^Q\,(o^b
SebastianusP.F.M.Roefs
STRUCTUREOFACIDCASEINGELS
Astudyofgelsformedafteracidificationinthecold
Proefschrift
terverkrijgingvandegraadvan
doctorindelandbouwwetenschappen,
opgezagvanderectormagnificus,
dr.C.C.Oosterlee,
inhetopenbaarteverdedigen
opvrijdag 11april1986
desnamiddagstevieruurindeaula
vandeLandbouwhogeschool teWageningen
ISW* iL/c/gyy-
BïBT.IOTTIT^r
'OF?-
f* ^o??o\
STELLINGEN
1.
Hoewel c a s e ï n e ' s macromoleculen z i j n , g e d r a a g t een zuur c a s e ï n e g e l z i c h fenomenologisch a l s een d e e l t j e s g e l .
Dit proefschrift.
2.
Rond pH=5,2 v e r a n d e r t h e t k a r a k t e r van m e l k e i w i t g e l e n a a n zienlijk.
Dit proefschrift.
3.
Bij h e t onderzoek n a a r de m i c r o s t r u c t u u r en de s t e v i g h e i d
van s t a n d y o g h u r t en op s t a n d y o g h u r t g e l i j k e n d e systemen
wordt t e w e i n i g a a n d a c h t geschonken aan fundamentele paramet e r s als caseïneconcentratie, ionsterkte, ionsamenstelling
en v e r o u d e r i n g s t i j d .
Taraime, A.Y., Kalab, M. and Davies, G. (1984). "Microstructure of setstyle yoghurt manufactured from cow's milk fortified by various methods".
Foodmicrostructure 3, 83-92.
Harwalkar, V.R. and Kalab, M. (1981). "Effect of acidulants and temperature on microstructure, firmness and susceptibility to syneresis of skimmilk gels". Scanning Electron Microscopy, 1981; I I I , 503-513.
4.
Bohlin e t a l . hebben t e n o n r e c h t e geen r e k e n i n g gehouden met
de i n v l o e d van de pH op de g r o o t t e van de dynamische moduli
van met s t r e m s e l b e r e i d e ondermelkgelen.
Bohlin, L., Hegg, P.-O. and Ljusberg-Wahren, H. (1984). "Viscoelastic
properties of coagulating milk". J. Dairy Sei. 67, 729-734.
5.
Bij de i n t e r p r e t a t i e van h e t v e r l o o p van de d r u k v a l b i j s t r o ming door poreuze media g e b r u i k t Ghoniem een k e n g e t a l ,
w a a r i n h i j de v e r b l i j f t i j d van h e t polymeer o n j u i s t i n r e kening b r e n g t .
Ghoniem, S.A.-A. (1985). "Extensional flow of polymer solutions through
porous media". Rheol. Acta 24, 588-595.
^
6. De eigenschappenvanbierschuim, zoals stabiliteitenhechtvermogenaandeglaswand, kunnenpasfysischgeïnterpreteerd
worden als de relevante reologische oppervlakte-eigenschappenbekendzijn.
Bamforth,C.W. (1985). "The foaming properties of beer". J. Inst.Brew.
91,370-383.
7. Hetnadenken overdebetekenis vaneenzwichtspanningzonder
datdebijbehorendetijdschaalbekendis,isverlorentijd.
8. Veellevensmiddelenbrekeninrekalsmeneropdrukt.
9. Het verschil tussen eengoede eneen slechte advokaat isaf
telezenaanhetgedragondergeringestress.
10. Delangstepolymeermoleculentrekkenaanhetkortsteeindje.
11. Voor eenverantwoord gebruikvanmedicijnenindeintensieve
veehouderij ishetvanbelang datdehonoreringvan deveeartsenwordtlosgekoppeldvandeverkoopvanmedicijnen.
12. LievereengoeddialectdanslechtNederlands.
SebastianusP.F.M.Roefs
STRUCTUREOFACIDCASEINGELS
Astudyofgelsformedafteracidificationinthecold
Wageningen,11april1986.
Voor mijn ouders
ABSTRACT
Roefs,Sebastianus,P.F.M. (1985). "Structureofacidcaseingels;
a study of gels formed after acidification inthe cold".Ph.D.
Thesis, Laboratory of Dairying and Food Physics, Agricultural
University, Wageningen. 209+9 pages, 68 figures, 11 tables.
EnglishandDutchsummaries.
Thestructureofacidcaseingelswasstudiedbyrheology,permeametry, electron microscopy and pulse NMR. Gels were mainly
formed by heating at rest of casein solutions acidified in the
cold (0-2°C).The structure of such gels involvesboth thespatial distribution of the structural elements and the interaction
forces between them.An acid casein gelhas an irregularparticulate structure. Gelation results from the aggregation ofcasein
particles,which themselves have acomplexinternalstructuredue
to the association ofnumerous different caseinmolecules.Dense
areas ofcoagulated particles are separatedbylargepores.Gelation at pH=4.6 appears to be subject to an activationHelmholtz
energy, which is largely due to the stabilizing effect of the
glycomacropeptide part of K-casein. At ageing temperatures above
283K, the dynamic moduli G' and G" linearly increase with the
logarithm of time.Their absolute values primarily depend onthe
heterogeneity ofthenetwork.Themodulidecreasewithincreasing
time scale ofmeasurement. From the effect ofvariation ofexperimental conditions (pH,ageing andmeasuringtemperatures,ionic
strength and ionic composition)itmaybeconcludedthatelectrostatic interactions andhydrophobic bonding areinvolvedinkeeping the network together. Moreover, Vander Waals attraction,
steric interactions andpossibly hydrogenbonds mayplay apart.
Differences inthe internal structure ofthecaseinparticlesappear tobeparamount indeterminingdifferences inthenumberand
character of the interparticle bonds;thiswas in agreementwith
results on the spin-spin relaxation time ofwater protons.Addition of rennet enables gel formation in amuchbroader rangeof
temperature and pH; the character of the gels changesconsiderablyaroundpH=5.2.
CONTENTS
Page
1 INTRODUCTION
1.1 Acidcaseingels
1.2 Casein
1.3 Outlineofthisstudy
2 MATERIALSANDMETHODS
2.1 Skimmilkpowder
2.2 Sodiumcaseinatesolutions
2.3 Acidificationandgelation
2.4 Whey
2.5 Varyingproteinconcentrationbyultrafiltration
2.6 Gelelectrophoresis
2.7 EstimationofsplittingofK-casein
2.8 Permeabilitymeasurements
2.8.1 General
2.8.2 Thetubemethod
2.9 PulseNMRmeasurements
2.10 Rheologicalmeasurements
2.10.1 Dynamicmeasurements
2.10.2 Measurementofacidcaseingels
2.10.3 Stressrelaxationmeasurements
2.10.4 Creepmeasurements
2.11 Electronmicroscopy
2.12 Solubilityofcasein
2.13 Particlesizemeasurement
3 FORMATIONOFACIDCASEINGELS
3.1 Introduction
3.2 Formationandageingofacidcaseingels
3.2.1 Ageingofacidskimmilkgels
3.2.2 Irreversiblecharacterofgelformation
3.2.3 Skimmilkgelsmadebyrapidheating
3.2.4 Differentkindsofacidcaseingels
3.3 Changesduringcoldacidificationofcasein
3.3.1 Introduction
1
1
3
7
9
9
9
11
13
13
13
14
14
14
15
17
18
19
21
22
23
24
25
27
29
29
30
30
33
34
35
37
37
3.3.2
3.4
Coldacidificationofskimmilk
39
3.3.2.1 Solubility ofcaseinatlow
temperature
40
3.3.2.2 Caseinparticlesize
41
3.3.2.3 Electronmicrographsofskimmilk
44
3.3.3 Coldacidificationofsodiumcaseinate
solution
46
3.3.4 Discussion
48
Networkmodel foracidcaseingels
50
3.4.1 Generaldescriptionofpossiblemodels
50
3.4.2 Experimental results
54
3.4.2.1 Storagemodulusasafunction
ofcaseinconcentration
54
3.4.2.2 Electronmicrographsofacid
caseingels
57
3.4.2.3 Permeabilityofacidcaseingels
60
3.4.3 Discussion
64
3.4.3.1 Schematicrepresentationof
anacidcaseingel
65
3.4.3.2 Comparisonofthemeasured
permeabilitywiththatofsome
geometricmodels
67
RHEOLOGICALCHARACTERIZATIONOFACIDCASEINGELS
4.1 Introduction
4.2 Rheologicalmeasurements
4.3 Interpretationofrheologicaldata
4.3.1 Relaxationspectrum
4.4 Interactionforcesinacidcaseingels
4.4.1 Hydrophobicbonding
4.4.2 VanderWaalsattraction
4.4.3 Electrostatic interactions
4.4.4 Hydrogenbonds
4.4.5 Stericinteractions
4.5 Experimental results
4.5.1 Introduction
4.5.2 Thedynamicmoduliasafunction
oftemperature
72
72
73
76
79
80
81
81
82
83
84
84
84
86
4.5.3
4.5.4
4.6
4.7
Variationwithmeasuringtemperature
88
Dynamicmoduliofacidskimmilkgels
asafunctionofpH
97
4.5.5 Variationwithioniccomposition
100
4.5.5.1 Roughestimateofionicstrength
ofacidskimmilk
100
4.5.5.2 TheeffectofaddedNaClon
acidskimmilkgels
103
4.5.5.3 TheeffectofNaClandCaCl2
onacidsodiumcaseinategels
107
4.5.6 Relaxationspectraofacidskimmilkgels
111
4.5.6.1 Computationoftherelaxation
spectrumandofasemi-permanent
networkmodulus
113
4.5.6.2 Thevalueofapseudo-stress
relaxationmodulusatlongtime
scales
115
4.5.7 Creepmeasurements
118
Estimationofthemodulusofastrandof
particles
120
Discussion
123
THESTRUCTUREOFCASEINGELSMADEBYACIDIFICATIONAND
RENNETACTION
128
5.1 Introduction
128
5.2 Proteolytic action
130
5.3 Resultsanddiscussion
132
5.3.1 TheeffectofrennetatpH=4.6
133
5.3.2 TheeffectofrennetatvaryingpH
143
5.3.2.1 Gel formationatdifferent
pHvalues
147
5.3.2.2 Influenceofthetimescaleof
thedynamicmeasurement
149
5.3.2.3 Effectofvariationofmeasuring
temperature
151
5.3.2.4 Proteolyticdegradation
157
5.4 Generaldiscussion
160
6 PULSENMRSTUDYOFCASEINSOLUTIONS
6.1 Introduction
6.2 PrinciplesofpulseNMR
6.3 TheeffectofmobilityofthenucleusonT 2
6.4 Experimental results
6.4.1 T 2ofskimmilk
6.4.2 T 2ofsodiumcaseinate
6.5 Discussion
162
162
163
168
170
171
174
176
7 CONCLUDINGREMARKS
185
Literaturereferences
Listofsymbols
Summary
Samenvatting
Curriculumvitae
Nawoord
191
197
200
203
207
208
INTRODUCTION
1.1 Acidcaseingels
Milk isone ofthemost important foods inmany countries all
over theworld.Besidesbeing drunk intheliquidform,assecreted by themammal,the nutritious substances ofmilk maybeconsumed in a series of derived milk products.Mostof theseproducts, now manufactured in highly equipped modern factories, are
stillprepared by empirical processes developed overtensofcenturiesfromtraditionalmethodsalreadyappliedbyancienttribes.
Examplesaredifferenttypesofcheeseandalargevarietyofsour
milk products such as yoghurts and quarg. All oftheseproducts
were developed in olden times as a means ofpreserving theeasy
perishable freshmilk.Note that inthis thesis theword milkis
used for the mammary secretion of healthy cows excluding colostrum.
Milk is a complex fluid containing many components in several
states ofdispersion (e.g.Walstra and Jenness,1984).Proteinis
amain constituent ofmany milkproducts,notonlybecauseofits
nutritional value, but also because of its contribution to the
physical structure of these milkproducts,this structuredetermining to aconsiderable extent the tasteperception oftheconsumer. The two most important groups of milk proteins are the
caseins (about 80%of total milk protein) and thewhey or serum
proteins.
Undertheconditionsofmilkserumproteinsaresoluble,mainly
separate molecules, whereas the caseins form aggregates of colloidal size (diametermay vary from 20to 300 nm), the socalled
casein micelles, whichmay contain up to thousands ofcaseinmolecules (WalstraandJenness,1984).Thesecaseinmicellesarethe
source of the colloidal blue white appearance of skimmilk. They
are stabilized under normal conditions inmilk (pH=6.7)bysteric
repulsion and a negative charge (Schmidt, 1982a, Payens, 1979,
Walstra, 1979). Upon acidification the structure and composition
of the caseinmicelles markedly alters;thereforethetermcasein
micelles willbeused here only forthecaseinaggregates inmilk
orskimmilkundernaturalconditions.Inallothercasesweprefer
toemploythetermcaseinparticles.
Due to rennet action (manufacture of cheese), acidification
(manufacture ofyoghurt)or acombination ofboth (manufactureof
quarg) the casein particles become unstable andmay coagulate to
form agel in anunstirred solutionwith casein asthemaincomponent of the gel network. Products like cheese, yoghurt, and
quargessentiallyarecaseingels.Howeverinspiteoftheeconomic importance the structure of casein gels has notbeenstudied
extensively. Only the spatial distribution ofthebasic elements
ofthe casein gelnetwork hasbeenstudiedtoanydetailedextent
byelectronmicroscopy (e.g.HarwalkarandKalab,1981,Knoopand
Peters, 1975,Glaser et al., 1980,andKalab,1981).Withrespect
to the manufacture of cheese further attention has beenpaidto
the structure and syneresis behaviour of rennet gels (e.g.Van
Dijk, 1982,Walstra et al., 1985,VanDijk et al., 1986)made at
naturalpHofmilk.Thisrelativelyscantyknowledgeofthestructure ofcasein gels is somewhat surprising,becausethemethodof
manufacture and the ultimate taste perception of products like
yoghurt, quarg and cheese depends notonlyonthechemicalcomposition, but especially on the physical behaviour of the casein
gelsformedinthecourseofmanufacture.
Theaimofthisworkistotakeafirststepinamorethorough
andfundamentalcharacterizationofthephysicalstructureofmilk
gels made by acidification.Because casein isthemain component
determiningthephysical structureofthistypeofgels (Roefsand
Van Vliet, 1984), we will denote them by the term acid casein
gels.To characterize the structure of agelwemustconsidertwo
main features; namely the spatial distribution of thebasic elements and the nature and the strength of the interaction forces
between thebasic elements.Due accountmustalsobetakenofthe
fact that the basic elements themselves have a certain physical
structure,which canchangewith the environmentalconditions.So
in factbasic elements and interaction forcesbetweenthemcanbe
distinguished atdifferentlevels.
Thespatialdistributionofthebasicelementsofagelnetwork
can be readily studiedbymeans of acombination ofpermeability
measurements, electron microscopy and concentration dependent
rheological measurements. The rheological properties and theeffect of experimental conditions suchasionic strength,temperature, pH etc.onthem provide information aboutthe structureof
and the interactions between thebasic elements.Thestateofwater (mobilized or immobilized)inagelnetwork,whichdependson
the structure and aggregation ofthebasic elements,may alsobe
studiedbypulseNMR.
1.2 Casein
As casein is the main component involved in the structureof
gelsmade frommilkby acidification (RoefsandVanVliet,1984),
specialattentionwillbepaidtoitinthissection.Thetermcasein includes awhole family of differentcaseinmolecules,whose
common characteristic isthat they are insolubleatpH=4.6.Under
thenaturalconditionsofmilktheyareaggregated inlargespherical particles, the casein micelles. Casein micelles consist of
water,casein,salts (mainlycalciumandphosphate)andsomeminor
components (WalstraandJenness,1984).
Four main groups of caseins maybe distinguished: a,-casein,
a 2-casein, ß-casein and K-casein. Within each group small,but
distinct variations may occur dueeither to small differences in
aminoacidsequence (veryoftenconstrainedtoavariationofonly
oneaminoacid)asaconsequenceofgeneticvariabilityortodifferences inmolecular residues attached to aminoacidsidegroups
(as e.g. a variable number of carbohydrate residues attached to
K-casein). Besides these fourmajor caseins,some2%oftotalcaseinexistsassmallerminorcaseins.Thesemostlyresultfromthe
proteolyticbreakdownofamajorcasein (e.g.-y-caseinisabreakdown product of ß-casein). In table 1.1 some data are given for
one genetic variant ofeach group ofcaseins,exceptforthedata
in the last two lines,which apply generally to eachgroup.The
casein composition ofmilkvarieswith season,withlactationperiod, from cowto cow andevenwith thetime oftheday (Walstra
andJenness,1984).Howevertheoverallcaseincompositionofbulk
milk,producedbyalargenumberofcowsisfairlyconstant.
None ofthe fourgroups of caseinhas ahighly organizedsecondary structure.Their conformation appears tobemuchlikethat
ofdenatured globularproteins,which ispartlyduetotherather
highproline content.Caseins containmany hydrophobicaminoacid
residues (see table 1.1).Ingeneral,theseresiduesarenotdistributedrandomlyalongthepeptidechaine.g.<xsl-caseincontains
three predominantly hydrophobic regions (residues 1-44, 90-113,
and 132-199,after Fox andMulvihill, 1983),whereasß-caseinhas
a soaplike characterbecause of ahydrophilicN-terminalpartand
ahydrophobicC-terminalpart.Asignificantfeatureofcaseinsis
thenumberofesterboundphosphateresidues,whichvariesconsiderably among the different caseins (see table 1.1).«„„-caseins
contain 10 to 13esterphosphate residues,whereas these figures
are8or9for a ,-casein,5forß-caseinand
1or2forK-casein.
r
si
Since the esterphosphate groups of caseinstronglybinddivalent
2+
ions (presumably Ca ,which
isthemostabundantdivalentionin
milk),especially athighpH,thenumberofesterphosphategroups
2+
determinesthestabilityofthedifferentcaseinsagainstCa induced precipitation. Thus a „- anda,-casein,but also ß-casein
aggregate and precipitate at very low Ca concentration (table
2+
1.1).K-casein,however,issolubleoverawiderangeofCa concentrations. K-casein is further characterized astheonlycasein
carrying carbohydrate residues, linked to the threonine residues
atposition 131,133,135 andpossibly136 (Swaisgood, 1982).The
carbohydratecontentmayvaryfrommoleculetomolecule.
All of the caseins tend to self-associate in solution inthe
2+
absenceofCa ,togiveakindof"polymers"orsoaplikemicelles
of fixed size (K-casein,Payens andVreeman,1982)orofsteadily
increasing size (<*sl-, a S 2 ~ a n d ß-casein)asconcentrationisincreased. The association behaviour of ß-casein, however, iscompletely different from that ofa g l - andas2-casein,particularly
in itstemperature dependence.o<sl- anda»-caseinassociateina
seriesofconsecutivesteps,whereasß-casein associatesmoretruly like soapmolecules to formmicellar aggregates. Inthe first
step of K-casein polymerization -S-S-linkages areinvolved.The
final K-casein "polymers" have a similar size as the ß-casein
"polymers" (Schmidt, 1982a). The degree of self association depends besides on concentration also on pH, temperature, ionic
Table 1.1 Properties ofthemain caseins
of -casein
si
molecularweight
B a »-casein A
ß"-casein
A2
K-caseinB
sz
19 ,023b
23 ,614
25 ,230
23 ,983
199
207
209
169
17
8
10
35
20
11
5
-
-
-
1
+
4.9
4.7
5.6
5.1
38
11
36
13
residuespermolecule:
amino acids
proline
esterphosphate
carbohydrate
hydrophobicity
%oftotal casein
lowestCa
2+
concentration
ofprecipitation inmmol
2
1
9
400
a.after various sources (Walstra and Jenness, 1984,Swaisgood, 1982,Schmidt,
1982a,Payens andVreeman, 1982).
b. exclusive of carbohydrate residues
c. these aregeneral figures,which refer tothewholegroup ofcaseins instead
ofthe individual geneticvariants.
strengthandkindofionsinthemedium (PayensandVreeman,1982,
Schmidt, 1982a). In mixtures of two or more different caseins
"polymers" (in fact aggregates) consisting of all available caseins will be formed.These aggregates generally aremore stable
than associations of any single casein. This is especially true
forK-casein,whichwillpreventprecipitationofa,-orß-casein
2+
aggregates by Ca ,stabilizing up totentimesitsownweightof
a
or
ß-caseinagainstprecipitation (WalstraandJenness,1984).
si~
Most of thecasein appears inmilk integrated intothecasein
micelles at or prior to secretion by the mammary glands of the
cow. Agreatdealofworkhasbeendoneonthestructureofcasein
micelles.Asweareonlyinterestedintherelativechangesofca-
sein micelle structure inthe course of acidification, itisbeyond the scope of this study totreatthestructureand,particularly,stabilityofcaseinmicellesindetail.Inpointoffactno
conclusivemodel forthestructureofcaseinmicelleshasyetbeen
proposed. Schmidt (1982a) has discussed what is known of its
structureextensivelyandhasbrieflyreflectedonseveralsuggestedmodels.
The diameter of casein micelles under natural conditions of
milk (pH=6.7 and 1-0.08 M) varies from 20 to 300 nm. They are
comprised of some40 to 150.000caseinmoleculesinafairlyconstantdistributionofthedifferentkindsofcasein.Caseinmicellescontain some 8gof inorganicmatterper100gcasein,mainly
calciumphosphate andsomeMg,Na,Kandcitrate,togetherforming
the socalled colloidal calcium phosphate,whichisindispensable
for the micellar structure. The colloidal calcium phosphate is
amorphous and occurs in small regions, dispersed throughout the
entire micelle. Under natural conditions casein micelles are
stableagainstcoagulation.Stabilityisascribedtoelectrostatic
andstericeffects.AtpH=6.7caseinmicellescontainasmall,but
significantnegative charge i.e. the zetapotential isaround-15
to -20 mV at 30 CC (Dalgleish, 1984). Payens (1979)has argued
that this value is too low to stabilize caseinmicelles inmilk
solely by electrostatic effects.Most of the K-casein, having a
very hydrophilic C-terminalpart, isthought tobelocatedatthe
outside of the caseinmicelles.These and otherhydrophilic protein chains are thought toprotrude from the caseinmicellesurfaceintosolution,thusstabilizingthecaseinmicellesbysteric
repulsion (Walstra,1979).
Upon acidification all casein will coagulate atpH=4.6,being
the isoelectric pH of the caseinparticles inmilk,because ofa
loss of charge itisthoughtthattheelectrostatic andpossibly
the steric repulsion will decrease aspH decreases.The isoionic
pH of individual isolated caseins may differslightly frompH=4.6
(Swaisgood, 1982).
1.3 Outlineofthisstudy
To simplifly the system, acid casein gelsweremade generally
from skimmilk,but sometimes from asolutionofsodiumcaseinate.
Milk fat was omitted, because changes in its content or in the
compositionofthemilkfatglobulemembranemayaffectthestructure of acid casein gels considerably (VanVliet andDentenerKikkert, 1983). To reduce experimental error due tovariationin
composition,skimmilkwasreconstituted fromthesamebatchoflow
heatskimmilkpowder.Sodiumcaseinatesolutions,too,werealways
madefromthesamepowder.Sodiumcaseinatepowdermerelycontains
purifiedcaseins.HClwasused foracidificationinsteadofbacterial enzymes, which are difficult to handle with respect to pH
control. As gel formation only can occur in solution at rest,
acidification by means ofHCl was carried out atlow temperature
(0-4 °C),where acasein solution evenatpH=4.6 (theisoelectricalpH)doesnotcoagulate.Aftertransferringtheacidifiedsolution to the measuring apparatus, gel formation was induced by
heating at rest. In some experiments casein gels were formedby
acidificationat30°CusingGlucono-Delta-Lactone (GDL),aslowly
hydrolyzing acidprecursor.Thiswasdonetosimulatemoreclosely
acidificationbybacteria.
The composition of the skimmilk and sodium caseinate powders
is reported in chapter II.All experimental procedures andapparatusaredescribed there,too.
Inchapter IIItheeffectofacidificationoncasein,especially at low temperature, isdescribed first.Particle size andcasein solubility in skimmilk were studied as a function ofpH.In
addition electron micrographs were made of skimmilk and sodium
caseinate solutions at different pH's. Next the formation and
ageingofdifferentkindsofacidcaseingelsatdifferenttemperatureswere studiedbymeans ofrheologicalmeasurements.Thedynamicmoduli G' andG"were determined. Inthe lastpart ofthis
chapter a model ispresented for the spatial distribution ofthe
basic elements of an acid casein gel. This model is primarily
based on the results of the concentration dependent rheological
andpermeability measurements, aswell as onelectronmicrographs
ofacidcaseingels.
Chapter IVdealswith the rheological characterizationofacid
casein gels. The dynamic moduli were measured over a frequency
rangeofthreetofourdecadesasafunctionofioniccomposition,
pH and measuring temperature at different ageing temperatures.
Special attention was given to the 'permanent1 network character
of acid casein gels. The contribution of the different typesof
interactionforces,involvedinacidcaseingels,isdiscussed.
The structure ofcasein gels,made byacidificationandrennet
actioninthepHrangeof4.4 to5.8,isthesubjectofchapterV.
The rheological properties atconstant ageing temperature (20°C)
were measured over the whole pH range, while ageing temperature
wasvariedatpH=4.6.
In chapter VI the application of pulse NMR to elucidate the
stateofwaterincaseinsolutionsisdescribed.Thespin-spinrelaxationtime,T 2 ,ofwaterprotonsinskimmilkandsodiumcaseinate solutionswasmeasured inthepH range of 6.7 to4.6 atdifferenttemperatures.
The most important results of this study are summarized and
discussedinchapterVII.
2 EXPERIMENTALPART
All low molecular weight electrolytes used were analytical
grade. Solutionswere generally prepared withdemineralizedwater
though sometimeswith destilled water.Therennetusedwasacommercial calf rennet (Leeuwarder kaasstremsel)with astrengthof
10.000units.Thiswasdiluted1:4beforeuse.
2.1 Skimmilkpowder
Forallexperimentsreconstituted skimmilkwasused.Ingeneral
thiswasmade from acommerciallow-heatskimmilkpowder(Krause,
Heino).Forsomeexperimentsskimmilkwasprepared fromalow-heat
skimmilk powder, supplied by theNetherlands Institute forDairy
Research (NIZO).Thecompositionofbothpowdersisgivenintable
2.1. The two kinds of powder gave similar experimentalresults.
The drymatter, casein, ash andfatcontentwererespectivelydetermined according to IDF standards 26(1964), 29(1964), 9A(1969)
and 90(1979). Undenaturated whey protein nitrogen (W.P.N.) was
determined according to themethod oftheAmericanDriedMilkInstitute (1971). The difference between the trueprotein fraction
and the sum ofthe casein and serumprotein fractionmustbeascribedtotheproteose-peptonecomponents.
Standard skimmilk was prepared by dissolving 12gr powder in
100gr of demineralized water giving a somewhat higher total
solids content (10.4%) than in normal bovine skimmilk. To allow
equilibrationthesolutionswerestirredat30°Covernight (16-20
hours)before use.Topreventbacterialgrowth100ppmthiomersal
also called thimerosal (C2H5HgSC6H4COONa, BDHChemicals LTD)was
addedasapreservative.
2.2 Caseinatesolutions
Two different sodium caseinate powders were available. Both
powdersmet the IDF standard 72(1974)forthecompositionofedible caseinate (extra grade), except for the fat content of one
powder.The firstwas aspraydriedpowdermadeinthelaboratory
of theUniversity. Onebatch ofpasteurized (20sat72°C)skim-
10
Tabel 2.1 Composition (inwt.%)ofthe low-heatnon-fat
driedmilkpowders employed inthisstudy.
powderA
powderB
96.8
96.9
ash
6.1
6.5
fat
0.6
0.9
33.8
34.8
drymatter
trueprotein
3)
casein
28.3
3.4
serumprotein
28.6
4.1
NPN
1.8
2.6
WPN
6.45
6.94
1) Obtained fromFa.Krause (Heino).
2) Obtained from theNetherlands Institute forDairyResearch.
3) Usually inliterature one speaks about totalprotein.This
includes trueproteinandNPN.
milk was acidified with 0.5 N HCl at 30°C until pH=4.6.After
separating the whey and pressing the curd three washing stages
withdemineralizedwateratrespectively40-50°C,60°Cand30°C
followed. The washed curdwas redispersed indemineralized water
andpassedthroughacolloidmilltogiveafinegrounddispersion.
Under gentle stirring the pH was increased topH=6.7with 0.5 N
NaOH. The dissolved caseinate was heated to 60-80°Cjustbefore
itwasspraydried.
ThesecondpowderwaskindlysuppliedbytheNetherlandsInstitute for Dairy Research. Pasteurized (10s at 72°C) skimmilk
(Ottenhof,pers. communication)wasmixedwith4NHCl inacontinuous flow process at relative low temperature (15-20°C).At
theend ofthisprecipitation stagedirectsteaminjectioncaused
ariseofthetemperatureto38-42°C.Thewheywasseparatedfrom
thecurdwith adecanter.Threewashingstageseachat45°Cwere
carried out. The washed curd was redispersed in ordinary water
and ground in a colloid mill, while 2-3 NNaOHwas added toin-
11
Tabel 2.2 Composition (inwt.%)ofsodium caseinatepowders
employed inthisstudy.
spraydried
freezedried
95.8
98.6
ash
3.7
3.9
fat
3.1
0.5
88.2
93.0
drymatter
trueprotein
casein
87.3
NPN
-
-
serumprotein
proteose -peptone
92.0
1.0
0.7
1.2
1.1
crease thepH topH=6.7. The temperature during thisprocesswas
kept below 70°C.The sodium caseinate solutionwas freezedried
at 55°C under low pressure. The composition ofbothpowdersis
given intable 2.2.Theywillbedistinguishedbythetermsspray
dried (madeatourlaboratory)andfreezedried (madeattheNIZO)
powder. The fat content of the spray driedpowder isrelatively
high and does not conform to the IDF standard 72(1974) for the
composition of (extra grade)edible caseinate.Togetherwiththe
higher moisture content thisproduces alowervalue fortheprotein content of the spray dried powder.No serum (whey)proteins
were detectable ineither powder.Thedifferencebetweenthepercentage of true protein and the sum of the casein andproteosepeptonepercentage isduetoexperimentalerror.
Standard sodium caseinate solutions contained 3grsodiumcaseinate powder per 100 gr solution and some NaCl and/or CaCl2.
Sodium caseinate did notdissolve aswell as skimmilkpowder and
therefore caseinate solutions were stirred at least 20 hours at
30°Cbeforeuse.
2.3 Acidificationandgelation
For acidification the caseinate and skimmilk solutions were
cooled in ice water baths and transferred to a low temperature
12
(4°C)room. The apparatus for automatic acidification consisted
of an autoburette (type ABU 13e),coupled with atitrator (type
TTT 60a)and astandard pHmeter (typePHM 62a),all fromRadiometer Copenhagen.The rate of acid additionwas regulated bythe
titrator and slowed near the pH end-point. For skimmilk 3NHCl
was used, but in sodium caseinate solutions toomany floeswill
be formedwith this acid concentration.Byusing0.5NHCl fewor
no floeswill be formed duringacidification.Generallythesolutions were titrated to a pH=4.6 end-point, though not in those
experiments where thepHwas thevariable of interest.Theacidified solutions (0-2°C)were transferred totheapparatusmaking
the experimental measurement ofinterest and heated at arateof
0.5 °Cperminute,unless otherwise stated.Intimedependentexperiments the time,atwhich thetemperatureroseabove4°C,was
chosen aszero time.Above 10°Cgelationstarted.Thefinalageingtemperaturesvaried from20to50°C.
Heating rate and temperature was controlled (within ± 0.1 °C)
by MGW LAUDA thermostatted baths (type K4RD and K2RD), coupled
with aregulating unit (PTRRegler,typeP20KorR20/3)andasocalled "Programmgeber" (typeP250/2orP250).
In experiments where thecombined effect ofpH and rennetactionwas studied, 50 \sl ofadilutedrennetsolutionwasaddedto
50ml of cold acidified skimmilk togiveafinalconcentrationof
250 ppm rennet. In these particular experiments the moment of
mixingwastakenaszerotime.
GDLinduced acidification
Glucono-ô-lactone (GDL)wasused as anacidprecursor toprepare acid casein gels (pH=4.6)with anacidification temperature
of 30°C. For gel preparation solid GDL (1.22wt.%for standard
skimmilk and 0.47 wt.% for standard sodium caseinate) was added
toskimmilkorsodiumcaseinateat30°C.Thesolutionwasstirred
thoroughly, before itwas transferred toanymeasuringapparatus.
Incase of skimmilk the firstflocculationwasseenafter1.8x10
s (~5hrs)atpH~4.90-4.95, followed bygelformationatlowerpH.
4
Finally after approximately 9x10 s (24hrs) the pH of skimmilk
solutionreached4.60-4.62andofsodiumcaseinate4.64.
4
13
2.4.Whey
Acid whey was prepared from fresh skimmilk, unless stated
otherwise.For thispreparation agelwasformed fromfreshskimmilk in accordance with the procedure described in section2.3.
After anappropriate gelation time ofabout16hoursthewheywas
separated fromthecurdbycentrifugation(inaCHRISTUJ3centrifuge)for 30min at3000rpm (~2300g).Thewheywasfilteredjust
before use.The kinematic viscosity q/Pw a s determinedwithaKPG
Ubbelohdeviscometer (Schott-Geräte,BRD)atthedesiredmeasuring
temperatures. The elution time was determined in the classical
way.
2.5 Varyingproteinconcentrationbyultrafiltration
Protein concentration was varied by ultrafiltrating standard
skimmilkinanAmiconconcentratormodelCH3,equippedwithahollow fiber cartridge (type H1P10). Allconstituentswithmolecular
mass above 10,000 Daltons were concentrated. The concentratewas
used directly except in the case of low protein concentrations
wherestandardskimmilkwasdilutedwiththeultrafiltrateobtained. The extent to which the protein was concentrated ordiluted
ascompared to standard skimmilk wasdeterminedbyKjehldahlanalysis and/or by a rapid infrared absorption technique using a
Milkoscan 104A/B (A/S N. Foss electric, Denmark). With thisinstrumentthe absorption of infrared radiationatA=6.46|jmbythe
peptide bonds is measured. Results obtained with the two techniqueswereingoodagreement.
2.6 Gelelectrophoresis
Theproteolytic actionofrennetona-andß-caseinasafunction oftime after enzyme additionwas studied by aquantitative
variant of PolyAcrylamide gel Electrophoresis (PAE)accordingto
the procedure described byDeJong (1975). Precooled glasstubes
werefilledwith0.5mlofanacidified skimmilksolution,prepared according to section 2.3, immediately after the addition of
250ppm rennet.Gel sampleswereobtainedbyheattreatmentusing
14
the standard procedure (section 2.3).After the appropriate time
interval each sample (0.5ml)was dissolved in3.5ml of aTrisHC1buffer (pH=8.5), containing about 9M urea,resulting ina8
M urea solution. From this solution,withaproteinconcentration
of approximately 0.5%, 50piwas taken forthegelelectrophoresis. The optical density of the stained caseinbandswasdetermined with the aid of a Shimadzu dual-wavelength TLC scanner
(model CS-910), coupled to a recorder (BBC Servogor 120).The
densitometeroperatedinthesingle-wavelength (at600nm), double
beammode,using atungsten lamp,withascanspeedof20mm/min.
The transmission wasmeasured with an illuminationbeam of 10mm
height and 0.2mm width. Both the optical density and theintegrated optical densitywere charted bythetwopenrecorder.From
the integrated signal the decrease in protein content could be
calculated.
2.7 EstimationofsplittingofK-casein
Withtheaidofhigh-performance liquidchromatographythefree
GlycoMacroPeptide (GMP) content, resulting from rennet actionon
K-casein, was determined according to themethoddescribedbyVan
Hooydonk and Olieman (1982). Glass tubes were filled with 2ml
acidified skimmilk, to which rennet was added. They were then
warmed at a rate of 0.5 °C per min to three different gelation
temperatures.At regular time intervals thereactionwasquenched
by adding 4ml 12% (m/m)Trichloracetic Acid (TCA)to theglass
tubes. The rate of GMP splitting was analysed, partly with the
apparatus oftheNetherlands Institute forDairyResearch (kindly
done by Van Hooydonk and Olieman), and partly atour laboratory
withaSpectraPhysicsSP1800liquidChromatograph.
2.8 Permeabilitymeasurements
2.8.1.General
Theresistanceofaliquid flowthroughaporousmediumdepends
onthespatialdistributionofthesolidphase.Incaseofalaminar flowthrough ahomogeneous fixedmatrixgenerallyDarcy'slaw
isobeyed. For a flow inonedirectiontheliquid flux,v,canbe
readas:
15
v=-B/nVP
(2.1)
v=liquidflux (i.e.volume flowrate/cross-sectionalarea)(m.s")
2
B=permeabilitycoefficient (m)
H=viscosityoftheflowingliquid (Pa.s)
VP - pressuregradient.InourcaseVPhasonlyone
componentinthex-direction (i.e. parallelto
themeasuringtubes).SoVP=dP/dx (Pa.m")
Thepermeability coefficientB depends onthegeometry,scaleand
spatial distribution ofthepercolated matrix.Forflowthrougha
porous medium a Reynolds number Re can be defined (Scheidegger,
1960):
Re=vpô/n
(2.2)
v=liquidflux (m.s~)
-3
p=densityoftheflowingliquid (Kg.m )
0 =viscosityoftheflowingliquid (Pa.s)
ô=adiameterassociatedwiththeporousmedium,
i.e somelengthcorrespondingtoanaverage
grainorporediameter (m)
Incase of laminar flow itisaprerequisite forapplyingDarcy's
lawthatReshouldnotexceedacertaincriticalvalue,whichvaries from 0.1 to 75 depending on theporousmedium (Scheidegger,
1960).
2.8.2 The_tube_method
By measuring the liquid flux,v, ofusuallywhey throughopen
glasstubesfilledwithcaseingels,thepermeabilitycoefficient,
B, couldbe calculated from the knownpressure gradient,VP,according to equation 2.1.The apparatus used was developed byVan
Dijk (1982)formeasurements on rennet gels. Glass tubes openat
both endswith aninnerdiameter of3.7mm and alength of25cm
wereplacedinaprecooledvat.Thetubesplacedinaholderrested on a plexiglass base. Acidified skimmilk or sodium caseinate
16
was added tothevattosuchanextentthatthetubeswerefilled
over alength of about10cm.The gelationvatwasheatedaccording to the procedure given in section 2.3. After the required
gelationtime atthe appropriate temperaturethetubeswerewithdrawn from the gelationvat,cleanedattheoutsideandplacedin
arack,whichwasplacedinthemeasuringvatmadeofclearplexiglass. The level of the percolating liquid inthemeasuringvat
(usuallywheyorasodiumphosphatesolution)wasadjustedinsuch
awaythattheinitialpressuregra3
dient was about4.5-6.0x10 Pa.m
1
-1
2
Thewheylevelinthetubeswasread
at regular time intervals with the
help of a travelling microscope.
_h_
The
lengthoftheintervalsdepended
whey
on the permeability of the gelma-h(t 2 )
-h(t,l
trix. From the five readings usually made fourpermeabilitycoefficients could be calculated. Theorder ofmagnitude ofthe flowvelocity, v, varied from 3xl0~ to
8x10 •8 ms -1
~. Assuming a v a l u e of
-7
10~' m f o r t h e p a r a m e t e r ô ( i . e . a
Fig. 2.1 Schematic representalow e s t i m a t e of t h e approximate d i a t i o n of permeability measurement.
in eq.
meter of casein particles)
For explanation see t e x t .
n~io"3
2.2, while p~103 Kgm -3 and
Reynoldsnumber,
Pa.s, the
Re,for
-7
the flow through casein gelsvaried from8x10
to3x10-9
;df
Taking
—fi
—R
>-5
forôaporediameterof10~ to10~ minsteadofaparticledia—7
meterof10 m,Rewillbe10to100timeslarger,butstillsufficientlysmall.Therewasthereforenoriskforturbulentflowin
3
our experiments. Variation ofthepressure gradient from4.0x10
3
-1
to 11.0x10 Pa.m didnot influence the calculated permeability
coefficients, so that the application of Darcy's law for flow
throughacidcaseingelsseemsallowable.
The calculation of B from the experimental readings issomewhat complicated, because thepressure gradient ischangingwith
time as the whey level intheglass tubes rises (see fig.2.1).
On the otherhand because of the rather homogeneous character of
L
17
the gel and the one dimensional direction of flow (x-direction)
thepressuregradientatacertainmomentisconstantandnegative
overthewholegelandisgivenby:
gill=.pg fh(<M-h(t)}
(2>3)
h(<»)=heightofthewheylevelinthereferencetube(m)
h(t)=heightofthewheylevelinthegeltube (m)
H
=lengthofthecaseingel(m)
-2
g
=gravitational accelerationms
Because ofthe largevolume outside the tubesh(°°)isassumedto
beconstant.Theliquid flux,v,alsochangeswithtime:
v(t)=f p 1
(2.4)
InthiscasetheequationofDarcy (eq.2.1)canberewrittenas:
v(t)=dh < t > =gP9W°°)-h(t)?
(2.5)
dt
n
H
Integration, solving the integration constant andrewritingleads
to anexpression forB,depending onh(t)att=t1 and t=t2 (Van
Dijk, 1982).
h(°°)-h(t)
B=
-TT
T~
(2.6)
pg(^-t-^
Within the experimental accuracy thepermeabilitycoefficient,B,
ofacidcaseingelsdidnotchangewithtimeduringtheexperiment.
2.9.PulseNMRmeasurements
The spin-spin relaxation timeT 2 ofseveralcaseinsampleshas
been measured. Measurements have been carried out with apartly
modified Bruker Minispec PC20 pulse NMR apparatus, operating at
20MHz and equipped with aNewport 7-in. electromagnet.ABruker
Aspect 2000 computer and aZ17Cpulseprogrammerwereused forre-
18
gulation of the measurements and storage of experimental data.
AllT ?experimentsinvolvedtheuseofaCarr-Purcell-Meiboom-Gill
pulsesequence.Eachmeasurementconsistedofone90°pulsefollowed by a number of 180° pulses.The lengths of the90°and 180°
pulseswererespectively 12.5and25 (JS.Thetimebetweenthe180°
pulses was 1.0 or 3.0 ms (formilk ultra filtrate samples).The
delay timebetween two consecutive measurementswasvaried from4
to 10sdepending on theT,ofthemeasuredsample.Thiswassufficientto allow thenuclear magnetizationtoreturntoitsequilibrium value. Each measurement resulted in anuclearmagnetizationdecaycurve,characterizedbyoneormoreT_relaxationtimes
(seeChapter 6). For a suitable signaltonoiseratio8to16decaycurveswere firstsummed and stored ondisk inthecomputer.
Each decay curve consisted of 2048, 3072 or 4096 samplepoints,
depending on the length of the pulse sequence.Nexttheaccumulated decay curvewas fitted with a single exponential according
to the method of McLachlan (1977). The inaccuracy inthecalculatedT„valueswas estimated tobeabout1%.Thiswasdetermined
by checking the computer fitting program with a generated decay
curve. Previous fitting with sums of more than one exponential
resulted inone single dominating exponential forthedecaycurve
ofskimmilkatdifferentpHandtemperature.
For thermostatting a Varian ESR dewar coupled with a Varian
temperature controller wasused.The dewarwasplacedthroughthe
cavity, which was centered between two large electromagnets. A
cold N2~flow, created byheating liquid nitrogen in adewarvat,
whichwas connected directly to theESR dewar,wasused toregulate the temperature.The samples wereheldintubesusuallymade
ofquartzbut sometimes ofglass,bothwith anouter diameter of
4mm. The inner diameter was 3mm and 2.2mm forthe quartzand
glass tubes respectively.Notwithstanding the considerablereduction involume the samples intheglasstubesstillshowedareasonablesignaltonoiseratio.
2.10 Rheoloqicalmeasurements
Skimmilk gels, made by acidification and/or rennet actionbehave as visco-elastic materials (van Dijk, 1982, and Roefs and
19
VanVliet, 1984). Thenumber oftechniquesforstudyingtherheological properties of this type of gels is limited, because by
transferring from one apparatus to another,e.g.fromabeakerto
arheological apparatus,thegelswillbreakand/orsyneresiswill
begin.Thusthegelsmustbemadeintheapparatusitself.
In this study two different rheometers were used. The first
was adynamic viscometer developed byDenOtter (1967)andDuiser
(1965) at TNO Delft. Except for dynamic measurements (section
2.10.1)itcan alsobeused for akind of stress relaxationmeasurements (section 2.10.3). The second rheometer was a constant
stress apparatus fromDeer LTDused forcreepmeasurements (section2.10.4).
2.10.1Dynamicmeasurements
The rheometer used hasbeen describedextensivelyelsewhereby
Duiser (1965), Den Otter (1967), Beltman (1975)andTeNijenhuis
(1977). Essentially the apparatus consists of two coaxialcylinders (seefig.2.2)betweenwhichthesampleisbrought.Theouter
cylinder made ofglass is fixedwhereas the inner cylinder,made
ofstainlesssteel,issuspendedbetweenatorsionwirefixedtoa
-driving shaft
-torsion wire
- inner cylinder
-sample
-outer cylinder
- thermostatted jacket
- strain wire
ie
-sample inlet
Fig.2.2 Schematic representationofthedynamic rheometer.
For explanation seetext.
driving shaft and a strain wire.A
sinusoidal rotational oscillation
canbeappliedtothedrivingshaft.
Thismovement istransferred tothe
inner cylinderby the torsionwire.
When the samplebehaves in alinear
visco-elastic fashion, the inner
cylinder alsoperforms asinusoidal
oscillation,showinghoweverasmaller amplitude than and aphasedifference with that of the driving
shaft. These differences depend on
the visco-elastic properties ofthe
sample, the elasticity of the torsionwire and themomentofinertia
oftheinnercylinder.
20
Ifthe oscillation e (rad)of the driving shaft isgiven by:
cL
e
where e
a = e ao s i n (u)t+,^,)
<2-7>
= the maximum amplitude (rad)of the oscillation of the
1
cLO
driving shaft, m =the angular frequency (rad.s - )of the oscillation, $ = the phase difference (rad) between the oscillations of
the driving shaft and the inner cylinder, and t = time (s),the
oscillation e (rad)of the inner cylinder can be writtenas:
e = e sinuit
c
e
(2.8)
CO
is themaximum amplitude (rad)of the oscillation of the inner
cylinder.
2
With I for the moment of inertia (Nms )of the inner cylinder,
D.. and D~ as the torsion constants of respectively the torsion
wire (Nm)and the strainwire (Nm),and E (m )as a characteristic
cylinder constant, the equation of motion of the inner cylinder
in this particular case is as follows:
D
D
l
2
r"
T
=±(e -£ )-=^£ -G'e -— t -±£ = 0
E ' a c ' E c
c w c E c
-1
Here i
(2.9)
*
'
-2
(rad.s )and £ (rad.s )are the first and second deriv-
ative of £ with respect to time t, G' is the storage modulus
-2
-2
(Nm ) and G" is the loss modulus (Nm ).In a more general description (Duiser, 1965) equations 2.7 and 2.8 are written as
complex functions, while equation 2.9 must be rewritten using the
_2
complex shear modulus G* (Nm ),which isdefined as:
G* =G' + iG"
(2.10)
Solving equation 2.9 G' and G"canbe calculated from the following equations:
£ cos <)>
G' =D 1 /E(-22
1)- D 2 / E + IuZ/E
(2.11)
CO
£ sin <)>
G" =D./E-22
1
(2.12)
e
co
21
E = a cylinder constant = 47thRi2R02/(R02-Ri2) (m 3 ), where h is
the length of innercylinder (0.15 m), R i isthe radius ofinner
cylinder (3.75xl0~3 m) and RQ is the radius of outer cylinder
(4.5xl0~3 m).
-3
The angular frequencywwasvaried over the range 10 to10
1
rad.s .This range corresponded to afrequencyrangeof1.6x10
to 1.6 s - 1 . The amplitudes e .e „ and the phase difference<|>
dO
CO
were measured by means of two light beams falling on a special
mirror system fixed on inner cylinderanddrivingshaft(Beltman,
1975). The constants D~ and I were calculated as described by
Beltman (1975) andDuiser (1965).D, was determined withweights
2
of exactknownmoment of inertia I 1 (Nms ),whichwere suspended
from thetorsionwire and thenbroughtintoharmonicoscillation.
Fromtheobserved frequencyv (s~)D,couldbecalculated asfollows:
D 1 =47i2I1v2
(2.13)
Temperature was controlled within 0.1 °C by a thermostatting
bath (MGM Lauda, see section 2.3),which was connected to the
thermostattedjacketaroundtheoutercylinder (seefig.2.2).
2.10.2 Measurementofacidcaseingels
After acidification and occasionally addition of rennet the
skimmilk and caseinate solutions cooled on ice were transferred
to the rheometer, which was precooled to approximately 2°C. A
funnel precooled in a refrigerator was used for filling. After
filling the rheometerwaswarmed to the chosen gelationtemperatures (see also section 2.3).In some experiments themeasuring
temperature was varied from 2 to 70°C. To prevent evaporation
gelswere coveredwithparaffin oil.Sinusoidaldeformationsusuallywerenotappliedbeforeagelwasformedtoavoiddisturbance
inthe firststage ofgelformation.Theamplitudeofthedriving
shaftwas kept sufficiently low toensurelinearbehaviourofthe
sample,whichappearedtoexistifthemaximumdeformationv<0.04.
Inthe case of linearbehaviourboththedeformationya n d the
shear stress a depend one and the distance R to the centerof
theinnercylinder,asfollows:
1
-4
22
2
7
R
£
c
-7
(R
i
-7
R
Ï
(2.14)
, R. < R < R 0
(2.15)
o >
2 £C|G*|
R2(R
, R± < R < R 0
2_R
Ö
2)
y varies from 4.545.e at the outercylinder to 6.545.e at the
inner cylinder. The average value of y over the whole sample
equals 5.545.e cand so<an average maximum shear deformationy
canbedefinedas5.545.E
CO
2.10.3 "Stressrelaxation"measurements
Setting the driving shaftof thedynamicrheometermanuallyat
a certain fixedposition insuchaway,thatthegelisstrained,
offers the possibility of measuring a pseudo-stress relaxation
_2
modulus,whichwewill call G(t)*(Nm ).Theproblem is thatin
case of visco-elastic solids when e isplaced ata fixedposition, e will change with time and also both y and a (seeeqs.
2.14 and 2.15). Therefore one cannot speak about a real stress
relaxation experiment, nor about acreep experiment. For thedeformationyandthestress a eqs.2.14and2.15 stillhold,except
thate ande areno longer sinusoidal functions oftime.Using
£'
of£ andce for the
uand e' instead
a
a amplitude ofrespectively
the inner cylinder and the driving shaft, the torsionmomentM,
(Nm.rad)exertedbythetorsionandthestrainwirecanbewritten
as:
M
l =D l (sa-£c>-D 2 e c
<2-16>
Replacing the complex shear modulus G* (eq. 2.9)by thepseudostress relaxationmodulus G(t)*, whichhasonlyarealvaluenow,
the total shearmomentM 2 (Nm.rad)exerted on the sample between
innerandoutercylinderisgivenby:
M 2 =EG(t)*e£
(2.17)
a
23
In case of an applied harmonic oscillation the differenceM 1 ~M 2
causes an angular acceleration ë (see eq. 2.9),assuming G*to
be constant. When e' is fixed andG(t)*isconstant,M,willbe
equaltoM 0 andë tozeroandsoe vanishesfromeq.2.9.Asim£
c
c
pieexpressionforG(t)*canthenbederived:
G(t)*=D,/E(-1-1)-D,/E
1
s
c
(2.18)
However in caseofvisco-elasticsolidswithvery long relaxtion
times there isno steady-state situation andG(t)*will decrease
with time, whereas £ and thus Y will increase causing a todecrease. Equation2.18 isno longer anexactsolution,becauseë"c
will have asmall,although negligible value.Thus e^ andthough
thisG(t)*shouldbewritten astimedependentfunctions.Inthat
case eq. 2.18 is still an excellent approach for measuring a
pseudo-stress relaxtion modulus over longer time scaleswiththe
concentriccylinderapparatus,describedabove.
2.10.4 Creepmeasurements
With this type ofmeasurement the strainof asample ismonitored as a function of time during application of a constant
stress.TheexperimentswerecarriedoutusingaDeerPDR81Rheometer, fitted with a coaxial cylinder geometry machined from
stainless steel and kept atthe desired measuring temperatureby
immersioninathermostattingbathincorporatedwithintheinstrument.A constant stresswas appliedbymeansofaninductiontype
electric motor.The rolling frictionwas reduced by using anair
bearingsupport.Angulardisplacementwasdeterminedbyanon-contacting electronic sensor, whichmeasured the distance betweena
circular ramp and the sensor.The diameter of inner cylinderwas
6mm and thatoftheouterone7.5mm.Thesamplevolumetotalled
2ml. Constant stress was applied to the inner cylinder at t=0
and the resulting displacementmeasured asafunctionoftimeand
monitored by means of a recorder. The applied stresswasvaried
over the range 1to 175Pa.Allmeasurements were carried outat
30°C.Toavoidinterferenceoftemperaturegradientsandaircur-
24
rents the apparatuswasplaced in aperspex cage.The instrument
was adjusted at30°C,subsequently cooledto2°Candafterfilling with skimmilk acidified in the cold, was heated again to
30°Catarate of 0.5 °Cperminute (see section 2.3).Afteran
ageing time of 18to 20hours each gelwas subjected toonlyone
creepmeasurementatoneparticularstress.
2.11 Electronmicroscopy
Transmission Electron Microscopy (TEM)using samplesprepared
by thin sectioning was applied toviewthestructural featuresof
skimmilk and sodium caseinate solutions inthe liquid and gelled
state instudieswhere temperature andpHwere thevariables.To
minimize the disturbing influence ofthepreparationprocedureon
the structure ofthe casein solutionsandgels,themicro-capsule
method, introduced by Salyaev (1968)and adapted tomilkbyHenstra and Schmidt (1970a andb)was employed. Agar capsules,made
by dipping glass rodswith adiameter of~1mm inahot3%sterilized agar solution (Diftobacter),were filledwithcaseinsolutions by withdrawing the glass rods from the formed capsules,
whichwereheldinthesolutionattheotherend,andthensealing
both ends with hot agar. In case of liquid samples solutionsof
desiredpH and'temperaturewereprepared afewhoursbeforefixation.Afterfillingthecapsuleswithacertainsolutiontheywere
stored in the same solution. In the case of gelled samples the
capsules were filled after acidification to pH=4.6 at ~2 °Cand
thenheatedinthesameacidifiedsolutiontothedesiredgelation
temperature (seealsosection2.3).
Aftertheappropriateageingtimethecapsulesweretransferred
for fixation to a1%0s0 4 solutionina0.1Mphosphatebufferof
the corresponding pH and temperature. The samples were kept in
the1%Os0 4 solutionfor16hours.Insomepreliminary experiments
thesampleswere firstprefixed in1.4%or2%glutaraldehydesolutionsforatleast6hoursandpostfixedin1%OsO.fortwohours.
This prefixing had no effect on the results.After rinsingwith
buffer and distilled water the capsules were dehydrated in a
graded alcohol series from 20 to 100%ethanol.For embedding the
samples were transferred to polyethylene capsules.Embeddingwas
25
carried out inthree steps.Step 1consisted ofatreatmentwith
a 1:1 mixture of alcohol and embedding medium (3partsn-butylmethacrylate and 2parts styrene), and then step 2withpureembedding medium, both without initiator.The final step consisted
of atreatmentwith embedding medium with 2%benzoyl peroxideas
initiator. For adequate polymerization the polyethylene capsules
were kept for atleast48hoursat50°C.After24hoursmoreembedding medium was added to the polyethylene capsules, because
shrinkingandevaporationofthemediumhadtakenplace.
Thin sections (thickness about 60 nm) were cut with a LKB
microtomeandpoststainedwithuranylacetate (7min)andReynolds
leadacetate (7min), and finally rinsedwith 0.01 NNaOH toprevent lead carbonate precipitation, which causes artefacts. The
sampleswereobservedunderaPhilipsElectronmicroscope (EM400T),
operatingat60KVandmicrographsweretakenon35mmfilms.
2.12 Solubilityofcasein
UsingthefacilitiesputatourdisposalbytheHannahResearch
Institute (Ayr,Scotland) thesolubilityofcaseinatlowtemperature was determined as a function ofpH.Caseinwasdefined as
soluble if it did not separate from acasein dispersion,whena
centrifugal force of 60,000 gwasapplied foratleasttwohours.
Fresh skimmilk was obtained from the bulk tank on the Institute
farm.The skimmilk was cooled to 2-4 °C and thepH adjusted toa
value inthe range from 6.7 to4.6byaddingHCl.Aftertheskimmilksampleshadbeenstored44hrsat5°C,theywerecentrifuged
at 60,000 g for 2hrs (temp.=4°C)in aSorvall Superspeed RC
2-B centrifuge. The supernatants were carefully poured off from
the pellets, which were drained and then redispersed inwater.
Bothpellets and supernatants were raisedtopH=6.7bymeansof1
MNaOH,treated with EDTA toremoveCaandwarmedtoroomtemperature.Afterdilutionina20mMimidazole,50mMNaClbuffer
1:The author wishes to thank the Hannah Research Institute for
the facilities provided and Dr. Dalgleish and Dr. H o m e for
stimulatingdiscussions.
26
(pH=7.0)the light absorptionwasmeasured at320nm and 280nm.
The light absorption at 280 nm (A-g«) arose from absorption by
aromatic amino acids in the casein molecules plus a turbidity
background, whereas the absorption at320nm (A 32Q )was onlydue
tosolutionturbidity.TheA 3 2 Q valuewasusedtocorrecttheA 2 8 Q
measurementusingtheequation:
A=A 2 8 0 -1.706A 3 2 0
(2.19)
whereAgavearoughmeasureofthecaseinconcentration.Thefactor 1.706 stemmed from the assumption thatturbidity wasproportionalto (wavelength).Ultimatelytheparameter,A,wasrecalculated inrelative units of absorptionper gram oforiginalsolution. Because the sum of light absorption of pellet and supernatantwasequal for all pH's,theamountofcaseininpelletand
supernatant could be expressed aspercentageoftotalcasein.But
as a correction for whey protein ateachpH the total lightabsorption was reduced by the value of A of the supernatant at
pH=4.6, which was entirely attributed to the whey proteinfraction. The exact protein concentration could not be calculated,
because the molar extinction coefficients of the individual caseins differ and the individual casein content of each fraction
wasnotknown.
In another experiment (kindly performed by Dr. Dalgleish of
theHannahResearch Institute)the fractionoftheindividualcaseinsinpelletsandsupernatantswasdetermined.Thesampleswere
prepared as described above, except that the acidified skimmilk
solutions were only stored for 20 hrs at5°C.After the casein
was isolated and purified from the supernatant and pellet,both
pelletandsupernatantweredissolved ina8Murea,20mMacetate
buffer (pH=5.0), towhich ß-mercaptoethanol wasadded.Theamount
of individual caseins was estimated bymeans ofcolumnchromatographyonaPharmaciaFPLcsystem.AMONO-Scolumnwithasolution
of20mM acetate (pH=5.0)in8M urea asbuffer Aandasolution
of buffer A + 1 M NaCl as buffer Bwere used (Dalgleish, tobe
published).The a ,-caseinanda„-caseindidnotresolveproperly
and were therefore taken together. Estimates of errors are±4%
for a - andß-Caseinand±6%forK-casein.
27
2.13 Partielesizemeasurement
The sizeofcaseinparticles asa function ofpHwasinvestigated by means of Photon Correlation Spectroscopy (PCS) at the
Hannah Research Institute (Ayr, Scotland). Thismethod relieson
thefactthatthefrequencyofthelaserlight,whichisscattered
from a moving particle is Doppler-shifted by the motion of the
particle relative to the observer.Thispropertyhasbeenusedto
determine Brownian motion of particles in solution and henceto
determine their translational diffusion coefficients. Detailed
descriptions of the design andprincipleofthetechniqueandits
application to milk particles are given elsewhere (Home, 1984,
Chu, 1974,Berne and Pecora, 1976, andHoltet. al., 1973).The
2-1
values ofthediffusion coefficient,D (ms ),forskimmilk,diluted in diffusate, were measured at different temperature and
pH. Inactual factsincetheparticlesarepolydisperseanaverage
value ofD, weighted by theintensityofthescatteredlight,was
determined.Thiscorresponded toaz-averaged D.Theparticlediameter, d (m), was calculated from the diffusion coefficient, D
2-1
(ms ),usingtheStokes-Einsteinequation
J
-
kT
37tnD
(2.20)
H=solventviscosity (Pa.s)
T=absolutetemperature (K)
k=Boltzmann'sconstant (Nm.K )
The photon correlator spectrometer (Home, 1984) consisted ofa
scattering photometer with temperature-controlled water bath
(within 0.1 °C) and variable scattering angle turntable,collection optics, and photomultipliertube followedbypulseamplification and discriminator and a Malvern K7026 60 linear channels
digital correlator. The correlator was operated in the singleclipped mode with clipping levels nevergreaterthan3.Thelight
sourcewasaSpectraPhysicsHe-Nelaser,model124B.Experimental
runs consisted of 1.67 to 2.5xl06samples.Measurementsweremade
atanangleof90°.Atlowmeasuringtemperatureaflowofgaseous
N 2 was blown along the glass window of the index-matching bath,
28
inordertoprevent condensation ofwater vapour on it.Thecorrelatorwas interfaced to aDEC11/02computer.Thecomputerdata
analysis was performed on-line within seconds of the completion
ofeachrun.
For samplepreparation large amounts ofstandardskimmilkmade
from skimmilk powder A (see section 2.1)were acidified at0-2°C
topH'svarying from 6.7 to4.6 (seesection2.3).Dialysistubes
filled with aliquots of standard skimmilk (10ml)or a4.5wt.%
lactose solution (25 ml) for the preparation of diffusate were
added tobeakers filled with 800ml of thepH-adjusted skimmilk.
For equilibration the sampleswere storedthreedaysundergentle
stirringat5°Cinacoldroom.
ForPCSmeasurements5(jlofdialysed skimmilkwasdilutedinto
2 ml diffusate ofcorresponding pH.Beforeusediffusatewasfiltered through cellulose nitrate membrane filters (Millipore)of
0.22 urnporesize.
29
3 FORMATIONOFACIDCASEINGELS
3.1 Introduction
Whetheracoagulating system formsageloraprecipitate,isa
very difficult question, largely unanswered by colloidchemists.
It is knownthat factors likeparticle shape,volume fractionof
particles and the ratio between the rate of aggregation andthe
rate of displacement of the particles, due to e.g. convection
streaming, sedimentation or stirring, are important. The gel
state, however, may be defined as one where both the dispersed
componentandthedispersionmediumextendthemselvescontinuously
throughoutthewholesystem.Onecandistinguishbetweengelswith
a reversible and gelswith an irreversible character as function
of e.g. temperature or pH. In fact a gel is usually a kind of
metastablesystembeingfarfromitsabsoluteminimumofHelmholtz
energy (see eq. 3.1),e.g. mostly a particle gel, disrupted by
stirring,willnotspontaneouslyreestablishinthesameway.
This study isconcerned with acid caseingels,made fromskimmilk or sodium caseinate solutions acidified inthe cold.Asalreadyimplicitlymentionedinthetitleofthisthesisandaswill
be shown further on, casein is the main constituent of the gel
network. Gel formationbyproteins ingeneral and casein inparticular depends on pH, temperature, ionic strength, ioniccomposition of the water phase, protein concentration and other more
obscure andmore difficult to define factors (suchastemperature
historyandmechanical agitation).
Preliminaryexperimentsshowedthatforgelformationbycasein
usingthemethoddescribed insection2.3 aminimumcaseinconcentration of about 1.0 wt.%is needed, whereas the ionic strength
should exceed roughly estimated 0.08-0.09M, both for skimmilk
diluted with ultra filtrate and sodium caseinate dissolved ina
salt solution. The critical temperature for gel formation at
pH=4.6 is about8-10 °C.Below this temperature onlypart ofthe
caseincoagulates leadingtoasediment.Therestofthecaseinis
stable against coagulation or coagulates very slowly. With the
methoddescribed insection2.3 gelformationat30°Cisrestric-
30
tedtothepHrangeof4.3 to4.9.AbovepH=4.9caseindoesnotcoagulate at 30°CandbelowpH=4.3 itcoagulates during theacidification process at 0-2 °C. Possible gel formation during that
stage of preparation would be disrupted immediately by stirring,
which isneeded for ahomogeneous distributionoftheaddedacid.
For smooth gel formation it is essential thatthe system isnot
stirred,whenitpassesthecoagulationpointduringheatingleading to gel formation. Convection is largely diminished by slow,
gradualheating.
Section3.2 treatstheformationandageingofacidcaseingels
in general, monitored by measuring the storage modulus,G', and
loss modulus, G", as a function of ageing time.As is knownthe
structure of the caseinparticles,thebasic elements ofthegel
network (section3.4.2 and3.4.3),drasticallychangesuponpHadjustment (e.g. Heertje et al., 1985). Therefore in section 3.3
specialattentionwillbepaidtothechangesoccuringinskimmilk
with respect to thecaseinparticles during acidification atlow
temperature. In section 3.4 amodel forthe acid casein gel networkbasedonexperimentalevidencewillbepresented.
3.2 Formationandageingofacidcaseingels
3.2.1 Ageing_of_§cid_skimmilk_gels
Inthefirstinstancetheformationandageingofacidskimmilk
gels was followedbymeasuringG' andG" (see section2.10.1and
2.10.2) as a function of time at different ageing temperatures
(angular frequency w=1.0 rad.s" ). Acidified standard skimmilk
(section2.3)washeated atarateof0.5 °Cperminfrom2°Cto
the desired ageing temperature. Unless otherwise stated skimmilk
inthischapterwasmadefromskimmilkpowderA (seesection2.1).
Theresultsaregiveninfig.3.1a andb.MeasurementswerestartedaftervisiblegelformationhadoccuredandthevalueofG'was
atleastlargerthan40Nm .Thedeformationwaskeptsufficientlysmall (see also section4.5.1)topreventmechanicalinterference. Gel formation started above 10°C (thatmeans around t=720
s, as t=0 was chosen at the moment thattemperature rises above
4 °C)andincreasedwithtemperature.ThecurvesofG'andG"were
largely similar.Experimentally G' couldbe determinedmoreaccu-
31
û'iNm' 2 )
600
Fig. 3.1a.StoragemodulusG'of
+ - 20°C
x - 25°C
i -30°C
a —tO°C
o —50°C
acid skimmilk gels plotted asa
,4'
4//
400H
function ofthelogarithmofthe
ageing time t(s)at different
ageing temperatures. Att=0the
heating of the acidified skimmilk solution (pH=4.6) at4°C
commenced at a rate of 0.5°C
200
per min. Ageing temperatures:
20°C (+),25°C(x),30°C(A),
40 °C (Q)and50°C (o).u»=1.0
, -1
rad.s
10'
10"
10D
10e
t (s)
F i g . 3.1b. Loss modulus G" of
the same gels as in f i g . 3.1a
p l o t t e d as a function of the
logarithm of the ageing time.
Conditions were the same as in
f i g . 3.1a.
r a t e l y . Between 10 and 20 °C a very strong temperature effect on
the r a t e of gelation was found; after ageing a t 10 °C for 16 hrs
G' had a value of a mere 13 Nm in c o n t r a s t with the value of
250Nm" -2
after ageing for16hrsat20°C.Afteraninitialpe-
32
riod, which included t h etime needed toheat thesystem from 4 °C
to t h emeasuring (and ageing) temperature, G'andG"tended to i n crease linearly w i t h t h e logarithm o f time, except fort h e gel
aged a t50°C. Even after 7 days (6x10 s )gelation still proceeded w i t h o u t a n ysign o f reaching a plateau v a l u e . Iti s thought
probable that t h esystem needs a nalmost infinitely long timeto
reach t h ep o i n t o fminimum Helmholtz energy inherent tot h em e t a stable state o ft h eg e l . T h enumber o fbonds b e t w e e n t h ecasein
particles, which m o s t likely arephysical protein-protein contacts, should increase w i t h ageing time d u et oslow p r o t e i n c o n formation rearrangements.
T a n ô (i.e. t h eratio o f G"/G') is depicted i n fig. 3.2asa
function o fageing time. A sc a nb eseen t a n6 decreased w i t h ageing time, resulting i napproximately thesame value (0.23) after
5x10 sfort h egels aged at2 0 ,2 5and3 0°C. Int h ebeginningo f
gel formation t h estrongest decrease o ft a nôw a sseen. Thisw a s
to be expected, because t a nô o fa solution ism u c h larger than
1.0. T h e final value measured fort a nô forthegels aged at4 0
and 50°Cw a s somewhat lower than 0.23. Apparently t h e elastic
character o fthese gels increased i ncourse o ftime. W ewillr e turn tothis p o i n t i nsection 4.5.3 and4.5.4.
tan6
0,35-
Fig. 3.2. The loss tangent,
+ — 20°C
x — 25°C
A — 30°C
f
!
tan 6, of the acid skimrailk
gels of fig. 3.1 plotted asa
function of the logarithm of
the ageing time t(s).Condi-
0.30-
%v
tions and symbols are thesame
as infig.3.1,except forthe
curveofthegelaged at40°C,
0,25-
which was taken from aduplicateexperiment.
0,20-
10J
1
1
r*
w
w
106
1- (s)
33
The small maximum, occuring after 4.5x10 s in the curve of the
gel aged at 50 °C ( f i g . 3.1a and b ) , can be ascribed to a combined
influence of heating and ageing. As we w i l l see in section 4 . 5 . 3 ,
G' and G" decrease with measuring temperature once a gel i s formed. Thus during heating from 20 to 50 °C the moduli tended to increase due to ongoing gelation, but to decrease due to an increasing measuring temperature. This r e s u l t e d in a small maximum
3
a f t e r 4.5x10 s, when temperature i s 40 °C, and in a small minimum
3
a f t e r 5.8x10 s, when temperature had reached the ageing temperature of 50 °C. The strong increase in G' after 10 s was not seen
for G" (compare f i g . 3.1a and 3.1b). This i s i l l u s t r a t e d more exp l i c i t l y in f i g . 3.2, where a t the moment t h a t G' s t a r t e d to increase more strongly in f i g . 3.1a, a dip in the curve of tan 6
versus ageing time was found. We cannot explain t h i s p a r t i c u l a r
ageing behaviour for the gel a t 50 °C.
3.2.2
l££ëYË£^ible_çharacter_of_gel_formation
Fig. 3.3 i l l u s t r a t e s the i r r e v e r s i b l e character of gel format i o n of acid skimmilk g e l s . A skimmilk solution (pH adjusted to
pH=4.6) was heated in the appropriate way (section 2.3) to 30 °C
and aged a t t h i s temperature. After 18 h r s , when G' had reached a
Fig. 3 . 3 . Storage modulus G'
(o) and loss modulus G" (o)
of an acid skimmilk gel p l o t ted
as a function
of
the
logarithm of ageing time t ( s ) .
After heating in the standard
manner the gel was aged for
18 hrs a t 30 °C, before
it
was stored 4 days a t 4 °C.
Subsequently i t was heated to
30 °C. The temperatures are
i n d i c a t e d . ui=1.0 r a d . s
.
34
value of 400 Nm ,temperature was lowered to 4°C and kept at
that level for four days. Instead of a dissolution of the gel
phaseG'enormously increased, implying adrasticincreaseinthe
number or strength ofthe elastically effectivebondsbetweenthe
protein molecules of different casein particles. Apparently an
acidified skimmilk solution atatemperature of0to4°Cmustbe
regarded as adispersion,which is stableinthecolloidchemical
sense,butthermodynamicallyunstable.
ThestrongincreaseofG'andG"upontemperature loweringwill
be discussed extensively in section 4.5.3. During the ageing at
4 °CG'tended to increase slightly,whileG"slightlydecreased,
giving the gel amore elastic character.Bringingthesystemback
to30°Cresulted inthe sameG'asbeforethecoolingprocedure,
which suggests that the increase inG'at4"Cwasnotduetothe
same effect of ageing as found for the gels aged attemperatures
varying from 20 to 50°C (described insection3.2).Probablythe
observed slight increase ofG'was due to some retarded temperature reversible protein rearrangements of the same kind asthose
whichcausedtheobserved increaseanddecreaseofG'uponrespectivelyloweringandraisingthetemperature.
AcidificationwasfoundtobereversibleinthataskimmilksolutionofpH=4.6 after readjustment topH=6.7bymeansof3NNaOH
exhibitednovisiblecoagulationandlookedstableat4and30°C,
but of course it isquestionable whether the original caseinmicelleswerereformedbythisprocedure.
3.2.3 Skimmilk_gels_made_bY_rap_id_heating
Ina fewexperiments the rheometer filledwithacidifiedskimmilkwasheated within 10-15 s inatemperature jumpfrom4°Cto
respectively 30,40 and 50°C.In fig.3.4themeasuredvaluesof
G' are depicted as a function of ageing time. Again a rather
linear increase of G' with the logarithm of the ageing timewas
found, which was in the case of ageing at30°Cvery similarto
the increase ofG' found for agelheatedatarateof0.5 °Cper
min (fig.3.5a, curve 1 and 3).The smaller increases ofG'with
the logarithm of time for the gels at40 and 50°Cprobably stem
fromthemuchcoarserstructureofthegelnetworkinthesenseof
35
Fig.3.4. Storage modulus G' of
acid skimmilk gels heated in a
single temperature jumpplotted as
a functionofthe logarithm ofthe
ageing time t(s)at three different ageing temperatures. At t=0
the skimmilk solution was heated
within 10 s from 4°C to theageing
temperature
graph). UD=1.0rad.s
(indicated in
•1
verylargeconglomeratesandpores,whichwereevenmacroscopically visible. Probably the large temperature gradient fromthermostattedjackettoinnercylinderduringtheinitialstageofgelation caused a more irregular coagulation, or perhaps convection
streamingresulted inamoreinhomogeneousnetworkstructure.
3.2.4 Different_kinds_of_acidcaseingels
Tohighlighttheinfluenceofthemethodofpreparationonacid
casein gelsG1 isdepicted as a function ofageing time forfive
different acid casein gels in fig. 3.5a. The ageing temperature
was30°CandthefinalpHvaried from4.60 to4.64.
Theageingcurvesforthegelsmade fromstandardskimmilkacidified in the cold and heated in a single jump (no.1)or ata
rateof0.5 °cperminute (no.3)aretakenfromfig.3.4and3.1a
respectively.Asimilartypeofageingcurve (no.2)wasfoundfor
a sodium caseinate gel (casein cone. 2.8wt.%)prepared according
tothesameprocedureasgelno.3.Thissimilarityindicatesthat
skimmilk gels areessentially caseingels (seealsosection 3.4.2
and 4.5.3). Curves 4 and 5weremeasuredongelsmadebyadirect
slow acidificationprocedure at30°C,as isdescribedinsection
2.3. For this purpose the slowly hydrolyzing acidprecursor Glucono-0-Lactone (GDL)wasused.For skimmilk (curve5)coagulation
was visible at 1.8xl04s after the addition of GDL and for the
sodium caseinate solution (curve4) after 3.0xl04s. Arbitrarily
these times were chosen as zero time in fig.3.5a. For skimmilk
38
s,
V
•1.5\
p/
0.5
^ /
J
a
35 25 15
/ \
•1.0
•6
\
•0.5
4°C
35°C
-4
/
/~\io°c
/
30°C
1
~^^~'- ~
ffi°C
s
5
55 6.0 65
TCO
4.5
pH
5.5
6.5
pH
Fig. 3.6. a: the "solubility" S of a - and ß-Casein as function of temperature
for fresh milk at physiological pH. S is expressed as fraction casein in the
serum after centrifugation at 190.000 g (after Reimerdes and Klostermeyer,
1976). b: The total serum casein concentration S as function of pH at two different temperatures for fresh skimmilk after centrifugation at 78.000 g. S is
expressed as mg casein N/ml (after Rose, 1968). c: the voluminosity, v, of casein as function of pH at three different temperatures for reconstituted skimmilk. v is expressed as gram water per gram protein in the pellet after centrifugation at 257.000 g (after Darling, 1982).
s o l u b l e t o t a l c a s e i n as f u n c t i o n of pH a t 4 and 35 °C ( s e e f i g .
3 . 6 b ) . At pH=6.7 t h e s o l u b i l i t y i n c r e a s e d by a f a c t o r 2 . 8 as temp e r a t u r e was lowered from 35 °C t o 4 °C. This a g r e e s w i t h t h e
above mentioned r e s u l t s of Reimerdes and K l o s t e r m e y e r . At 35 °C
t h e serum c a s e i n c o n c e n t r a t i o n i n c r e a s e d only v e r y slowly over t h e
pH range of 7.0 t o 5 . 0 . However a t 4 °C a s t r o n g i n c r e a s e i n serum
c a s e i n c o n c e n t r a t i o n was found w i t h d e c r e a s i n g pH u n t i l pH=5.4,
where a c l e a r maximum was o b s e r v e d . At t h i s pH t h e s o l u b i l i t y a t
4 °C has i n c r e a s e d by a f a c t o r 5.6 as compared t o 35 °C. Another
i n t e r e s t i n g f e a t u r e i s t h e v o l u m i n o s i t y of c a s e i n p a r t i c l e s as a
f u n c t i o n of pH. Voluminosity (g w a t e r p e r g c a s e i n ) can be c a l c u l a t e d from t h e water and c a s e i n c o n t e n t of t h e p e l l e t s l e f t aft e r c e n t r i f u g a t i o n ( c e n t r i f u g a t i o n f o r c e >_ 70.000 g for s e v e r a l
h r s ) of skimmilk samples a t d i f f e r e n t pH and t e m p e r a t u r e (Tarodo
de l a Fuente e t a l . , 1975, D a r l i n g , 1982 and Snoeren e t a l . ,
1984). As can be seen i n f i g . 3.6c ( a f t e r D a r l i n g , 1982) a t lower
t e m p e r a t u r e a maximum i n t h e v o l u m i n o s i t y was a l s o found around
pH=5.4. According t o D a r l i n g t h i s maximum v a n i s h e d a t 30 °C or
39
higher,whereagradualincreasewithpHwasobserved,whereasVan
Hooydonk (1986,tobepublished)still observed asmall,butsignificantmaximum inthevoluminosity at30°CaroundpH=5.4.Further the voluminosity tended to decrease with temperature.
Strikingly thepH, atwhich themaximuminvoluminosityofcasein
at 10°C was reached (Darling, 1982), coincides with thepH,at
which the optimum insolubility at4°Cwasreached (Rose,1968).
However, at30°CVanHooydonk observed themaximuminsolubility
tobe atpH=5.6 ascompared tothemaximuminvoluminosity,which
he observed atpH=5.4. Inthis respect twomain questionsimportant forthis studymaybeput forward; firstly,whathappensto
the structure of the casein particles during acidification to
pH=4.6, and secondly,which caseins andhowmuchofthemdissolve
from thecaseinparticles around pH=5.4?Weshalldealwiththese
twoquestionsinthenextsections.
3.3.2 Çold_acidification_of_skimmilk
In the standardized procedure forthepreparation oftheacid
casein gels askimmilkor asodium caseinate solutionwas cooled
down in a bath filled with ice and water to a temperature of
0-2 °Candkeptthusaround20to60minutesbeforethefirstacid
was added (section 2.3).The subsequentpH-adjustmentwascarried
out in 30 to 60 minutes. The acid additionwas slowed downconsiderablyneartheallottedpHtoensureequilibrium.Afteracidification to pH=4.6 thepH sometimes increased alittle,butnormallyby less than 0.05 unit ofpH.Oneshouldrememberthatdissolution of colloidal calcium phosphate (CCP) and especially of
casein areprocesses which take time. Inthecontextofthissection the same procedure was always followed. Skimmilk and sodium
caseinate solutionswere acidified to apHintherangeof6.7to
4.6.Thesolubilityoftotalandindividualcasein (section2.12),
the caseinparticle size and the intensityofthescatteredlight
(section 2.13) were studied for skimmilk samples stored atleast
24 hrs atlowtemperature.The size and structure ofcaseinparticles in skimmilk and insodium caseinatesolutionsatdifferent
stages of acidification were also studied by means of electron
microscopy (section2.11).
40
3.3.2.1 Solubility
of casein at low temperature
The amount of non-centrifugable casein (centrifugal force
60.000g for 2 hrs) was determined in two ways (section 2.12):
namely by measurement ofthe light absorption of supernatantand
redispersedpellet,andbyquantitativecolumnchromatography.The
last method also afforded the estimation of the soluble fraction
of the individual caseins. Both methods were applied to fresh
skimmilk (section 2.12) and agreed well (comparecurve1tocurve
2 in fig. 3.7a). Inthis graph the fraction of non-centrifugable
total casein isdepicted as a function ofpH after storage times
of 20 hrs (curve1) and 44 hrs (curve2)at5-8 °C.Whether the
smalldifferencesbetweenthecurvesareduetoaneffectofstorage time is not known. Upon acidification the amount of soluble
casein first increased gradually to a maximum of approx. 60%
around pH=5.4 agreeing with the results of Rose (1968, seefig.
3.6b). Between pH=5.2 and 4.8 a very steep decrease of casein
solubilitywasobserved.
In fig.3.7b thebehaviour ofthe soluble fraction oftheindividual caseins after 20hrs.storage isdepicted as a function
ofpH (Roefs et al., 1985). The shape of the solubility curveof
each individual casein was very similar to that of total casein
withamaximumsolubility aroundpH=5.4.AtpH=6.7thefractionof
soluble total casein consisted mainly of ß-casein (70%)withonly
21% of a-casein, which agreed with the results ofReimerdes et
al. (1976,see fig. 3.6a). AtpH=5.4howeveronly51%ofthesoluble caseinwas ß-casein,while the contributionofa-caseinhad
increased to 38%.This considerable increase ofsolublea-casein
at pH=5.4 as compared to pH=6.7 (by a factor 5overall)wasthe
most remarkable result of thisexperiment.The K-caseinfraction
ofsolubletotalcaseinremained fairlyconstant (around10%)over
thewholepH-range.BelowpH=5.4thefastestdecreaseofsolubilitywasseenfor a -andK-casein.
s
Itisprobablethatthedissolutionofcaseinactuallyobtained
duringtheacidificationstageofacidcaseingelpreparationwill
be lower because this stage of lowering the pH from 6.7 to 5.0
takesplace inonly 10 to 20min.However we assume that theobservedtrendswillalsohold forthissituation.
41
soluble total casein(%
Fig. 3.7a. The fractionoftotal soluble casein as a function of pH at
5-8 °C. The amount of soluble casein
was determined (see section 2.12) by
means ofcolumn chromatography (curve
1) and light absorption measurements
(curve 2 ) .The sampleswere storedat
5-8 °C respectively 20hrs (2)and44
hrs(1).
soluble individual casein (%)
Fig. 3.7b. The fraction of soluble
individual caseins as a function of
pH after 20hrsof storage at5-8 °C.
The amount of soluble casein was determined bymeans ofcolumnchromatography. The total soluble caseincurve for these samples is depicted as
curve 1of fig.3.7a.
3.3.2.2 Casein particle
size
Infig.3.8a thecaseinparticlediameter,3,measuredbymeans
ofphoton correlation spectroscopy (section 2.13), isdepictedas
a functionofpHatfourdifferenttemperatures (seealsoRoefset
al., 1985). Samples were prepared by dialysing at 5-8 °C small
amounts of skimmmilkofnatural pH againstlargeamountsofskimmilk directly acidified inthecold.Thisbulk skimmilkwasmade
42
from the same skimmilk powder A (see section 2 . 1 ) . A s a l t diffusate was simultaneously prepared by dialysing an appropriate l a c tose solution against the acidified skimmilk. For measurements a t
temperatures higher than 8 °C the dialysed skimmilk and s a l t diffusate were f i r s t incubated separately a t the measuring temperature and mixed together (5 pi of skimmilk into 2 ml of s a l t diffusate) j u s t before use. Coagulation of casein (below pH=5.0) and
p r e c i p i t a t i o n of calcium phosphate (in the s a l t solutions of pH
below 6.0 and above 6.3 a t 35 °C) r e s t r i c t e d the range of pH
values, at which measurements were possible (see f i g . 3.8a and b ) .
d (nm)
F i g . 3.8a. The average diameter,
d, measured by photon c o r r e l a -
325
tion
spectroscopy,
of
casein
p a r t i c l e s in skimmilk as a func-
300
t i o n of pH. Temperatures are ind i c a t e d . The samples were pH ad-
275-
j u s t e d by means of d i a l y s i s for
40 h r s . The dashed curve r e f e r s
250
to d i r e c t l y a c i d i f i e d bulk milk
a f t e r storage for < 70 hrs a t
225
45
5-8 °C. The e r r o r in the mea5.5
Fig. 3.8b. The intensity I of
the scattered light as a function of pH for the samples of
fig. 3.8a. Measuring temperatures are the same as in fig.
3.8a.
65
surements was < 10 nm.
pH
43
The particle diameter (fig.3.8a) tended to increase slowlywith
pH and to decrease with temperature, which correlates with the
voluminositybehaviourathighertemperatures (seefig.3.6c).The
differences found are relatively small,ifone considers theextended scale on which 3 is plotted. Clearly atall temperatures
investigated no dip in the particle diameter was found around
pH=5.5, which suggests that the dissolution of casein was not
accompanied by complete disintegration of the caseinparticles.
The corresponding intensity, I, of the scattered laser light,
plotted asafunctionofpH (fig.3.8b),showedonlyasmallminimumaroundpH=5.1-5.2at7.8 and15.7°C.Thisminimumvanishedat
25°C. This almost constant particle diameter upon acidification
inspiteoftheconsiderabledissolutionofcaseinagreeswiththe
optimum involuminosity aroundpH=5.5foundbyDarling (1982).
Incontrasttotheparticlediametertheintensityofthescattered light is the same at 7.8 °C and 15.7°C. The relatively
strongincreaseofIat35°Cmustbeascribedtoprecipitationof
CCPonthecaseinparticles.ActuallyalargerminimumofIaround
pH=5.5 than found atT=7.8 and 15.7°Cwouldbemoreinlinewith
expectations, since aconsiderable amountofcaseintendstodissolve from the casein particles at lower temperature (see fig.
3.7a). Surprisingly thiswas found for thescatteredintensityof
thebulkmilksamplesat7.8 °C(fig.3.8b).Thisminimum isrelatively much deeper thanthe smallbut significantminimum inthe
particle diameter,whichwas alsonoticed aroundpH=5.5forthese
samples (seefig.3.8a). Inthiscaseprobablysomedisintegration
of particles had occurred, butthe observed decrease indiameter
of the caseinparticles inbulkmilkatpH=5.5isstilltoosmall
tobe correlated directly to the largeamountofcaseinsolubilized atthatpH.On the otherhandthelargedecreaseinintensity
of the scattered light at pH=5.5 seems to correlate directly to
thelargeincreaseofsolublecaseinatthatpH (seefig.3.7a).
Itisthoughtthattherateofacidification,whichdiffersbetween direct acidification and dialysis regulated acidification,
maybe responsible for the observed differencesbetweenbulkmilk
anddialysedmilk,sincethedissolutionofCCPandofcasein,and
the rearrangement of casein molecules aretimedependentprocesses.
44
In summary itappears thatthe optimum involuminosity ofcaseinparticlesaroundpH=5.5atlowtemperature istheresultofa
dissolvingofcaseinandCCPfromparticles,theparticlesretainingapproximatelythesamediameter.
3.3.2.3 Electron
micrographs
of
skimmilk
Electronmicroscopy isoneofthemostcommonlyusedmethodsof
studying the structure and size of all kinds ofproteinsystems.
It has oftenbeen applied tomilk andmilkproducts (e.g.Kalab,
1981 and Schmidt, 1982b). In this study Transmission Electron
Microscopy (TEM)wasused to study the caseinparticles inskimmilk (made from skimmilk powder A, section2.1).RecentlySchmidt
(1982b)has discussed the problems andpossibilities of applying
TEMtomilkandmilkproducts.Thedehydrationandembeddingsteps
mayinfluencetheobservedproteinstructures.Particularly atlow
temperature someprotein denaturation mustbe takenintoaccount,
because the hydrophobic and electrostatic bonds in proteins are
sensitivetothesepreparationsteps.
Fig. 3.9 showselectronmicrographsofthreedifferentskimmilk
samples,namelypH=6.7at30°C,pH=5.3at4°CandpH=4.6at4°C.
The samples were prepared according to section 2.11. At pH=6.7
freecaseinparticles (approximatediametervarying from70to250
nm)canbedetected (fig.3.9a), agreeingwithresultsreportedin
literature (Henstra and Schmidt, 1970a and b and Davies et al.,
1978). The observed particle diameter is anunderestimate ofthe
true value, because the embedding medium used (amixture ofstyrène and n-butylmethacrylate)tends to shrink duringpolymerisation (Glauert,1975).
Apart from casein particles with a less compact structure a
largeamountoffinelydispersedcaseinisseenatpH=5.3and4°C
(fig. 3.9b). The finely dispersed casein particles probably stem
fromdissolvedcaseinmolecules,whichhavereaggregated toacertainextent,andfrommoreorlesscompletelydisaggregatedcasein
particles. No apparent change was seen in the diameter ofthose
larger particles still present.A similar effectwas observedby
Heertje et al. (1985)inelectronmicrographs of skimmilkacidifiedbymeans ofGDL at30°Cand 43°Cto apHvarying from 6.7
45
.M
#
+ *¥•
'
**L « r
* *
• :* 4
•
^ W . * rf * >*> j *'sJ*P;' **
-.f*
(a)
• ç • 'é. »
9»
1
(b)
* •f
f'
Fig. 3.9. Electron micrographs of
•-.' w
standard skimmilk at different pH
'(•-.
\.
*
and temperature, a: pH=6.7, 30°C.
-*»
b: pH=5.3, 4°C. c: pH=4.6, 4°C.
The magnification is indicated.
- —» 3 F
-•• 5 „. tim _
(c)
to4.8.Howeverthey reported adisaggregation ofcaseinparticles
aroundpH=5.2-5.4,whichwasevenmorepronounced thanobserved in
thisstudy.
At pH=4.6 the finely dispersed casein has reaggregated again
(fig. 3.9c).Whenextrapolating theseE.M. resultstothe standard
46
acidificationprocedureofskimmilk (section2.3),whichtookonly
30-60min,ithastobeconsideredthatintheE.M.experimentthe
samples were kept several hours atpH=5.2before the pH-endpoint
of4.6wasreachedandfixationwasstarted.
3.3.3 Çold_acidification_of_sodium_caseinate_solutions
Theappearanceofasodiumcaseinatesolutionchanges,whenits
pH is lowered, from rather clear,greylikeatpH=6.7tocolloidal
white and turbid atpH=4.6,where itisnolongerdistinguishable
from skimmilk. Hardly anyvisible coagulation occurs and thepHadjusted solution is colloidally stable at0°C for severaldays
atleast.Obviously the transition from arathertransparenttoa
turbidcaseinsolutioniscausedbytheformationofcaseinaggregates of considerable size (diameter probably largerthan20nm),
in which probably individual casein molecules or smaller aggregatesofthesamesizeasthesocalledcaseinsubmicellesareinvolved.
This formation of aggregates was confirmed by electronmicrographs of sodium caseinate solutions (in 0.16 M NaCl) at three
stages of acidification (fig. 3.10). At pH=6.7 and 4°C (fig.
3.10a) casein was visible as very finely dispersed, somewhat
threadlike structures. It is possible that protein denaturation
resultinginthethreadlikestructureshasoccuredduringthepreparationprocedure,aswassuggestedbySchmidt (1982b).Usingthe
same micrograph preparation procedure Schmidt obtained identical
(threadlike) structures for disintegrated casein micelles. These
he believed were casein submicelles. Applying a freeze-etching
techniquetospecimensofspray-frozensolutionsthesesubmicelles
were visible as small spherical particles (Schmidt, 1982b). Obviously considering fig. 3.10a and the clear grey appearance of
sodium caseinate onemay conclude that atpH=6.7sodiumcaseinate
molecules are present as individual molecules or as smallaggregates.
AtpH=5.3 and4°C (fig.3.10b)thecaseinislessfinelydispersed and the first visible casein aggregates are formed. At
pH=4.6 and 4°C (fig.3.10c)all casein is aggregated into small
particles, as were also observed in skimmilk samples ofthatpH
(fig. 3.9c). Based on themicrographs thediameter of theaggre-
47
*
r
<
....
(a)
J^*
J!L*
|%X
t
Î A ^ î f t
k,fflr"< P v
"%\ *% •.
^ ^ ^ ..
(b)
'-•••
fc
,
* . •**•#'•*'
*
*• ^k*
"^"' • -v/ ^ " « L
« • *« *
Fig
' 3 ' 10 " E l e c t r o n micrographsof
sodium caseinateatdifferentpHa:
pH=6.7,b:pH=5.3, c:pH=4.6.Tem'
perature 4°C. NaCl conc. 0.16mol
per kg dispersion. Themagnificationisindicated.
*
(c)
gatesmaybeestimatedtobe20to40nm.Theactualdiameterwill
belargerbecauseofthepossibleshrinkageduringsamplepreparation mentioned in section 3.3.2.3. In fig.3.10c some of thecasein particles seem tohave coagulated.Apparently at4-5 °Cthe
casein particles formed in sodium caseinate solutions atpH=4.6
are no longer colloidally stable and tend to coagulate after a
48
longer storage time. Before fixation the sample at pH=4.6 was
stored forseveralhoursat4-5 °C.
3.3.4 Discussion
Inregarding the aggregation ofcaseinmoleculesleadingultimatelytotheformationofagelonehastorealizethatdifferent
stagesandlevelsofaggregationcanbedistinguished;namely,the
aggregation of individual casein molecules leading to theformation of small aggregates, which probably quite often aggregate
further to larger,under certain circumstances metastableparticles;theseparticlesmayaggregateintostrandsandconglomerates,
whichultimatelywillformacontinuousgelnetwork.Thestability
against coagulation of these metastable casein particles isdirectly related to their internal structure,which depends onthe
mutual interactions between the different casein molecules and
abovepH=5.4alsoontheinteractionsofcaseinwithCCP.Probably
inbothcasesthe.caseinparticles formedarenotcompletelyhomogeneous. Acidification and temperature variation will alter the
internal structure. On acidification not only CCPwilldissolve,
but the extentof aggregation andprobablythearrangementofthe
caseinmolecules insidetheparticleswillchange,too.
Differentinteractionsase.g.VanderWaalsattractiveforces,
hydrogen bonding, hydrophobic bonding, electrostatic interactions, aswell as steric factors,willbeinvolved.Hydrophobic
bonding may be of crucial importance, as it strongly increases
withtemperaturebetween0andabout40°C(e.g.VanVliet,1977).
The interaction between charged areas depends on factors suchas
pH,ionicstrengthandsaltcomposition,whilethesolventquality
stronglyinfluencesthestericterms.
In general the change ininteraction between caseinmolecules
inside casein particles during acidification is governed by two
main mechanisms: a tendency to aggregatewith decreasing pH (the
proteinisbroughtclosertoitsisoelectricpoint)andatendency
to disaggregate because ofdissolution ofCCP. Inabsence ofCCP
onlythefirstmechanismplaysapart.Forsodiumcaseinateaggregation of casein molecules was found to start justbelowpH=6.0
andwascompleteatpH=4.6.Thisisschematicallydepicted infig.
3.11.
49
Fig. 3.11.Schematicalpictureofthe"solubilsolublecasein(%)
ity"ofcaseinatlowtemperature(0-4°C)asa
^On
functionofpHforskimmilk( )andsodiumcaseinate solution ( ).Caseinwhichcannotbe
pelleted by centrifugation at60.000gisregarded as soluble. The curve for skimmilkis
derivedfromfig.3.7a.
Disaggregation ofcaseinmolecules isobserved inskimmilkbetween pH=6.7 and pH=5.5 at low temperature (section 3.3.2). All
three kinds of casein investigated (a-, ß-and K-casein)dissociate from the casein particles (see fig. 3.7b), while theparticle diameter remains fairly constant (fig.3.8).Somedisintegrationofcaseinparticlescannotbeexcluded atpH=5.5and5°C.
Howeverthiswillbefarfromcomplete,whereasdissolutionofCCP
atpH=6.7leadstoacompletedisintegrationofcaseinmicelles.
TheextentofcaseindissociationatpH=5.5coulddependonthe
rateofacidification,asissuggestedbythedifference inintensity of the scattered light as function of pH between dialysed
milk andbulkmilk (fig.3.8).Rapid acidificationmay lead toa
faster dissolution of CCP, followed by a larger dissociation of
casein.Perhaps then inthepH range around 5.5 the time forthe
individual casein molecules wouldbe too short to compensate the
lossofinteractionwithCCPbymutualcasein-caseininteractions,
whichmight require protein conformational rearrangements.Casein
dissociation possibly will be decreased, when the rate ofacidificationisdecreased,sinceproteinrearrangementsmaycompensate
thedissolutionofCCP.Attheotherhandwhenrapid acidification
is carried outuntil apHbelow 5.0 casein dissociation mightbe
decreased,too,sincethelossofCCPmaybecompensatedbyanincreased amountof+- ionic interactions.Suchadependencyofthe
molecular structure and size of the casein particles on pH and
perhaps their temperature history demands painstaking studiesto
revealpreciselywhatoccurs.
Twopossiblemechanismscanbepostulatedtoexplainthefairly
constant particle size during acidification to a pH around 5.4.
Firstly andmost likely, the dissolution ofCCPandcaseinisac-
50
companied by a swelling ofthe residual casein. Secondly, casein
particles consistof a framework ofprotein,whichismostlyassumed to consist of one or twoofthedifferentkinds ofcasein
(e.g.Linet. al., 1972), filledwithmorelooselyboundprotein.
Inourview the results depicted infig.3.7 and3.8particularly
favour the first mechanism. BelowpH=5.5 the amount ofdissolved
caseinsteeplydecreases.Electronmicrographs (fig.3.9 and 3.10)
suggest that soluble casein not only reassociates with already
existing particles,but alsomay formnew aggregates of thesame
sizeasfound forsodiumcaseinate.
Sothe final result ofthemechanismsdescribed aboveisthat,
although the casein particles above pH=6.0 and below pH=5.0 are
complete different entities,they havemore orlessthesamediameter;thisdiameterisalsofoundinthetransitionregion.
3.4 Networkmodelforacidcaseingels
3.4.1 General_descrip_tion_of
_p_ossible_models
Continuityofstructureandpermanencyofthatstructureisthe
general feature of a gel, apart from a relatively large volume
fraction of the continuous liquid phase. Flory (1974) distinguishes four different types of gels: 1, ordered, lamellar gels
(e.g.soapgelsandphospholipids);2,networksofcovalentcrosslinked flexible polymers (fig. 3.12a); 3, networks of flexible
polymers with crosslinks formed byphysical aggregation (seefig.
3.12b);4,particulatedisordered gelse.g.flocculatedclaysand
b. \
\
Fig. 3.12. Highly schematic representation
of four different types of gels, a: a polymer networkwithpermanent covalentcrosslinks, b: a polymer network with semi-per-
d.
m
manent crosslinks formed by physical aggregation, c: A particulate structure consisting of strongly anisotropic particles,d:a
particulate structure consisting of identical hard spheres (afterPapenhuizen, 1972).
51
most partly crystalized fats (fig. 3.12c and d ) .Inreality the
spatial arrangement of the basic elements in the last mentioned
systemsismuchlessregularthandepicted infig.3.12c andd.
The nature, size, shape and spatial distribution ofthebasic
elements forming the network, the permanent or non-permanent
character of the junction points, and the entropie or enthalpic
natureoftheinteraction forcesarethemainfeaturesforfurther
classification of agel.For acomprehensivetheoreticaldescriptionofproteingels,whichisnotachieveduntilnow,elementsof
theories forbothmacromoleculargels (fig.3.12a andb)andparticlegels (fig.3.12c andd)willberequired.
Deformation of protein gelswill lead to an increase inHelmholtz energy, A, arising from both a decrease ofentropy andan
increase of internal energy (van Vliet and Walstra, 1985). The
change in Helmholtz energy, dA, at constant temperature, T, is
writtenas:
dA=dU-TdS
(3.1)
whereUisinternalenergyandSisentropy.Sincebothvolumeand
pressureareconstantinourexperiments,theHelmholtzenergy,A,
equals theGibbs energy,G, and theenergy,U,willequaltheenthalpy,H.
Deformation causes astretching ofthe strandsofthegelnetwork. If one considers a network, to which anexternal forceis
applied in the direction x, one can according to van Vliet and
Walstra (1985)derive the following equation forthemodulusGof
thenetwork:
G=CN^
d2A
dx^
(3.2)
whereN isthenumber ofstrandsperunitareainacrosssection
perpendicular to x bearing the stress (i.e. the force per unit
area). C is a characteristic length determining the geometry of
the network. In the case of anetwork ofparticle strands dAis
the change in Helmholtz energy (eq. 3.1),when theparticles in
thestrandsaremovedapartoveradistancedx.
52
Equation 3.2 is generally valid for small deformations (Van
Vliet and Walstra, 1985), because the force exerted should be
proportional tothedeformation.Fromeq.3.2 itisclearthatthe
elasticorshearmodulusG (andalsothedynamicmoduliG'andG")
depends on the homogeneity of the gel network expressed in the
number of stress carrying strands,N; further it depends onthe
character and number of bonds between the basic elements inside
the strands, asexpressed inthe change oftheHelmholtzenergy,
dA.Thecharacterofthebondswillbedeterminedbythenatureof
the interaction forcesbetween thebasic elements.Inthecaseof
a network of particles,which arehomogeneously distributed over
the available space,allparticles will contributetothenetwork
modulusGtothesameextent.Nwillthenbedirectlyproportional
to thevolume fraction ofparticles,<(>.Inthecaseofaninhomogeneous distribution only a fraction of the particles (see e.g.
fig. 3.12d)will carry the stress andNwillbenolongerproportional to <)>.Insuch circumstances Gwill beproportional to<j>x,
wherex>l (VandenTempel,1979).
In a gel of aggregated particles (fig. 3.12c and d) such as
margarine or flocculated clays the interaction forcesareonlyof
enthalpic nature. Then on deformation the increase of Helmholtz
energy stems from anincrease of internalenergyratherthanfrom
adecreaseofentropy.
This is not the situationwith idealpolymer gels (fig. 3.12a
andb)e.g. rubber gelswhich consistoflongflexiblemacromoleculescrosslinked atpermanent or semi-permanentjunctionpoints.
The chain segments between the crosslinks are so long thatthey
haveaverylargenumberofpossibleconformationsimplyingasubstantial conformational entropy. They will behave as statistical
coilsandtheenergeticorenthalpiccontributionstotheincrease
ofHelmholtzorGibbsenergyondeformationofthesegelsarenegligible. Then the increase ofHelmholtz energy stems only froma
decreaseofentropy.
Oftenproteinmolecules,althoughlongchainmolecules arefoldedintoacompactandcomplicated structure,whichcanbeclassified as secondary, tertiary and even quarternary structure.Such
compactfoldedproteinmoleculesmayberegarded asparticleswith
a non-uniform structure and surface.Most denaturedproteins,al-
53
though almost without secondary structure, are still constrained
in their spatial arrangement by the diverse character of their
amino acids and are far less flexiblethanordinaryhomopolymers.
Upon aggregation they,too,willbehave toalargeextentasparticles andnot as flexible macromolecules. Bothadecreaseofentropy and mostly amore important increase ofenthalpy willcontributetoanincreaseinGibbsenergy,whensuchproteingelsare
deformed.Onlyinafewproteingelsasforexampleelastin(Norde
et al., 1985) and gelatin (Te Nijenhuis, 1979) is the entropie
contributiontodAinequation3.1dominant.
A casein gel originates from the coagulationofparticlesconsisting of at least several hundred of casein molecules.These
particles, consisting of 70-80 wt.% of water, are probably not
homogeneous inthat the distribution of thedifferentcaseinsmay
change from the outside tothe coreoftheparticles.Theyshould
probably also be regarded as easily penetrable and deformable,
dynamic entities.After coagulation the formation ofsemi-permanent bonds between casein molecules at the boundary of adjacent
particles will be very likely.The formation of entanglements as
inthe case of long flexible homopolymers seemslessprobable.It
isunlikely that all coagulated particles willcontributeequally
to themacroscopical gelproperties.Some oftheparticlesmaybe
•incorporated in large non contributing conglomerates or aggregates, as illustrated schematically in fig. 3.12d for a gel of
hard spheres. Indications of an aggregate-like structure ofacid
casein gels have been given e.g. by Harwalkar and Kalab (1981).
Suchinhomogeneitywilldrastically influencethemechanicalproperties of the gel formed (see above).TouseanoldDutchsaying:
the strength of awhole chain equals the strength of theweakest
link. Therefore the mechanical properties of acid casein gels
dependnotonlyonthenumberandnatureofbondsbetweentheparticles,butalsoonthespatialdistributionoftheparticles.The
last factor determines that fraction ofthetotalnumberofbonds
which effectively contributes to the mechanical properties. To
study the spatial distribution bothpermeability measurementsand
rheological measurements (measuring the dynamicmoduli G'andG")
as a function ofconcentration ofthebasic elements ofthenetworkweremade.Allparticles,whichpossiblycantakepartinthe
54
gelnetwork areregarded asbasic elements.Permeabilitymeasurements give information about the large inhomogeneities at the
level of the gelnetwork (VanDijk, 1982). To these measurements
anE.M.studyofacidcaseingelswasadded.Toavoidconfusionwe
will distinguish between heterogeneity at the level of the gel
network and at the level of the structure oftheproteinparticles. For amore extensive discussion see section 3.4.3 andsection4.6.
3.4.2 Exp_erimental_results
Inorder to obtain information aboutthebasicelementsofthe
networkinanacidcaseingelandabouttheirspatialdistribution
thepermeabilityanddynamicmoduli (G'andG")ofdifferenttypes
ofacid casein gelswere measured asafunctionofcaseinconcentration. The size and shape ofthebasic elementswas studiedby
meansofelectronmicroscopy.
3.4.2.1 Storage
modulus as a function
of casein
concentration
To study the role ofdifferentmilkcomponents,acidgelswere
madeasafunctionofcaseinconcentration followingthreedifferent procedures. The results are shown in fig.3.13,where G'is
plotted as a function of casein concentration on adoublelogarithmic scale.All gelswere aged for16hrsat30°Cbeforemeasurement.
Curve1 refers to gels made by dissolving skimmilk powderB
(section2.1) in demineralized water. Along with the casein the
concentration of all othermilk components (e.g.salts)variedto
the same extent.The resultwas acurvedlineexhibiting astrong
dependenceofG'onthecaseinconcentration.
For curve2 the casein concentration was varied by means of
ultra filtration atpH=6.7 (section 2.5). This allowedtheselective separation of casein micelles with bound CCP andwheyproteins from lactose, salts andwater.With this technique thecaseininstandardskimmilk (caseincone,is30gperkgdispersion)
was concentrated at 30°C and the separated ultra filtrate was
used to lower the casein concentration below that of standard
skimmilk by dilution. Inthiswayprimarily theconcentration of
55
Fig. 3.13. Storage modulus G' as afunction
of casein concentration C (gram per kgdispersion) for three different types of acid
casein gels. 1:skimmilkpowderdissolved in
demineralized water. 2: a standard skimmilk
solution concentrated ordilutedbymeansof
ultra filtration. 3: sodium caseinate dissolved in 0.12 M NaCl. Gels were aged at
30°Cfor 16hrs.ui=1.0rad.s".
50
100
C(gkg"1)
components w i t h m o l e c u l a r m a s s greater t h a n 10,000 w a s varied.
Thus a t p H = 6 . 7 the ionic strength and composition could b e kept
almost c o n s t a n t w i t h v a r i a t i o n in p r o t e i n c o n t e n t . H o w e v e r a t
pH=4.6 the ionic strength and composition still varied because of
the CCPd i s s o l v i n g from thec a s e i n particles during acidification.
This v a r i a t i o n , h o w e v e r , w a sfarless than incurve 1.A sa c o n s e quence of the smaller v a r i a t i o n o f I, curve 2 is less b e n t than
curve 1. Furthermore the m i n i m u m casein concentration at w h i c h a
gel could b e formed w a s lower for skimmilk gels made b y dilution
w i t h u l t r a filtrate (curve 2 , minimum casein concentration <12
g/kg) t h a n for gels m a d e b y dissolving skimmilk powder in different amounts o f water (curve 1, minimum casein concentration ~ 1 5
g / k g ) . These differences are probably due to a higher ionic
strength a t l o w casein concentration i nt h eskimmilk diluted with
ultra filtrate. A d d i t i o n o fNaCl toa skimmilk solution (according
56
to curve 1)with a lowcasein concentration sothat theionic
strengthwasraised tothesame value asofa solution madeby
diluting standard skimmilk with ultra filtrate, resulted inthe
samevalueforG'asforagelofcurve2atthesameproteinconcentration.Theionic strengthatthelowestcaseinconcentration
of curve1 and2 that agelcould bemade wasnearly thesame
(approximately 0.09M and 0.1M respectively), although these
minimumcaseinconcentrations (~15g/kgand~11g/kgrespectively)
differed significantly (seefig.3.13). This indicatestherelativelymoreimportantroleoftheionicstrength.Anestimationof
the ionic strength of standard skimmilk atpH=4.6 is givenin
section4.5.5.1.
Inthethirdprocedure gelsweremadefrompuresodiumcaseinateandaslittle saltaspossible.Noothermilkcomponentssuch
as lactose and serum proteins were present. To obtain agela
minimum levelofNaCl (~0.10M)wasfoundnecessary.Forthisexperiment alsoasmall amountofCaCl2 (~0.007M,i.e.fivetimes
lessCathanthelevelinstandardskimmilk)wasadded.Replacing
this small amountofCaCl_byNaClandkeepingtheionicstrength
constantdidnotinfluencesignificantlythevaluesofthedynamic
moduli obtained. Theresult forG'asa function ofthecasein
concentration wasastraight line (curve 3)withaslopeof2.6
fallingslightlyhigherthantheothercurves (seefig.3.13).
Similar resultswere obtained forG"asafunctionofthe casein concentration. ForgelspreparedbyallthreemethodstanÔ
varied between 0.21and0.24overthewhole casein concentration
range.
From thesimilarityofthethree curvesmaybeconcluded that
the gelnetworkwasprimarily builtupofcasein. Serum proteins
and lactosewerenotimportant.Theamountofsaltplayed aprominentpart,whereasthetypeofsaltseemedtobelessimportant.
The difference inslopebetweenthethree curves couldbedueto
different variations of ionic strength. This will be discussed
moreextensivelyinchaperIV(section4.5.5.2).
FromthestrongexponentialdependenceofG'onthecaseinconcentration(G'~c')itcanbeconcludedthatthenumberofstress
C3.S
carrying strands, N (seeeq.3.2),wasnotproportional tothe
volume fractionofcaseinparticles,andsothenetwork formedwas
57
veryheterogeneous.The heterogeneity ofthe spatialdistribution
ofthebasicelementsformingthegelnetworkwillbeinvestigated
inmoredetailinthenexttwosections.
3.4.2.2 Electron
micrographs
of acid casein
gels
To study the spatial structure of the acid casein network,
electronmicrographsofgelsmadefromacidifiedskimmilkandfrom
acidified sodium caseinate solutions (section2.3),wereprepared
asdescribed in section 2.11.The gelswere aged for atleast16
hrsat30°Cbeforefixation.A fewtypicalexamplesofthemicrographs obtained are shown in fig.3.14.Thepictures oftheacid
skimmilk gels (fig.3.14a andb)areverysimilartothoseofthe
acid sodium caseinate gels (fig.3.14c and d), whichmightbeexpected from the similarity inrheological properties (fig. 3.5a,
fig.3.13 and section 4.5.3 to4.5.5)andsupportstheconceptof
casein as main constituent of the network in acid skimmilk gels
(section 3.4.2.1). The electron micrographs are very similar to
those reported by Harwalkar and Kalab (1981) for acid skimmilk
gels, made by heating coldly acidified skimmilk to 40°C, using
HClandcitricacidasacidulants.
Both types ofcasein networks consist ofcoagulatedparticles,
which have only partly fused. The coagulated particles are not
homogeneously distributed over the available space.They tendto
begroupedindenseareas,whichcanbeconsidered aslargeaggregates and conglomerates.Onthe other hand the areaswithoutcasein represent the relatively large meshes of the gel network.
Only a fewparticulate strands are seen,which isnot surprising
if one remembers the thickness of the thin sections (60-100nm,
seesection2.11).
The diameter of the particles of acid sodium caseinate gel
(d=50-100 nm) seems to be slightly smaller than in case of the
acid skimmilk gel (d=80-300 nm).In the acid skimmilk gel most
particles have adiameter ofaround 100nm.Onmicrographs taken
fromacidskimmilkgelswitheitherhalfordoublethecaseinconcentrationparticles had roughly the same size.Comparingthegel
situation with that existing prior to aggregation i.e. comparing
the size ofthepartly fusedparticles in fig.3.14 with thatof
58
(a)
(b)
mm
Ü^.
i
» **-•*
4Er
<*
V
#5»
(c)
V
V *
(d)
Fig. 3.14.Electronmicrographs ofacid skimmilk gels (aandb)and acid sodium
caseinate gels (c and d ) .pH=4.6. The sodium caseinate gels were aged for 16
hrs at 30°C. The skimmilk gels were aged for 25 hrs (a)and 170 hrs (b)at
30°C.
0.5um
59
theparticles of fig.3.9c (skimmilk atpH=4.6and4°C)andfig.
3.10c (sodium caseinate solution at pH=4.6 and 4 °C)suggests,
particularly for sodium caseinate,an increase indiameterofthe
proteinparticlesduringgelationinducedbyheating,whereasfrom
voluminosity and particle size experiments (fig.3.6c and fig.
3.8a) adecrease inparticle diameter withincreasingtemperature
wouldbe expected, ifone assumes thediameteroftheseparticles
tobechangedreversiblywithtemperature.Bearinginmindpossible experimental error involved in the preparation procedures,
theseresultssuggestthat,particularly, forsodiumcaseinate,it
is small casein particles which first coagulate to form larger
particles.Thesesubsequentlytakepartintheformationofbigger
aggregates and strands of particles ultimately resulting in the
formation of agel.To confirm thisphenomenonmanymoreelectron
micrographs will be necessary using other E.M. techniques.With
the datapresently available itisvery difficult to give areasonableexplanation fortheobservedphenomenon.Howeveraneffect
of acidification rate cannot be excluded. In the preparation of
the E.M. samples the acidification rate was much higher forthe
gels (fig. 3.14) than forthe samples ofnon-aggregated skimmilk
atpH=4.6 and 4°C (see fig. 3.9c).Becauseofthehigherrateat
which thepH range from 6.0 to 5.0 waspassed,possibly lesscaseindissociated fromthecaseinparticlesatapHaround5.4than
suggested infig.3.9b andc (seealsosection3.3.2.2),resulting
in larger particles at pH=4.6 before and after heating. On the
otherhandoneshouldrememberthatreachingapHend-pointinthe
range 5.2 to 6.0 atahigheracidificationratewillpossiblyincrease the amount ofdissociated casein. Itishoweverclearthat
caseinaggregationoccursinstepsandatdifferentlevels,dependingonchangingconditionssuchastemperature,pHetc.
Inmost ofthe electronmicrographs adegree of anisotropy is
seen. This isprobably due to aslight sample deformation during
the cutting of the thin sections with the microtome (section
2.11).Atthemarginoffig.3.14c thecontoursofthreesmallfat
globules can be seen,their surface partly consisting ofcasein.
These fat globules are incorporated in the gel network and in
principle they should enlarge the rigidity ofthe gel (vanVliet
60
and Dentener, 1983). However because of the low fat content
(around 0.1 wt.%or less)the effectonthedynamicmodulishould
benegligible.
3.4.2.3 Permeability
of acid casein
gels
..
2
. . .
Thepermeabilitycoefficient,B (m ),ofacidskimmilkandacid
sodiumcaseinategelswasdeterminedusingDarcy'slawforlaminar
flowthrough aporousmedium (eq.2.1,section2.8).AsBdepends
on the homogeneity and geometric structure of theporousmedium,
inprinciple informationabouttheseparameterscanbeobtainedby
measuring B. An equation for B as a function of the geometric
parameters can be derived assuming arather simple networkmodel
(seesection3.4.3.2).
Inthissectionexperimentalresultswillbepresented. Ineach
experiment 10 to 14 tubes were used with 4 consecutivemeasurementsofBpertube.
In fig. 3.15 the permeability coefficient B of acid skimmilk
gels is depicted as a function ofcaseinconcentration,bothona
logarithmicscale.Thecaseinconcentrationwasvariedbymeansof
ultra filtration (section 2.5).As can be seen the permeability
exhibited avery strong dependence on thecaseinconcentration.A
straightlinewithaslopeof-3.3wasfound,whichimpliesthatB
-33 the heterogeneity at the
is proportional to [casein] '. Thus
levelofthegelnetworkwasverymuchconcentrationdependent.
In fig. 3.16 the permeability coefficient B of acid skimmilk
gels is depicted as a function of the measuring temperature for
gels aged for 16hrs atrespectively 20°C, 30°Cand 40°C.All
experiments were carried out twice, except for the gel aged at
30°C and measured at 40°C, which was measured only once.The
standard deviation in each experiment varied from 0.05 to
0.25x10-13m2,while the difference between twoduplicateexperi-13 2
mentswas0.04x10
m atmost.
It is clear that ageing temperature affected Bmuchmore than
the measuring temperature. The relatively small variation with
measuringtemperaturemaybeascribedtoadecreaseinvoluminosity with increasing temperature (e.g. Darling, 1982 and see fig.
3.6c). The great influence of the ageing temperature onBshows
61
Fig. 3.15. Permeability coefficient, B (ra) ,as
a function of casein c o n e , C (gper kg dispersion), foracid skimmilkgels.The caseinconcentration was varied by means of ultra filtration
(section 2.5).The gels were aged for 16 hrs at
30°C,beforemeasurement at30°C.
10
20
50 100
C(gkg-1)
thatthetemperature atwhichinitialgelformationtakesplaceis
ofgreatimportance forthespatialdistributionofthebasicelements. This was confirmed by measuring the permeability of acid
skimmilk gels heated at different rates to 30°C, followed by
ageing at30°C (table 3.1).Coagulation andgelformation,which
startabove10°C,need acertaintimeforcompletion.Thusatthe
lowest heating rate gel formation should occur atlowertemperature. In agreement with the results shown in fig.3.16 a lower
temperatureduringgelformationresulted inalowerpermeability.
Unfortunately theexactmechanismofhowthecoagulatingparticles
form the network has not yet been elucidated.Wewill returnto
theeffectoftemperatureonpermeability insection3.4.3.
All experiments on acid casein gelspointtothefactthatthe
permeability of these gels after initial gel formation hardly
changed with ageing time in contrast to rennet gels (VanDijk,
1982), indicating that possible rearrangements of the gelnetwork
62
B(KT13m2
2.0
Fig.3.16.Permeabilitycoefficient,B(m),
as a function ofmeasuring temperaturefor
acid skimmilk gels. The gelswereagedfor
1.5-
16hrsattheindicatedtemperatures.
1.0-
after that stage were only very local and did not influence the
overall structure. After 16 hrs ageing time acid casein gels did
not show syneresis. Nor did B increase with time due to the pres3
-1
sure gradient (between 4.5 to 6.0x10 Pa.m ),as found for rennet
gels, which are sensitive tomicrosyneresis (see section 2.8).The
heating of the gelation vat used in the permeability apparatus
(section 2.8) always lagged behind that of the thermostatted bath
because of a slow heat transfer. Therefore the actual heating rate
in the vatwas lower than the programmed one.This isprobably the
reason for the small difference in the values found for B, when
acid skimmilk was heated at rates of 30 and 12 °C/hr (table3.1).
However within each experiment this delay in temperature rise was
always the same, so that the determined trends are real. However
the absolute value of the measured permeability coefficients is
probably too lowbecause gel formation occurred at a lower temperature than the programmed one.Therefore for comparison Bwas measured for acid skimmilk gels made in tubes placed in a graduated
cylinder. This cylinder was heated in direct contact with the
liquid of the thermostatted bath (table 3.2). In agreement with
the results given above a significant increase of B from 1.5 to
-13 2
m was seen. Using another gelation vat with a faster
2.0x10
heat transfer also resulted inhigher values for B; for gels, aged
63
Table3.1 Theeffectofheating rateonthepermeabilitycoefficient,B(ra),
ofacidskimmilkgels.TheskimmilkwasmadefrompowderB(section2.1).After
heating the gelswereagedat30°Cfor16hrs.Thenumberofexperimentsis
giveninbrackets.
B(10~13m2)
Heatingrate(°C/hr)
30
1.4710.18(3)
12
1.43+0.16(2)
4
1.15+0.09 (2)
at respectively 25 °C and 30 °C, B increased to 1.37x10
13
m
2
(section 5.3.1) and 1.78xl0~ m (section4.5.5.2) instead of
-13
2
m
(estimated from fig. 3.16) and
approximately 1.15x10
1.5x10 ^ m .
The permeability coefficients of acid sodium caseinate gels
—13 2
m , see table 3.2) are considerably lower
(1.06 and 1.04x10
than those of acid skimmilk gels of the same casein concentration
(1.8xl0~ 13 m 2 for 2.62 wt.% and 2.0xl0~ 13 m 2 for 2.76 wt.%, as
derived from fig. 3.15). The fact that the two sodium caseinate
samples had equal permeabilities, while they differed in casein
concentration, may be due to experimental error. The explanation
for these results is not clear. The tendency of a smaller B for
acid sodium caseinate gels agrees with the slightly smaller particle diameter observed on the electron micrographs of these gels
(fig. 3.14c and d ) , assuming that the total volume fraction of
particles is more or less the same. Besides, the considerably
smaller diameter observed at4 °C after acidification (fig.3.10c)
and the fact that an acidified sodium caseinate solution tended to
coagulate at lower temperature suggest that formation of a more
homogeneous gel network should bepossible.
Finally in table 3.2 two values are given for the permeability
of acid skimmilk gels made at 30 °cwith GDL. The permeability of
GDL induced gels was slightly, but significantly higher than that
of standard acid skimmilk gels. The difference may be due to the
lower temperature atwhich gel formation starts in skimmilk acidi-
2
66
Fig. 3.17. Highly schematical two dimensional p i c t u r e of the d i s t r i b u t i o n of
casein p a r t i c l e s in an acid casein gel (pH=4.6). The casein p a r t i c l e s have d i a meters of 80 to 200 nm. The dashed l i n e surrounds a conglomerate of coagulated
p a r t i c l e s . The p i c t u r e may be regarded as a p r o j e c t i o n of a t h i n s e c t i o n of the
gel network (with a thickness of a few p a r t i c l e s ) on the horizontal plane. The
cross sections of a l l strands in the d i r e c t i o n perpendicular to the plane are
omitted.
not showing the cross sections of a l l strands in the d i r e c t i o n
perpendicular to the horizontal plane.
The exact mechanism for gel formation in acid casein gels i s
not yet known. I t i s clear t h a t i t occurs in different s t e p s ,
which depend p a r t i c u l a r l y on temperature and pH. During a c i d i f i c a tion a l l individual casein molecules aggregate f i r s t into casein
p a r t i c l e s , which d i f f e r strongly from the casein micelles in milk
of natural pH. Upon heating the casein p a r t i c l e s w i l l coagulate
and small strands and small conglomerates w i l l formed. Out of
these l a r g e r conglomerates with a l e s s dense s t r u c t u r e are formed.
Subsequently the gel network consisting of the strands and of the
small and large conglomerates of p a r t i c l e s w i l l be formed. That
formation of a very open network s t r u c t u r e i s possible in t h i s
way, has been indicated by Sutherland and Goodarz-Nia (Sutherland,
1967, Sutherland and Goodarz-Nia, 1971, Goodarz-Nia and Sutherland, 1975), who simulated by means of computer c a l c u l a t i o n s the
floe s t r u c t u r e in a system of coagulating p a r t i c l e s .
67
The spatial structurewith its largeporesandthusthepermeability of acid casein gels isdetermined by the ageingtemperatureinthefirststageofgelformation.Differentfactorsmaybe
involved inthe formation ofthe spatialstructure,i.e.thediffusion rate of the coagulating particles, the activation energy
for coagulation, the interaction energy after coagulationandfor
rearrangementofthegelnetwork.AthighertemperaturestheactivationHelmholtz energy for aggregationwill decrease,whichpossibly will lead to a coarser network. As will be discussed in
chapter V (section 5.4.3.2)rearrangement of acaseingelnetwork
as inthe case ofmicrosyneresis ofrennetgels (VanDijk, 1982)
will only occur at high values of tanô, which for acid casein
gels are only found attheverybeginning ofgel formation (fig.
3.2). However,when only a fewbonds orweakbonds existbetween
theparticlesofastrand,thechancethatallbondswillbreakat
the same time increases strongly.Then spontaneousruptureofgel
strands despite a low value of tanômay occur. Soonly athigh
temperatures,wherethedynamicmodulihavedecreasedsignificantly (section4.5.3),canrearrangementsoccurtogiveacoarsergel
network.
Inthenextchapterweshalldiscussinmoredetailthedifferent interaction forces responsible for aggregation offirstlyindividualcaseinmoleculesandsecondlycaseinparticles.
Inthe next sectionwe shall comparethemeasuredpermeability
valuesinrelationtothebuiltupoftheacidcaseingelsasdiscussedinthissection.
3.4.3.2
Comparison of the measured permeablitu
geometric
models
with that of some
Van Brakel (1975)and Scheidegger (1960)attemptedtodescribe
thestructureofaporousmediumusingageometricalmodel,having
thesamemacroscopicalpropertiesasforexamplethepermeability.
Each geometric model is a simplification of the real spatial
structure. We will compare thepermeability coefficient ofthree
models (Scheidegger, 1960)with the experimental values foracid
caseingels.
68
Themostwidely used equation forthepermeabilityofaporous
medium is the so called Kozeny-Carman equation (Scheidegger,
1960).Thevoidstructureoftheporousmedium isrepresentedbya
bundleoftortuous,non-interconnectingchannelsofvariouscrosssectionsbutof adefinite length.Thepermeability iscalculated
from the flowthrough the channels and inthe first instanceexpressed intermsofthespecificsurfaceareaandtheporosity (e)
oftheporousmedium.Forasystemofspheresthespecificsurface
area may be converted into the volume surface average diameter,
d ,whichresultsinthefollowingequationforB (m )(VanDi]k, 2
1982):
c3H2
ed
B=
——,
(3.3)
180(l-er
However theporosity, e, shouldbe smallerthan0.5 (Scheidegger,
1960). This condition is at first sight not met in an ideally
homogeneously built up acid casein gel. From fig. 3.6c (after
Darling, 1982) a total volume fraction of approximately 0.1
(e=0.9)canbe calculated for the acidcaseinparticlesatpH=4.6
and30°Cinstandardskimmilk.Thisisinthesamerangeasfound
for unrenneted casein micelles at pH=6.7 and 30°C (Walstra,
1979).
A refinement of thismodel maybefoundinthesocalled "cutting and joining model", recently proposed by Maghoub et al.
(1982). In thismodel thebundle ofchannels is slicedperpendicular to their length and thenthecutisrejoinedafterarandom
rotation.Howeverthismodelrequiresaporesizedistributionobtained from a capillary pressure curve and, because of this,is
notapplicabletoacidcaseingels.
The theory of Iberall, which may be called a "drag theory"
(Scheidegger, 1960) and which holds only fordilute systems,appearsmore attractive at firstsight.Theporousmedium isrepresented by arandom distribution ofcircularcylindrical fibresof
thesamediameter,6.Thepermeability iscalculated fromthedrag
force needed tomove liquid along thefibres.Thisistakentobe
equal to the flow resistance oftheporousmedium.Theseparation
between the fibres and the length of the individual fibresmust
••
69
bothbe large compared to the fiberdiameter,ô.Alsothedisturbance due to adjacent fibres on the flow around any particular
fibermustbenegligible.Bisgivenby:
B
=3 / 1 6 f ! j i ^ | §
(3.4)
where Re istheReynolds number (seeeq.2.2) asdefined insection2.8.1.
ThetheoryofBrinkmanalsohasitsbasisinthedragtheoryof
permeability. The solidmatrix is assumed toconsistofspherical
particleswithradius,R,keptinpositionbyexternal forces.The
permeability coefficient,B, iscalculated from thedampingforce
exertedbytheparticlesonthevelocityoftheliquidflowaround
themandcanbewrittenas:
îïï(3 + l k - 3 V(îV3)]
B=
<3"5>
A firstrefinement of this theorywouldbetheincorporationofa
particle size distribution. Equation 3.5 is applicable to media
withbothlowandhighvolume fractionsofparticles.
If one estimates that the porosity, e, of ahomogeneous acid
casein gel of standard casein concentration is 0.9 and thatthe
average diameter of the particles or strands is roughly between
100 and 200nm (fig.3.14)Bcanbecalculatedwithequations 3.3
to 3.5. These calculations give values for B which are far too
low.Thisisclearlyillustrated infig.3.18,whereBisdepicted
asafunctionofthevolume fraction, ty(=l-e),ofthecaseinparticles (both on a logarithmic scale) for the three models mentioned.Forparticlediameter (eq.3.3 and3.5)orstranddiameter
(eq.3.4)avalueof200nmwaschosen.SinceBisproportionalto
the square of the diameter, itwill strongly increasewithpart-15 2
ielesize.At<)>=0.1thecalculatedB's,varying from9x10
m to
-14 2
6x10
m , are almost an order of magnitude smaller than the
-13 2
values for acid casein gels (1.0-2.0x10
m ).Moreovertheconcentration dependence at<)>=0.1(theslope ofthecurvesherevariesfrom-1.15to-2.7,seefig.3.18)ismuchsmaller (exceptfor
theKozeny-Carmanmodel)than that found experimentallywherethe
70
Bim?)
1.
12
10 2.
Fig. 3.18. Permeability coefficient, B (m ) ,
3
io
13
\
as a function ofvolume fraction ofthedis1
persed solid phase, <j>, calculated forthree
1^-1.15
different model systems. Themodels used are:
I
\
1. Kozeny-Carman. 2.Iberall. 3.Brinkman.T h e
V/ \
slope ofthe tangent ofthe curves at(p=0.1is
Y*-2.7\
*>-*-
-16/* l\\
I >A
I \
\
\
indicated. The diameter o fthe particles (cur\
ve 1and3 )or strands (2)w a schosen to b e
200 nm.
10*-
tr*-
i
0.01
0.1
1.0
slope was -3.3 (see fig.3.15). Obviously the geometric models
describedabove,representamuchmorehomogeneous systemthanthe
acid casein gel.Van Dijk (1982)proposed that the structurally
very similar rennet gels can be considered as particle gelsbut
withmuch largerparticle diameters than thoseoftheprimarycasein particles (whose diameter is around 100-200 nm).If these
large particles (actually the product of aggregation of primary
caseinparticles)areassumedtoconsistofdenselypackedcasein,
their permeability will be negligible compared to the largevoid
spacesbetween the largeparticles,where noproteinisfound.An
obviouschoiceisthentotakethedenseregions (largeconglomerates) in fig.3.17 as the permeability determining units. The
dense regions areconsidered as spherical withatleastatenfold
largerdiameter (1-10^m)thantheprimarycaseinparticles.Since
the diameter has increased, somusttheeffectivevolumefraction
beincreased,becausethelargeconglomeratescontainalotofextra liquid.Recalculating thepermeability coefficient,B,witha
tenfoldlargerparticlediameter (eq.3.3.and3.5)orstranddia-
71
meter (eq.3.4)showsthatthecurvesinfig.3.18willbeshifted
vertically tohigher values ofB over atleast two decades.Ata
volume fraction of 0.4 to 0.5 the correct permeability isfound
according to the models ofbothBrinkman andKozeny-Carman.Also
atthisvalueof0,theslopeofbothcurveshasdecreasedtoeven
below-3.3,whichconfirmstheapplicabilityofboththesemodels.
Moreover, the minimum porosity requirement of the Kozeny-Carman
modelisalsomet.
Our general conclusion isthat the acidcaseingelcanberepresentedbyaporousmedium,consistingofsphericalaggregatesof
caseinparticles.The diameter ofthese aggregatesisoforderof
micrometers and the effective porosity is approximately 0.5.The
diameter of the poreswill then approximately equal thediameter
oftheaggregates (seefig.3.17).
72
4 RHEOLOGICALCHARACTERIZATIONOfACIDCASEINGELS
4.1 Introduction
As discussed intheprevious chapter acasein gel isbuiltup
of partly fusedparticles,which intheir turnconsist ofaggregated casein molecules. Such a gel has a rather inhomogeneous
structure,both atthe level ofthe gelnetwork and atthelevel
of the particles themselves. It exhibitsviscoelastic properties
i.e. (Ferry, 1980) it exhibits both the viscous properties ofa
fluid and the elastic properties of asolid. Suchproperties are
most fruitfully studied using rheological techniques. Inrheology
one studies the deformation of amaterial inrelationtoboththe
applied force and to the time scale overwhich that force isapplied and the deformation ismeasured. Rheologyisalsoconcerned
with thosematerial properties which determine thedeformationas
afunctionofforceandtime (Darby, 1976).
Therheologicalpropertiesofanacidcaseingelwilldependon
the spatial distribution of the contributing particles and the
kindandnumberofbondsbetweenandwithintheparticles (section
3.4.1 and3.4.3).Differenttypesofinteraction forcesmaybeinvolved in the formation of bonds between and within the casein
particles.The type,number andmagnitude ofthedifferentinteraction forces largely influence the rheological behaviourofacid
casein gels. In anequilibrium situation, the lifetime (thetime
ofexistence)ofthebonds,whetherstressedornot,isofparticularly crucial importance for the ratio between the viscous and
elasticcharacterofthegel.Moreover,thespatialstructureofa
gel network, such as a casein gel made from skimmilk by rennet
action atpH=6.7 (VanDijk, 1982), may changewithtime,duetoa
constantbreaking and reformation ofbonds. Inanideallyelastic
solid allbondshave apermanent character,whileideallyviscous
behaviour indicates that all bonds have an ephemeral character,
suchthatthelifetimeofthebondsisseveralordersofmagnitude
smaller than the time scale of deformation. Inrelation tothese
aspects one has to realize that the measurement of rheological
propertiesisalwaysconstrainedtoacertainlimitedtimescale.
73
In this chapter acid casein gels are characterized mainly by
one type of rheological measurements i.e. dynamic measurements.
Special attentionwillbe given to arheological characterization
of viscoelastic properties and to the different types of interactionforcesinvolvedinbuildingupthegelstructure.
4.2 Rheologicalmeasurements
A sample maybe deformed invariousways (such aselongation,
bending,compressionetc.).Aparticularlysimpleandcommonlyapplied typeofdeformation isthe socalledsimpleshear,whichis
mathematically relatively easy to describe (Darby, 1976). The
principle of simple shear is illustrated in figure4.1a. A force
is applied parallel to the surface of a rectangular body. The
force per unitof surface area,called the shear stress, a(Pa),
causes a deformation expressed in the shear deformation, y.For
an ideally elastic body (a so-called Hookean body), where all
bondshaveapermanentcharacter,onecanwrite:
a/y =G
(4.1)
where G (Nm )-2
is called the shear modulus or elastic modulus.
Aftertheshearstress a isappliedthebodywilldeforminstantaneouslytoafixeddeformationy.Theoppositebehaviour isdemonstrated by an ideally viscous fluid, where the lifetime of the
bonds is several orders ofmagnitude smaller thanthe time scale
ofdeformation.ForanideallyviscousfluidNewton'slawholds:
a=ndy/dt=n i
(4
'2)
where n (Nsm )is the viscosity. As soon as a stress o isapplied,theliquidwillstarttoflowataconstantrate (dy/dt=y).
However forviscoelasticmaterialstherelationbetweenstressand
deformationcannotbesimplygivenbyequations4.1 or4.2.Usuallyevenacombinationisnotsufficient,becausebothGandnwill
dependontheappliedstressandonthetimescaleofthemeasurement, as a result of breakage and formation of bonds (whether
spontaneous or forced)inthe time scale ofdeformation. Inthis
context one can distinguish between static and dynamic experi-
74
•y=tana
Fig.4.1a Illustrationof simple
Fig. 4.1b
shearonacross sectionofa
strain and stress as a function of
Sinusoidal variation of
rectangular body, a (Pa)isthe
time foraviscoelastic material (for
shear stressand y=tan a isthe
further explanation,see text).
sheardeformation.
merits.Instaticexperimentstheshearstressa,thedeformationy
orthedeformationrateyarefixedatt=0andeithery(t)ora(t)
aremonitored as a function of time.Indynamicexperiments aand
y are varied with time in an oscillatory, generally sinusoidal
fashion. The deformation is usually kept sufficiently small to
prevent disruption ofthe gelnetwork andsoensurelinearviscoelastic behaviour, which implies that a isproportional to yfor
all applied deformations. In terms ofbonds, linearviscoelastic
behaviour means that the measurement (i.e. the applied deformation)mayinnowayinfluencethespontaneous formationandbreaking ofbonds,or the strength of thosebonds.Neither may formationorbreakingofbondsbeinduced.Thetimescaleofthedeformations can be adjusted very easily by changing the frequency of
deformation.
When a viscoelastic material is deformed sinusoidally at a
frequencyw (rad.s )accordingto:
y(t)=yQsinwt
(4.3)
where yQ is the maximum deformation (deformation amplitude), the
shearstress a isgivenby:
a(t) - aQsin(ujt+ô)=a (sinwtcosô+coswtsinô;
(4.4a)
75
wherea isthemaximumstress (stressamplitude)and6,thephase
difference between deformation and stress (see fig.4.1b),originatesfromtheviscouspropertiesofthematerial.Duringadeformation cycle, stress carrying bondswill spontaneously break and
new stress-free bonds will be formed. In this way part of the
energy stored inthe system willbe dissipated asheat.Whenthe
deformation y passes through y=0, a number of bonds,whichwere
formed in the preceding half of deformation cycle, have already
been deformed in the opposite direction. Therefore a(t) passes
througho=0atatime ô/m priortothispoint (seefig.4.1b).The
stress functiono(t)therefore runs ahead ofthedeformationy(t)
byaphaseangleô.
In the case of an ideally elastic solid ô equals zero and
stress is exactly inphase with deformation. For an ideally viscous fluid ô equals l/2n and stress is completely out of phase
with the deformation,but inphasewith the rateofdeformation,
dy/dt. In this respect equation 4.4a may be split up into an
elasticpartandaviscouspart.Forlinearviscoelasticmaterials
a willbeproportional toy .So4.4a canberewrittenas:
a(t)=y (a/ycosôsinwt+a/ysinôcoswt)
elastic
(4.4b)
viscous
The first term at the right hand side ofequation4.4b contains
thepart of the stress inphasewiththestrain,i.e.theelastic
part of the stress. This corresponds to the elastic or storage
modulusG',whichisdefinedas
G'(u>)=CTo/yQcosô
(4.5a)
G' is a measure of the energy stored and released per cycle of
deformation. The second term at the right hand side ofequation
4.4b containsthepartoutofphasewiththestrain,i.e.theviscouspart of the stress.This correspondstothelossmodulusG",
whichisdefinedas
G"(ut)=ao/yosinÔ
(4.5b)
76
G" represents theviscous character ofthematerial,itisameasureoftheenergydissipatedorlostasheatpercycle.Theratio
ofthemaximum shear stress, a , tothemaximumshearstrain,Y
equalstheabsolutevalueofthecomplexshearmodulusG*:
lG*l =V*o
(4.6a)
whereG*canbewrittenas:
G*=G1 +iG"
(4.6b)
In this study special attention is given to the loss tangent
tan6,whichisdefinedas:
tan ô(u>)= G"(u))/G'(u))
(4.7)
4.3 Interpretationofrheologicaldata
The way in which energy is stored or dissipated in a system
during aperiodic application of stress dependsonthetimescale
of this process.Formacromolecular gels arelationmaybe found
for G' and G" as a function ofw as shown schematically infig.
4.2.Thecurvesforthreedifferenttypesofpolymeraredepicted.
Fig. 4.2 Schematicpicture ofdynamic
logG.G (Nnf2)
moduliG' (solid lines)and G" (dashed
lines) as a function of w, bothona
@
G'
/''" "\G"_
@.®,'
^v
M
(b)
/,
\\
\\
\
\
\
\t
(£)//
logarithmic scale,fornot chemically
crosslinked polymers of rather high
(b)and low (c)molecular weight and
for aslightlyvulcanized rubber(a).
The slope of G' and G" forcurve (b)
logeu
atsmallw is indicated.
77
Curves b and crefer topolymers ofrespectively ratherhighand
lowmolecularweightbothwithoutchemicalcross-linkages.Curvea
refers to a slightly vulcanized rubber, which has a permanent
character even atvery small u>.The curve ofG'particularly for
case a, may be characterized by two plateau regions:therubber
plateau, which isthe lower, and theglassy region,which occurs
at very high frequencies. These plateaus are linked by a glass
transition area.Thepartof the curvesatlowwwhereG"exceeds
G' (case b and c) iscalled the terminal zone. Inthis studywe
areinterestedinthetimedomainwhichcorrespondstotheso-called rubber plateau. In contrast with the ideal systemb infig.
4.2 the lifetime ofthephysical bondsinacidcaseingelsvaries
considerably,whichcausesanincreasseofthedynamicmoduliasa
functionoftuovertheentirefrequencyrangestudied.
In the time scale considered in this study the magnitude of
the storage modulusG' is approximately proportional totheelastic modulus G and so to the effective number ofbonds (equation
3.2, section 3.4.1). Inprotein gelswecanconsiderasbondsall
protein-protein contacts whether of a permanent or a temporary
character.Thesebonds will beboth intramolecularandintermolecular. Moreover in acid casein gels,which inmany respectshave
the features of a particle gel (section 3.4.3), intermolecular
bonds between protein molecules in differentparticles determine
certainly in the first stage ofgelationtherheologicalpropertiestoalargeextent.
During aperiodic application of stress (orstrain)energycan
be stored in a bond. The lifetime of a bond, whether it breaks
spontaneously or by an applied stress,isusually called therelaxation time.Generally speaking strongbonds withalargeenergy content will have along relaxation time.Theywill establish
thepermanent orelastic character of agel.Weakbondswillgenerally break and reform spontaneously over much shorter time
scales. They will contribute to the temporary character of the
gel network. Inacid casein gelsbondswith alargevariation in
energy contentwillbepresent causing awidevariationinrelaxationtimes.
Inthis respectthe lifetime of abondmustbecorrelatedwith
the oscillation time of the applied deformation. Therefore the
78
time scale (i.e.the frequency)ofthedynamicmeasurementsisof
crucial importance. Non relaxing bonds only contribute to G',
whereas rapidly relaxing bonds only contribute toG". Bondswith
relaxation times in the time scale of the measurement willcontribute to both G' and G". Because at short time scales fewer
bonds might relax than at longer time scales,an increase ofG'
withfrequencycanbeexpected (seee.g.fig.4.2).
Forpolymers such asvulcanized orunvulcanized rubbersG"can
be ascribed to the spontaneous formation and breaking of bonds
causedbypolymer backbone configurational changes (Ferry,1980),
e.g. rotation ortranslation ofcomplete chains (atthebeginning
ofthe rubberplateau in fig.4.2) orchainsegments (intheglass
transitionareainfig.4.2).Foraproteingelwithahighliquid
contentnotonlyprotein-proteinbutalsoprotein-waterbondsmust
be considered, since energy is also dissipatedbyliquidmovement
alongthestrandsandconglomerates,andbyliquidmovementinand
out of the strands and conglomerates. Water-water bonds do not
havetobetakenintoaccountbecauseoftheirveryshortlifetime
(~10 -13
s).However themost important contribution probablystems
from the dissipation of energy caused by the protein-protein
bonds (VanVliet,1977)relaxingduringadeformationcycle.
In an inhomogeneous gel network such as that of acid casein
gels (fig. 3.17) many of the particles, incorporated into the
largeconglomerates,willnotcontributeeffectivelytothemagnitudeofthemoduliandotherrheologicalproperties.Thereforethe
effective number of bonds,which depends on theparticleconcentration and spatial distribution (section 3.4),willbeconsiderably smaller thanthe total actual numberofbonds.Thevaluesof
bothmoduli,G'andG" at acertainuuwill depend onthespatial
distributionofthebasicelements,thisdetermining theeffective
number of bonds,and onthe relaxationbehaviour of thosebonds,
thisbeingrelatedtotheirenergycontent.Itseemsreasonableto
assume thatthe dependence ofG' andG"on the spatial distributionwillbemore or less the same.This causes the ratio G"/G'=
tanôtobealmostindependentofthespatialstructure.Therefore
tan ô will be more related to the nature of the bonds and the
relative importance of the different types ofbonds.Sotanômay
be amuchmore sensitive parameter thanG' and G" for indicating
79
1
n
'
! VWV 4 —Q -
Figi4.3Themaxwellelement.
changes inthenature ofthebondsorinthecontributionsofthe
different typesofbonds.
4.3.1 Relaxation_sgectrum
Usually inrheology thedistribution ofallbondswithrelaxation times, t,isdescribed bymeans oftherelaxation spectrum
H ( T ) (Darby, 1976andFerry, 1980). H(t)indicatesineach interval ofxbetween tandt+dt thenumber ofbonds with relaxation
times in that interval, multiplied bythemodulus belongingto
thosebonds.Inprinciple H ( T )canbederived partlyorcompletely
from allmeasured rheological parameters. Different rheological
parametersintheir turncanbeexpressedineachother usingH(r)
(Ferry, 1980). In such a theoretical approach bonds aremostly
describedbyamechanical analogue e.g.themostcommonly usedis
the maxwell element, consisting of a spring anda dashpot in
series (seefig.4.3).Themaxwell element,inwhich theapplied
stress isuniformly distributed, ischaracterized byamodulus Gof thespring andaviscosity ru ofthedashpot.Therelaxation
time T• isgivenby:
t i•= t]i/Gi
(4.8)
Based on this analogy, mathematical relations between H(t)and
G'(w) resp. G"(w) can be derived foran experimental system
(Ferry, 1980):
+»
22
ƒ H(t)
G'(u»)=G e+ƒ H(t)
*"I 2 Jü-t
dinT
-o°
1+uTT'
(4.9)
where G isthesocalled permanentnetworkmodulus,whichrepresents thebonds which donotrelax even att=». Inthis respect
t=» does notcorrespond to infinity, buttoextreme long times.
OtherwisethedefinitionofG Q wouldberedundant.
e
80
+00
G"(u))=ƒ H(T) "*I2 dinT
-oo
(4.10)
1+U) T
Itisclear that for agiven H ( T ) bothG'andG"dependonu>and
on x-. At each frequency w the bonds relaxing at T~1/W are of
specialinterest.Theyareresponsible fortheincreaseofG'with
increasingiuinthatparticular time domain.SoanincreaseofG'
with iupoints to an increasing number of bonds, which are no
longer able to relax during one deformation cycle. Bonds witha
relaxation time close to1/wwill alsogivethelargestcontributiontoG" atthat frequencyw,because thesebondswill be able
tocarry stress for aconsiderable time and to relax inthe same
deformationcycle,andsotodissipateafairamountofenergy.
4.4 Interactionforcesinacidcaseingels
The conformation of an isolated protein molecule depends not
only on intramolecular solute-solute interactions, but also on
solvent-solute andsolvent-solventinteractions.Thepresenceofa
secondsolute,e.g.lowmolecularweightelectrolyte,alsoaffects
conformation. The structure and conformation ofcaseinparticles
willalsodepend,inadditiontotheabove-mentionedinteractions,
on intermolecular protein-protein interactions. Basically these
intermolecular interactions are no different from the intramolecularones.Therewillbeacompetitionbetweenthem.Themain
interaction forces, which give rise to these interactions,are:
hydrophobic bonding, formation of hydrogen bonds,Van der Waals
attraction and electrostatic interaction. Steric interactionsmay
also be involved. These types ofinteraction forceswillbriefly
be discussed below. In the case of unfolded orrandom coil like
protein molecules, bonds may also be formed by entanglements,
whicharetheresultofmultipleinteractions.Althoughsimilarin
nature the mathematical formulation will be different for all
interaction forces except hydrophobic bonding in the case of
interaction between different casein particles. Interactions, in
2+
wich Ca bridges are involved, can be considered as a special
case.
81
4.4.1
SYçlroghobiç_bonding
The term hydrophobic bonding refers to the tendency ofnonpolar groups to aggregate inwater,therebydecreasingtheextent
of their interaction with the surrounding water. In fact, the
hydrophobiceffectarisesprimarily fromtheentropygainofwater
molecules no longer surrounding a non-polar surface (Tanford,
1973). The attraction ofthenonpolar groupsforeachotherplays
onlyaminorpart.
Thermodynamically, hydrophobic bonding is characterized by a
positiveenergeticorenthalpiceffect (oftheorderof1.5kJ/mol
at25 °C)and alargerpositive entropieeffect (ca.3kJ/mol at
25 °C),which results inanegative Helmholtz orGibbs energyof
formation (seeeg.3.1)oftheorderof1.5 kJ/molat25°C(Némethy and Sheraga, 1962). The entropy gain is attributed to adecreasednumberoforderedwatermoleculesafteraggregationofthe
solutes, whereas the positive enthalpic term would arise from a
decrease in hydrogen bonds between thewatermolecules.The free
energy for the formation ofhydrophobic bondsatmoderatetemperatures becomes more negative onraising the temperature.Nemethy
and Sheraga (1962) predicted an interaction maximum for hydrophobicbondingofaliphaticandaromaticgroupsatresp.331Kand
315K.VanVliet (1977)foundaninteractionmaximum forpartially
esterfiedpolymethacrylic acidat~325K.
4.4.2 Yän_der_Waals_attraction
TheVanderWaalsinteractionbetweenmoleculesarisesfromone
or more of a family of generally attractive forces,namely:permanent dipole-permanent dipole interactions (described by the
Keesom equation), permanent dipole-induced dipole interactions
(described by the Debye equation) and induced dipole-induced
dipoleinteractions (describedbytheLondonequation).Thepotential energy for all three types of interaction isrelated tothe
intermolecular distance x by an inverse sixth power dependence
(Hiemenz, 1977).ThepotentialenergyofthevanderWaalsattractionbetweenparticlesofmolecularsizeisgivenby:
V a =-ß/x6
(4.11)
82
where ß is a constant representing the various constants inthe
Deye, Keesom and London equations. For large particles at relatively small interparticle distances the LondonVanderWaalsattraction energy can be calculated to a fair approximation by
(Hiemenz, 1977):
V =-Ar/12H
(4.12)
a.
whereA istheHamaker constant, ristheparticlediameterandH
is the shortest distance of separationbetween theparticles.As
canbeseentheVanderWaalsattractionforlargeparticleshasa
longrangecharacter.
4.4.3 Electrostatic_interactions
Even attheir isoelectric pH the caseinscontainseveralresidues carrying either positive ornegative charge. Inthe caseof
simple coulombic interactions, which areof a long rangenature,
the potential energy (negative or positive)between such groups
would be inversely proportional to their distance apart.However
in asalt solutionpartof thechargewillbescreenedbycounter
ions,which arepartlymobile intheneighbourhoodoftheprotein
molecule or partly bound as ionic pairs (Oosawa, 1971). The distributionofcounter-ionsoverbothclassesdependsonchargedensity, ionic strength, I,and nature andvalencyofthesaltions.
Oppositely-charged groups will attract each other andintramolecularandintermolecularsaltbridgeswillbeformed. Inthiscontext even originally equally charged groups may attract one anotherwhen the charge ofone ofthemisalteredbyanassociation
of a divalent counterion such as for example Ca binding2+to a
negatively charged phosphate residue. Because of the high Ca
concentrationatpH=4.6theformationofsuchCa 2 + bridgesisvery
muchapossibility.
When aproteinmolecule as awholeispositivelyornegatively
charged, then, under certain conditions, the interaction between
twoproteinmolecules or aggregated proteinparticlescanbedescribed by the so-called DLVO-theory (Hiemenz, 1977). In this
theory the attractive term arises from van der Waals attraction
2+
83
(eq.4.12). Thegenerally repulsive electrostatic termisrelated
among other things to the electricalpotential atthe surfaceof
the charged species and to the thicknessoftheelectricaldouble
layer,i.e.thedistanceoverwhichtheelectricalpotentialdrops
to1/etimesitsvalueatthesurface.However,forvalidapplicationoftheDLVO-theory, the distancebetweentheindividualsurface charges should be much smaller than the thickness of the
electricaldoublelayer.Thisconditionwillnotbemetforcasein
atpH=4.6.For caseinmicelles atpH=6.7,wheretheycarryaconsiderable negative zeta-potential (e.g. Dalgleish, 1984), Payens
(1979) calculated a thickness of only 1.1 nm for theelectrical
double layer.This is asmallvalue ascompared to the irregular
molecular structureattheboundariesofthecaseinmicelles.Upon
acidification the surface potential will decrease due to thedecrease of charge and the ionic strength will increase (section
4.5.5.1). Both factors will diminish thedouble layerthickness,
while the distance between individual chargeswillincrease;thus
atpH=4.6theDLVO-theory isnolongervalid.Probablymostofthe
chargesatpH=4.6willoccurseparatelyorinsmallpatches.
The ionic strength determines the extension of electrostatic
interactions and thereby the decrease ofpotentialwithdistance.
Atincreasingionicstrengthbothelectricalrepulsionandattractionwillbe lowered;when the repulsiveelectricaleffectsdominate,thismayleadtoamorecompactproteinconformation;aless
firmprotein conformation is foundwhen theattractiveelectrical
forces dominate. During acidification of casein in skimmilk the
number of negative charges will decrease, whereas the number of
positive charges will hardly increase.At thesametimetheionic
strengthwill increase due to the dissolutionofCCP.Thusduring
acidification the +- electrostatic attraction may possibly only
increase as a result of rearrangement of protein molecules.At
pH=4.6 the electrostatic interaction between and within casein
particles will depend on the interaction between individual
chargedgroupsorsmallchargedpatches.
4.4.4 Hydrogen_bonds
Hydrogenbonds,althoughhaving arelatively largeenergycontent, very often are of minor importance, because they require
84
fixed spatial positions for the contributing molecular groups.
Moreover, there is always a competitonwith hydrogen bonding to
water molecules in an aqueous environment. Therefore hydrogen
bonds areprobably only important intheapolarcenterofprotein
moleculesorinstructuredproteins.Schmidt (1971)couldonlyexplain the formation of tightly bound dimers of a ,-casein at
pH=2.5 by assuming a contribution from hydrogen bonds. One may
thereforeassumethatforacidcaseingels (pH=4.6)hydrogenbonds
cannotbeneglected.
4.4.5 §teric_interactions
Particles with flexible,hydrophilic macromolecules protruding
fromtheirsurfaceintosolutionmaybeprotected againstcoagulationby arepulsive mechanism due tothesemacromolecules.Ifthe
particles approach closely, theprotruding chainswillinterpenetrate (Walstra and Jenness, 1984) or become compressed; this
causes loss of conformational entropy and thus produces interparticlerepulsion.Repulsionbyhydrationmayalsooccuronclose
contact of the individual hydrophilic macromolecular chains.The
total effect iscalled steric repulsion and itsmagnitude maybe
oftheorderofafewkTpermolecularchain (WalstraandJenness,
1984).
Steric stabilization, originating from all kinds offlexible,
hydrophilic (charged or uncharged) casein fragments,willbeinvolved inthe stabilization ofcaseinparticles.AtpH=6.7steric
repulsion may even be the main factor in the stabilization of
casein micelles (Walstra, 1979). At pH=4.6 steric repulsion may
still contribute considerably to the stability ofthecaseinparticles.SinceitsGMP-portionisnegativelychargedatpH=4.6 (see
section 5.3.1), K-casein mayplay aparticular role inthisstability,whilstthesoap-likestructureofß-caseinmayalsoplaya
part.
4.5 Experimentalresults
4.5.1 Introduction
In thispartofthe study theproperties ofacid casein gels,
prepared from skimmilk and sodium caseinate solutions (according
85
to section 2.1 to 2.3),weremainlytestedwiththedynamicrheometer, described insection2.10.1 and 2.10.2.The effectofpH,
measuringtemperatureandionicstrengthonthedynamicmoduliwas
studied in order to elucidate the role of the different interaction forces inthe formation and structureofacidcaseingels.
The effect of ageing temperature has already been dealtwithin
section3.2.
Gelswereagedforatleast16hrsattemperaturesvaryingfrom
20 to 50 °C before the dynamic moduliwere measured.Thesemeasurements involved avariation ofmeasuring temperature from5to
50 °C,while the frequencyu>waskeptconstantat1.0rad.s ,or
-3 rad.s1 atconstant
-1
a variation of frequency from w=10 to 10
temperature (notnecessarily the ageing temperature).Whenpossible the results of the rheological measurements were related to
permeability experiments in order to obtain independentinformationoftheextentofinhomogeneities inthegelnetwork.
The average maximum shear deformation \ (section2.10.2)was
a
keptsufficiently smalltoensurelinearbehaviour,v corresponds
a.
to an average value of y (see equation4.3),since y variesa
little frominnercylindertooutercylinder (seesection2.10.2).
For linearbehaviour tohold,by definitionthesheardeformation
y should beproportional to the shearstressai.e.G'andG"may
not change uponvariation of a andy.Linearity waspreservedby
keepingy smallerthanorequalto0.035,whichisillustratedin
fig.4.4,whereG1 andG"aredepictedonalogarithmicscaleasa
function of y for two gels, onegelwithrelatively smallmoduli
a
and onewithmoduli ofcommonmagnitude. Itis clear thatG' and
G" tended to decrease only very slowly with increasing applied
deformationevenatlargev .TheratioG"/G'(=tanô)wasconstant
a.
overthewholerangeofy .Rememberingthatresultsbetweenidena.
ticallypreparedgelsvariedbyupto10%,itisobviousthateven
aty=0.1reliablemeasurementscouldstillbeperformed.Therefore
avalue fory of0.035wasregarded asasafechoice forallgels
a
-?
withG'varyingfrom50to1000Nm .
The experimental part was completed with some staticmeasurements. Using avariant ofordinary stressrelaxationmeasurements
(see section 2.10.3)a kind of pseudo-stress relaxation modulus
G(t)* was determined. The value ofthispseudo-stress relaxation
86
G',6"(Nm-z)
1
500-
1
°OOCCM>0-CHXK>0000
l
1
l
i
200-
1
100- • • • • • • • ^ • • ^ • T
1
501
1
1
20-
l
1
'
1
0,05
1
1
0,10
1
YQ
Fig. 4.4 Storage modulus G' (open symbols) andloss modulus G" (filled symbols)
as a function of the average maximum shear deformation y fortwo different
a
acid skimmilk gels. ThepH of the gels was resp. 4.6 (o,»)and4.9 (•,•).The
gels were aged for 7.9x10 s (22hrs)(o,*)and6.5x10 s (18.5hrs)(0,B)hrs
at 30 °C. Measuring temperature was30 °C andw=1.0 rad.s .Thedashed vertical line indicates the maximum value of "y applied during the rheological
a
measurements.
modulusagreedwellwiththevaluesofthedynamicmodulimeasured
4 5
inthe same time scale.At longtimescales (10-10 s)akindof
pseudo-permanentnetworkmoduluswasfound,whichagreedwellwith
predictions from theoretical computations carried out using the
experimentalvaluesofthedynamicmoduli.
Thebehaviour of acid casein gels atconstantstressandlarge
deformation was studied by employing ofcreepmeasurements (section 2.10.4). Assuming a simplified spatial distribution of the
casein particles, it is possible to calculate the modulus G of
anindividualstrandofcaseinparticles.
4.5.2 The_dvnamic_moduli_as_a_f
unction_of
_f
reguency_
Strikingly the frequency dependence of the dynamic moduli was
rather similar for all acid casein gels tested. Both G' and G"
tended to increase with the angular frequency u>over the whole
87
101
1
<JÜ( r a d s" )
Fig. 4.5 Storage modulus G' and loss modulus G" of an acid skimmilk gel (pH=4.6)
as a function of the angular frequency tu ( r a d . s ) . The gel was aged a t 30 °C
4
for 5.6x10 s (16 h r s ) and subsequently t e s t e d a t the temperatures i n d i c a t e d .
-3
1
-1
This i s i l l u s t r a t e d in f i g .
range t e s t e d from 10 to 10 r a d . s
4.5 and 4.6.Infig
4.5 G' and G" are shown as a function of w
(rad.s )onadouble logarithmic scaleforanacidskimmilkgel,
agedat30°Cfor16hoursandmeasuredatrespectively20,30and
40°C. Infig.4.6areshownthemoduliofanacid skimmilkgel,
G'G"(Nm-2)
10-
50°C
io2H
x
„--•X'
10'
10":
10"'
x
x •~.-* '
. x - - x —•-" '
-"- x ——'~
10"1
10u
101
u)(rad s" 1 )
Fig. 4.6 Storage modulus G' and loss modulus G" of an acid skimmilkgel
(pH=4.6)asa function oftheangular frequency ui(rad.s ) .Thegelwasaged
at50°Cfor5.3xl05 s(147hrs)andsubsequently testedat50°C.
88
whichwas firstaged for 147hrsat50°Candsubsequentlymeasuredatthesametemperature.
Acid skimmilk gelsmeasured at30 °Cshowedalinearrelationship between bothmoduli and frequency,whenplotted on adouble
logarithmic scale (see fig.4.5).At 30 °Cthis linearrelationship was always found for acid casein gels, whether they were
made from skimmilk or sodium caseinate solutions, and whether
theywere acidified at2 °Cbymeans ofHCl or at30°Cbymeans
ofGDL (section2.3).The slope ofthelinearcurvesat30°Cwas
alwaysaround0.15 forbothG'andG".Asoftenaswehavechecked
it, we have always found the shape oftheG' andG"curves asa
function of mtobe independent ofthemanner, inwhich theacid
casein gels were made; more or less straight lines were found
with aboutthe same slope,butwithconsiderablydifferentmagnitudesforthemoduli.
The increase of G' and G" with w pointed to a relaxation of
bonds over the time scale of themeasurements.Apparently atall
temperatures aconsiderable number ofeffective bondswithrelax3
ation timesvarying from-0.6 to 6x10 swaspresent,
becauseG'
increased by a factor2.5 to4.5,whenuowaschanged from10 to
10 1 rad.s"1.
4.5.3 Y§Ei§£i22_yiyj_ïïꧣüïi29_£êmE§ï§£yEË
Acid casein gels show apeculiar temperaturebehaviour.G'and
G" tend tovaryvery strongly withmeasuring and ageingtemperature when measured at w=1.0 rad.s" . Further the shape of the
curve representing tanôas afunction ofuuchanges considerably
with the measuring temperature. Both aspects will be treated in
detailinthissection.
The effect of the measuring temperature (T)on the dynamic
moduli is shown in fig. 4.7a andb for acid skimmilk gels after
ageing for aperiod of 16to 20hrs atconstant temperature.The
moduliwere measured atiu=1.0rad.s" .Thegelswereagedattemperatures from 20to 50 °C.Reproducibility was good, except for
gels aged at20 °C,which showed arather largevariation inabsolute values of the dynamic moduli; however the temperature
dependence foundwasalwaysthesame.Agelwaskept15to30min.
at the desired temperature, while the dynamic moduli weremea-
-3
89
G'(Nm1000
800
•A
600
x\
s
\>
Bv \
400
—^O-sSX.
200
^ 0
A
1
0
1
1
1
~—X
1
-r
J
10 20 30 40 50 60
Tm (°0
(a)
G"(Nnf2)
250
0
10
20
30
40
(b)
Fig. 4.7a andb.StoragemodulusG' (a)and lossmodulus G" (b)ofacid skimmilk
gels (pH=4.6) as a function of the measuring temperature, T .The ageing temperatures of the gels were respectively 20°C (+),25°C (x),30°C (A),40°C
(•) and 50°C (o).w=1.0 rad.s .The ageing time varied between 5.8x10 s
(16hrs)and 7.2xl04 s (20hrs).
90
sured. The moduli did not change significantly during thistime,
except for the gels aged at20 and 25 °C,whenmeasured at40to
50 °C. In general a considerable decrease of the dynamicmoduli
withincreasingT wasfound.However,ahigherageingtemperature
led tohighermoduli,whenmeasured atthesameT .ForG'andG"
m
asimilartemperaturedependencewasfound.Thedecreasewithmeasuring temperature tended to become stronger with longer ageing
times and higher ageing temperatures.The curves were completely
reversible,except for the gels aged at20 and 25 °C.As soonas
temperature was raised above 35 °C (forthegelagedat20°C)or
40 °C (for the gel aged at25 °C)gelationwas accelerated and,
after the initial decrease of G' and G" caused by heating, a
strong increase ofthemoduli was seen atthese temperatures itself. Probably gelation as such i.e. the formation of effective
bonds is subject to anactivationHelmholtzenergy,whichsharply
decreaseswithincreasingtemperature.Attemperaturesbelow10°C
it prevents gel formation. This decrease inactivationHelmholtz
energy with increasing temperature may lead to a faster gelation
athighertemperaturesespecially duringthefirsthours.Buteven
aftersometime,whentheincreaseofG'andG"withlogtbecomes
nearly independent of ageing temperature for ageing temperatures
between 20 and 40 °C (see fig.3.1a and b), itislikelythatthe
moduli of a gel aged at 40 °Cwould increase more stronglywith
time, when measured from time to time at30 °C ,than for agel
agedandmeasured at30°C.
The small maximum in the G' andG" versus logtcurves (fig.
3.1a and b) for the 50 °Cgel att=4.6xl03 s (actual temperature
atthatmomentwas40°C)couldbetheresultantofanincreasein
dynamic moduli caused by ongoing gelation andastrongerdecrease
due to the continuing rise of the measuring temperature, asthe
system was heated from 2 to 50 °C. The small minimum was found
3
after5.6x10 s,whentheultimateageingtemperatureof50°Cwas
reached.
As canbe concluded from thebehaviour of tanô (see later in
this section), the character ofthe interaction forceswillprobably not depend on ageing temperature, when the moduli aremeasuredatthesametemperatureT .However,thecontributionofthe
differentinteraction forcestotheeffectivebondspossiblycould
91
vary with ageing temperature, although the rheologicalproperties
measuredatw=1.0rad.s didnotsuggestthisfortheinteraction
forcesdominatingaroundthetimescalecorrespondingtothatfrequency.The character ofthebonds atthesameT willnottherefore change with ageing temperature. This implies that the increase ofthemoduli with ageing temperaturewillprobablynotbe
due to achange intheHelmholtzenergy (equation3.2),buttoan
increaseinthenumberofeffectivebondsN.
From section 3.4.2.3 and fig. 3.16 it is clear that larger
moduli at higher ageing temperatures are accompanied by alarger
permeability. Thismeans that the strongest gelsarethemostinhomogeneous atthe level ofthe network.Thisseemscontradictory
to the general rule thatgel strength and thedynamicmodulidecrease with increasing inhomogeneity ofthe gelnetwork.However,
the magnitude of themoduli depends onboth the number ofeffective bonds between theparticles and the spatial distributionof
those particles, whereas the permeability depends on the dimensionsofthelargeporesbetweenthedenseareasofparticles (see
section3.4.3).Asdescribed inchapter3inhomogeneitywilloccur
notonlyatthelevelofthegelnetwork,butalsoatthelevelof
the casein particles themselves and at the level of the strands
and the small conglomerates of casein particles. Apparently the
number of effective bonds strongly increases at higher ageing
temperatures.Morecontactsbetweentheparticlesareformed,possibly involving previously useless particles (i.e.thosenoteffectivelycontributingtothegelnetwork),sothattheproportion
of such useless protein particles decreases. In this respect it
wouldbeworthwile to investigate thepossibleincreaseoffusion
ofthe aggregated caseinparticles with increasingageingtemperature.
Tan6 (G"/G') was found nearly constant (w=1.0 rad.s" )over
thewholetemperaturerangestudied,exceptforthesampleagedat
50 °C. for this sample tan6significantlydecreasedatT>50°C.
This was also found forgels agedathighertemperatures (results
not shown), but this range ofT wasnot studied extensively.So
therewas no indication of aclearchangeinthecharacterofthe
bondsinthetimescalearound6s(w=1.0rad.s" ),causedbyrise
of T from 2 to 50 °C. Inany case,most interaction forces are
92
not so strongly temperature dependent. In the case of a direct
effect involving hydrophobic interaction, an increase
of G' and G" with T would have been expected instead ofadecrease (VanVliet and Lyklema, 1978). In the region between two
particles there will always be acompetitionbetween intermolecularinteractionsbetweenproteinmoleculesbelongingtodifferent
particles andthosebelongingtothesameparticle,andacompetitionbetweenintermolecularandintramolecular interactionswithin
a particle. Therefore it is difficult to give a straightforward
explanation in terms ofmolecular interaction forces for theobserved temperature behaviour, because a competition as indicated
abovedependsonthebalancebetweenthedifferenttypesofinteraction forces.Moreover, the interaction forcesmaybe effective
not only inadirectway,but also in amore indirectmannervia
the conformation ofproteinmolecules and thestructureofcasein
particles.Theresultantofthecompetitionmentionedwilllargely
determine G' and G". But again, as said above most interaction
forces inproteinmolecules areonly slightlytemperaturedependent, thatis,exceptforhydrophobic interactionswhichgotheoppositeway.Asmallshiftinthebalanceoftheinteractionforces
may have alarge effecton theconformationofaproteinmolecule
andsoonthestructureofparticlesofaggregatedprotein.Apparently the structure of the casein particles, which form thegel
network is of crucial importance.This structure isprobably not
homogeneous (section 3.3.4 and 3.4.3). Itseems justified toassume that it will change from the outside to the inside. The
structure of these casein particles will depend strongly on the
conformationofandtheinteractionsbetweentheindividualcasein
molecules. A small change in interaction forces can cause large
changes in conformation ofcaseinmolecules and so in thestructure of theparticles.Undoubtedly besides theothershydrophobic
interactions are involved in determining theconformation ofcaseinmolecules.Ourhypothesis isnow thattheobservedtemperaturebehaviour isnotdirectly but indirectlycausedbyhydropobic
interactions,whichprobably induceamorecompactconformationof
the casein molecules with increasing T and thus a shrinking of
the casein particles. This shrinking in its turn influences the
balancebetween interparticle (only intermolecular)and intraparticle (both intra-and intermolecular)bonds.Probablythenumber
93
of interparticle bondswill decreasewithT .Furthertheshrinkingofcaseinparticleswillbereflected inthedecreasingvoluminosity ofcaseinwith increasing temperature (Darling,1982,see
fig. 3.6c). We will further elaborate this discussion insection
4.6.
The same temperature dependence was observed for acid casein
gels whether, made from sodium caseinate solutions acidified in
the cold, or from respectively a skimmilk or asodium caseinate
solution acidified at30 °Cby hydrolysis ofGDL.This isillustrated in figure4.8,where G' isdepicted as a function ofmeasuringtemperatureT .Thesodiumcaseinatesolutionsacidifiedin
the coldwere aged atrespectively 20,30 and40 °C.For thegel
aged at20 °Cthedecreasewithmeasuringtemperature (ofthedynamic moduli) was partly neutralized by an accelerated gelation
above30°C.Thisresultedinsomeirreversiblebehavioursothat,
aftercooling down againto 20 °C,the samevalue forG'wasobtained as for the gel aged at30 °C.The gelsmade withthehelp
of GDL are those already shown in fig.3.5a. They exhibited the
same decreasing temperature dependence although atmuchlowerabsolute values. This is better seen when log G' is plotted as a
functionofT (not
m shown),
As stated before tanôis aparameter which isvery sensitive
tochanges ofG' andG"with respect to eachother.A highvalue
oftanô (>1.0)points to amore liquid like character inasystem, while a low value oftan ô (<0.1)points to amore elastic
character.Moreover, tanô is related moredirectlytothenature
of the bonds than G' or G" (section4.3).Athigher frequencies
(w=10 to 10 rad.s" )tan ôdidnotchangesignificantlyeither
withageingtemperatureormeasuringtemperature,aslongasthese
temperatures were keptbelow 50 °C.Atameasuringtemperatureof
60 °Cand also after longer ageing times at 50 °C (see fig.3.2)
tanô tended to decrease strongly.Allvaluesoftanôcalculated
from themoduli depicted in fig.4.7 and4.8 (u»=1.0rad.s-1)rangedbetweentan6=0.20 and0.30withthemajorityaroundtanô=
0.25.This spreading was due to experimental errorascanbeseen
inthefollowingfigures.
94
G' (Nuf2)
Fig. 4.8 Storage modulus G' as a function of measuring temperature T for
acid casein gels, made from sodium caseinate solutions acidified in the cold
(G,H,A) and made from skimmilk (V) and
sodium caseinate (•) acidified by means
of GDL. The sodium caseinate solutions
acidified in the cold (casein cone.=2.6
wt.% and CN „,=0.12 mol per kg dispersion) were aged for 6.5x10 s (18 hrs)
at the indicated temperatures. The GDL
gels (the same as in fig. 3.5a) were
aged for resp. 2.6x10 s (skimmilk) and
2.3x10 s (sodium caseinate) at 30 °C.
U)=1.0 rad.s
In f i g . 4 . 9 t a n ô i s shown as a f u n c t i o n of t h e a n g u l a r f r e quency u) for a c i d skimmilk g e l s aged a t 30 °C and measured a t
r e s p . 20, 30 and 40 °C. These a r e t h e same g e l s whose moduli a r e
p l o t t e d i n f i g . 4 . 5 . At low f r e q u e n c i e s t a n 6 i n c r e a s e d w i t h d e c r e a s i n g measuring t e m p e r a t u r e T . Consequently t h e c a s e i n g e l s
became more l i q u i d - l i k e a t low t e m p e r a t u r e and more e l a s t i c (or
s o l i d - l i k e ) a t high t e m p e r a t u r e . This e f f e c t of T on t a n ô c a n n o t
be i d e n t i c a l t o t h a t r e l a t e d t o t h e t e m p e r a t u r e time s u p e r p o s i t i o n
as d e s c r i b e d by F e r r y ( 1 9 8 0 ) . P o s s i b l y i t i n v o l v e s some form of
i n t e r a c t i o n l e a d i n g t o bonds w i t h r e l a x a t i o n t i m e s of t h e o r d e r of
3
10 s , which cause an i n c r e a s e i n t h e r a t i o of G" over G' a t
_ _3
_i
uj-10
rad.s
upon a d e c r e a s e of measuring t e m p e r a t u r e . Probably
t h i s d i f f e r e n c e i n t h e e f f e c t of Tm on t a n ô a t low and h i g h ui and
t h e f a c t t h a t a t e m p e r a t u r e time s u p e r p o s i t i o n cannot be a p p l i e d ,
i n d i c a t e t h a t a t l e a s t two d i f f e r e n t i n t e r a c t i o n f o r c e s each w i t h
d i f f e r e n t time dependence a r e i n v o l v e d . Since t h e e l a s t i c c h a r a c t e r of a c i d c a s e i n g e l s i n c r e a s e s w i t h T i t seems l o g i c a l t h a t
hydrophobic bonding i s one of them.
95
tan5
w (rads"1)
Fig. 4.9 The loss tangent,tan6=G"/G',asafunctionoftheangular frequencytuforthegelsoffig.4.5.Measuring temperature isindicated.
tan5
10u
Fig. 4.10
101
u)(rads'1)
The loss tangent, tan ô = G"/G' , as a function of the angular fre-
quency u) for the gel of f i g . 4 . 6 . Measuring temperature T was 50 °C.
For a g e l aged for 147 h r s a t 50 °C t h e d e c r e a s e of t a n ô a t
small tu was much more pronounced ( f i g . 4 . 1 0 ) . The dynamic moduli
G' and G" of t h i s g e l a r e d e p i c t e d i n f i g . 4 . 6 .
98
4.5.4 DYnamic_moduli_of_acid_ski^ilk_gels_as_a_function_of_gH
The effect ofpH on the dynamic moduli of acid skimmilkgels,
made from skimmilk powder A (section 2.1),was studied. Thegels
were aged for 18 hrs at 30 °C,measured atthe same temperature
and tested at w=1.0 rad.s" .Above pH=4.9 no gels were formed.
This agrees with the results obtained by GDL induced gel formation,which started atpH=4.94 (section 3.2.4).AtpH=4.9arelativeweak gelwas formed (fig.4.13).BetweenpH=4.8and4.3only
a slightvariation inthevalue ofthemoduliwasseen.AtpH=4.5
asmallmaximumoccurred.AlmostanidenticalcurveforG'wasobtainedbyVanDijk (1982),whousedskimmilkpowderB,althoughhe
did not find the small maximum around pH=4.5. In his case the
moduli kept increasing from 4.8 to 4.3. This small difference
could, however,be easily explained by agreaterexperimentalinaccuracy at low pH.AtpH=4.3 thepermeability increased sharply
(VanDijk, 1982)pointing to amuch coarser gel network.ExperimentallyitwasfoundthatatlowpHcaseinparticleswerealready
tending tocoagulate atlower temperature,justbeforetheendof
the acidification procedure (T<2°C)orduring thefillingofthe
rheometer. Although at that moment stirring and streaming will
prevent gel formation, the average particle size could increase
sharply leading to a much coarser gel network after subsequent
heating without stirring. From these experimental resultsonemay
conclude that at lower pH the number of effective bondsbetween
twocoagulated casein particles willincrease.Particularlythe
G',G"(Nnr 2
Fig. 4.13 Storage modulus G' (o)and
«)(H
gels asafunction ofpH.The gelswere
loss Modulus G" (ü) of acid skimmilk
aged for 6.5x10 s (18 hrs) at 30 °C.
Measuring temperature was 30 °C and
U)=1.0rad.s
200H
4.2 4.44.64.8 5.0
pH
99
repulsive forces due tonegative chargeswillbe decreased.However themore inhomogeneous character of thegelnetworkwilldecrease the magnitude of the moduli, since the number of stress
carrying particles will decrease. The balance between these two
phenomena will determine the absolutevalue ofG' andG". Subtle
differencesinexperimentalperformancemayberesponsible forthe
observed differences between the curve for G1 of this studyand
thatobtained byVanDijk (1982). Probably thestrongincreaseof
G' for some samples atpH=4.3 asfoundbyvanDijkwasduetothe
formation of large dense floes,which could reach from the inner
totheoutercylinderofthemeasuringapparatus.
For all pH's the dynamic moduli G' and G" increased linearly
-2
1 - 1
with uj(uuvarying from 10 to 10 rad.s )when depicted ona
doublelogarithmicscale.Thelineswereparallel forallpH'sand
theslopewasthesameasinfig.4.5 fortheacidskimmilkgelof
pH=4.6measured at30°C.
The values of tan ô at ou=1.0 rad.s" rangedbetween 0.24 and
0.28 as thepHwasvaried from4.3 to4.9.Thisspreadwaswithin
-2
experimental error; tan ô as a function of w (from 10 to 10
rad.s" )forpH'sbetween4.3 and4.8gavewhenmeasuredat30°C
straighthorizontal lines.Thisbehaviour isthesameasthatalready found for all acid casein gelsprepared (pH=4.6),however,
when measured at 30 °C (see fig. 4.9, 4.11 and 4.12). Only at
pH=4.9wasaslightincreaseintan6foundatthelowestfrequencies.
Itisprobable that thepH ofthesystemaffectstheeffective
number of bonds rather than the nature of the interactions. In
this context it should be repeated that we are concerned with
bonds and interactions whose relaxations extend overatimescale
3
of roughly 0.6 to 6x10 s, since, except from the bonds with a
more permanent character, these determine the values of themoduli.Typically athigher pH's (4.5to4.9)decreasingmoduliare
accompaniedbyadecreasingpermeability (VanDijk, 1982).Thegel
with the lowest permeability i.e. the fewest largepores appears
tobe theweakest one.ItisprobablethatthepHaffectstheobserved values ofthemoduli indirectly bymodifyingthestructure
oftheparticipatingparticles (similar to theeffectofthemeasuring temperature T ,see lastsection)anddirectlybyaltering
1
100
the number ofbondsbetween theparticles. Inthis contextelectrostatic interactions betweenpositive andnegative chargesseem
to be involved. We will deal furtherwith this inthenextsections.
4.5.5 Yaïi§£i22_2£_i2Qi2_£22)E2§i£i2D
The ionic strength of the water phase has amarked effecton
the formation of acid casein gels (e.g. section 3.4.2.1, fig.
3.13). Itwasfoundthataminimum saltconcentrationof~0.10mol
NaClper kgdispersionwas required tomakeagelfromsodiumcaseinate solutions by acidifying in the cold and subsequently
heating. Adding less salt causes casein precipitation at pH=4.6
even at 0 °C. Moreover it was found that adding too much salt
(>0.24molNaClperkgdispersion)preventedgelformationevenat
elevated temperatures. Bivalent cations, particularly Ca ,
stronglybind to casein (see section 1.2 andtable1.1).Theturbidity of sodium caseinate solutions ofpH=6.8sharply increased
2+ ionic strength being maintained
upon the addition of Ca ions,
2+
constant.Thepresence ofCa induces theformationoflargeaggregates ofcoagulated casein, sedimentable under gravity.Therefore it seems reasonable to assume that ionic strength and the
typeof salt ions are importantparameters intheformation,stabilityandstructureofcaseinparticlesatpH=4.6.
First ot all in this section wemake arough estimate ofthe
ionicstrengthinacidskimmilkatpH=4.6.Theeffectoftheionic
strength ontheproperties of acid skimmilkgelswasmainlystudiedbymeasuring the dynamic moduli andthepermeabilityofthese
gels atdifferent levels ofextra addedNaCl.However,theeffect
ofsaltsonsodiumcaseinategelswasstudiedintwoways:firstly
the total NaCl concentrationwithno other ionspresentwasvaried, and secondlyboth theNaCl andCaCl.concentrationwerevaried,whiletheionicstrengthwaskeptconstant.
4.5.5.1 Rough estimate of ionic strenth
of acid skimmilk
The ionic strength isoneoftheconditionsinskimmilk,which
undoubtedly will change upon acidification.AtpH=6.7 theeffective ionic strength, I, for natural skimmilk is estimated tobe
2+
101
0.08 M (Walstra and Jenness, 1984). During acidification Iwill
increase dueparticularly to the dissolution ofColloidalCalcium
Phosphate (CCP). Because of the enormously complexcompositionof
the water phase of skimmilk it is almost impossible to give an
exact estimate of I at pH=4.6. Extensive computer computations
taking into account all dissociation and association equilibria
between the electrolytes present would be necessary. The result
obtained would then onlybe applicable atthetemperatureimposed
forthatcalculation,becausealltheequilibriainvolvedaretemperature dependent.Moreover, itwould only applytotheanalysis
of aparticular sample,since ionic composition isdifferent for
everymilksampleduetonaturalvariations.
Based on the average ionic composition of natural skimmilk
(Walstra and Jenness,1984)we shall attempt to give aroughindicationoftheeffectiveionicstrengthatpH=4.6ofthestandard
skimmilkusedinthisstudy (section2.1 and2.3).Firstthemaximum possible I for the aqueous phase of standard skimmilk at
pH=4.6 was calculated. The following assumptions and correction
factorswereapplicable:
in a first approach all ionic complexes were considered as
splitintoanionsandkations.
2+
allCCPwasregarded asdissolvedandsplitintoCa andphosphateacidresidues.
the charge of the acidic residues was governed by their dissociationconstantsintheaqueousphase,
allactivitycoefficientsweretakenequalto1.0.
of the HCl added during acidification the chloride ion was
takenintoaccountbuttheH wasnot.TheaddedH wasthought
asbeingusedtodissolveCCPandneutralizeproteincharge,
a correction factor was introduced to account for the higher
total solids concentration in the standard skimmilk of this
studycomparedtonaturalskimmilk.
another correction factor was introduced for the dilution
broughtaboutbyacidaddition.
- the association of ions to macromolecular species,presumably
theproteinswasnottakenintoaccount.
- no contribution of the protein to I was taken into account
since we seek first an estimate of the ionic strength ofthe
aqueousphaseofskimmilk.
102
Table4.1:CalculationofIofthesalt solutioninstandard skimmilkatpH=4.6.
Cone,xvalency (cz)ofallpositively
charged ionsatpH=4.6intheaqueous
phaseofnatural skimmilk
idem,ofnegatively charged ions.
Cl" addedduring acidification
total solidscorrection factor
dilution factorduetoacidification
0.139M
0.088M
0.058M
1.15
1.02
a: all ionic complexes are thought tobesplit into ions.Chargeofacid residues depends ondissociation constants.All ion concentrations are taken from
WalstraandJenness (1984).
allionicconcentrationswereexpressedinmolarconcentrations.
When allvalues aresummed andcorrected fortheconcentration
effects (see table 4.1),we obtain an estimated maximum ionic
strength of 0.20 M forthe salt solution i.e.saltdialysateof
standard skimmilk. Forthe true Iin thesaltsolution onealso
has to take into account the ionactivity coefficients andthe
ioniccomplexes formed.Woodetal. (1981)havepublishedcomputer
calculations on the ionic composition, including allassociation
and dissociation equilibria, of salt solutions with an overall
composition very similar to that ofour skimmilk dialysate.For
one of their systems, containing slightly more Ca andphosphate
andconsiderably lesschloridethanoursystem,butwithaboutthe
same amount ofcitrate, sodium andpotassium, Wood etal.calculated an effective ionic strength of 0.15 M, whereas with all
ionic complexes now dissociated inthis solution amaximum ionic
strength of 0.22 M canbe calculated. Their experimentally measuredpH (=4.19)agreed well with theircalculatedpH (4.11).Assuming thesame 30%reduction ofIduetoionic complex associationtheeffective ionic strength Iwouldbeestimatedat0.13to
0.14Minoursalt solution. Instandard skimmilksomeofthedi2+
9+
valent cations (Ca andMg )maybe associated withproteins.
Therefore therough estimate ofIpresentedherewillprobablybe
amaximumvalueforstandard skimmilkatpH=4.6.
103
4.5.5.2 The effect
of added NaCl on acid skimmilk
gels
Standard skimmilk (powderA,3.0wt.%casein,section2.1)was
acidified topH=4.6 at0-2 °C (section2.3). Subsequentlydifferent amounts of NaCl were added. After dissolving the NaCl by
thoroughstirring,thesolutionsweretransferredtotherheometer
and heated intheappropriateway (section2.3)to30°C.Assoon
as gel formation had started, the dynamic moduli G'andG"were
measuredasafunctionofageingtime.
Fig. 4.14 Storagemodulus G'asafunctionofthelogarithm oftheageingtime
t(s) for acid skimmilk gels with different amounts ofNaCl added. At t=0and
4 °Ctheheating oftheskimmilk solutionwasbegun.AmountofNaCl added:zero
(o), 0.025 (x),0.050 (A),0.071 (o),0.084 (V),0.100 (•) and0.125 (•) molper
kgdispersion.
In fig.4.14thestorage modulusG'isdepicted asafunction
ofthelogarithmofageingtimet(s)fordifferentamountsofNaCl
added (varying from 0.0 to 125mmol ofNaClperkgdispersion).
ForG"thepathofthecurveswasvery similar.AdditionofNaCl
had adistincteffectonthevaluesofthedynamicmoduliofacid
skimmilkgels.Althoughmeasurablegelformationbeganatapproxi3 s,when3
matelythesametime (between2x10 and3x10
thetempera-
104
G,G (Nnr 2 )
400Ö
'0.^
300-
\
200-
\
\
100-
Fig. 4.15StoragemodulusG'andloss
modulusG"after8.6x10 s(24hrs)as
afunctionofaddedamountofNaClfor
thegelsofFig.4.14.
:—0—o^.G
a-
c)
50
100
150
CNQC1(mmol/kg dispersion]
ture approached 30 °C),the slope ofthe ageing curves decreased
with increasing amount of NaCl added. However the value of the
moduli after a fixed ageing time did not decrease linearlywith
the amount,ofNaCl added, as is illustrated more clearly infig.
4.15. At low levels of added NaCl only a slow decrease of the
moduliwas seen,which onthe additionofmoresaltpassed intoa
steep decrease above 50 mmol NaCl added per kg dispersion. The
upper limit for gel formation at 30 °C seemed to be around 150
mmol NaCl added per kg dispersion. By this level of addedNaCl,
the ionic stength of the systemwillhavebeen,roughly,doubled.
Tan ô fluctuated between 0.23 and 0.26 independent of added salt
concentration.
Significantly, the permeability of similarly prepared acid
skimmilkgels also decreased as a functionoftheaddedamountof
NaCl (see fig.4.16). Thepermeability coefficientBwasmeasured
at 30 °C after an ageing time of 18 hrs at 30 °C.Again lower
values of the dynamic moduliwere accompanied by a lowerpermeability, i.e. agel network with fewer and/or smaller largepores
(section3.4,seealsosection4.5.3 and 5.3.1).AddingextraNaCl
apparently decreased the effective number ofbondsinvolvedinG'
and G" in the gel network formed. Since the overall tendency of
thegelnetworkistobecomemorehomogeneous,thenumberofbonds
105
B(1(T13m2)
2.0
Fig. 4.16 Permeability coefficient B
1.5-
of acid skimmilk gels (pH=4.6) as a
function of added amount of NaCl. The
gels were aged for 6.5x10 s (18 hrs)
at30°Candmeasured at30°C.
1.0-
C N,.(mmol/kgdispersion)
between two coagulated particles after a certain ageing time will
probably decrease with the NaCl concentration. However, the effect
of NaCl can be not only a direct effect causing fewer interparticle +- interactions but also an indirect effect by influencing
the structure of the casein particles.
The decrease of G' in fig. 4.15 and of B in fig. 4.16 occurs
according to respectively a convex and a concave curve. A simple
explanation can be given for this behaviour. At low amounts of
NaCl added the decrease of the number of contacts between the
particles is probably counterbalanced by an increasing number of
particles contributing to the modulus G', since the gel network
is becoming more homogeneous. Above 50 mmol NaCl added per kg dispersion the gel network can become only slightly more homogeneous
with increasing NaCl concentration. The decrease of the effective
number of bonds is then no longer counterbalanced and G' decreases
more rapidly.
From these results and from the pH influence it is clear that
ionic interactions are very important in acid skimmilk gels.
Whether they act directly via attraction between positively and
negatively charged groups on different casein particles is less
clear. Neither from the frequency dependence of tan ô at 30 °C
106
G'(Nnr2)
Fig. 4.17 StoragemodulusG'asafunction of measuring temperature for some
600
of the gels of fig. 4.14. The symbols
refer tothe same gels asinfig.4.14.
u)=1.0 rad.s .The measurement of the
curve for the gel with 0.125 mol NaCl
400-
per kgdispersion addedwas interrupted
during 15 hrs at 30 °C,while thesample was kept at this temperature (see
200
text). Ageing time was respectively
7.5xl04 s (o),8.1xl04 s (A),9x10 s
(•),9.5xl04s (•) and9.1x10 s(•).
0
10
20
30
40
50
Tm TO
(not shown), nor from avariation of the dynamic moduli withthe
measuring temperature (fig. 4.17) was any indication found that
theformofinteractionsdeterminingthemodulihadchangeddueto
••
-2
addition ofNaCl. Tanômeasured as a function ofi»(10 to10
rad.s" )gavestraighthorizontallinesaroundtan6=0.25 forall
gels. The lines of G' and G" ranparallel atdifferent absolute
values. The decrease ofG'with themeasuring temperature T for
gelswithdifferentamountsofNaCladded (varyingfrom0.0 to125
mmolNaClperkgdispersion)isillustrated infig.4.17.Thegels
are those forwhich the ageingbehaviour was shown in fig.4.14.
The decrease ofG'as a functionofT isverysimilartothatof
m
-*
ordinary acid skimmilk gels.The absolute slopeofthecurvesdecreased with increasing amountofNaCl added.However, therelative decrease ofG1 with T ,whichisapparentlywhenG'isplottedasafunctionofT onadoublelogarithmicscale (notshown),
was aboutthe same for all gels.Above40°Ctherateofgelation
increased enormously, particularly at thehighest amount ofNaCl
added. This also occurred with acid skimmilk gels with noadded
NaCl,whentheywereagedat20and25°C (section4.3).Apparent-
1
107
ly the added NaCl increased the activation Helmholtz energy for
the formation of interparticle bonds (section 4.5.3).Thiseffect
could be neutralized by raising temperature,which decreased the
activation energy for gel formation.Thevalues oftanôfluctuatedbetween 0.22 and 0.27 withnoregularity andirrespectiveof
T value orNaCl concentration.Thisvariationwaswithinexperimentalerror.
4.5.5.3 The effect
gels
of NaCl and CaCl„ on acid sodium
caseinate
As discussed in section3.4.2.1aminimumionicstrengthanda
minimum casein concentration are necessary for the formation of
acid casein gels. Forboth acid skimmilkandsodiumcaseinatethe
minimum level of Iafter acidification to form agel isapproximately 0.11 M. Itis alsoprobable thatgel formation dependson
the type of ionspresent.NaCl will only affect I.However CaCl,
2+ only affects the ionic
(especially when present as Ca ) not
strength, but also may react with negatively charged acid residues,mainly phosphate groups (pK=1.5 and 6.5 inunfoldedpeptide
chains, after Walstra and Jenness, 1984), on the proteins and
therebyaffectproteinconformationandcaseinparticlestructure.
In a first series of experiments sodium caseinate was dissolved in solutions containing only different amounts of NaCl.
After acidification and heating gelswere formed with addedNaCl
in the range of 0.10 to 0.24 M. In these systems acidification
increased Ibyapproximately 0.01Mbecauseoftheadded0.5NHCl
(see section 2.3),so that after acidification Ivariedapproximately between 0.11 and 0.25 M. Infig.4.18 G' and G" ofsodium
caseinate gels, aged for 16 to 20hrsat30°Cbeforemeasurement
at30°C,aredepicted asafunctionoftheNaClconcentration.
The same trend is seen as for acid skimmilk gels (fig.4.15).
The dynamic moduli decreased with increasing NaCl cone, while
tanô (not shown) had a constant value of~0.25. Again thepermeability coefficientB decreased with increasing NaClcone,(see
table4.2).
108
G'G"(Nuf2'
Fig. 4.18T h edynamic moduli G' (solid
line) and G" (dashed line) of acid
sodium caseinate gels asa function of
total NaCl concentration. T h egels were
aged for 5.8 to 7.2x10
s (16to20
h r s ) at30° C .w = 1 . 0 r a d . s " .
120
160
200
C NnC1 mmol/kg dispersion
Figs. 4.15 and4.18 suggest anoptimum ionic strength orsalt
concentration for gel formation, since no gels can be formed at
low I. Such an optimum salt concentration will depend onpHand
casein concentration. For skimmilk this optimum seems to be approximately at the concentration found in standard skimmilk
(1-0.13 to 0.14 M)with no added salts.A further indication of
the existence of anoptimum saltconcentration for acid skimmilk
gels was found in fig.3.13 (section 3.4.2.1). Adding extraNaCl
(0.07 M) to skimmilk solutions of half the casein concentration
(1.69 wt.%) of standard skimmilk (curve 1), implying that Iis
alsolower,increasedthedynamicmoduliconsiderably.Underthese
conditions (lower casein concentration and lower ionic strength)
the systemwas atthe other side (left side)ofthe optimum suggested in fig. 4.15. The bending of curves 1and 2 in fig. 3.13
can be explained by an increasing ionic strength over thewhole
casein concentration range. Curve 3 suggests a straight line in
the case ofconstant ionic strength.Thevariation of Iwithcasein concentration forthe gelsmeasured for curve 1 isobvious.
Forthegelsmeasuredtogivecurve2,IatpH=4.6stillincreased
with casein concentration because of the dissolution ofCCP from
theincreasingamountofcaseinparticlesdispersed inthemilkul-
109
Table 4.2. Permeability coefficientBofacid sodium caseinate gelsasafunctionofNaCl concentration. The gelswere aged for16hrsat30°C. Spray dried
sodium caseinate (section 2.2)was used.The standard deviationisindicated.
B (10" 13 m 2 )
1.64±0.08
1.04±0.06
0.79±0.02
C
NaClm m o 1p e rkg d i s P e r s i o n
0.095
0.12
0.19
tra filtrate.For the gels of curve1and2atlowcaseinconcentrations (atthe left side of the saltoptimum)an increase inI
causedarelatively strongerincreaseinG'thanexpected fromthe
casein concentration alone atconstant I.TheslopesofG'versus
thecaseinconcentration fromcurves1and2werethereforesteeper than thatofcurve 3 atlowcaseinconcentrations.Athighcasein concentrations the salt concentration lay to the right-hand
side of the salt optimum, so that depending onthe exactconditions a relatively smaller increase ofG' with caseinconcentration was found, compared to that expected from the casein concentrationdependencealone.
For sodium caseinate with only NaCl present the optimum salt
concentration was smaller than 0.10 MNaCl. However atthis salt
level the attractionbetween caseinparticles wassostrong,that
they were already coagulated at 0-2 °C during the acidification
procedure.Thereasonforthisdifferenceinbehaviourbetweenthe
acid skimmilk gels and the sodium caseinategelsisnotknown.As
shownin section 3.3.3 the size ofthecaseinparticles atpH=4.6
and0-2 °Cwasalsodifferent.Maybetheseeffectswererelatedto
differences intheioniccomposition,whichcouldbeofparticular
importance in the formation of the casein particles during the
acidificationprocess.
In a second series of experiments sodium caseinate was dissolved in solutions containing both NaCl andCaCl2.Gelformation
was possible when Ivaried between 0.11 and 0.17 M.However the
effects of CaCl2 andNaCl were notcomplementary. This isillustrated infig.4.19,wherethedynamicmoduliG'andG"aredepic-
110
Fig. 4.19 Storage modulus G' (o)and
loss modulus G" (D)asa functionof
the concentration of added CaCl„and
NaCl for acid sodium caseinate gels
(casein cone. 2.76 wt.%). The ionic
strength
after
acidification
only
varied between0.13and0.14molperkg
dispersion. The gels were aged for
6.1x10 s(17hrs)at30°C.Measuring
0
20
40
CCaC| (mmol/kg dispersion)
120
r
temperaturewas30°Candu>=1.0rad.s
60
(mmol/kg dispersion)
tedasafunctionoftheioniccomposition.Theionicstrengthwas
maintained approximatelyconstantbetween0.13 and0.14M,whereas
theratiobetweenNaClandCaCl,varied from0.0 to1.0.Betweena
CaCl2 concentration of 10mmol/kg dispersion and 20mmol/kg dispersion a strong decrease of the moduli was seen,pointing toa
specific effect of CaCl-. Such an effect has already beenseen,
when the casein was dissolved at around pH=6.8. There, above a
CaCl- concentration of 10mmol per kgdispersionthecaseinmolecules tended to aggregate strongly and large particles of colloidal dimensions were formed. At those CaCl- concentrations the
sodium caseinate solution had acolloidal white,milklikeappearance (even atpH=6.7)and the largestparticles formed tendedto
sediment. These particles were much larger than the caseinparticles in skimmilk. Itisprobable thattheywere disrupted only
partially,ifatall,byacidification,resultinginaverycoarse
gel network onheating, aswas confirmedbypermeabilitymeasurements (table4.3).
Above a certain critical CaCl2 concentration (-20mmol perkg
dispersion) it isprobable that addition ofmore CaCl2 no longer
affected the formation of large casein aggregatesatpH=6.8.Consequently there wasno furthervariation inthe structure ofthe
caseinparticlesatpH=4.6andwiththatnofurtherchangesinthe
values of themoduli and thepermeability of the resulting gels.
Ill
2
Table 4 . 3 . Permeability c o e f f i c i e n t B (m ) of acid casein gels made from sodium
caseinate dispersed in d i f f e r e n t s a l t solutions with the same ionic s t r e n g t h
(1=0.13-0.14 M). The samples were aged for 17 hrs a t 30 °C. The standard deviation is indicated.
B (10
-13 2
m)
s a l t solution
1.06 ± 0.09
NaCl: 0.12 mol per kg dispersion
9.22 ± 0.42
NaCl: 0.063 mol per kg dispersion aad
CaCl.: 0.021 mol per kg dispersion
The replacement of NaCl by CaCl_ had no effect on tan ô. This
fluctuated between 0.22 and 0.24 for a l l the gels whose values of
G' and G" are given in f i g . 4.19.
Summarizing the specific Ca effect may be explained by i t s i n fluence on the size and s t r u c t u r e of the casein p a r t i c l e s formed
before and during a c i d i f i c a t i o n . In the subsequent gel formation
and ageing these properties are more or l e s s frozen. From the experiments described i t i s not clear whether there was also a spec i f i c Ca effect a t pH=4.6 on the casein p a r t i c l e s already formed.
In order t o obtain t h i s information the CaCl2 should be added
after a c i d i f i c a t i o n .
4.5.6 5?ia5â£i2S_ËEê£t£â_2f-âSi^-ËlSïSîïïiuS-SêiË
For a complete c h a r a c t e r i z a t i o n of the rheological behaviour of
acid casein gels various other rheological techniques in addition
to dynamic measurements such as constant s t r e s s and constant
s t r a i n measurements would be needed, unless one i s able to r e c a l culate the d i f f e r e n t rheological parameters as a function of the
time scale into one another. In p r i n c i p l e t h i s can be done quite
e a s i l y by using the relaxation spectrum, H(x), calculated from one
type of rheological parameters. However, such a spectrum can only
be calculated completely, when the time scale i s known a t which
the so-called terminal zone ( f i g . 4.2) i s reached. In t h i s region
theory p r e d i c t s t h a t G' and G" should approach zero a t a slope of
112
respectively2and1withdecreasinguu,thiswhenG',G"andware
plotted on adouble logarithmic scale (fig.4.2).Forlinearviscoelastic materials, such as aphysically cross-linked gel,this
in principle occurs always as w approaches zero. Such a linear
viscoelastic system maybe simulated by asystem ofmaxwell elements (fig. 4.3) with different relaxation times.However quite
oftenphysically cross-linked gels show over longertimescalesa
semi-solid-like or permanent character i.e. G' approaches some
constantvalueG atthe lowestmeasurablew (seefig.4.2,curve
a). In fact the presence of a permanent modulus G depends in
principleonthelongesttimescaletakenintoconsideration;i.e.
itdependsontheratio ofthelongesttimescaleofthemeasurementwith respectto the longest lifetimeofthebondsinthegel
network.Insuchcaseitmightbemuchmoredifficulttocalculate
the relaxation spectrum in an unequivocal manner. One way to
deriveH ( T )thenisbycalculatingitfromG"usingeq.4.10.Subsequently G' isrecalculated fromH(t)using eq.4.9. Thecalculated and experimental values of G' should agree then,whenthe
possibility of apermanent network modulus G istaken intoconsideration. Permanent refers inthis case tothe longestexperimentaltime.
Sincethetime/temperature superpositionprinciplecouldnotbe
appliedtoacidcaseingelsandsinceexperimental limitationsalways constrained the computed relaxation spectrum toarelatively
small range ofw (4decades atmostinthis study),atbest,only
asemi-permanentnetworkmoduluscouldbecalculated.
Inthecontextofthisstudywewereinterested inthepossible
presence of aso-called permanent network characterinacidskim3
5
milk gels over time scalesbetween 10 to10 s(0.25to25hrs).
It is,however, alsopossible thatover these time scales G'and
G"keep decreasing atmore or lessthesameslopeorthatthegel
behavesasaliquid,G'andG"approachingzeroataslopeofrespectively2and1.
Thepresenceofapermanentnetworkcharactercanbetestedexperimentallybymeasurementsoververylongtimescales.Different
methodsareavailable,butstressrelaxationmeasurementsaremost
convenientforthispurpose.Att=0acertainconstantdeformation
y is applied suddenly and the shearstressa(t)ismonitored asa
113
function of time. The shear stress will decrease with time and
eventually itwill relax toa=0orto aconstantvalue o=ax. The
permanentnetworkmodulusisdefinedas:
G = aA
(4.14)
Bymeans ofthis typeof experimentitcanbecheckedwhetherthe
valueofG derived fromtheexperimentaldynamicmodulibyapplying eqs.4.9 and 4.10 is areasonable one.Inthis sectionsome
results of computer simulations on the dynamic moduli of acid
skimmilkgels (kindlyperformed byProf.B.deCindio,Université
degli studi diNapoli)will firstbepresented.Thesetheoretical
calculations suggested thepossibility that asemi-permanentnet3
workmoduluswaspresentbeyond the timescaleof6x10 s.Therefore acid skimmilk gels were tested over longer time scales by
meansofavariantofastressrelaxationexperiment.Thisvariant
howeverhadsomedisadvantages,becausebotha(t)andy(t)changed
withtime.
4.5.6.1 Computation of the
permanent network
relaxation
modulus
spectrum
and of a
Acid casein gelswere considered as asystem ofparallelmaxwell elements. As a first step the relaxation spectrum H(t)was
derived from the lossmodulus G"bymeans of an iterative method
(deCindioetal., 1977),usingeq.4.10 overatruncatedfrequencyrange:
ln(T2=l/w2;
G"(u))= / H(x)
m
l 9 dinT
1+U) TT
(4.15]
1
-1
-3
-1
where w, (=10 /2n s )andw- (=10 /2n s )are themaximum and
minimum experimental value ofw.The calculations begin fromthe
experimental values of G" and H(x) is calculated ina firstapproach.SubsequentlyG"isrecomputed from H ( T ) , whichiscontinually adjusted to obtain thebest fitbetween the experimental G"
and itsrecomputed value. In fig.4.20 anexampleofacalculated
semi-
114
H(Nm-2)
Fig. 4.20 The relaxation spectrumH(ï)
calculated from the loss modulus G"
(see text) for the acid skimmilk gel
of fig.4.5,whichwastested at40°C.
relaxation spectrum isshown. Inthe situationwhere H ( T ) iscompletely known andG iszero,G'andG"canbeconverteddirectly
into eachother.However, inthis studyH(x)wastruncated atthe
lowest measurable frequency, which implies that the curve oflog
G"versus logwwas assumed tohaveaslopeof1inthefrequency
rangebelow the truncated frequency.Therefore G wouldbedueto
4
all bonds having arelaxation time greater than~10 s.Formany
macroscopicalproperties,whichareofinterestformanufactureon
afactoryscale,thisisequivalenttoaninfinitelylongtime.
G'maybederivedthenfromH(t)accordingtotheintegralterm
ineq.4.9 (for the truncated frequencyrange)andthedifference
betweencalculatedandexperimentalvaluesofG'ascribedtoG*:
ln(x 9 =l/uj,)
22
exp
H(x)
U)T
dint
(4.16)
u 22
1+U) t
ln(T1=l/iu1)
where G* e is a semi-permanent network modulus. The word semi is
used to indicate among other reasons that G* wasobtained from
only avery limited frequency range.For acid casein gels asubstantial value forGe*was found.Thisvalueshowedlittlevariationovertheexperimental rangeofwasopposedtothevariations
ofG'and G" (fig. 4.21), which favours thevalidity of the calculation.The constantvalue ofG*asafunctionofwimpliesan
r
e
increaseintheproportional contributionofG*totheexperimentalvalues ofG'atsmall values ofw, as is illustrated infig.
115
Fig. 4.21 The semi-permanent network
modulus G* as a function of angular
frequency tu,calculated from the storage modulus G'and the relaxationspectrum H ( T ) (seetext)fortheacid skimmilk gel of fig. 4.5, which wastested
at40°C.
co(rad.s-1
4.22. Inthis figure3 the ratio ofthe calculated value ofG*to
experimental value ofG'isdepicted as a function ofw forfour
different acid skimmilk gels. Curve 1refers to anacidskimmilk
gel,whichwasagedfor147hrsat50°Candsubsequentlymeasured
at50 °C (fordynamicmoduli,see fig.4.6).Curves 2to4refer
toacidskimmilkgels,whichwereagedforapproximately18hrsat
30 °C and subsequently measured atresp.40 °C,20 °Cand 30°C
(for dynamic moduli see fig. 4.5).For the gels aged at 30 °C
(curves 2to 4)Ge*varied between80and150Nm (seefig.4.21
forthe gelmeasured at40°C),whileforthegelagedat50°Ca
-2
straight line atGe*=300Nm was found.Ofcourse thevalueobtained forG*willbeverysensitivetothesmallesttu,wherethe
rangewastruncated. Itappearsthatatthetimescalesconsidered
the gel aged at 50°C showed a more pronounced solid-likebehaviourthanthethreegelsagedat30°C,whichallshowedasimilar
more liquid-like behaviour with atendency tobemoreliquid-like
at low T .This conclusion was also obtained more qualitatively
fromthebehaviouroftanôasafunctionofmeasuringtemperature
atlowfrequency (section4.5.3).
4.5.6.2 The value of a pseudo-stress
time scales
relaxation
modulus at long
The dynamic viscometer was used to roughly testthepermanent
character of acid skimmilk gels (section 2.10.3) at long time
scales. For thispurpose the driving shaftwassetatitsmaximum
displacement.This corresponded tothemaximum amplitudeusedfor
e
116
G!/G'
I.U
?\^^
0.8-
0.6-
^\\ ^ " ^ \
\ \ \
^ \
\\ \
^ \
\ \ \
\
0.4-
v^ X
N.
•--. —-
^->-
\
0.2-
^""^d 3.
4.
0-
TO"4
10"
10-1
10'
10'
o) (rad s-1 )
Fig. 4.22 The r a t i o G*/G' as a function of angular frequency m ( r a d . s ) .
e
5
Curve 1 refers to the gel of f i g . 4 . 6 , which was aged for 5.3x10 s (147 hrs)
a t 50 °C and subsequently t e s t e d a t 50 °C. Curves 2 to 4 refer to the gels of
f i g . 4 . 5 , which were aged for 5.8x10
s (16 hrs) a t 30 °C and subsequently
t e s t e d at resp. 40 °C, 20 °C and 30 °C.
dynamic measurements within the l i n e a r region. The displacement of
the inner-cylinder was measured as a function of time. Because of
the v i s c o - e l a s t i c character of the gel both y(t) and a ( t ) w i l l
change with time. As the amplitude of the inner-cylinder i n creases, a ( t ) w i l l decrease and y ( t ) w i l l increase. Therefore we
define a pseudo-stress relaxation modulus G(t)* as:
G(t)* = o ( t ) A ( t )
Ultimately G(t)*will reach a limit value G^*,whichmay beregardedasaparametercharacteristic ofthepermanentcharacterof
agelnetwork.Forthatreasonwewillcall Gx*apseudo-permanent
networkmodulus.
In fig.4.23 G(t)*isdepicted as a function of the logarithm
of time fordifferent acid skimmilk gels (madefromskimmilkpowder A, section 2.1).One series of gels were aged for 19to25
hrs at 30 °C and subsequently tested at resp. 10, 20, 30 and
40 °C. One gel was aged for 175 hrs at 40 °C and subsequently
testedat40°C.
(4.17)
117
GmiNin-2)
400
10°C o
30020°C x.
200" ^
WC
100
X)1
W'
10"
t) 5
t (s)
Fig. 4.23 The pseudo-stress relaxation modulus G(t)* as a function of the logarithm of measuring time for five different acid skimmilk gels. Four gels
(D,x,o,V) were aged for 6.8x10 s to 9.0x10 s (19 to 25 hrs) at 30 °C, before
G(t)* was measured (measuring temperatures indicated at the left handside of
the figure). The remaining gel (measuring temperature indicated at the right
handside of the figure) was aged for 7.3xl0 5 s (175 hrs) at 40 °C, before G(t)*
was measured.
G ( t ) * d e c r e a s e d w i t h time for a l l g e l s t e s t e d , b u t even a f t e r
10 s (30 h r s ) a c o n s i d e r a b l e v a l u e of G ( t ) * remained, confirming
a kind of permanent c h a r a c t e r i n t h e s e a c i d skimmilk g e l s . The
-3
-1
-2
computed v a l u e s of G * a t w=102
rad.s
( v a r y i n g from 100 Nm a t
40 °C ( f i g . 4 . 2 1 ) t o 150 Nm" a t 20 °C) were of t h e same o r d e r of
3
magnitude as t h e v a l u e s of G ( t ) * a f t e r 6x10 s . However a t l o n g e r
t i m e s G ( t ) * d e c r e a s e d f u r t h e r i n d i c a t i n g t h a t for t h e c a l c u l a t i o n
of G * t h e frequency range had been t r u n c a t e d a t v a l u e s of w which
were t o o l a r g e . In t h i s c o n t e x t i t would be i n t e r e s t i n g t o compute
G and H ( t ) from f i g . 4.23 and compare t h e s e r e s u l t s w i t h t h e d a t a
c a l c u l a t e d from t h e dynamic moduli a c c o r d i n g t o e q s . 4 . 1 5 and
4 . 1 6 . C l e a r l y more r e s e a r c h i n t h i s f i e l d i s n e c e s s a r y .
The r a t h e r g r a d u a l d e c r e a s e of G ( t ) * w i t h t h e l o g a r i t h m of
118
time (fig.4.23) forthe gels aged at30 °Cwashalted atlonger
timesprobablypartlybecauseofanongoinggelation,whichtended
to increase the modulus G(t)*. The gel aged for 7.3x10 s (175
hrs) at 40 °C showed a substantially higher G(t)*and an almost
linear decrease ofG(t)*with the logarithmoftime.Inthiscase
G' hardly increased during theG(t)*experiment,whereas forthe
gels, aged for 6.8 to 9.0x10 s at 30 °C, the increase ofG'
duringtheG(t)*experimentranfrom15%at10°Cto60%at40°C.
Apparently G(t)*increased athigher ageing temperaturesandlonger ageing times;this agreedwith thetheoreticalcalculationof
G *fromthedynamicmodulusforthegelagedfor147hrsat50°C
withrespecttoGe*forthegelsagedat30°C(seefig.4.22).
Significantly the decrease ofG(t)*with thelogarithmoftime
forthegelsagedat30°C(fig.4.23)wasmorepronounced atlowertemperature.HoweverthedynamicmodulusG'ofthesegelsafter
_2
ageingwasequalto355Nm at30°Cexceptfortheonetestedat
20 °C,where G' was equal to 310Nm"2 at30°C.The tendency of
thestoragemodulitodecreasefasterwithdecreasing frequencyat
longer time scales for lower T wasalreadyseeninfig.4.5.Obviously morebonds relaxed faster inthetimescalebelowroughly
4
10 satlowertemperature,whichagreedwiththemoreliquid-like
character at lower measuring temperatures as indicated by the
highervaluesoftanôatlowerangular frequency (section4.5.3).
4
After 10 s G(t)*seemed to be almost independent of measuring
temperature.
4.5.7Çreep__measurements
Thebehaviourofacidskimmilkgelsprepared fromskimmilkpowder B at large deformations was studied by constant stressmeasurements (section 2.10.1). Before themeasurement the gelswere
aged for 16hrs at30 °Candsubsequently testedatthesametemperature. Att=0 aconstant stress a, varying from 10 to 175Pa,
wasapplied.Thesheardeformationy(t)wasmeasured asafunction
oftimeforloadingtimesupto900s(15min).Theseresultswere
the so-called creep curves.A fast initial increase of y, dueto
the elastic character of the gel,was followed by aslow gradual
increaseofy,duetoitsviscouscharacter,until fractureoccurred.Each gelwas used only once.Infig.4.24 thesheardéforma-
119
Fig.4.24Thesheardeformationyasafunctionoftheshearstress aderived
from creep measurements for acid skimmilk gels (pH=4.6). Each gel,agedfor
4
5.8x10 s(16hrs),at30°C,wasmeasured onlyonceat30°Catoneconstant
shearstress
CT.
Theloadingtimeisindicated.
tion y(t)is shown as a function of the applied constant stress at
different time intervals. y(t) tended to increase gradually but
less than linearly with a until the network was broken. Independently of the loading time macroscopic fracture occurred at ay of
0.5-0.6. Incontrast toy, a at the point of fracture strongly de_2
the gel network
pended on the loading time. Below a a of 80 Nm
remained macroscopically intact for at least 900 s, while the
-2
caused fracture after ca. 20 s.
highest applied CT of 175 Nm
Qualitatively this picture was the same as that found by Van Dijk
(1982) for rennet gels. However quantitatively there was a large
difference. The deformation at fracture for rennet gels was much
larger namely ca. 1.5, while the stress at fracture was much lower
-2
.
.
e.g. 10 Nm for a loading time of 900 s. Significantly this dif-2
ference in stress at fracture (90 Nm
in contrast to 10 Nm )
.
-2
120
afterloadingtimesof900swaslargerthanthedifferenceinthe
_2
storage modulus, which equalled approx. 400 Nm for the acid
-2
skimmilk gels and approx. 110 Nm for rennet gels, indicating
that these parameters were notdirectly related.Rennet skimmilk
gels probably have a much less permanent network character than
acid skimmilk gels; thisconclusion is supported by thevery low
valueofG*,whichcanbecalculatedaccordingtosection4.5.6.1
from the dynamicmoduli ofrennetgels (VanVlietand deCindio,
unpublishedresults).
The maximum deformation of0.5 to 0.6 found inthese constant
stressmeasurementsagreedwellwithamaximumdeformationvarying
from 0.5 to 0.8 found in stress overshoot experiments (notpresented in this study). Inthose experiments the shear stressa(t)
wasmeasured asafunctionofthesheardeformationy(t)onapplyingaconstantshearratey.
The less-than-linear increase ofywith a indicates thatwith
higher applied a.the shear modulus G should increase. At first
sight this seems tobe incontradictionwith fig.4.4,wherethe
dynamicmoduliG'andG"slightlydecreasedwithy.Howeverinthe
constant stress experiments not enough data in the low yregion
wereobtainedtocheckwhetherasigmoidshapedcurvewasfoundat
lowy.Infactthevery limiteddataobtaineddonotexcludesuch
a shape. The increase of Gwith ymightbe due tobentstrands,
which only contribute at larger deformations, when they are
stretched. At increasing y the number of stress-carrying strands
will increase,although the strands already stretchedatt=0will
break.
From the slope ofthe yversusacurveafter1s,extrapolated
to y=0 and a=0, a shear modulus G of approximately 500Nm was
calculated. This isofthe same orderofmagnitude asG'foracid
skimmilkgelsathighw.Inthiscalculationthealreadymentioned
possibility of asigmoid shape of theyversus a curveatsmally
wasnottakenintoaccount.
4.6 Estimationofthemodulusofastrandofparticles
Themodulus of an inhomogeneous acid caseingelwilldependon
the number and the strength of the strands,connecting thelarge
121
aggregatesofcaseinparticles.Assumingaverysimplefiedspatial
distribution itispossible to estimate theorderofmagnitudeof
themodulusofastrandofparticles.
The gelnetwork isthought tobebuiltup of acubic arrayof
strands, which extend in three perpendicular directions. Each
strandreachesfromonesideofthenetworktotheother.Atregular distances,i.e. atthe angular pointsofthecubicarray,the
strandsofparticleswillintersecteachotherformingcrosslinks.
Only a fraction f' of the total number of available caseinparticleswillbebuiltintothestrands.Theremainderofthecasein
particlesarethoughttobeaccumulated atthecrosslinksandthus
forminglargeaggregates.Averyschematictwo-dimensionalpicture
of such anetwork isgiven infig.3.12d.Thesegmentofastrand
between two crosslinks maybe represented byacylinderoflength
Landdiameterd.Thisdistheactualdiameterofthesegmentsof
the strand between the large aggregates ofcaseinparticles.This
implies that only part of the aggregates at the crosslinks is
thought to be effective incontrolling themechanical properties
of thegel.Thevolume of such asegmentof strand willbegiven
2
3
by ndL/4. Suppose we have N cylinders per m ,then the volume
fraction<j»'ofsegmentsandsoofallstrandscanbewrittenas:
i'= 1 / 4Nnd2L
(4.18)
ThetotallengthofstresscarryingsegmentsofstrandsamountsNL
3
perm oftotalgelvolume.Rememberingthatthestrandsextendin
threeperpendicular directions,thenumber of segmentsofstrands
2 •
carrying atensile stress across onem isas a firstapproximation,givenby:
1/3 NL=^ I
(4.19)
3;tdz
When the gelnetwork is sheared strands carrying atensile force
willbeelongated.Theelongation forcefforasegmentofstrand,
whenitiselongated fromLtoL+dL,canbewrittenas (VanVliet,
1977)
122
f = 3GA Y^
S
(4.20)
Li
2
where A is the cross section area (=nd/4) and G the modulus of a
strand. G
is considered to have the same value over the whole
strand and for all strands.Macroscopically the shear stress a may
be coupled to the elongation force fby (VanVliet, 1977):
a=^ 4 f
3nd^
(4.21)
where ty is the total volume fraction of casein particles and f'is
a correction factor for the fraction ofparticles not contributing
to the strands. In fact f'<t>, which equals <)»' in eqs. 4.18 and
4.19, is thevolume fraction ofparticles,which form the strands.
At small deformations a simple relation between the macroscopical
shear deformation y an<ä the elongation dL/L may be derived (Van
Vliet, 1977):
Y = 2j£
(4.22)
Using equation 4.20 to4.22 the shear modulus G canbe writtenas:
G =o/Y = f'Gs <t>/2
(4.23)
or
G s =| ^
(4.24)
Thus a simple relationship between the shear modulus G and the
modulus of a strand G
is found. The factor 2 may be somewhat
variable, in that it depends on the arbitrary assumptions made
regarding the geometrical structure assumed in the model. Kamphuis
(personal communication, and Kamphuis, 1984) derived a similar
relationship to equation 4.24 with a factor 5 instead of 2, when
he assumed a more random distribution of strands. Equation 4.24
seems to be only valid for calculating the order of magnitude of
G_.
123
To apply equation4.24 to acid skimmilk gels requires arough
estimate of f'.From e.g.permeability measurementsandtherelationship foundbetweenG'andthecaseinconcentration (chapter3)
it follows that acid casein gels are very inhomogeneous; this
implies that only arelatively smallpartof the casein actually
contributes to the mechanical properties of the gel. Ifwe say
thatf'isaround0.1,i.e.effectively 90%oftheparticlesdonot
carry an applied stress, that <|>is also~0.1 andG is~500Nm
5
(see previous section), then G will be approximately 10 Nm
Thus G will be at least two orders ofmagnitude larger thanG,
which seems reasonable. Inside the strands theproteinconcentrationwillbeatleastaround25wt.%.Almostnodataareavailable
for themoduli of such concentrated proteingels.Proteingelsof
10% heat denatured lysozyme or ovalbumin exhibit moduli of ap4 - 2
•
proximately 10 Nm (Graham, 1976). The differenceinmodulusof
a factor 10 seems reasonable since the concentration is arounda
factor 2.5 lower (see also section 3.4.2). VanKleef (personal
communication)andVanKleefetal.(1978)founddynamicmoduliof
2xl03 to 7xl03 Nm -2 for 10wt.% and 105-4xl05 Nm"2 for 25wt.%
4
4-2
heat-setovalbumingelsandof1.5x10-5x10 Nm for25wt.%soya
proteingels.
4.7 Discussion
The rheological properties of acid casein gelswill depend on
the interactions between the particles and their spatialdistribution throughout the gel network. The spatial distribution of
strands ofparticles and especially the effectofinhomogeneities
in this distribution has been discussed in section 3.4.3.1. In
this sectionwewill discuss the differentinteractionforcesinvolvedintheformationofacaseingelnetworkandtheconsequencesforthestructureofthestrands.
The interactions between the particles i.e. the formation of
interparticle bonds strongly depends on the structure and state
of aggregation of the individual casein molecules. In this context a hierarchy of protein aggregation can be distinguished at
three levels i.e. intramolecular leading to the secondary structure and tertiary structure of proteinmolecules,intermolecular
-2
-2
124
inside the casein particles leading to the structure of these
casein particles and intermolecular between distinct particles
leading to coagulation. As discussed in chapter 3 and section
4.5.5.3the structure oftheparticles andprobablytheextentof
fusionbetweenthem aftergel formationdependsontheconditions
(pH, temperature, kind of salt ions present and I)duringtheir
formation.
Differentinteractionforcesbothatmolecularandatcolloidal
levelwill be involved.Hydrophobic bonding, electrostaticinteractions,vanderWaalsattractionandprobablyhydrogenbondswill
contributetotheconformationofthecaseinmolecules.
The contribution ofhydrogenbonds to thespatialstructureof
the casein particles isvery difficult to estimate. Inprinciple
their contribution can increase aspH islowered from6.7 to4.6,
since the number of protonated carboxylic groups will increase;
because of their large energy content only a fewhydrogenbonds
canhave alarge effect.However, intherelativelyrandomstructure, ascaseins have,therewill alsobeacompetitionofhydrogen bonds formed with water molecules. Because of the varying
charge distribution and different hydrophobic character of the
various caseins the relative importance of the other mentioned
interactionsonthespatialstructureofthecaseinparticleswill
varywiththetypeofcasein.Furtheronehastotakeintoaccount
thepossible formation ofCa-bridges,as«,-,a»-andß-casein,
all of which contain serinephosphate rich amino acid seguences,
..
2+
areverysensitivetoCa (DalgleishandParker,1980,Parkerand
Dalgleish, 1981). Itisprobable thattheseCa-bridgesaremainly
involved indetermining the size and structureofthecaseinparticlesandnotdirectlyintheinterparticle interactions,because
the rheological properties of acid sodium caseinategelsprepared
in the absence of Ca are very similar to those of acid skimmilk
gels.Themuchweakerdynamicmoduliofacidsodiumcaseinategels
preparedwithCaCl2 ascomparedtothosepreparedwithNaClatthe
sameIareprobablyduetothemuchlargerparticlesalreadyformedathigherpH (pH=5.0-6.8),whiletan6,whichisinsensitiveto
variationsinthespatialdistribution,remainsthesame.Electrostatic interactions are very important incontrolling thestructureofthecaseinparticles.Thiscanbeconcluded frombehaviour
125
seenduringacidificationofskimmilkwherecaseinmoleculesfirst
tend to dissolve from the caseinparticles,butclosetotheisoelectricalpHalldissolvedcaseindisappeared fromtheserumonce
more.Thesameaggregationeffectoccursinsodiumcaseinatesolutions, where casein tends to aggregatebetweenpH=6.0 and 5.0 to
form caseinparticles.Of course partofthisaggregationwillbe
due to a decrease ofelectrostatic repulsionbetween theprotein
molecules,sincethenetnegativechargeofthecaseinsdecreases,
when pH is being decreased to pH~4.6. Without doubt hydrophobic
interactionsarealsoinvolved.Caseinmoleculesarefairlyhydrophobic (Walstra and Jenness,1984)andthedecreaseinvoluminosity with increasing temperature canbe accounted forby simplya
change inhydrophobic interactions. Inaddition totheseinteraction forces the ever-present van derWaalsinteraction forcesand
steric interactions are also involved inthe intra- andintermolecularprotein-proteininteractions.
All these types of interaction forceswill be involved inthe
formation of bonds between caseinparticles.However the results
of this study arenot conclusive enough to give anestimation of
thecontributionofeachtypeofinteraction forces.Theformation
and character ofthebonds will dependonthebalancebetweenthe
interaction forces.Each change inthe conformationofthecasein
molecules will affect theparticle structure andsoitspossibilities for the formation of interparticle bonds.However the experimental results clearly offer the possiblity of some simple
speculations.The formation ofdirect electrostatic bondsbetween
oppositelychargedgroupsondifferentcaseinparticlesisstronglysuggestedbythespecificpHdependence andthelargeeffectof
extra NaCl, added after acidification, on the magnitude of the
dynamic moduli.The ever-presentvan derWaalsattractionmayenhancetheformationofthesebonds.Therearenoclearindications
of the presence of direct interparticle bonds due tohydrophobic
bonding, since the dynamic moduli decrease with increasing measuring temperature in the temperature range from 0 to 50 °C.
However in somepreliminary experiments atlargedeformationsand
long loading times a positive temperature effect was found. In
these experiments, which were carried out according to section
4.5.6.2, at a large constant deformation (-y>>0.04)applied for
126
severalhoursG(t)*didincreasewithtemperature.Howevernoconclusion can be drawn astowhether thispositive temperatureeffect is due to entropie contributions or hydrophobic bonding or
both. Another temperature effectwas seenwith tanô atlow fre-1
-1
quency (10 -3to 10 rad.s
).
Themore liquid-likecharacter at
low temperature expressed inthehigher valuesoftanÔ(seefig.
4.9, 4.11 and 4.12) and in afaster decrease ofG(t)*(seefig.
4.23) isprobably simply due to relatively fasterrelaxinghydrophobicbonds at low temperature.As discussedinsection4.5.3 we
assume that the large effect of T on thevalues of thedynamic
moduliisatleastpartlyduetoanindirecteffectofhydrophobic
interactions.Animportantcontribution fromhydrogenbondsisnot
obviously expected since they need specific spatial orientations
ofcarboxylic groups on different caseinparticles.Stericinteractions stillplay an importantpart atpH=4.6,aswillbe shown
in the next chapter. Splitting off the glycomacropeptide partof
K-caseinconsiderablyreducesthestabilityofcaseinparticlesat
pH=4.6 (seenextchapter).
Itshouldbeemphasizedthatmostprobably,thenatureandnumber of interparticle bonds depends in the first instance onthe
conformation ofthe individual caseinmolecules andthestructure
ofthe caseinparticles.This structure willprobablychangefrom
the outside to the inside of these particles. Changing asystem
parameter such as pH, I, T and type of ions,will first affect
the casein particles and subsequently the nature and number of
interparticle bonds. For example: as discussed in section 4.5.3
changes inproteinconformation upon temperature rise,leadingto
a more compactproteinmolecule,may thenproduce amore compact
casein particle. This could ultimately result in fewerinterparticlebonds.
Ifwe consider, the amino acid sequencesoftheindividualcaseins, ß-casein probably will be involved relatively more in
hydrophobic bonds, whereas a-caseins will be involved more in
electrostatic bonds.Perhaps, ß-casein inparticular maybe able
tomigrate reversibly from the outside ofthecaseinparticlesto
thecoreastemperature israised,therebydecreasingtheparticle
voluminosity and particle stability due to a decrease of steric
repulsion. K-casein will still be located at the outside ofthe
127
casein particles at pH=4.6 and contribute to the stericstabilizationofthecaseinparticles.Itisdoubtfulwhetheritcontributesmorethantheothercaseinstotheformationofinterparticle
bonds,aslongasGMPisnotreleased.
Os>
128
5 THE STRUCTURE OF CASEINGELSMADE BYACIDIFICATION AND RENNET
ACTION
5.1 Introduction
Rennet isused inthemanufacture ofmanykindsofdairyproducts. Several of them are acidified to apHbetween 5.0 and 6.0
before rennet action takes place, e.g. quarg and some types of
cheddarcheese.
Steric repulsion is expected tobe involved inthestabilization of casein particles,even atpH=4.6.Thehydrophilic glycomacropeptide (GMP)partof K-casein will especiallycontributeto
the stabilization of casein particles.Addition of rennetoffers
the possibility of studying the stabilizing effectofGMP atlow
pH, since the rate of scission ofGMP ismuch fasterthanother
proteolyticreactionsofrennet,evenatlowpH.
Ordinarycommercialrennetsamplescontainprimarilytheenzyme
chymosin and some pepsin.Both these enzymes are so-calledendopeptidases. Bovine pepsin is roughly similar in action tochymosin.Themostnoteworthy property ofrennetistherapidandspecific manner in which it splits K-casein between the aminoacid
residues Phe (no. 105) and Met (no. 106) (Walstra andJennness,
1984). This reaction ishighly temperature dependent.The Q,Q is
about3.The chain of amino acidresidues106-169,resultingfrom
proteolysis, iscalled GMP,because itcontainsalloftheglycosyl residues found in K-casein. These are attached to threonine
residues, particularly those found inposition 131,133,135and
possibly136 (Swaisgood, 1982).
Itiswell documented thatGMPplaysakeyroleinthestability ofcaseinmicelles atpH=6.7,butvery little isknown about
itsrole atlowpH (below 5.2).Itisgenerally acceptedthatthe
coagulationofcaseinmicellesinthefirststageofcheesemaking
is induced by rennetaction onK-casein, resulting inpara K-casein and GMP.The stabilizing effect ofGMP atpH=6.7 canbeattributed to two mechanisms: steric stabilization and chargestabilization.GMP has astrong hydrophilic characterandanegative
charge,which depends on thenumber ofboundsialicacidresidues
129
(Walstra and Jenness, 1984). Renneting causes adrop inZetapotential of casein micelles at natural pH to about two thirdsof
its original value (Dalgleish, 1984). At this pH a charge of
—10.5 or —9.5 (depending on the geneticvariantA orB ofthe
K-casein)canbeattributedtothepeptidebackboneofGMP(Swaisgood,1982,WalstraandJenness,1984). Foreachsialicacidresidue one negative charge must be added. Taking anaverage ofone
sialicacidperK-caseinmolecule (WalstraandJenness,1984)this
wouldgiveachargeof— 1 1 fortheGMPpartofK-caseinatpH=6.7.
A similar calculation at pH=4.6, using the pK-values for the
acidic and hydroxylic side groups, the serine phosphate and the
N-acetylneuraminic acid (sialic acid) as given by Walstra and
Jenness (1984)and Swaisgood (1982), results inanegativecharge
ofapproximately-4fortheGMPpartofK-casein.
Inpassing wenote thattheoverall Zetapotential of thecaseinparticlesatpH=4.6 (T=2°C)isfoundtobezero (Darlingand
Dickson, 1979), but theseparticles are of arather complicated,
indeterminatestructure.
Inthisparticular studywewere interested inthestabilizing
effect of GMP onthecaseinparticles formed after acidification
atlow temperature (0-2°C)to apHbetween4.4 and5.8.Thiseffect was studied with the help of rheological and permeability
measurements ofgels formed after (successively)acidificationto
thedesiredpH,additionofrennetandheatingatarateof0.5°C
per minute to the desired temperature. Gels can be made over a
muchbroader range ofpH's and temperaturesbythementionedcombined effect of acidification and rennet action thanbyacidification alone (see section 4.5.4). The rheological properties of
acid casein gels differ little in the pH range between 4.3 and
4.9, overwhich acid casein gels canbeformedat30°C(seesection 4.5.4). However these properties differ significantly from
those ofcasein gelsmade by rennetactiononskimmilkatnatural
pH (Zoon, 1984). Therefore the effect of pH incombinationwith
rennet addition was investigated to seek atransition inrheologicalpropertiesbetweenacidcaseingels (aroundpH=4.6)andrennet gels (natural pH).This transition wasnotexpectedtobedue
to the release ofGMP,buttothepropertiesofthecaseinparticlesinwhichCawasinvolvedeitherinionicformorascolloidal
130
calciumphosphate (CCP).
Ingeneral,rennetactiononmilkproteinsincludestwostages:
a fast first stage in which GMP is split off and asecond slow
stage inwhichproteolytic cleavage of only« s l _ andß-caseinoccurs (seenextsection).Thisslowproteolysiswillonlyinfluence
gel properties atlonger time scales,while the influence ofGMP
splitting will be seen atthebeginningofgelformation.According to Pierre (1983) at 32°C the proportion of GMP, which was
releasedatthemomentofmilkclotting,decreased from92%to43%
aspHwasdecreased from6.7 to5.0.Althoughintheexperimentof
Pierre, milk was acidified atelevated temperatures, itisprobable that a similar trend may be expected formilk acidified at
2 °C,but the absolutepercentages hydrolysed willdependontemperature.
5.2 Proteolyticaction
After the rapid cleavage of the protein bond betweenPhe 105
and Met 106 of K-casein rennet action does not stop. <*„-i-and
ß-casein are hydrolysed in a slow process which continues over
weeks innormal cheesemaking practice,butparaK-caseinand a 2~
caseinsuffernofurtherdegradation.
Recently Visser (1981), Pélissier (1984) and Grappin et al.
(1985) have reviewed the proteolysis of the caseins. They paid
detailed attention tothe rennet-inducedhydrolysis.Thedegradationof a ,-andß-casein isquitecomplicated.Therateofdegradation and the type of products formed depend very much onpH,
ionic strength and temperature.These factors notonlyaffectthe
enzyme activity, but predominantly the conformation and state of
aggregation ofthe caseinmolecules and therebytheaccessibility
of bonds for proteolytic cleavage.For example soluble caseinis
hydrolysed much faster than micellar casein (Ledford et al.,
1968). Above 40°Crennet israpidly inactivated, theQ,Q ofthe
inactivationreactionbeingabout2.5 (WalstraandJenness,1984).
A suitable technique to trace the degradation of a ,- and
ß-casein is Polyacrylamide gel electrophoresis (Ledford et al.,
1966, DeJong, 1975 and Grappin et al., 1985). Most experiments
described in the literature havebeen carried outwith solutions
131
ofisolatedcaseins (MulvihillandFox,1977,1979a,1979b,Creamer,
1976, Creameretal.,1971,VisserandSlangen,1977),withsodium
caseinate (Fox,1969)orwith cheese-like substrates (DeJongand
De Groot-Mostert, 1977, andNoomen, 1978). From theseresults it
is clear that the accessibility of the proteins and therefore
their state of aggregationplay akeyroleintheproteolyticaction of rennet. Both «,- and ß-casein are not hydrolysed into
many small peptides in a one step process,but in a multi step
process.Ateverystepasmallpeptideissplitofftogivemacropeptides ofdecreasing length,utimately resulting inaseriesof
smallpeptides.
The degradation of a,-and ß-casein and thehydrolysisproducts formed are schematically depicted in figure 5.1.agl-casein
is first cleaved at the N-terminal end of its peptide chain to
give a..-Icasein (residue 24or25to 199,Pélissier, 1984). At
leastsixotherproteinbondsareknowntobesensitivetorennet.
According to Mulvihill and Fox (1977 and 1979a)Ö - I - H caseinis
splitoff from<*-.-Icasein atpH=5.8ina2%o<,-caseinsolution
and in the next stage « S l - H casein is further hydrolysed to
or..-III
anda,-IV
si
sicasein.AtpH=4.6rontheotherhand,wherethe
substrate is aggregated, oi,-I casein ishydrolysed toa,-Vcaseinonly (seefig.5.1)andsmallpeptideswhichcannotbedetected with Polyacrylamide gelelectrophoresis. In this case (a 2%
a ,-casein solution after 12 hrs incubation time at T=30°C)
a ,-caseinbreakdownisoptimalatpH=5.8andminimal atpH=4.6.
ß-casein is degraded from its C-terminal end to give successively ß-l casein (residue 1-189 or 192),ß-II casein (residue
1-165 or 166)and ß-III casein (residue 1-139). Detection ofthe
ß-II and ß-III casein bands in the electrophoretic patterns of
milk products ishampered because oftheposition ofthesebands
justbeforeandafterthebandofa,-casein (seefigure5.1).The
rate of hydrolysis ofboth a ,- and ß-casein (Fox, 1969,Creamer
et al., 1971, andCreamer, 1976)increaseswith temperature,a,
hydrolysis faster than ßso that atincreasingtemperaturesrelatively more agl-casein is degraded. At 10°C (Creamer et al.,
1971) the degradation productß-I ishydrolysed much slowerthan
at37°c.
Proteolysis of « s l - and ß-casein in a sodium caseinate solution
132
Fig.5.1 Schematic picture of Polyacrylamide gel electrophoretic patterns of different caseinsamples,whetherhydrolysed by
rennetornot.
1.total caseinwithoutrennet.
2. a ..-caseinhydrolysedby rennetatpH=5.8.
3. a ..-caseinhydrolysed by rennetatpH=4.6.
4. ß-casein hydrolysed by rennet (nospecificpH).
1 2
3
4
(Fox,1969)shows anoptimum atpH=5.8.Thiswasalsofoundbyde
Jongetal. (1977)forsodiumparacaseinate.
5.3 Resultsanddiscussion
This section isdivided intwoparts.Thefirstpartdescribes
experimentswithskimmilkgelsmadeatpH=4.6andvaryinggelation
temperatures.Thesecondpartdealswithexperiments inwhichgels
weremadeat20°C,butwithapHvaryingfrom4.4to5.8.
All gels were prepared according tothe standardprocedure as
explained in section 2.3. Skimmilk, reconstituted from skimmilk
powderA (section2.1),wascooleddownto0-2 °Candsubsequently
acidified tothedesiredpH intherange of4.4 to 5.8.Therate
of acidification was made slow enough to assure astablepH.At
t=0 rennet was added to the cold, acidified skimmilk to afinal
concentration of250ppm. Immediately themeasuringapparatuswas
filled as quickly aspossible andheated to the desired gelation
temperature at a rate of 0.5 °C per min.Thedelay timebetween
the moment of rennetaddition andthemoment oftemperature rise
above4°Cvaried from4to16minutes.
In preliminary experiments arough testwasperformed tofind
the pH and temperature at which stable, intact gels could be
formedusing theprocedure described above. Incontrastwithacid
skimmilk gels made without rennet addition (section 4.5.4)the
133
combined use of acidification and rennet allowed gel formation
over theentire range ofpH tested, from4.4 to 5.8.AtpH>5.0a
minimum temperature of approximately 8°Cwas necessary,whileat
temperatures above 20°C a severe breakdown of the gel network
(especially around pH=5.2) was noticed, starting within a few
hoursaftergelformation.AtpH=5.2andatatemperatureof30°C
the gel network firstcollapsed and after30hourshadcompletely
disappeared. Syneresis,i.e. mainlymicrosyneresis, andproteolytic breakdown of caseinweremostprobably responsible forthese
effects. At apHof around 6.7 Zoon (1984)found thatrelatively
stable gels could alsobemade athigher temperatures (T<40°C).
AtpHvalues from4.4to5.0gelswereformedattemperaturesfrom
0to30°C.
5.3.1 The_effect_of_rennet_at_gH=4^6
The results of the measurements of G' of skimmilk gels at
pH=4.6 and inthepresence of 250ppm rennet as a funtionofthe
ageing time t(s)are shown in figure5.2 forsixdifferentageing
temperatures (2,5,10,15,20and25 °C). Forcomparisonwealsoshow
(dashed line) the ageing curve of an acid skimmilk gel made at
30°Cwithoutrennet.Thishadthelargestmoduliforthiskindof
gels (see also figure 3.1a). Two gels aged at30°C (notshown)
initiallyshowedanageingcurveverysimilartothecurveobtain4
edat25°C,butcollapsed afterapproximately 10 s.
Theapparentdiscrepancybetweentheearlyportionsofthecurves at25°Cand20°Cwas duetoashorterdelaytimeof3x10 s
between rennet addition and the startofthe heating forthegel
agedat20°C.RennetactionatpH=4.6hasamarkedeffectonformationandageingofacidskimmilkgelsascanbeseenfromacomparison of figure 5.2 with figure 3.1a. Two pronounced features
canbe noticed due to thepresenceofrennet:firstly,gelformation can takeplacebelow 10°C (evenat2°C)and secondly,the
gels formed at higher temperatures (15 to 25°C) have a much
larger value of G'.Moreover, the linear relationship betweenG'
and logtwasnot found apart from alimited range of lowtemperatures. In the presence of rennet the shape of the (G1 versus
ageingtime)curvechangeswithtemperature.Belowwewilldiscuss
the shape ofthe curve inmoredetailinrelationtothecleavage
134
G (Nm"z)
600
<h2Sl^a
20°C
400-
200
10J
Fig. 5.2
t (S)
The storage modulus G' as a function of ageing time t for acid skim-
milk gels (pH=4.6) made with 250 ppm rennet and aged a t d i f f e r e n t
temperatures.
Ageing temperature varied as i n d i c a t e d . Rennet was added at t=0 s. The dashed
curve refers to an acid skimmilk gel made without rennet and aged a t 30 °C
(derived from f i g . 3 . 1 a ) . UF=1.0 rad.S
. Measurements were made a t the ageing
temperature.
of GMP and the hydrolysis of ß-casein and a , - c a s e i n .
Below 15 °c gel formation showed a kind of lag phase (figure
5.2). I t began only when a c r i t i c a l minimum proportion of GMP had
been freed as can be seen from a comparison of f i g . 5.2 with 5 . 3 .
In figure 5.3 the percentage of GMP released i s depicted as a
function of time a f t e r rennet addition (see section 2 . 7 ) . Experimental conditions were the same as for figure 5.2. At 25 °C the
heating was retarded in the early s t a g e s . This produced the i n i t i a l slow increase of GMP released. At 5 °C gel formation had a l 3
ready s t a r t e d a f t e r 5x10 s, when 60% of the K-casein was cleaved.
From a comparison of figure 5.2 with 5.3 i t also follows t h a t a t
low temperatures the G' versus log t curves became l i n e a r , when a t
l e a s t 90% of the GMP was released. For the 5 °C curve e.g. t h i s
135
%GMP released
Fig.5.3
The percentage of
GMP, splitoff from K-casein,
as a function of time for
acid skiramilk gels (pH=4.6)
aged at three different temperatures. At t=0 250 ppm
rennet wasadded totheacidified skimmilksolutions.
1.5
2.0
tdO 4s)
occured at a time of about 1.2 to1.5x10 s,when 90to 95%had
beenhydrolysed.
ApparentlyGMPstillhasaconsiderableeffectonthestability
of caseinparticles atpH=4.6.Thismustbeduetoitssmall,but
significant negative charge atthispH and to itsoverallhydrophilic character which probably at pH=4.6 also gives rise to a
smallbutsignificantstericrepulsion.
The slope of the linear increase ofG'withlogtincreasedas
the ageing temperature was increased from 2 to 10°C. This increase of slopecannotbe related directlytothelossofstability caused byGMP cleavage,because the change in slope occurred
afterallGMPhadbeensplitoff.Apparentlytherateofageingof
gels formed from the para casein particles increased much more
strongly with temperature than in case of acid skimmilk gels
formed from ordinary casein particles without rennet action (see
fig.3.1).A highly speculative explanation canbegivenforthis
phenomenon. After the GMP is released, the activation Helmholtz
energyforaggregationofcaseinparticlesispossiblylargelydue
to the stabilizing effectof ß-casein chains protruding fromthe
surfaceoftheparticles.Thesechains,causingacertain,butinsufficient steric repulsion, aremoved to theinteriorofthecasein particles, when temperature israised and so the activation
Helmholtzenergy foraggregationislowered.
Above and at 15°C the situation was somewhat different. GMP
splitting was no longer a prerequisite for gel formation, aswe
136
havealready foundthatacidskimmilkstartstogelassoonasthe
temperature is raised above 10°C. At that moment (after about
3
1.3x10 s)only asmallproportion ofGMP,approximately25%,has
been split off (fig. 5.3).During heating the casein particles
willbecomeincreasinglymoreunstablebecauseofboththeacidity
ofthesolutionandthecontinuingrennetaction;whenG'wasmeasuredat15and25°Cforthefirsttimeatleast60to70%ofGMP
3
had been released (after 2.7x10 s).As can be seen in fig. 5.2
rennet action still had a significant effectontheageingcurves
of the gels at 15°Candhigher.The lossofGMP led to alarge
increase in the initial value of the dynamic moduli (compare
figure 5.2 to figure 3.1a) and to amuch steeper increase ofG'
with log t. However except for the gel at15°C for ageingtime
below 3x10 s there was no longer a linear increase of G' with
logt. The lines were curved, especially at 25°C. Permeability
measurements (see below) on these gels gavepermeabilitycoefficients which did not increasewithmeasuring time,indicating an
absence of microsyneresis. This contrasts with the behaviour of
rennet gels, as found by VanDijk (1982). These were subjectto
microsyneresis andBincreasedwithtime.
AmoreobviouscauseforthecurvatureinG'versuslogtplots
couldbeproteolyticcleavageofa-,-andß-casein.Infigure5.4a
and b theresidual proteinconcentration ofa.- and ß-casein is
depicted as a function of time after rennet addition for three
different temperatures (5, 15 and 25 °C). The proteolysis (see
section 2.6) was followed forup to 5x10 s,whereas allrheological measurements (fig. 5.2 and 5.5) were carried out within
2x10 s. Therefore only the hydrolysis of the caseins within
2x10 s can be important for the curvature of the lines infig.
5.2. Inthisperiod of time amoderate,butsignificantproteolysisofa,-andß-caseinhadoccurred.Thedegradationofß-casein
showedlittletemperaturedependence (fig.5.4a):therewashardly
difference between measured levels at 5°Cand 15°Cand thehydrolysiswasonlyalittlehigherat25°C.Astrongertemperature
dependencewasfoundfor a ,-casein (fig.5.4b):at5°Cless a,than ß-casein washydrolysed, while at25°Crelativelymore a,casein was degraded. After 2xl05 s (55 hrs) at25°C 50%ofthe
initial a-.-casein concentration and 60%of the intial ß-casein
137
concentration remained. The base l i n e for the residual casein conc e n t r a t i o n in figure 5.4a and b was approximately 8% for ß-casein
and 18% for a , - c a s e i n . A r e l a t i v e increase in the breakdown of
a -casein in r e l a t i o n to the breakdown of ß-casein, as temperat u r e was raised, was also found by Fox (1969) for sodium caseinate
a t pH=4.6. The p a t t e r n of degradation products also changed with
temperature (not shown). At 5 °C more ß-I casein was l e f t uncleaved, whereas a t 15 and 25 °C l e s s ß-I casein and more ß-II casein
and ß - I I I casein were found. The same effect was found by Creamer
e t a l . (1971) in a solution of pure ß-casein a t pH=6.5. ß - I I I casein was d i f f i c u l t to detect in the e l e c t r o p h o r e t i c p a t t e r n .
residual fraction p-casein
1.0-
Fig. 5.4 The r e s i d u a l concentrat i o n of ß-casein (a) and a . - c a sein (b) in acid skiiranilk gels
(pH=4.6) made with rennet as a
function of time for three different ageing temperatures. Ageing temperatures are i n d i c a t e d .
250 ppm rennet was added a t t=0 s .
t ( 10ss )
(a)
residual fraction a s l -casein
t (10 5 s)
(b)
138
From the degradation products ofa,-caseinonly« s l _ I casein
was clearly visible.Above the<xsi-I caseinband twominorbands
couldbe detected, one ofwhichmightbeascribedtoc s l _ vcasein
(Mulvihill et al., 1977). At25°Casl-I caseinwasmore rapidly
hydrolysedthanatlowertemperatures.
Inviewofthesignificantcaseindegradationduringtheageing
ofthe gels one could conclude thatthebending of theG'versus
logtcurves after longer ageing times atT>15°Cmightbedueat
leastpartlytocaseinhydrolysis.Thefactthatthelineat25°C
was curved from thebeginning,when degradationwasatmostafew
percent, showsthatother effectsmust alsobeinvolved.Maybeat
this temperature thebending ofthe curveatshorterageingtimes
was caused by changes intheproperties ofthe aggregated casein
particlesduetotheon-goingreleaseofGMP,whileatlongerageing times itwas causedbyproteinbreakdown.Apossiblepositive
role of the very hydrophobic para K-casein (Walstra andJenness,
1984), left after release ofGMP,must alsobe considered.Moreover, at pH=4.6 para K-casein will be positively charged, since
itsisoelectricpHisaroundpH=9-9.5 (Vreemanpersonalcommunication).
As the bending of the G' versus log t curves increased with
temperature inparallel with thebreakdown of a ,-casein (compare
fig.5.2 tofig.5.4b),itsuggeststhata,-caseinisamaincomponent of the casein gel network. Inthis respectnoconclusion,
positive ornegative,canbe drawn aboutapossibleroleofß-casein,because ß-caseinbreakdown showed averyslighttemperature
dependence (fig.5.4a).
The rheological properties of the acid skimmilk gels made in
the present of rennet were further characterised by calculating
tanô as a function of ageing time,andbymeasuring thedynamic
moduliG'andG"andcalculatingtan6bothasafunctionofangularfrequency mandofmeasuringtemperatureT.
A rapid decrease of tanô in the early stages of ageing was
3 in
found.Thispassed intoaslowdecreaseafter5x10 sresulting
tanô values varying from 0.24 to 0.28 after 10 s (see table
5.1). Similar behaviour was found for acid skimmilk gels made
withoutrennet (seefig.3.2,section3.2).
139
Table5.1 Tanôofacidskimmilkgels(pH=4.6)madeinthepresenceof250ppmrennetasafunctionofageingtemperatureafteranageingtimeof10 s.UJ=1.0rad.s
T(°C)
tanô
2
0.24
5
0.26
10
0.24
15
0.27
20
0.27
25
0.28
The dynamic moduli G' and G" showed avirtually linear increase
with the angular frequency u>on a double logarithmic scale with
the same slope (around 0.15) as was found for acid casein gels
made without rennet. For tan ô as a function of w straight horizontal lines were found at 30 °C while at lower temperatures a
slight increase at small u>was observed.
Once agel was formed the dynamic moduli G' and G" strongly decreased, when the measuring temperature was increased (see fig.
5.5, where G' is depicted as a function of measuring temperature
for gels aged at least 25 hours atdifferent ageing temperatures).
This behaviour was similar to that found for normal acid casein
gels (see fig.4.7, section 4.5.3). Although G'was measured after
different ageing times, the picture remains clear. The smaller
decrease with measuring temperature found at 25 and 30 °C for the
5 °Ccurve was thought tobe due to an accelerated gelation during
the measurement. This started above 20 °C and is thought to arise
from a faster rearrangement of protein molecules in the casein
particles forming the strands and aggregates of the gel network.
Probably these protein rearrangements take place at the outer
region of the casein particles. These rearrangements which cause
an increase of the dynamic moduli athigher measuring temperatures
obviously only occur for gels aged at low ageing temperature (see
also section 4.5.3).
140
G'lNnr 2 )
1000-
600-
200"i
r-
10
20
30
Tm CC)
Fig.5.5 The storage modulus G' as a function of measuring temperature, T,
for acid skimmilk gels (pH=4.6)made with250ppm rennet and aged atdifferent
temperatures. Ageing temperaturewasvaried asindicated.Theageing timeswere
°C, 1.7xl05 s; 15°C, 1.05xl05 s; 20°C,
respectively: 5°C, 1.9x10 s; 10
5
4
-1
1.2x10 s;25°C,9x10 s.Angular frequencyw=1.0rad.s .
To explain the difference inthe absolute values ofG' andG"
and intheG1 versus logtcurvesbetweenacidskimmilkgelsmade
with and without rennet, information concerningpossible changes
inthespatialdistributionofthebasicelements (i.e.thecasein
particles) upon rennet action atpH=4.6 isvery relevant.Therefore at 25°C thepermeability coefficient of acid skimmilk gels
with and without rennet was measured simultaneously. The permeability increased by a factor of two in the presence of rennet
(seetable 5.2).This suggests that amuchmoreinhomogeneousgel
networkwasformed.Thevalueofthedynamicmodulialsoincreased
significantly. This is again aremarkable result,which canonly
be explained by an increase in the number of bonds between the
caseinparticles;since ingeneral amoreinhomogeneousdistributionof thebasic elements of agelnetworkresultsinlowernetwork moduli (see section 3.4).This feature, that acoarsergel
network is formed inthe case ofprobably ahigher number ofinterparticle bonds,was noticed before for acid casein gels (see
e.g. section 4.5.3, and section 3.4 andfigure3.15).Partofthe
141
Table5.2 The permeability coefficient B of acid skimmilk gels (pH=4.6)made
with (+)and without (-) rennet (250ppm) at 25 and 10°C. The gels, made at
25°C with and without rennet, were measured simultaneously at 25°C. The
ageing time was respectively 19 hours (25°C)and20hours (10°C).Thevalues
of column 1are the average values of severalexperiments,thenumber ofwhich
is given in column 4. In each experiment at least 8 tubes (see section 2.9)
were used. The variation between the average values in each experiment isindicated.
T(°C)
B(10
-132
m)
rennet
numberof experiments
25
1.3710.05
-
3
25
2.7610.03
+
3
10
1.7810.04
+
2
increase of permeability may however be due to a decrease of
voluminosity of the caseinparticles as aresultofGMPcleavage.
It ispossible for inhomogeneity to increase atthe level ofthe
gel network, while at the level of the particle strandshomogeneity may increase due to a more extensive fusionofthecasein
particles, when GMP is released. Electronmicrographs (fig. 5.6)
support this suggestion. In figure 5.6 micrographs (see section
2.11) of three different casein gels are depicted: anacidskimmilk gel without (fig. 5.6a) and with rennet (fig. 5.6b), anda
rennet gel (fig. 5.6c). The samples forelectronmicroscopy were
all prepared inthe sameway (seesection 2.11). AtpH=6.7thick
strands consisting of completely fused para-casein micelles are
found, while at pH=4.6 without rennet individual particles are
still recognizable and areonlypartly fused.The strands ofthe
acid casein gels are alsomuch thinner.Inthesamplewithrennet
present at pH=4.6 (compare fig. 5.6a and b) particle fusionincreases, the strands seem to be more compact andmoreover fewer
freeparticles,notcontributingtoastrand,seemtobepresent.
Thepermeabilityofanacidskimmilkgelprepared at10°Cwith
rennetwasalsomeasuredat10°C.Thispermeabilitywassignifie-
142
«
(b)
(a)
Fig. 5.6. Electron micrographs of
three d i f f e r e n t skimmilk g e l s . The
E.M. samples were prepared as described in section 2 . 1 1 . The magnif i c a t i o n i s given in the graphs,
a: acid skimmilk g e l , pH=4.6, made
without rennet, aged a t 30 °C for
4
7.2x10 s (20 h r s ) ; b: acid skimmilk g e l , pH=4.6, made with 250
4
ppm rennet and aged for 5.5x10 s
(16 hrs) at 25 °C; c: rennet gel
0.5um
made
from skimmilk
(pH=6.7) by
rennet action at 30 °C. Ageing time
i s 2.2x10 s (ca 6 h r s ) .
(c)
antly lower than t h a t of a similarly prepared sample a t 25 °C (see
t a b l e 5.2), but s t i l l higher than the permeability of acid skimmilk gels made without rennet at 25 °C. A decrease in B with decreasing ageing temperature was also found for acid casein gels
made without rennet addition (see section 3 . 4 . 2 . 3 ) .
143
5.3.2 The_effect_of_rennet_at_varYing_gH
The rheological properties of acid skimmilk gels prepared in
thepresence of rennetwere studied atdifferentpHvaluesinthe
range of 4.4 to 5.8. To ensure that the chosen pH was constant
during the measurement, sufficient timewas taken foracidification. Particularly around pH=5.2 acidification was a time consuming process, because of the retarded dissolution ofcolloidal
calcium phosphate and the formation of all kinds of soluble Calcium phosphate complexes.A final check ofthepH at20°Cafter
thegelshadbeenagedforatleasttwodaysshowedamaximumrise
inpH of less than 0.1 unit. Inall cases ageing temperaturewas
keptconstantat20°C.Totracegelformation,thedynamicmoduli
were measured as a function of ageing time and pH. For further
rheological characterization, measuring temperature andmeasuring
frequency were varied. The effect of proteolytic activity was
testedbyfollowingthedegradationofa,-andß-casein.
In table 5.3 a summary is given of the measurements made on
these gels. For sake ofclarity onlyaselectionoftheavailable
experimentaldatawillbedepicted inthefigures5.7to5.13.
5.3.2.1 Gel formation
at different
pH values
ThedevelopmentofG'asafunctionofageingtimeatdifferent
pH's is shown in fig.5.7.As canbe seen thepH ofthesolution
had a large effect. Both the shape of the ageing curves andthe
magnitudeofG'stronglydependedonpH.BelowpH=5.0theshapeof
theageingcurvesresembledthatfoundforpH=4.6at20°C(figure
5.2). AbovepH=5.0 not only thevalueofG'butalsotheshapeof
theageingcurvesmarkedlyaltered.Insteadofamoreorlessparallel shift to lower values of G',the curves had amore convex
shape. At pH=5.2 and 5.4 a maximum was found after 10 s,after
whichG'decreasedslightly.
Forclarity,G'afteranageingtimeofrespectively 10 s(ca.
3hrs)and 10 s (ca.28hrs)isdepicted as a function ofpHin
figure5.8 (seealsotable5.3).Amaximum inG1 wasfoundbetween
pH=4.7and4.8 incontrasttoacidskimmilkgelsmadewithoutrennet,wheretheoptimumwasfoundaroundpH=4.5 (fig.4.13,section
144
Table 5.3 A summary of the rheological p r o p e r t i e s of a l l gels made by the combined action of a c i d i f i c a t i o n and rennet p r o t e o l y s i s in the pH range from 4.4
to 5.8. The rennet concentration was 250 ppm. Ageing temperature was 20 °C and
angular frequency u) was 1.0 r a d . s
gelno.
pH
G'(Nm~2)
after 10 s
tan6
G'OJm"2)
tanô
after 10 s
after 10 5s
after 10 s
1
4.40
240
0.26
433
0.24
2a
4.59
290
0.27
512
0.24
2b1
4.60
310
0.30
538
0.27
3
4.70
362
0.27
613
0.24
4
4.83
316
0.29
572
0.26
5
4.92
248
0.32
490
0.25
6
5.01
150
0.37
330
0.28
7a
5.10
102
0.43
222
0.30
7b
5.16
70
0.49
98
0.34
8a
5.20
63
0.47
61
0.39
8b
5.20
73
0.42
38
0.42
8c2
5.20
-
-
50
0.41
8d
5.20
63
-
82
0.39
9
10
5.40
0.38
0.31
60
140
0.36
5.60
82
124
11
5.83
136
0.28
188
0.27
1: data taken from section 5.3.1
2: t h i s g e l , a f t e r ageing a t 20 °C for 6.5x10
0.29
4
s (18 h r s ) , was only used for
measurement of tan Ô and G' as a function of w. The given values of G' and
tan ô were measured a f t e r 6.5x10
s.
4 . 5 . 4 ) . Moreover, without rennet the pH dependence around the optimum was much l e s s pronounced. Obviously t h i s small s h i f t of optimum pH was due to the cleavage of the s l i g h t l y negatively charged GMP, which r e s u l t s in a small s h i f t of the i s o e l e c t r i c pH of
the para-casein p a r t i c l e s remaining. I t i s probable t h a t the
maximum size of the dynamic moduli s t i l l coincides with charge
145
G'(Nm2)
pH47
600-
"a%
400
200-
1
10d
1
1
1 I I I II
IO*1
-i—i
i i i i|
1
r
103
t(s)
Fig.5.7 The storage modulus G' as a function of ageing time t (s) forskimmilk gels made by the combined actionofacidification and 250ppm rennet.The
gelswereaged at20°C.pHwasvaried asindicated.w=1.0rad.s
neutrality inthe aggregating particles aswasfoundforacidcasein gels prepared without rennet (see section4.5.4). Comparing
thepH dependence ofG'of acidskimmilkgelsmadewithoutrennet
at 30°C (fig.4.13, section4.5.4)with that of gels made with
rennet at20°C (fig.5.8) and rememberingthatatanageingtemperature of20°Cmuchweaker gelswere formedthanat30°C(see
e.g. fig.4.7, 5.2 or 5.5),itisclearthatoverthewholerange
of pH=4.4 to 5.0 rennet action caused much stronger gels to be
formed.Thesameconclusionhasalreadybeenreached forgelsmade
with rennet atdifferent ageing temperatures atpH=4.6insection
5.3.1.
At thebeginning of the ageingprocessthecurvesofG'became
measurable at the same time and had approximately the samevalue
forG 1 ,independentofpH.Howevertanô (=G"/G')dependedstrongly on the pH (fig. 5.9 and table 5.3) indicating apH-dependent
146
G(Nm 2 )
600-
M)0-
200
6.0
pH
Fig.5.8 The storagemodulusG'afterageing timesof respectively 10 s (
and 10 s (
)
)asa functionofpH forskimmilk gelsmadeby combinedacidifi-
cation and rennet (250 ppm) action. Ageing temperature was 20°C and UFI.O
, -1
rad.s
relaxation behaviour of the bonds in the gel network (w=1.0
rad.s"1).
Thedatapresented in fig.5.8 and5.9 showthataroundpH=5.2
aminimum inG' and amaximum intanÔwas found.BetweenpH=4.9
and 5.2 G' decreased dramatically with increasingpH,whiletanô
showed a drastic increase. After a longer ageing time this increase was shifted to between pH=5.1 and 5.2. Hence the ageing
curves forG' and tanô atpH=5.10 (sample7a,seetable5.3)had
a shapemuchmore like that forpH=5.0,whilethecurves foundat
pH=5.16 (sample7b)resembledthosefoundatpH=5.2.Significantly
the increase inG'and the decreaseintan6,foundwithincreasingpHatpHabove5.2,occurredmuchmoregradually.
As canbe seen from fig.5.9notonlythevalueoftanôafter
aspecifiedageingtimebutalsotheshapeoftheageingcurvesof
tanô versus log t varied strongly with pH. All curves have to
begin attanô above 1.0 because ineverycasethestartingpoint
was a skimmilk solution at t=0 s. The latter behaves as anewtonian liquid (VanVliet andWalstra, 1980). Attheboundariesof
thepH range studied (pH=4.4 and 5.8)tanôalreadyhasdecreased
147
tan5
0.50
0.40-
0.30
Q20-
103
- 1 —
i,
10*
10'
t(s)
Fig.5.9 The losstangenttan6 (=G"/G')asafunctionofageing timet(s)for
skimmilk gels under the same conditions as infig.5.7.pHwasvaried asindicated.
to substantially lowvalues (<0.30)atthemomenttherheological
3
measurementswerebegun (tthenhadavalueofaround3x10 s).In
the course ofageing only aslight further decrease intanôwas
seen.WhenpHwaslowered from5.8to5.4thehorizontalcharacter
remained,butthe curveswere shifted tohighervalues.AtpH=5.2
ahorizontal curve intheearly stages (until1.5x10 s)wasfollowed by a significant decrease.AtpH=5.1 thehorizontal domain
was shorter and the subsequent decrease steeper. InthepHrange
from 4.6 to 5.1 atransition inthe rheological character ofthe
gels as expressed in tanô occurred over the time span of the
measurements.Tan6stronglydecreasedovertheentiretimerange,
e.g. at pH=5.0 from approx. 0.50 after 3xl03 s to 0.28 after
10 s.TheaboveobservationimpliesthatinthepHrangefrom4.6
to 5.1 the elastic character of the gels increased significantly
withtime,whereasbelowpH=4.6andabovepH=5.4thechange froma
150
net andmeasured at20°C (see fig.4.9,4.11 and4.12).Aslight
increase,whichwas hardly ifat allsignificant,wasobservedin
the final frequency decade (1.0 to 10 rad.s" ).AthigherpHthe
curves shifted to higher values for tanô and the decrease of
tanôwith increasingtuatlower frequenciesbecamemorepronounced with a maximum effect at pH=5.2. At this pH the viscous
character of thegel strongly increased atlow rates ofdeformation. Further pH rise caused again adecreaseinthemagnitudeof
tanôbut the shape ofthe curvesremainedthesame.Thecurveof
pH=5.8 resembled very closely the tanôversusu>curve, foundby
Zoon (1984) for skimmilk gels, made from skimmilk of natural
pH(=6.7)by rennet action at 25°C. Itwillbe shownbelowthat
the small difference inthe shape oftanôversuswcurvebetween
pH=4.9and5.8 forwbelow10~ rad.s" isofsignificance forthe
differencebetween acid casein gels and rennetedcaseingels.The
transitionagaintookplaceatapHofaround 5.2.Theincreaseof
tanô withdecreasingtubegan for allpH's atw=10~ rad.s" .As
already suggested in section 4.5.3 for acid casein gels, it is
possible that this involves some form of interactions leadingto
interparticle bonds with relaxation times in theorder of 10 s.
It is also possible that these interactions aremore or lesspH
independent.
5.3.2.3 Effect
of variation
of measuring
temperature
As indicated previously (section4.5.3)themeasuringtemperaturemaybe avery valuable parameter forcharacterizing acidcasein gels, once formed and after acertainageingtime.Thevalue
of the dynamic moduli of such formed acid casein gels (pH=4.6)
tendedtodecreasestronglyastemperaturewasraised (seesection
4.5.3). There isoneprerequisite:the gelsmusthaveaconsiderable age,so thatG'only increasesslowlyduringthemeasurement
becauseoffurtherageing.
Inallexperimentstemperaturewasvariedinthefollowingman5
ner: after ageing at20°c for•approximately 10 sthe gelswere
cooled down first in steps of 5°C to a lowest temperature of
5 °C. The rate of cooling and heating was always 0.5 °Cperminute. After each temperature change a waiting time of20-30min
was allowed, before G'and tanôwere measured. Subsequently the
3
151
Table 5.4 G'andtanôofanumber ofgels with varying pH,beforeandafter
the measuring temperature experiment.T=20°Candw=1.0rad.s .Theageatthe
beginning ofthetemperature experiment isgivenins.
gelno.
PH
age
5
10 s
G'(Nm"2)
G'(Nm"2)
tanô
tanô
before
after
before
after
1
4.40
1.85
456
386
0.24
0.28
4
4.83
1.85
550
391
0.25
0.32
6
5.01
0.85
319
262
0.28
0.31
7a
5.10
0.77
170
0.30
0.30
40
0.36
0.39
8
0.40
0.42
7b
5.16
0.85
209
94
8a
5.20
0.80
61
9
5.40
0.80
68
2
0.36
0.36
10
5.60
0.85
137
11
0.30
0.29
11
5.83
0.85
189
18
0.26
0.27
system washeated in steps of 5°C firstto 20°Cand thenultimately to40 °C.Atthe end thegelswerecooleddownto20°Cin
a single step and the residual valueofthemoduliwasdetermined
(seetable5.4).
Infig.5.11a and5.11bG'isdepictedasafunctionofmeasuringtemperature firstonalinearandthenonalogarithmicscale.
AtlowpH,i.e.4.4-4.8,thesametemperaturedependencewasfound
asforacidcaseingelsmadewithoutrennet (comparetheseresults
and fig. 5.5 with fig.4.7 and4.8):a fairly linear decrease of
G'withmeasuringtemperatureT wasnotedespeciallyabove20°C.
No explanation can be given for the relative increase atpH=4.4
between35°Cand40°C.Itisprobablynotduetoincreasedgelation,becauseG'waslowerafterthetemperatureexperiment(table
5.4). Above pH=4.8 the temperature behaviour changeddrastically.
A maximum value of the dynamic modulus was seen between 15 and
20°C and G'tended to decrease as temperature was lowered below
15°C. Inthe range ofpH=4.9 to 5.1 G1 decreased above 20°Cas
expected for acid casein gels. Although the moduli of the gels
lost a considerable part (about 20%)of their value afterbeing
heated from20°Cto40°C (table5.4),theywerestillcharacter-
154
creased hydrolysis with temperature may be expected to occur at
eachpH,probablywithasmalloptimumaroundpH=5.2-5.4(seenext
section), but certainly notwith such astrong transition asobserved inthis experiment.Thus itmaybeexpectedthatincreased
hydrolysiscouldonlyexplainasmallpartinthesharpdropG'.
The lack of microsyneresis is one of the characteristics of
acid casein gels at pH=4.6 (see chapter3 and 4 ) .On the other
hand from cheese making practice it is known that syneresis is
stimulated by heating and acidification. VanVliet and VanDijk
(tobepublished)pointed outthat forrennetgels(pH=6.7)there
is possibly a relation between the value of tan6 and the susceptibilitytomicrosyneresis.Gelswithahighertan6valueover
-2
1
-1
the frequency rangeof 10 to 10 rad.s tended to show anincreaseinrateofmicrosyneresis.Microsyneresis leadstoacoarsening ofthe gel network (VanDijk, 1982).Forthegelsformedat
pHvalues>5.1thiswasultimatelyvisiblemacroscopically,asthe
colloidal white appearance of the gels had changed into agrey
appearanceafterthetemperatureexperiment.
The behaviour of tanô as a function ofmeasuring temperature
at five differentpH's (w=1.0rad.s"1)isshowninfig.5.12.The
values of tanô and G' before and after the temperatureexperiments are given in table 5.4. The results at 20°C before and
after cooling to 5°Cwere equalwithin experimental error.This
also applied to the tanô values after the heating cycle. The
seemingly largedeviations atpH=4.4 and4.8 arestillwithinexperimentalerrorlimits.
Fig. 5.12 shows that at 5°C there was little variation in
tanô (from0.25 to0.30 forallpH's), aspHwasvaried,whileat
40°C a dramatic effect of pH was registered.At lowpH (4.4to
4.9)horizontalcurves (0.20<tanô<0.30)were foundfortanôasa
function of measuring temperature. At higher pH tan6 gradually
increased with temperature with a maximal increase at pH=5.2.
After a further increase in the pH to 5.8 the increase intanô
became smaller again especially at T below 30°C. Above 30°C
therewasstillarelativelystrongincrease.Thiseffectwasalso
found by Zoon (1984) for rennet gels. From table 5.4 and fig.
5.11b one canconclude that the relatively strong decrease inG'
with temperature and the concurrent increased lackofreversibil-
155
0.20-
Fig.5.12 The losstangent tanôasafunctionofmeasuring temperatureT for
-1
thegelsof fig.5.11h. pHvalues are indicated.u)=1.0rad.s
ity inthevalue ofG'afterthetemperatureexperiment,beganat
apHofaround5.16.AtpH=5.16avalueof0.75 fortan6at40°C
wasfound.Comparing fig.5.11b andfig.5.12withtable5.4shows
thatahighvalueoftanôathightemperaturecorrelateswiththe
above-mentioned decrease of G1 and the increased lackofreversibility inG'. Ingeneral the decrease ofG'occurred when tanô
was greater than 0.45-0.50, whereas microsyneresis should result
inacoarseningofthegelnetwork.Thereforeprobablythefallin
G' during the temperature experiment was accompanied more by a
decrease in thenumber of interactions i.e. thenumber ofinterparticlebonds,whichwould correspond to acoarseningofthegel
network,thantoachangeinthenatureoftheinteractions.
The resemblance of the curves for pH=5.1 and 5.6 (fig. 5.12)
showed that the correlation between enhanced microsyneresis and
value oftanô atui=1.0rad.s" asafunctionofmeasuringtempe-
156
tan 6
Fig. 5.13 The loss tangent tanÔ as a
function of frequency U)(rad.s ) for
s
^
renneted skimmilkgels (pH=6.7)atthree
M)°C
OA-
30°C
different measuring temperatures (after
25°C
102
li-1
Zoon, 1984). Theobserved effect isin10"
li1
dependentofageing temperature.
u)(rad.s"')
rature was not complete.Although they had a similar tanôcurve
theylargelydifferedintheobserveddecreaseofG'.Inthefirst
instanceitisquestionablewhetheritispermissibletocorrelate
microsyneresisonlywiththetanôvalueatw=1.0rad.s ,because
onemay also expect syneresis processes tooccuroverlongertime
scales. Rennet gels (pH=6.7) for example had approximately the
samevalue fortanô attu=1.0rad.s" inthetemperaturerangeof
20 to 30°C,while atloweru>thevaluesoftanôdifferedsignificantly (see fig. 5.13, after Zoon, 1984).Themicrosyneresisof
rennet gels is enhanced considerably when their temperature is
raised from 20to 30°C.Moreover atpH=5.6thecolloidalcalcium
phosphatewillbeonlypartiallydissolved.Thereforethecompositionof the caseinparticles andprobablythetypeofinteraction
forcesbetweenthemwilldifferbetweenpH=5.1and5.6.
In general it is clear from the results ofthis sectionthat
enhancedmicrosyneresisuponheatingdependsonthetanôvalueof
thepreformedgelatelevatedtemperaturesandperhapsalsoonthe
pH-determined composition of the basic elements (casein particles). The small decrease inG' foundatpH<5.1aftertheheating
cyclewaspossiblynotduetomicrosyneresis.Thiswillbediscussedfurtherinthenextsection.
Afinalremarknotdirectlyrelatedtothediscussionabove,is
thatnoneofthegelsdemonstrated atemperaturebehaviourcharacteristicofanidealrubbergel.Acidcaseingelsthereforedonot
behave as ideal elastic gels andboth energetic and entropieeffectscontributetotheHelmholtzenergy (seeeq.3.1).
157
5.3.2.4 Proteolytic
degradation
Theamountofresidualß-anda,-caseinwasdeterminedaccordr
si
ingtosection2.6.Thegelsampleswerepreparedbytheprocedure
used inthe rheological experiments.ThepHofthesamplesvaried
from4.5 to 5.9.AteachpHthedegradationwasfollowedasfunctionoftimeover5x10 s(~140 hrs).
In fig. 5.14a and b, respectively, the residual amountofßanda..-caseinisdepicted asafunctionofpH.pHwasmeasuredat
20°C.Thebaseline forthe residual caseinconcentrationinfig.
5.14a and b was approximately about 8% forß-caseinand 18%for
a„T-casein.
si
Both a .,-and ß-casein were hydrolysed to a considerable extent.Itisprobablethattheinitialdegradationproducts
(fflsl-I'
ß-I, ß-II casein, etc.) still contributed considerably to the
structure ofthe gel network,but itisalsopossiblethatcasein
moleculesnotinvolved innetworkbondsweremorereadilyattacked
byrennetandsoweredegradedmorerapidly.Both a ,- andß-ca% residual a s l- casein
100
% residual ß-casein
100
3.6.tes
• N > ~
yB
8.6 NTS
fi
1.8.10 3 s
*«-,
50
50y»
1,3. WS
•N*-._
4.5
5.0
5.5
6.0
4.5
5.0
5.5
pH
(b)
Fig.5.14 The percentage of residual ß-casein (a)and a -casein (b)concentration in skimmilk gels made by the combined action of acidification and 250
ppm rennet reaction as a function ofpHat fourdifferent ageing times.Rennet
was added att=0.Ageing timesare indicated.
6.0
pH
158
seinshowedaboutthesamepH-dependenceofproteinbreakdown,although a,-casein was hydrolysed somewhat faster (fig. 5.14). A
maximum degree ofproteolysis occurred aroundpH=5.2-5.4for Ö S 1 caseinandaroundpH=5.4-5.6 forß-casein,whichwassomewhatdifferent from the results ofFox (1969)who used sodiumcaseinate,
Fox andMulvihill (1977 and 1979a)whousedapure«--caseinsolution or DeJong (1977) who used sodium paracaseinate. All of
these workers reported a maximum degree of proteolysis around
pH=5.8.
Forcomparison with themeasurements shown infig.5.7onehas
to restrict oneself to theproteolysis occurringduringthefirst
2x10 s. As argued already insection 5.3.1 the deviation froma
linear increase ofG'with log t found atpH=4.6upon rennetactionwasprobably partly due to caseinhydrolysis.Thesameargumentsmaybe applied to thebending of the other G'versus logt
curvesatapH£5.1.Howeverthebendingofthegelationcurvesat
pH values greater than 5.1, which was already underway within
3
4x10 s,cannotbe due to increased hydrolysisalone.Norcanhy4
drolysisexplain the largeeffectofpHonG',e.g.after10 and
10 s (fig. 5.8), ashydrolysis varies relativelylittlewithpH.
4
Besides for all samples the protein hydrolysis after 10 swas
still very small. It is more probable that the significant increase of asl-casein hydrolysis, when pH was raised from 5.0 to
5.2 had the same root cause as the large decrease in G' around
these pH's: i.e. achange inthe structure andproperties ofthe
caseinparticles,which form thegelnetwork,andthusanalteration inthe availability ofthe caseinsforproteolyticactivity.
This change would enhance microsyneresis and cause the large
bendingandloweringoftheG'versuslogtcurves.
The electrophoretic pattern varied withpH.AtpH=4.5ß-Icaseinwasonlyvisibleasasmallband,whichmeantthatß-Icasein
in its turn was hydrolysed relatively rapidly. The ß-IIcasein
band was clearly visible, whereas the ß-III casein band could
hardly be detected. Of the a ,-casein degradation products only
a
s l _ I c a s e i- nw a s clearlyvisible.AtthispHonlytracesofoneor
two other degradation products of a.-casein could be seen. At
pH=5.2 to 5.4more ß-I and relativelylessß-IIcaseinwasdetected, even a trace of ß-I11 casein could be seen. Probably the
159
degradationofß-Icaseinwasslowedrelativetotheotherprocesses.Amore intenseasl-Icaseinbandbutagainhardlyanytraces
of other a,-casein degradation products were seen. As pH increasedtopH=5.9thelevelofß-IIcaseinwasreducedtoatrace,
while ß-I casein appeared as an intense band. <*sl_I casein was
again the single detectable degradation product of agl-casein.
Within experimental error, itwasnotpossibletodetectanycorrelationbetweenthepatternofdegradationproductsandtheTheologicalpropertiesofthegelsatanypH.
5.4 Generalremarks
The number and strength ofbondsbetween caseinparticles and
the spatial distribution of the particle strands determine the
value of the dynamic modulus G' (chapter 4). The loss tangent,
tanô,dependsmuchmore on the relativenumberandthecharacter
of the different bonds between the casein particles thanonthe
spatial distribution of the strands. The shape and magnitude of
theG'versuslogtcurvesandthe (ageingandmeasuring)temperaturedependenceofG'aredeterminedbyfivefactors:
1. Themolecularconformationoftheindividualcaseinmolecules
and themolecular structure ofthe caseinparticlesconsistingof
aggregatedcaseinmolecules.
2. The spatial distribution of the stress carrying strandsand
thelargeconglomerates,bothconsistingofcoagulatedcaseinparticles.
3. The ratio oftherates ofprotein-proteinbond formationand
cleavageintheregionbetweenthecoagulatedcaseinparticles.
4. Theratesofhydrolysisofa,-andß-caseinmolecules,which
effectively contribute (directly or indirectly) to the intêrparticlebonds.
5. Theoccurrenceofmicrosyneresis,whichisverymuchtemperature and pH dependent, depending as it does on the structureof
the casein particles and the relaxation behaviour of the interparticlebonds.
From the results of thischapter itcanbeconcluded thatGMP
has a largeeffecton the stability ofcaseinparticles over the
entire pH range from 4.4 to 6.7. The character of the skimmilk
160
gels made by the combined action of acidification and rennet
changedabruptlyaroundpH=5.2.
Below pH=5.2 the gels formed were subject only toproteolytic
hydrolysis and not tomicrosyneresis.At and around theisoelectric pH ofcaseinparticles thevalues ofthe dynamicmoduliincreased considerably (fig. 5.2 and 5.8) as GMP was released and
skimmilk gels could be formed even at low temperatures (<10°C).
However, these gels consisted of amuch coarser gelnetwork than
in case of acid skimmilk gelsmadewithout rennet.Therefore the
number of bonds between the caseinparticles musthave increased
drastically,becausethecharacterofthebondsremainedthesame,
as tan6 didnotchange upon rennet action.Particle fusionwill
be enhanced and more homogeneous gel network strands will be
formed.
Above pH=5.1 the skimmilk gels became subject to both proteolytic hydrolysis and microsyneresis. Microsyneresis may occur
because of a sharp change incaseinparticlestructureandrelaxationbehaviour of the interparticle bonds aroundpH=5.2.Particularlyathighertemperatures (>30°C)therelaxationbehaviourof
the interparticle bonds altered as indicated by higher values of
tan6. It is suggested that this isdue to achange inthecontributionratherthanthenatureofthedifferenttypesofinter-
T( •C)
Fig.5.15 Schematicpicture of syneresis
40-
behaviour of skimmilk gels made by combined action of acidification and rennet
no
1
rapid
syneresis
|
syneresis
asafunctionofpHandtemperature.
30-
• slow
S
'syneresisy'
/ no
-r syneresis
20-
45
5.5
6.5
pH
161
action forces.The occurrence ofmicrosyneresismaybecoupledto
the behaviour oftan6,although not atthe angular frequencyof
1.0 rad.s" appliedinthisstudy.
Based on the results ofthischapter aschematicalpictureof
the occurence of microsyneresis in skimmilk gels can be drawn.
This isdone in figure 5.15 withtemperatureandpHasvariables.
In this graph we have made no distinction between syneresis and
microsyneresis. The most remarkable feature isthe sharptransition from the region ofrapid microsyneresistothatofnomicrosyneresis at pH=5.2, a transition which is hardly temperature
dependent.
162
6 PULSENMRSTUDYOFCASEINSOLUTIONS
6.1 Introduction
NuclearMagnetic Resonance (NMR)spectroscopy is awidelyused
non-invasive,relatively rapid, spectroscopical technique. InNMR
measurements onemakes use of the specificmagneticpropertiesof
thenucleiofcertainatoms.Hydrogennucleiarethemostabundant
and appropriate nuclei forthispurpose,butrecentlymuchattention has been given to carbon-13, phosphorous-31, nitrogen-14,
deuterium-2,fluorine-19andoxygen-17.TheNMRtechniquenowadays
is employed in many variations, of which ordinary wide lineand
pulseNMRarethemostfamiliar.
InthisstudyonlypulseNMRisappliedtohydrogennuclei.Two
characteristic relaxation times,which depend onthe environment
and mobility of thenuclei, aredetermined: the spin-latticerelaxation time, T,, and the spin-spin relaxation time, T 2 . The
large difference in T_ betweenmobile and immobile nuclei offers
thepossibility ofmonitoring thebehaviour ofhydrogennucleiin
all kinds of heterogeneous systems.Becausewatermolecules i.e.
the main constituent of all biological species consists of two
hydrogen nuclei and one oxygen nucleus,pulse NMR canbe avery
suitable technique for determining the amount and mobility of
those water molecules. Special interest has been focused on the
physical state of water in biological systems such as protein
solutions,orcellularsuspensions andtissues (e.g.Packer,1977,
Lynch, 1983, Fullerton et al., 1982). In such systemsmore than
one type ofwater canbe distinguished on thebasis of theirmobility (e.g.boundandfreewater). Sometimesthisdistinctioncan
be extended to three orevenmore different fractions (Fullerton
et al., 1982). Even the flow of water through the vessels of
plants may be measured (vanAs and Schaafsma, 1984). Furthermore
the solid/liquid ratio or the solid fat content insystemscontaining oils and fats such as margarine, butter oroil inwater
emulsions (van Boekel, 1980)canbe determined very easily using
pulseNMR.
163
Recently Brosio et al. (1983, 1984) and Leung et al. (1976)
studied water-binding to powdered milk and to three different
dried milk protein species i.e. casein, albumin and Y-gl°bulin.
Brosio et al. divided thewater content into aboundwater anda
freewater fraction,the amountofwhichtheywereabletocalculate. Each fraction was characterized by itsownT2-value,which
changed in adifferentway foreachprotein species,asmoisture
contentwas raised.At the lowestmoisturecontentthevaluesobtained for powdered milk were very close to those obtained for
albuminandonlyathighermoisturecontentwerethevaluescloser
tothoseobtained forcasein.Inotherexperimentsonmilksystems
Lelievre and Creamer (1978) observed no changes in relaxation
times,whenliquidskimmilkwaschangedintoarigidgelbyrennet
action,aslongasnovisiblesyneresisoccured.
This study focuses onthe effect ofpH and temperature onthe
spin-spin relaxation time (T2) of hydrogen nuclei of the water
moleculesofcaseinsolutionsandskimmilk.Thebehaviourofthese
water molecules strongly depends on the protein-water interactions.Therefore pulseNMR canprovide agreatdealofinformationconcerning theproperties ofcaseinmolecules.Anadditional
advantage ofpulse NMR arises fromthelargesignalresponsefrom
theabundantwaterprotonsincontrasttowidelineNMR,wherethe
lessabundantproteinprotonsarestudied.
6.2 PrinciplesofpulseNMR
A treatment of the basic principles of NMR hasbeen givenby
Dwek (1973),andFarrarandBecker (1971).Manyatomicnucleipossess a spin and thereby, anassociatedspinangularmomentum.The
possession of both spin and charge confers a magnetic momenton
the nucleus. As only hydrogen nuclei are of interest in this
study, we will limit this treatment to hydrogen nuclei andprotons.
A number of electromagnetic properties of nuclei, although
based on quantum mechanical restrictions, can be very easily
visualizedbyaclassicalapproach.Whenanucleusanditsspinis
placedinastrongexternal (homogeneous)magneticfield,H ,only
two possible orientations for itsmagnetic moment,u andM,}OWn
164
Fig.6.1 Schematic picture ofthemagnetic
moment vectorsofhydrogennucleiinthetwo
spin states (spin-upandspin-down)inclined
at an angle 0 relative tothedirection xof an applied magnetic field H .Themagnetic moment vector will precess aroundthe
direction x,attheLarmor frequency w .To
induce transitions betweenthetwostatesH
must be perpendicular t o H and a l s o r o t a t i n g a t the Larmor frequency w .
(see f i g . 6 . 1 ) , are allowed by quantum mechanical theory. The
magnetic moment p w i l l i n c l i n e a t a fixed angle 8 p a r a l l e l or
a n t i - p a r a l l e l to H . Popular terms for these o r i e n t a t i o n s are
commonly termed the spin-up and spin-down p o s i t i o n s . The torque
exerted by the magnetic f i e l d , H , causes the nuclear magnetic
moment to precess about H (in Tesla) a t the so c a l l e d Larmor
):
precession frequency, to ( r a d . s
*H r
(6.1)
where yisthemagnetogyricratio (rad.s- .Tesla"),afixedconstant foragivennucleus.Thetwopermitted orientations differ
inenergy,eachorientationbeing characterizedbyafixedenergy
level.Thedifferencebetweentheenergylevels,AU(J), dependson
theexperimentally fixed field-parameterH andisgivenby:
AU = YJÖL
inwhich#is h/2n, wherehisPlanck'sconstant (6.6256xl0~34Js).
The spin-upposition,whichisparallel tothemagnetic fieldH,
hasthelowerenergy.Inpracticalsystems,thereisalwaysanensemble ofa largenumberofnuclei,possessing magneticmoments,
allprecessing atthesameornearlythesameui (seefig. 6.2).
The small energy difference (eq.6.2) between the two energy
levelsresultsinaverysmalldifferenceinpopulation.Theratio
(6.2)
1
165
of energy level populations isgoverned by Boltzmann'sdistributionlaw:
N u /N d =exp(Y*ffl0/kT)
(6.3)
whereN d andN are respectively thenumberofspinsinthespindown and themorepopulated spin-upposition,kbeing theBoltzmann's constant (1.3807x10
JK )andT isabsolutetemperature
(K).Theslightlylargernumberofspins,alignedinthedirection
of the external magnetic field (along thex3~axisofthecoordinatesystemoffigure6.2)causesanetmagnetizationM ,whichis
also orientated along thex_-axisofthe coordinate system.From
equation6.3 anexpression forM canbederived (Abragam, 1961):
M 0 =Nv2Jrf2H0/4kT
whereN=N+N,isthe total number ofspinsinthesystem.Because
the system is inthermal equilibrium transitions between thetwo
energylevelscontinuouslyoccur.Thesetransitions areinducedby
interactions with the surrounding medium, interactions whichare
generated by local dipolar magnetic fields.Thesemagnetic fields
are fluctuating, since they mostly originate from other nuclei,
both intramolecular and intermolecular. They disturb to a small
extentthelargeexternal fieldH towhichthenucleusissubjec-
Fig. 6.2 Precession of an ensemble ofmagnetic moments of hydrogen nuclei. The net
macroscopic magnetization M is oriented
along the x, axis, the direction oftheappliedmagnetic fieldH
(6.4)
166
ted. These disturbances are responsible forthecontinuouslyoccurring transitions between the spin levels, and they are the
reason why the magnetic moments of an ensemble ofnuclei donot
precess inphase and atexactly thesamefrequency.Ifallmagnetic moments didprecess inphase and atthe same frequency,this
would imply that in fig.6.2 thepositionofallmagneticmoments
could be visualized classically by two arrows, one representing
themagnetic moments inthe spin-up positionandoneforthosein
the spin-down position, both rotating around the x3~axis. This
wouldresultinanetmagneticmomentwithacomponentrotatingin
the x,x2 plane. However, in reality, the spins will be out of
phase and inthecase of anensemble of spins atthermalequilibrium nonetmagnetization canbe detected inthex,x2-planeperpendiculartothedirectionoftheexternal field (seefig.6.2).
Transitions between the two energy levels can alsobe induced
by aradio frequency field,H,,whichisappliedperpendicularto
H in the x2x3-plane of the coordinate system (see figure6.1).
Energy is absorbed from this radio frequencyfield,H-.,onlywhen
the frequency of this field equals theLarmorprecessionfrequency' w 0 < of the nuclei. Upon energy absorption thepopulationof
the two enegy levels is changed. When the H, field is switched
off, the spin system relaxes back to the equilibrium Boltzmann
distribution. Two different relaxation processes may be distinguished, characterized by two different relaxation times: the
spin-lattice relaxation time, T,, and the spin-spin relaxation
time, T 2 . These relaxation times canbe determined separatelyby
means of two different pulse techniques. Inboth techniques the
distributionofthemagneticmomentsoverthetwoenergylevelsis
disturbed,butinadifferentway.ThedifferencebetweenaT,and
T 2 measurementcanbepartlyclassicallyvisualized. Inbothcases
a large K'^field is applied suddenly and for ashort time i.e.a
pulseofradiationisgiven.
In a so called T-^ experiment the population of the energy
levels is exactly inverted by a pulse of definite length and
strength. Classically this canbevisualized (fig.6.2) by anet
magnetizationM x3 (t)pointingalongthe-x.-axisimmediatelyafter
theH-j^fieldisswitchedoff.TherelaxationofM3 (t)backtothe
equilibrium situationischaracterizedbythespin-latticerelaxationtime,T,:
167
M x3 (t)=Mo(l-2exp(-t/T1))
(6.5)
where M is the original equilibrium magnetization along the
+x3-axis. Thus att=0M„3(t)is -M .During this relaxationprocess, which iscausedby interactions with the small localfluctuatingmagnetic fields,energy istransferred fromthespinsystem to the surrounding medium,which is also termed thelattice.
T-,isthenmeasuredbymonitoringtheamplitudeandsignofM„3(t)
using anadditional specialpulse sequence.T,isalsocalledthe
longitudinalrelaxationtime.
InaT 2 experiment ashorterpulse isgiven.This leadstoan
equal occupation ofbothenergy levels.Besidesthefactthatthe
magnetic moments are thereby all fixed inthesamephase,asdescribed above,this creates anetmagnetizationM,2 (t)a t t = 0 ^ n
the x,x2~plane of figure 6.2.When theH-.field is switchedoff,
two processes will occur,bothcausedby interactions with small
localfields.Firstthespinswilllosephasecoherencepartlybecauseofspin-spininteractionsbetweenlikenucleiandsothenet
magnetization in the x,x?-plane will vanish. In solid materials
the loss of phase coherence is almost completely due to direct
spin-spininteractions.ThecharacteristictimeT 2 forthisrelaxationprocess istherefore mostly called thespin-spinrelaxation
time,but the term transverse relaxation timeisalsoused.Itis
definedbytheequation:
M
xix2<t> =Mxlx2.0eJtP<"t^2>
(6
-6)
whereM x l _ _isthenetmagnetizationinthex,x2planeatt=0at
themomentH,isswitchedoff.
T 2 is measured by monitoring the net magnetization in the
x1x2~plane. The population of the two energy levels does not
change because of the relaxationmechanisms involved only inthe
T 2 processes and the loss ofphasecoherenceisnotattendedbya
transferofenergyfromthespinsystemtothesurroundingmedium.
However, simultaneously with the relaxation mechanisms justdescribed transitions will occur from thehighertothelowerenergy
level to restore the equilibrium Boltzmann distribution,governed
168
by the relaxation time T,. These transitions also decrease the
phasecoherence (secondprocess)and,onthecontrary,areattendedbyatransferofenergyfromthespinsystemtothesurrounding
medium. Thus any process, which is involved in the spin-lattice
relaxation (T.,)processes,willalsobeinvolved intransverserelaxation (T2) processes. Consequently T 2 always will be smaller
thanorequaltoT,.
6.3 TheeffectofmobilityofthenucleusonT~
T,andT~directlydependonthemobilityofthemoleculescontainingthehydrogennuclei.Thismobility isusuallyexpressedin
acorrelationtimet .ThegeneralrelationshipbetweenT,,T~and
t for a homogeneous and isotropic nuclear spin system isshown
schematically in figure 6.3. Theparameter t isacharacteristic
time to describe the motion of a molecule and, depending onthe
stateofthemolecule,itcanberegarded aseitherthetimeneeded tomove translationally over adistance equal to its owndiameter, to rotate through anangle ofoneradianorastheaverage
time between molecular collisions. The T 2 of hydrogen nuclei in
aqueous systems varies very strongly with the mobility of the
watermolecules. Itis also strongly influencedbytheabilityof
hydrogen nucleion different water moleculestoparticipatein
T-,.1l? Is)
Fig. 6.3. Schematic dependence of
104
/ \
relaxation times T. and T„ onmoi
/
lecular correlation time, x ,for
' c
1
1
1
1-
a homogeneous and isotropic nu-
i
clear spin system. Ordinate and
i
/
\ & <p
1(f-
\
\
abscissa values are only approxi-
i
i
mate. (A): non viscous liquid,
i
!
T 1 =T 2 . (B):viscous liquid,T^T^.
T
h
in8-
1
10"'
1
10"°
r
1
1
(C): non rigid solid,T 1 » T 2 - (D):
'
10"'
T.C Is)
rigid lattice, T » T „ .
169
spin-spin exchangeprocesses. Inthis studywewill focusourattention ontheT„ ofwaterprotonsinsolutionsofcasein.Noattentionispaidtothehydrogennucleiofproteinsorothermacromolecules, because not only do theypossessvery shortT 2 values
but also theymake only asmall contribution to the totalnumber
of hydrogen nuclei present in a casein solution (viz.10.4wt.%
drymatter for skimmilk and 3wt.%caseinforskimmilkandsodium
caseinate solutions). It iswidely accepted thatthemobility of
water decreases sharply in the vicinity of protein molecules or
othermacromolecules.Thecorrelationtime x mayincreasebysome
orders of magnitude,when awatermolecule istransferred froma
bulk solution to a water layer close to the surface oftheprotein,sothatthisisgenerallydenotedasboundwater(Berendsen,
1975).However,thesewatermoleculesstillpossessaconsiderable
mobility and particularly the hydrogen nuclei rapidly exchange
withthebulksolution.Infactwaterinamacromolecularsolution
should be regarded as amulti-phase system. Itis then dependent
on the exchange ratebetween thesephaseswhether oneormoreT 2
processes can be detected. This means that thecurve ofthedecreasing transverse magnetization measured as a function oftime
canbefittedwithoneormoreexponentials.
In the case of rapid exchange i.e. when the interchange time
betweenphases is short incomparison totherelaxationtime,the
spinsystemwilldisplayasinglerelaxationrate:
1/T2= I P i / T 2 i
(6>7)
whereP•isthefractionofspinsinthei phaseandT0•there•
th
"*"
laxationtimeof the i phase.Thetransversedecaycurvecanbe
fitted with asingle exponential,whose characteristicdecaytime
is aweighted average of relative spinpopulationsP-andrelaxation timesT2.. Inthe case ofslowexchangethetransversedecay
curve becomes multiexponential and is built up of separate contributions fromeachphase:
W
xlK2^
= f Mxlx2,oiexp(-t/T2i)
(6.8)
170
where M,~(t) is the total transverse magnetization relaxing to
.
.th
zeroandM,isthetransversemagnetizationofthe1 phase
XXX^/Ox
att=0afterapplyingthepulse.
In practice, however, the exchange rate between the water
phasesveryoftenwillbeintermediaterelativetothedecayrates
ofthephases.Inthat situation, fittingthedecaycurvebecomes
very complicated and the T_- values found often vary asprotein
concentration is varied. Brosio et al. (1983 and 1984)distinguished two water phases intheir study ofwater-binding tomilk
proteinsresultinginabiphasictransversedecaycurve.Butthere
therelaxationtimeT-ofbothboundandfreewateralsotendedto
increasewithwatercontent.
6.4 Experimentalresults
All skimmilk (standard concentration) and sodium caseinate
solutions,respectivelyreconstituted fromskimmilkpowderA(section 2.1) and freeze-dried sodium caseinate (section 2.2) were
acidified to pH's varying from 6.7 to 4.6 according to section
2.3.The highestpH among the sodiumcaseinatesolutionswas6.9.
All pH values givenweremeasured at0-2 °Cafter theacidification stepwas completed, some solutions latershowedincreasedpH
values (see later). Milkultra filtrate wasobtained asdescribed
insection2.5.Themeasurementswerecarriedoutwiththeapparatusdescribed insection2.9.
Usingextensivecurve-fittingcalculations,preliminaryexperiments with skimmilk (pH=6.7)and acid skimmilk gels (pH=4.6)revealed only one dominant exponential (^96%of total amplitude),
except when a small layer of condensed water or syneresis fluid
had developed. All latermeasurements were fitted with oneexponential, which could be adequately corrected for the smalloverlyingliquidlayer.
Themeasuringtubeswerefilledimmediately afteracidification
andforanyparticulargel,thesametubewasusedatalltemperatures.Temperature inaccuracy waswithin 0.5 °Catlowertemperaturesandabout0.5 °Cathighertemperatures.Repeatmeasurements
ofT 2 for asample inthe same tubevaried by atmost0.5%.Differenttubescontainingthesamegelsamplesometimesshoweddevi-
171
ations of a fewpercent.All sampleswere firstequilibrated for
at least one hour at the measuring temperature, unless stated
otherwise.Ifnotused forlongertimestheywerestoredat4°C.
6.4.1 T„ofskimmilk
After acidification the skimmilk sampleswere storedat0-4°C
overnight.Experimentswerecarriedoutattherateoftwotemperatures per day.Figure 6.4 shows theT 2ofskimmilkasafunction
ofpHmeasuredatrespectively4,10.5,20,30,40and49.5 °C.In
the sample ofpH=5.2 at49.5 °Cthemilkproteinhad flocculated
and toomuch syneresis fluidwas formed togive areliablevalue
forT 2 .
TherewasaverystrongeffectofpHonT-ateverytemperature
investigated. A maximum inT 2 is foundbetweenpH=5.0andpH=5.2.
These pH values were somewhat arbitrary,because thedissolution
of colloidal calcium phosphate was a time consuming process at
pH's above 5.0 (see section 3.3).Ifwehadwaited alongertime
beforemeasuring thepH after acidification thepH-valueobtained
would have been shifted upwardby approximately 0.1 to 0.3 units
dependingonthetemperature.
AnincreaseofT_withtemperatureasfoundwasexpectedasthe
correlation time t ofthe hydrogennucleidecreaseswithtemperature (seefig.6.3).
Themaximum found intheT~valuewhenpHofthe skimmilkwas
varied (fig 6.4),must be ascribed to the skimmilkproteins and
perhaps to the CCP, but not to the salt solution. This follows
when we compare the results shown in figure 6.5 formilkultrafiltrate with those of figure 6.4 for skimmilk.Thismilkultrafiltrate,obtained atroomtemperature fromstandardskimmilk,was
acidified at 0-2 °C according to section 2.3.Asacheck,wealso
used ultrafiltrate obtained at4°C from skimmilk whichhadbeen
first acidified to the rangepH=5.0to5.2.TheT 2values forthe
ultra filtrates were about five timeshigherthanforthecorrespondingskimmilkandareveryclosetotheT 2valueofpurewater.
No clear influence ofpH onT 2wasfound.TheT„valuesofultrafiltrateobtained fromskimmilkacidifiedtopH=5.2and5.0 agreed
well with those ofultrafiltrate made fromskimmilkofpH=6.8and
acidifiedtothesamepH (seefig.6.5).
172
TheultrafiltratesampleofpH=6.8showedaremarkabledecrease
in T 2 during themeasurement at49.5 °C.Thismusthavebeendue
totheformationofacalciumphosphateprecipitate (seealsosection 3.3.2.2). Prolonged heating at50°Cenlarged thedecrease,
which after extended waiting time led to a T ? value of about
1.6 s. The temperature dependence was almost the same for all
pH's.
At lowpH the decrease inthevalueofT ? ofskimmilkwithdecreasing pH might be related to an increasing gelation ofthese
skimmilksolutions,especiallyathighertemperatures,sincegelationtendstodecreasetheT 2 .Thisisillustrated infig.6.4for
pH=4.6,wherethefilledsymbolsbelongtoaskimmilksample,which
T 2 (ms)
600
Fig.6.4.The T„ (ras)of acidified skimmilk as a function of pH. Thetemperature wasvaried as indicated.The filled symbols atpH=4.6belong toaskimmilk
solution, which was aged 10 hrs at 30°C before the first measurement (see
text).
173
wasgelled at30 °Cover 10hrsandthencooled forthe firstmeasurement at4°C. It shows that there was a small but noticeable
difference in T,between gel and solution of skimmilk atpH=4.6,
especially atlowtemperature. TheT„ofthegelwas significantly
smaller.Thedifference vanished asthe solutionbecame agelduring themeasurements at20 °Cand higher.At49.5 °Ctherewasno
difference anymore. However, as we shall show later it ismore
likely that the observed pH dependence is due to aggregation of
caseinmolecules inside thecaseinparticles rather thantoaggregation of these particles themselves (see for further discussion
chapter 3andsection6.5).
T2 (ms)
3000TI°C)
49.5 O
40.0
O-
a
cP-o
-CD-0.
2000
-O—O
30.0
20 0
1000-
4.0
O-
10.5
O-
4.5
O-
-O—O
O-
-o-o-
-°-°A"
fA—o-
5.0
6.0
7.0
pH
Fig. 6.5 The T„ (ras)as a function of pH for milk ultrafiltrate obtained at
room temperature from standard skimmilk of natural pH and subsequently acidified (o).Also included are the T- values of milk ultrafiltrate, gained from
skimmilk acidified to pH=5.2 (A)and pH=5.0 (D).Temperature wasvaried asindicated. For the sample with pH=6.76 at 49.5 °C,where T„ strongly decreased
during themeasurement,thehighestvalueobtained isgiven (see text).
174
6.4.2
T~ofsodiumcaseinate
Inorder to studythe influence ofthecaseinontheT 2values
in absence of colloidal calcium phosphate and serumproteins the
sameexperiments were repeated with solutions ofsodiumcaseinate
inwater (see section 2.2 and 2.3).Thecaseinconcentrationvariedslightly from2.8to2.9wt.%,dependingonthevolumeofacid
added.Figure6.6 showstheresultsforsodiumcaseinatedissolved
inasolutionof0.13molNaClperkgdispersion.TheT 2valuediminished with decreasingpH.Nomaximum withpHwasfound,unlike
the behaviour of skimmilk.The drop inT 2 with decreasing pHbecame more pronounced athigher temperatures especially inthepH
regionbetween5.0 to6.0.AtlowpHtheT 2valuewasonlyslightly largerthanforskimmilk, whileat higherpHtheT 2valueof
Fig.6.6 The T„ (ms)of acidified sodium caseinate solutions asafunctionof
pH. Temperaturewasvaried as indicated.The casein concentration was2.8-2.9g
per kg dispersion. The caseinate was dissolved in a solution of approximately
0.13 molNaClper kgdispersion.
175
sodium caseinate solutions was much larger. Part of the difference, especially at low pH, will be due to the absence of serum
proteins andallother smaller milk components.
T~ again increased with temperature. At lowpH (£5.1)theincrease was more or less identical tothat shownby skimmilk.However, at higher pH's the rise in T- as a function of temperature
was much larger than at lowpH's,incontrasttothebehaviour of
skimmilk solutions.
Upon acidification at 0-2 °C the appearance of the sodium caseinate solutions changed from a rather clear, greyish colour to
colloidal white andturbid (just like milk)atpH=4.6 (seesection
3.3.3). This must have been caused by the aggregation of casein,
and could also be observed on electron micrographs (fig.3.10,
section 3.3.3). The transition from smaller to larger casein aggregates, which took place between pH=5.8 and 5.2, is paralleled
only athigher temperatures byasteep decline inT- value.
When sodium caseinate was dissolved in a solution of0.066mol
NaCl and 0.022 mol CaCl,per kgdispersion (1-0.13 M ) , large protein aggregates were already present at pH=6.6. These tended to
sediment when stirring was stopped. The solutionhadthesame colloidal white appearance as skimmilk (see also section 4.5.5.3).
Figure 6.7 shows theT_ value of sodium caseinate dispersed inthe
above mentioned mixture of NaCl and CaCl_ as a function ofpH at
three different temperatures.These results areless absolute than
those given previously, because some sedimentwaspresent inevery
tube.No attempts at curve fitting were applied todistinguish a
T2(ms)
Fig.6.7.TheT„ (ms)asafunction ofpHforsodiumcaseinate,
dispersed inasolutionof0.066
1000-
mol NaCland0.022mol CaCl,per
kg dispersion and then acidified. Temperaturewasvariedas
indicated.
500-
176
separate T ? value forthehydrogennucleiofthewatermolecules
trapped in the sediment. The T_ value shown probably belongsto
the supernatant caseinate solution, this solutionobviously ata
lowerproteinconcentrationthanthecorrespondingcaseinatesolutions dissolved in pure NaCl. T_ again generally decreased with
decreasingpHbutshowedasmallmaximum aroundpH=6.0at32.5°C.
Although absolute values cannot be compared there is a striking
difference in pH dependence caused by the presence of calcium
ions.
6.5 Discussion
The large effectofpH on theT 2 value of skimmilk and sodium
caseinatesolutionsprovesthattheT„valueofhydrogennucleiof
water is avery usefulparameter formonitoringtheprotein-water
interactions inthese systems.The large differenceinT-between
milk ultrafiltrate and skimmilk or sodium caseinate solutions
proves thepresence of atleast twowaterphases:freewater and
socalledboundwater.Theboundwatermustbesituatedonthecasein (orcaseinmicelles),serumproteinsandperhapsontheamorphous colloidal calcium phosphate (CCP). Rapid oratleastmoderate exchange must be responsible for the T 2 values obtained for
skimmilk.
Brosio et al. (1983 and 1984)distinguished aboundandafree
water fractionwith amultiphasic transverse decaycurveforpowderedmilkandmilkproteins.HowevertheT ?valuesofbothphases
increased with water content, whichpoints toexchange processes
within the time scale of the NMR measurements.The change ofT_
valueuponacidificationcouldbeduetoachangeintheamountof
bound water,butcould alsobe theresultofachangeintherate
of exchange between bound and free water or to a change inT~
value itself of that bound water. According to Berlin et al.
(1970) the amount of bound water should be 0.55 g/g casein and
0.50 g/g total whey protein as estimated by aDSC technique. In
the same way Riiegg et al. (1974)estimated the amount of bound
water tobe 0.44 g/g casein forcaseinmicelles,paracasein,and
acidprecipitatedcaseinalso.UsingNMRtechniques,theamountof
non-freezable water was estimated to be 0.3 g/g dried casein
177
micelles (LelievreandCreamer,1978)and0.26 g/gpurifiedcasein
(Leung et al., 1976). Thus the amountofwaterverytightlybound
toindividualcaseinmoleculesmayvary from0.25 to0.55 gramper
gram caseindepending onthemeasuring method.Basedontheabove
literature data it is difficult to say whether the amount of
tightly bound water changes with the state ofcasein;nor isit
possible to say what will be the size of the total bound water
fraction incasein solutions.Concentration dependent experiments
willbenecessarytorevealthestateofwatermoreexplicitly.In
this way it may be possible to correlate themeasured T 2 values
withthehydrationandvoluminosityofcasein.
Recently Fullerton et al. (1982)proposed a model with three
water phases to explain results on tissue and cellular suspensions.Thebound water fractionwas splitupintoahydrationwater phase and acrystalline waterphase.A large hydrationwater
layer will slow the exchange between crystalline water and free
water,thisexchangedeterminingtheT ?ofthefreewater.Accordingtothemodelanincreasinghydrationfractionwouldleadtoan
increasing T 2 value. Concentration dependent experiments willbe
necessary to check the applicability of this model to skimmilk
solutions.
Thereforewiththeresultspresentedintheprevioussectionit
isnotyetpossible to give aconclusivemodelwhichwillusethe
measured T 2 parameter, the spin-spin relaxation time,todescribe
the behaviour ofwater incasein systems interms ofbound, free
orevenmorewaterphases.Thuswewilltrytoexplainourownresultsinmoregeneralterms.
Skimmilk is a complicated system containing mainly proteins
(chiefly casein and serum proteins) and lactose dissolved ina
mixture of several kinds of salts.The composition of the salt
mixture will change upon acidification, when CCP dissolves from
thecaseinmicelles.TheT 2valueofthesaltsolutionhoweverwas
hardly affectedbypH orby dissolutionofCCP (fig.6.5)Asdiscussed in section 3.3 the structure of the casein particles
changes drastically during acidification from pH=6.7 to 4.6.
RoughlyspeakingabovepH=5.2thecaseinispresentintheformof
caseinmicelles or the relics ofcaseinmicelles,thesebothcon-
178
sisting of aggregated casein molecules and amorphous CCP. Below
pH=5.2thecaseinparticlesnolongercontainCCP.Asdiscussedin
chapters 3 and4,casein aggregation isaccompaniedbytheformation of protein-protein bonds at three levels: intramolecular,
leading to the secondary and tertiary structure oftheproteins,
intermolecular inside the casein particles and governing the
structure of those casein particles, and intermolecular between
different particles. The latter reaction is in fact coagulation
and may be followed by gel formation. CCP ismainly involved at
thesecondlevel.Allofthedifferentcomponentsofskimmilkwill
influencethestateofwater,butalltodifferentextents.
Lelievre and Creamer (1978)determined theT_ values ofskimmilkandrennetwheyatnaturalpH (T=34°C)atthesamefrequency
of the magnetic field (=20 MHz, see section 2.9) as we used in
this study. For skimmilk they found an identical value for T„
(=0.17 s)ascanbe derived fromfig.6.9 forreconstitutedskimmilk (pH=6.8)at34°C.Thevalue they found forwhey (T2=1.3 s)
was smaller than the T ? of our corresponding milk ultrafiltrate
(containinglactoseandalldissolved salts),whichweestimateto
be 1.9 s (fig.6.5).Thedifference betweenthosetwovaluesmust
be ascribed to thepresence of serum proteins andglycomacropeptides inthewhey.However,thedifferenceinT,betweenwheyand
milk ultrafiltrate (1.3 and 1.9 s., respectively) is small when
compared to thedifference between skimmilk andwhey (0.17s.and
1.3 s. respectively).This implies that,certainly atnaturalpH,
the T 2 of skimmilk depends to a large extent on the casein and
maybe on theCCP.Moreover itmustcertainlyalsodependontheir
mutual interaction as reflected intheir interaction withwater.
For atpH=6.7 ahigher value ofT,wasfoundforthesodiumcaseinate solutions (fig.6.6) than for skimmilk.Itseemsreasonable
to suppose that atother pH's, too,theT,ofskimmilkandsodium
caseinate solutions will (largely) depend on the interaction of
water molecules with casein and for the skimmilk athigherpH's
also directly or indirectly on the CCP. Supporting evidence for
this statement is foundby comparing the small change ofT„with
pHformilkultrafiltrate (fig.6.5)withthestrongpHdependency
of T 2 found for sodium caseinate solutions (fig. 6.6) and the
peculiar effect ofpH onT 2 for skimmilk (fig.6.4).Furtherthe
179
curvesofT,versuspHforpuresodiumcaseinate (fig.6.6)showa
greatsimilaritytothecurvesofskimmilkatlowpH,butastrikingdifferenceathigherpH's (abovepH=5.2).Thisdifferencemust
be due to the absence of CCP inthe sodium caseinatesolutions.
The strong increase of T„ with decreasing pH for skimmilk at
pH>5.2 runs parallel to the dissolution of CCP from the casein
micelles. The question remains unanswered, whether this increase
in T ? stems directly from a change in the interactions between
amorphous CCP andwater,orwhether itdepends indirectly onthe
dissolution ofCCP,because of achangeofthecaseinaggregation
induced by it,orwhether itdependsonbothprocesses.DissolutionofCCPprobably results inapartialunfoldingofthecasein
particles accompanied at least at low temperature by a partial
dissolution of casein molecules (section 3.3).Such a change in
casein aggregation from within the caseinparticles will alsobe
manifest in the voluminosity of casein as a function of pH and
temperature (section3.3).
The maximum around pH=5.1 in fig. 6.4 became more obviousas
temperature was raised. This implies that the changes in T- of
skimmilk as function of pH and temperature do notcorrelatedirectly with changes inthevoluminosity ofcaseinmicelles (fig.
3.6, section 3.2).According to Darling (1982), Snoeren etal.
(1984) and Tarodo de la Fuente et al. (1975) a maximum in the
voluminosity of casein micelles was found around pH=5.4,particularly at temperatures below 30 "C. However in cjntrast to the
maximum in T_ this one disappeared at temperatures above 30°C
(see fig.3.6a afterDarling, 1982), orbecamesmaller (VanHooydonk,1986).AteachpHabovepH=5.2anequilibrium existsbetween
dissolved and undissolved CCP at all temperatures. Temperature
rise will enhance the reformation of amorphous CCP, as itshifts
the balance between dissolved andundissolved to theundissolved
species. Therefore temperature will affect T ? not only via the
water-proteininteraction,butalsoviathewater-CCPinteraction,
which vanishesbelow pH=5.2.No guess canbemade aboutthecontribution of thedirectwater-CCP interaction.Moreresearchwill
be necessary, before more definite conclusions canbe drawn.The
sharp drop in T 2 value caused by the formation ofcalcium phosphate precipitates in themilkultrafiltrate sample ofpH=6.7at
180
49.5 °C (fig.6.5) also indicates apossibledirecteffectofCCP
ontheT ? ofskimmilk.
Below pH=5.0, when all CCP isdissolved, all ofthe dissolved
casein reaggregates once more and casein particles of distinct
structure are formed, leading to lowerT 2 values. Infactcasein
aggregation can be distinguished atdifferent levels i.e. atthe
level of individual caseinmolecules,attheleveloftheparticlesandthelevelofthestrandsandconglomerates formingthegel
network (see also chapter 3 and 4 ) .Theinternalstructureofthe
casein particles rather than coagulation or gel formation will
determine T 2 , since Lelievre and Creamer (1978) found the same
valueforT~ofskimmilkatnaturalpH,whetherornotithadbeen
gelled by rennet action.As long asno syneresis had occured gel
formation did not change T 2 . The T ? of skimmilk acidified to
pH=4.6andmeasured at4 °Cwasslightly,butsignificantlyhigher
thanthatofthe corresponding skimmilk gelagedfirstfor10hrs
at30°Cand then alsomeasured at4°C.Thedifference,however,
isprobably causedby irreversible changes intheinternalstructure of thecaseinparticles caused byheatingandsubsequentgel
formation and not to gelation as such;since caseinparticles at
pH=4.6 after acidification at2°C are thermodynamicallyunstable
as shown by the irreversible character ofgel formation (section
3.3.2).
SinceproteinaggregationanddissolutionofCCPwillbetemperature dependent, itmaybe enlightening toconsiderthetemperature dependence of T 2 for sodium caseinate and skimmilk inmore
detail. Fig. 6.3 suggests a linear relationshipbetweenT 2 andt
(plotted on adouble logarithmic scale)forfastmovingmolecules
such aswater molecules inthebulkwaterphase. InthatcaseT 2
will be proportional to n/T (Carrington and Mclauchlan, 1969),
wherenistheviscosityofthemedium andTabsolutetemperature.
This proportionality stems from contributions to T 2 from rotational and translational motions, these together resulting in
Brownianmotion.Thecorrelationtimex willalsobeproportional
ton/T- However,forwatermoleculesboundtoasurface,molecular
motion will be constrained and only rotational motions will be
allowed.Thusx c shouldbewrittenas (Dwek,1973,Lynch,1983):
181
T c =T°exp(-Ua/kT)
(6.9)
whereU istheactivationenergy forrotationalmotion.According
to eq. 6.9 log t will be proportional to1/T. Inheterogeneous
systemswith atleastonebound water phase T 2 of thebulkphase
will depend ontheboundphase.ForthatreasonT 2 ofbiological
systems (Lynch, 1983, Bryant and Shirley, 1980)isgenerallydepicted on a logarithmic scale as a function of 1/T on a linear
scale. Inthecase of fastexchange betweenbulkwater andbound
water (Lynch,1983)logT 2ofthebulkphasewilldecreaselinearly with 1/T. This linearity maybe lostwhen an intermediateexchange rate exists or when the fraction of bound water changes
withtemperature.Ifthebulksolutioncanbeconsideredasaviscous liquid (region A, fig. 6.3),theory then predicts alinear
decrease of T 2 with increasing r\/1, both depicted on a double
logarithmicscale.
Except for the sample at pH=6.76 (particularly at 49.5°C)
straight lines (not shown) were found for milk ultra filtrate,
whenT 2 wasdepicted on alinear scale asa function ofn/T- T n e
T ? valueswereclosetothoseofpure,freewater.
For sodium caseinate solutions and skimmilk itisunrealistic
toexpect alineardecrease oflogT 2withincreasing1/T forall
samples. Several phenomena will be involved as temperature is
raised.Firstly,asmentioned abovethecorrelationtime T ofthe
hydrogen nuclei will decrease leading tohigher values ofT 2 for
all water phasespresent,but the exchange ratebetween thedifferent water phases may also change. Secondly the calcium phosphate equilibria will shift towards the undissolved species resultingdirectly,orindirectlythroughachangeinproteinaggregation, inalowerT_.This effectwillonlyplayapartinskimmilk at pH values above 5.2. Thirdly the aggregation of casein
molecules will increase with temperature leading to a firmerinternal structure of the casein particles. Upon increased casein
aggregation onemay also expectthe amountofboundwater toincrease;sothatT 2willdecrease.Thislattereffectwasespecially seen with sodium caseinate, when pH was varied at constant
182
temperature (fig.6.6).BelowpH=5.8 the formationofcaseinparticles in a sodium caseinate solution was accompanied by ahuge
drop inT 2 .The sum ofallthephenomenamentioneddeterminesthe
changeinT 2withtemperature.
Infig.6.8T 2 isdepictedlogarithmically asafunctionofthe
inverse temperature,1/T, forsodium caseinate solutionsatseven
differentpH's.Thesevalueswere derived fromfig.6.6.Sincewe
haveonlysodiumcaseinatepresentonlythefirstandthirdeffect
plays a part. A more or less linear decrease of logT 2 with 1/T
wasfoundforthesamplesofpH=5.4andabove.Hereitispossible
that the amount ofbound water and the exchange rate remainconstant.Thedeviation from linearity forthesesamplesatthelowestvalue of 1/T (pH=6.94and 5.80)wasprobably due to aninaccuracy in the measurement of the experimental temperature. At
lower pH values only over a portion of the depicted curves is
therealineardecrease.Herethedeviationfromlinearitywillbe
duetoanincreased aggregationofcaseinmoleculesinsidethecasein particles as temperature israised.This increased aggregationmay cause an increase ofthefractionofboundwaterleading
tolowerT2~values, butthedropinT 2 mayalsobeduetoadif-
Fig. 6.8. The T„ (ras)of sodium
caseinate solutions depicted ona
logarithmic scaleasafunctionof
1/T ( K _ 1 ) . The pH of the samples
is indicated. The values are derived from thedata of fig. 6.6.
i
1
r
107TIK1)
183
ferent exchange ratebetweenbulkwater andbound water. Inthis
context itshould bementioned that as ageneral trend theslope
ofthecurves also tends todecreasewithdecreasingpH;possibly
the rate ofcasein aggregation inside thecaseinparticlesatlow
pHincreaseswithtemperature.
In fig. 6.9 T~ of skimmilk is depicted logarithmically as a
function ofthe inverse temperature,1/T,forsixdifferentpH's.
Thesevalueswerederivedfromfig.6.4.ExceptforpH=5.4moreor
less parallel curves decreasing with the inverse temperature are
found. For all samples alinear decreaseislackingandatpH>5.0
theslopeofthecurvesismuchsmallerthanincaseofthesodium
caseinatesolutions.SignificantlyatpH=4.6,whereCCPisnolongerpresent,the curves of skimmilk andsodiumcaseinatehavealmost identical slopes.AtpH=5.4,which isclose to thepH limit
for the dissolution ofCCP,thecurveofT 2versus1/T levelsoff
above 20°C.At this and higherpH not only increased caseinaggregation,but also reformation of amorphous CCPmustbeinvolved
on raising the temperature, resulting in a large deviation from
linearityandlesssteepcurves.AtallpH'sachangewithtemperatureintheextentofcaseinaggregationinsidethecaseinparticles may be expected.Atmoderate pHvalues and low temperatures
this maystem partlyfrom amigration ofthecasein,dissolved
T2 (
Fig.6.9.TheT2 (ms)ofskimmilk
depictedonalogaritmicscaleas
afunctionof1/T(K_1).ThepHof
thesamplesisindicated.Thevaluesarederived fromthedataof
fig.6.4.
TIS)
500-
'
\
V
. „ . ^
400300-
>.îCN
48
6
V 54
a
a-
200-
0
^
46
-^ .
150" " ^ ° ^ - o 6.8
I
30
I
32
I
1
34
1
I
I
3.6
103/T(K~1)
184
during acidification at 2 °C, back to the casein particles, or
from the formation ofnewparticles outofthatdissolvedcasein.
The voluminosity of the caseinparticles decreaseswithtemperature for allpH's (fig.3.6, section 3.3).Inso far asthisdecrease reflects anincrease incasein aggregationthiswillcause
areducedincreaseofT,withtemperature.
However the observed temperature effects are smallcomparedto
the observed pH-effects. Gel formation hardly affects T2-Therefore itcanbe concluded thatT 2 andprobablytheamountofbound
water depend to a large extent on intermolecular electrostatic
interactionsbetweencaseinmoleculesinsidethecaseinparticles,
inwhichCCPmaybeinvolvedathigherpH.pHaffectsT 2muchmore
thantemperature.TheeffectoftemperatureonT 2willprobablybe
duemore tohydrophobic interactions inside thecaseinparticles.
This agrees with the speculations of section 4.6 that electrostatic interactions, whether repulsive or attractive, are of
primaryinterestincontrollingthestructureofcaseinparticles,
whilehydrophobicinteractionsareinvolvedinalterationsofthat
particlestructureontemperaturerise.
185
7 CONCLUDINGREMARKS
This study focuses onthe structure ofacidcaseingels,which
involves the spatial distribution of and the interaction forces
between the structural elements. Itismainlyconcernedwithgels
formed by heating atrestof casein solutions,whichwereacidified chemically in the cold. Gel formation caused byheatingan
acidified casein solution is an irreversible process (section
3.2.2). Itwasfoundthatnotonlycaseinconcentration,pH,ionic
strength,type of ions inthewaterphase,ageingtimeandageing
temperature,but also the conditions during acidificationarethe
mainfactorsdeterminingthestructureofacidcaseingels.Essentially the same kind of gels are formed from skimmilk and from
sodiumcaseinatesolutions (seee.g.section3.2.4,3.4.2.1, 4.5.3
and 4.5.5.3), which points to casein being the basic elementof
acidcaseingels.
Wheyproteins did not affect the formationofacidcaseingels
(section 3.4.2.1); however, the skimmilk and sodium caseinate
solutions (reconstituted from the corresponding powders)werenot
heat-treated prior to use, in contrast to industrial practice
wheremilkismostlypreheated toinvokedenaturationofwheyproteins.
Acid casein gels could onlybe formed over a limitedpH range
(4.3-4.9, see section 4.5.4) and at temperatures above 10°C
(pH=4.6, see section 3.2.1). Addition of rennet,however,enabled
gel formation inthe entire pH rangefrom4.4 to6.7 at20°Cand
also in the temperature range from 0 and 10°CatpH=4.6 (ChapterV ) .
In fact acid casein gels can be considered tobeparticulate
gels (Chapter 3), originating from the coagulation ofcaseinparticles. The diameter of particles eventually forming the strands
and conglomerates of the gel network may vary from 50to 300nm
(section 3.4.2.2). Inthe case ofsodium caseinate gels theconstituting casein particles are not "caseinmicelles", but arise
from the aggregation of casein molecules or oligomers during
acidification (section3.3.3). In skimmilk the situation ismuch
more complicated: starting at pH=6.7, acidification causes the
186
dissolutionofcolloidalcalciumphosphate (CCP)whilepartofthe
casein molecules dissociate from the casein micelles (section
3.3.2.1), whereas thediameter ofthe caseinparticles appearsto
stay about constant (section3.3.2.2 and 3.3.2.3) and few particles seem todisintegrate completely (section 3.3.2.3).Maximum
solubility of casein is seen around pH=5.4-5.5,whereas closeto
pH=4.6 all casein has disappeared from the serum (section
3.3.2.1). Although having approximately the same size as casein
micellesinskimmilkofnaturalpH,theinternalstructureof(not
yet aggregated) casein particles at pH=4.6 must be different
(section3.3.4).Boththesimilarity ininternalstructurebetween
caseinparticles inanacidified skimmilk andinasodiumcaseinate solution, and the change of that internal structure during
acidification were confirmed by the results ofpulseNMRmeasurements (section6.4.1, 6.4.2 and 6.5).The spin-spin relaxation
time, T 2 , of the hydrogen nuclei of the water molecules in the
serumappearstodepend (certainlyatlowpH)primarilyontheinteraction of the water molecules with casein inside the casein
particles, and thereby also onthe internal structure ofthecaseinparticles.
An acid casein gelmaybe characterized asaheterogeneousgel
network. Heterogeneity may be distinguished atdifferentlevels,
sinceitresults fromlinkagesatdifferentlevels:intramolecular
bonds inindividual caseinmolecules,aggregation ofcaseinmolecules inside the caseinparticles andbondsbetween caseinmoleculesofdifferentparticles,thelatterleadingtocoagulationof
casein particles. In the first step of coagulation strands and
small conglomerates of particles will be formed. Subsequently
thesewillaggregatetoformanetworkoflargeconglomeratesconnected by strands and separated by large pores. In fig.3.17 a
highlyschematicrepresentationisgiven.Thisdescriptionissupported by concentration dependent rheological (section3.4.2.1)
and permeability measurements (section3.4.2.3), and by electron
micrographs of acid casein gels (section3.4.2.2).Thepermeability coefficient, B, will particularly depend on the size ofthe
largepores,whereasthedynamicmoduli,G'andG",willdependon
thecharacter (relaxationtime)andeffectivenumberofbonds.The
effective number of bonds is determined by the number of bonds
187
between adjacentparticles and thenumber ofparticleswhichcome
under stress ifthenetwork isdeformed.Thelatternumberhighly
depends onthe spatial distribution of thesestresscarryingparticlesandismuchsmallerthanthetotalparticlenumber,because
ofnetworkinhomogeneity.Thespatialdistributionasreflectedin
the permeability of an acid casein gel seems tobemore orless
fixed in the first stage of gel formation, hardly changingwith
timeormeasuringtemperature (section3.4.2.3and4.5.3).
If other factors,such aspH and ionic strength, areconstant
the temperature during the earlier stages of gel formation predominantly determines the permeability of the gel network. Considering the large conglomerates (being actually dense areas of
casein particles) as spheres of approximately the same diameter
(inthe order of a fewjjm)asthe largepores,themeasuredpermeabilities roughly agree with calculations according to models
fortherandompackingofspheres (section 3.4.3.2).
After initial gel formation, the dynamic moduli of all gels
studied tended to increase with time forperiodsevenlongerthan
a week (section3.2.1, 4.5.4, 4.5.5 and 5.3.1). Aggregation as
such is probably subject to anactivationHelmholtzenergy (section 3.4.1), which decreases with increasing ageing temperature
(section3.2.1 and 4.5.3), since the increase of the dynamic
moduli (particularly occuring during the firststageofgelation)
increases with ageing temperature, when measured at the same
temperature. This activation Hemlholtz energy tends to increase
withionicstrengthatpH=4.6 (section4.5.5.2)andwithpHinthe
pH range of4.5 to 5.0, ifnorennetisadded (section4.5.4).It
must at least partly be due to asteric stabilization effectof
the GMP part of K-casein, since even at2°C acid skimmilkgels
may be formed after release of GMP (section5.1 and 5.3.1).The
other factors determining this activation Helmholtz energy are
lessobvious.Possibly,thereisamuchsmallertemperaturedependentstericstabilizationcontributionofß-casein,whichdecreases athigher temperature,where ß-casein tendstomovetotheinteriorofthecaseinparticles (section5.3.1).Differentacidcaseingelshadincommonthathigherdynamicmoduliwentalongwith
higher permeabilities (section3.4.2.3, 4.5.3, 4.5.4 and 5.3.1).
Probably,adecreaseoftheactivationHelmholtzenergyresultsin
188
largerpores,whereastheeffective number ofinterparticlebonds
between adjacent particles must increase. Anyhow more research,
particularly on the kinetics of the aggregation and subsequent
gelation process, arenecessary tobeable todrawmore definite
conclusions.
Partofthebonds inanacidcaseingelhavearelaxationtime
3
intherange from0.6to6x10 s(section4.5.2).Anothercharacteristic featureofacidcaseingelsistheratherpermanentchar4
acter over longer time scales (>10 s).The existence of a
pseudo-permanent network modulus, which resulted from thecalculationoftherelaxation spectrum (section4.5.6.2), couldbeexperimentally verified (section4.5.6.1). The calculated pseudopermanent network modulus andthemeasured pseudo-stressrelaxa4
tionmodulus (timescale>10 s)formedaconsiderablepartofthe
3
dynamicmoduli inthetime scaleof0.6to6x10 s.Possibly,the
more permanent network character ofacid casein gels ascompared
to rennetgels isthereason thatruptureofacidcaseingelsoccurs atasmaller deformation andalarger stress thandorennet
gels (section4.5.7).
Theparameter tanô (=G"/G')maybeaveryusefulparameterin
furtherrheologicalcharacterizationofacidcaseingels,sinceit
hardlydependsonthespatialdistributionofthegelnetwork,but
almost exclusively on the character of the interparticle bonds
(section4.3). It is concluded (section4.7) that the character
andnumberofbondsbetweentwoparticlesisdeterminedbytheinternal structure ofthe casein particles involved. The internal
structure ofcaseinparticles results from abalancebetweendifferent interaction forces (section3.3.4)i.e. hydrophobic bonding,electrostatic interactions,hydrogenbonds,VanderWaalsattractionandstericinteractions.Thebehaviouroftanôatlonger
timescalesdiffersfromthatatshortertimescales.Tanôinthe
rangeof0.1to10rad.s" doesnotchangewithageingtemperature
(T<50°C, section3.2.1), measuring temperature (T also <50°C,
section4.5.3), I (section4.5.5), type of ions (section4.5.5)
andpH(section4.5.4),aslongaspH<_5.1(section5.3.2),i.e.as
long as thegelhasthe character ofacid casein gels.Thisimpliesthatthereisnoindicationofadrasticchangeinthecharacter of thebonds with relaxation times intherangeof0.6to
189
60s as a function of the mentioned parameters. At longer time
3 ôtended todecreasewithdecreasing
scales (60to6.0x10 s)tan
measuring temperature, T ,this decrease being the strongest in
thelongesttimerange (section4.5.3).Atlowermeasuringtemperatureprobablymorebondsareformedwitharelaxationtimeinthe
3
order of 10 s, since the value of the dynamic moduli increases
withdecreasingmeasuringtemperature (section4.5.3).
The decrease of themoduli with increasing T canonlybeexplained from ashift inthebalance between the differentinteraction forces governing the internal structure ofthecaseinparticles. Conformational rearrangements, particularly at the boundaries of the casein particles, are held responsible for anincrease in the number of interparticle bonds.At least electrostatic+-interactions (saltbridges)andhydrophobic interactions
are involved in both the intra- and interparticle bonds. When
temperature islowered,hydrophobicbonding insidethecaseinparticles isexpected to decrease,causing conformationalrearrangements of the protein molecules, ultimately resulting in an increase in particle voluminosity (section3.3.2)and possibly an
increase inthe number of interparticle bonds,thussuggestingan
explanation fortheobservedoppositetemperaturebehaviourofthe
dynamic moduli. Increasing temperature leading to astrongerhydrophobic bonding inside the casein particles, is also the most
obvious explanation for the effects noticed in the temperature
dependent T„ measurements (section6.5). An increasing ionic
strength, which lowers the values of the dynamic moduli, would
decrease the number of attractive interparticle electrostaticinteractions (section4.5.5.2). It is put forward that attractive
electrostatic interactions maybe responsible for theratherpermanentcharacterofacidcaseingels (section4.5.6 and4.7).
The rheological parameters of skimmilk gels,madeby thecombinedactionofacidificationandrennetinthepHrangeof4.4to
5.8,indicated acleartransitionincharacteraroundpH=5.2(section5.3.2). Above pH=5.1 the gels are subject to microsyneresis
and a rise of measuring temperature causes an irreversible decreaseofthedynamicmoduli.Theoccurrenceofmicrosyneresismay
possibly be related directly to the value of tan6 (section
5.3.2.3and 5.4), sincebothdependontherelaxationbehaviourof
190
theprotein-protein bonds.At andbelow pH=5.1skimmilkgelsmade
by combined acidification and rennet actionbehave like ordinary
acidcaseingelswith,however,considerably highervaluesofthe
moduli. Even at pH=4.6, the glycomacropeptide part of K-casein
considerably contributes to the stability of casein particles.
Proteolytic degradation of a,- and ß-casein affects the ageing
curves at longer time scales,but does not affect significantly
otherrheologicalproperties.
The interaction ofwater protons with thecaseinparticles,as
studied inthepulseNMR experiments,couldnotbedescribedbya
simple twophasemodel.Certainly more thanone kind ofboundor
immobilized water phase should be taken intoaccount.Itisclear
(section6.4.1, 6.4.2 and 6.5) that theT~ofskimmilkandsodium
caseinate solutions depends on water-protein interactions inside
thecaseinparticles.InskimmilkabovepH=5.2CCPplaysaspecial
role,butwhetherdirectorindirectisnotclear.Caseinparticle
aggregation leading togel formationhardly affectedtheT~(section6.4.1), whereas casein aggregation leading to the formation
ofcaseinparticles (section6.4.2)considerablyloweredtheT-•
191
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Vliet, T. van and Dentener-Kikkert, A. (1982). Neth. MilkDairy
J. 36, 261-265.
Vliet, T. van and Walstra, P. (1985). Neth. Milk dairy J. 39,
115-118.
Vliet,T.vanandDijk,H.J.van (1986).Tobepublished.
Vreeman,H.J. (1985).Personalcommunication.
Walstra,P. (1979).J.DairyRes. 46, 317.
Walstra, P.andJenness,R. (1984). "DairyChemistryandPhysics".
JohnWiley&Sons,NewYork.
Walstra, P., Dijk,H.J.M,van andGeurts,T.G. (1985)Neth.Milk
DairyJ. 39, 209-246.
Wood, G.B., Reid, D.S. and Elvin, R. (1981). J. Dairy Res. 48,
77-83.
Zoon, P. (1984). M. Sei. Thesis,Agricultural UniversityWageningen,theNetherlands.
197
LISTOFSYMBOLS
A
A
A
Hamakerconstant
lightabsorption
Helmholtzenergy
J
2
B
D
d
d
'2
D,
E
D„
d
f
f'
G
G
G'
G"
G*
G(t)*
Gœ*
Ge
Ge*
Gg
H
H
H
HQ
H-^
J*
h
h
h
I
I
I
permeabilitycoefficient
..
diffusioncoefficient
particlediameter
averageparticlediameter
torsionconstantoftorsionwire
cylinder
constant
torsion
constant
ofstrainwire
volumesurfaceaveragediameter
force
correctionfactor
Gibbsenergy
shearmodulus
storagemodulus
lossmodulus
complexshearmodulus
pseudo-stressrelaxationmodulus
pseudo-networkmodulus
permanentnetworkmodulus
semi-permanentnetworkmodulus
modulusofastrand
lengthofacaseingel
enthalpy
relaxationspectrum
strongexternalmagnetic field
radio frequencyfield
h/2n
Planck'sconstant
lengthofinnercylinder
heightofwheylevel
momentofinertia
ionicstrength
intensityofscattered light
m
2 -1
m.s
m
m
Nm
Nm m
m
3
N
J
Nm
Nm
Nm
Nm
Nm
Nm
Nm
Nm
Nm
m
J
Nm
Tesla
Tesla
Js
Js
m
m
Nms
M
_?
_2
_2
_2
_2
_2
_2
_2
_2
198
k
M
M
M
l
2
o
W)
^1x2^)
M
xlx2,o
M
xlx2,oi
N
Nu
N
d
P
P
i
R
R
i
o
R
e
S
S
T
R
T
m
l
T
2
T
2i
t
tanô
U
T
V
V
X
V
Y
ïa
Boltzmann'sconstant
torsionmomentexertedbytorsion
andstrainwire
totalshearmoment
netmagnetizationofalarge
number
ofmagneticmoments
netmagnetizationalongthex
--axis
netmagnetizationinthex,x~
-plane
netmagnetizationintheX-.X-plane
att=0
netmagnetizationinthex-,x,
-plane
4-1-
JK"
Nm.rad
Nm.rad
i. £.
ofthei phaseatt=0
totalnumber
numberofspinsinthespin-upposition
numberofspinsinthespin-downposition
pressure
fractionofspinsinthei
phase
radius
radiusofinnercylinder
radiusofoutercylinder
Reynoldsnumber
entropy
solubility
temperature
temperatureofmeasurement
spin-latticerelaxationtime
spin-spinrelaxationtime
i t h phase
spin-spinrelaxationtimeof
time
losstangent
energy
liquidflux
voluminosity
direction
sheardeformation
shearrate
averagemaximumsheardeformation
Pa
m
m
m
JK"1
°CorK
°CorK
s
s
s
s
J
ms"
g.g"1
s"1
199
Y
ô
e
e
magnetogyric ratio
diameter
porosity
rotation ofdriving shaft
rad.s .Tesla
m
rad
cl
e
e
e
co
e'
maximumamplitudeofrotational
oscillationofdrivingshaft
rotationofinnercylinder
maximumamplitudeofrotational
rad
rad
c
oscillation ofinnercylinder
radial displacement ofdriving shaft
rad
rad
ét
e'
H
8
K
H
(j
Mdown
p
a
T
TC
<|>
u)
w
radialdisplacementofinnercylinder
viscosity
anglebetweenmagneticmomentof
nucleusandexternalmagneticfield
wave length
magnetic moment ofa nucleus
magnetic moment parallel to the
external magnetic field
magnetic moment anti-parallel to the
external magnetic field
density
shearstress
relaxationtime
correlationtime
volume fraction
angular frequency
Larmor precession frequency
rad
Pa.s
|jm
kg.m -3
Pa
s
s
rad.s
rad.s"
200
SUMMARY
Gel formation is involved in the manufacturing of many dairy
productssuchascheese,quargandyoghurt,andlargelydetermines
thephysical structure of them.Thestructureofsuchfoodsisof
considerable importance for the perception of taste and texture
bytheconsumer.Theaimofthisstudywastoelucidatethestructure of acid casein gels, made of skimmilk and sodium caseinate
solutions. By structure notonly the character, size and spatial
distribution of the structural elements is meant, but also the
interaction forces between them. These interaction forcesdetermine the nature (strength and lifetime)ofthebondsformedina
gelnetwork.
In chapter 1 a general introduction to the subject isgiven.
The properties of the four different groups of caseinmolecules
are given in some detail, since casein isthemain componentof
acidcaseingels.Attheendanoutlineofthestudyispresented.
Inchapter 2the experimental approachisdescribed.Theexperimentswere carried outwith skimmilkandsodiumcaseinatesolutions that were reconstituted from standard powders.The samples
weremostly acidified by addingHCl inthe cold (0-2°C)to apH
of about 4.6, i.e. the isoelectrical pH of casein in milk. Gel
formation was inducedbyheating the acidified solutions atrest
to temperatures inthe range of20to50°C.Thestructureofthe
gelswasmainly studiedby rheologicalmeasurementswithadynamic rheometer, permeametry, electron microscopy and pulse NMR
methods.
The formation and spatial arrangement of acid casein gelsare
discussed in chapter 3. Skimmilk and sodium caseinate solutions
givegelswithessentiallythesameproperties.Gelformationdoes
not occur below 10°C and above 10°C at firstvery sluggishly;
but it is an irreversible process and once agel is formed,the
values of the dynamic moduli (G' and G") even considerably increaseifthetemperature isdecreasedtobelow10°C.Thedynamic
moduli, after a short lag period tend to increase linearlywith
the logarithm of the ageing time inthe temperature range of20
to 40°C. Gelation appears to be subject to an activationHelmholtz energy, which is higher for lower ageing temperatures.A
201
pronounced contribution to the activationHelmholtzenergyarises
from the stabilizing effect of the glycomacropeptide part of
K-casein.
Acid casein gels show an inhomogeneous,particulatestructure.
After acidification inthe cold thecaseinparticles inskimmilk
or sodium caseinate solutions have approximately the same size
distribution as the casein micelles in the original skimmilk;
nevertheless their internal structure is different. The inhomogeneous structure of the gel results in part from aggregation
existing at different levels: intramolecular, intermolecularbetween casein molecules of the same particles and intermolecular
between casein molecules of different particles.The gelnetwork
ultimately formed consists of dense areas of casein particles
alternating with large pores. The dense areas are built up of
smaller conglomerates and strands of aggregated particles, with
small pores inside the conglomerates.Thenumber and diameterof
the large pores (between the dense areas) determine thepermeabilityofthegel.
Chapter 4 isconcerned with the rheological properties ofthe
gels,which depend on the characterandeffectivenumberofbonds
in the gel network. The effective number ofbonds is determined
by (a)thenumber ofbondsbetweenadjacentparticlesand (b)the
number ofparticles which come understressifthenetworkisdeformed.The latter number highly dependsonthespatialdistribution and ismuch smaller than the total particle number,because
of the inhomogeneity of the gel network. Different interaction
forces,particularly hydrophobic bonding and electrostaticinteractions (salt bridges), andprobably hydrogenbonds andVander
Waals attraction will be involved in bond formation. Moreover
stericinteractions (e.g.viatheconformationofthecaseinmolecules)must alsoplay apart.Fromvariationofexperimentalconditions,suchasageingandmeasuringtemperature,ionicstrength,
ionic composition andpH clear conclusionsabouttherelativeimportance of these interactions cannotbe drawn. Itwas,however,
concluded that the internal structure of thecaseinparticles is
paramount in determining the number (and possibly life time)of
the interparticle bonds. This internal structure results from a
subtlebalancebetweenthedifferenttypesofinteractionforces.
A considerable proportion of the bonds in an acid caseingel
202
has arelaxation time inthe range of 0.6 to 6000 s.Thecharacter of the bonds may be evaluated from the loss tangent tanô
(=G"/G'), which parameter is almost independent of the spatial
distribution and thus of the number ofbonds.Intherange from
0.6 to 60sthe characterofthebondsdidnotchangedrastically
with temperature, as it did inthe range of 60to 6000 s,where
3
more bondswere formedwith arelaxationtimeintheorderof10
s when temperature was decreased; this implies the rheological
characterbecomingmoreviscous,althoughbothmoduliarelarger.
Acid casein gels thusbecome relativelymoreviscousatlonger
timescalesiftemperatureislowered,buttheyalsoshowdistinct
elastic behaviour, even at time scales of 10 sor longer.This
followed from the pseudo-stress relaxation modulus, as measured
at longtime scales;althoughmanybonds relaxed between 10 and
10 s, asignificantproportion remained longer.The timedependence of this relaxationmodulus agreedwiththerelaxationspectrumascalculated fromthedynamicmoduli.
Whenrennet is added to skimmilk acidified inthe cold, agel
canbe formed inthewholepHrangefrom4.3 to6.7 (T=20°C)and
even at 2°CatpH=4.6.Apparently theglycomacropeptide partof
K-casein, which is split offby rennet,considerably contributes
to the stability of the caseinparticles,even atpH=4.6.Around
pH=5.2 a pronounced transition inrheological properties wasnoticed. Below this pH the gels made with rennet and acid behave
like all other casein gels,whereas above thispH theyhaveproperties similar to those of normal rennet gels, for instance
showing enhanced microsyneresis at higher temperatures. The occurrence of microsyneresis was clearly correlated with thevalue
oftanô.
Theresultsofchapter6,onthespin-spinrelaxationtime (T2)
ofwater protons incasein solutionsasafunctionofpHandtemperature, confirm the change of internal structure of thecasein
particles caused by acidification. T~ depends almost exclusively
on the water-protein interaction inside the caseinparticles,in
whichcolloidalcalciumphosphate,ifpresent,willplayaspecial
part.
The most important results and conclusions are summarized and
discussed inchapter7.
3
203
SAMENVATTING
De structuur van een levensmiddel isvan grootbelang voorde
smaakgewaarwording en debeoordeling vanhetuiterlijk envande
consistentie door de consument. Een produkt waarvan deze eigenschappen niet aandewensenvan deconsumentvoldoen,zalweinig
afzetvinden,ookalisdevoedingswaardeoptimaal.Allerleimelkproduktenzijngelen,endestructuurdaarvanhangtafvandevorming en opbouw van het gel. Beheersing van degelvorming isdan
ookwezenlijkbijhetbereidingsprocesdaarvan.
Dit onderzoek is gericht op de structuur van zure caseïnegelen.Onder structuurwordthiernietalleenaard,afmetingenen
ruimtelijke rangschikking van de bouwstenen van het gelnetwerk
verstaan, maar evenzeer het karakter (levensduur ensterkte)van
debindingen tussen dezebouwstenen.Verschillende soorteninteractiekrachten, zoalsvooral hydrofobebinding enelectrostatische
interactie,maar ookwaterstofbruggen,Van derWaalsattractieen
sterische interacties kunnen hierbij een rol spelen en bepalen
medesterkteenlevensduurvandebindingeninhetgelnetwerk.
Caseïne is een verzamelnaam voor 4 verschillende groepeneiwitten, die samenongeveer 80%vanhettotalemelkeiwituitmaken.
Serumeiwitten spelen bij de hier bestudeerde gelen geen rolvan
betekenis, aangezien deze alleen door verhitting met de caseïne
kunnen reageren en degebruikte oplossingen nietwerdenvoorverhit.
Inditonderzoekwerdgebruikgemaaktvanondermelkennatriumcaseïnaatoplossingen, bereid uit standaardpoeders van constante
samenstelling. Zoutzuur werd toegevoegd, bij een zodanig lage
temperatuur (0-2°C)datgeenvlokking optrad,toteenpHvanongeveer4,6,globaaldeisoëlectrischepHvancaseïneinondermelk.
Gelvorming werd geïnduceerd door opwarmen tottemperaturenvariërend van 20 tot 50°C. De toegepaste experimentele technieken
staaninhoofdstuk2beschreven.Devoornaamstewaren:reologische
metingen met een dynamische reometer, permeabiliteitsmetingen,
electronenmicroscopieenpulse-NMRonderzoek.
In hoofdstuk 3wordt ingegaanop devorming ende ruimtelijke
opbouwvan zure caseïnegelen.De snelheidvangelvormingbleekaf
204
te hangen van een activerings-Helmholtz-energie, die afneemtmet
toename van de temperatuur.Deze activeringsenergie kanvooreen
grootdeel toegeschreven worden aandestabiliserendewerkingvan
het glycomacropeptide-deel van de K-caseïne.Gelvorming dooropwarmenvaneen inde kouaangezuurdecaseïne-oplossing iseenirreversibel proces. Afkoelen van een reeds gevormd gel doet de
elasticiteitsmodulus zelfs sterk toenemen.Beide dynamischemoduli G'enG"blijken na een korte aanloopperiode ongeveer lineair
toetenemenmetdelogaritmevandetijd.
Een zuur caseïnegelbestaatuiteeninhomogeenruimtelijknetwerk van caseïnedeeltjes. Deze deeltjes, die uit duizenden caseïnemoleculen kunnen bestaan, hebben ongeveer dezelfde diameter
(80-300 nm) als de caseïnedeeltjes in de originele ondermelk
("caseïnemicellen"), maar de inwendige structuur van dedeeltjes
isanders.Hetcaseïnegelbestaatuitgebiedenmeteenhogedichtheid aan caseïnedeeltjes, afgewisseld met relatief groteporiën.
De eerstgenoemde gebieden zijn weer opgebouwd uit conglomeraten
en strengen van geaggregeerde deeltjes,met daartussen relatief
kleineporiën.
De permeabiliteit van de gelen is vooral afhankelijk vanhet
aantal endediametervan degroteporiën,terwijldereologische
eigenschappen (hoofdstuk 4) afhankelijk zijn van het karakter
(sterkte en levensduur)enheteffectieveaantalbindingeninhet
gelnetwerk. Het effectieve aantal bindingen wordt bepaald door
(a)hetaantalbindingentussentweemetelkaarinaanrakingzijnde deeltjes en (b)door het aantal deeltjes dat onder spanning
komtte staan alshetgelwordtvervormd,m.a.w.hetaantaldeeltjes dat effectief aan de "sterkte" van het netwerk bijdraagt.
Door de onregelmatigheid van het netwerk zal dit laatste aantal
slechts een gering deel van het totale aantal deeltjes zijn.De
mate van onregelmatigheid is dus een belangrijke factor in de
sterkte van het netwerk.Uitmetingen ondervariabele omstandigheden,zoalsvormings-enmeettemperatuur,pH,ionsterkteenionsamenstelling, bleek dat meerdere soorten interactiekrachten in
en tussen de caseïnedeeltjes werkzaam zijn. Hydrofobe bindingen
enelectrostatische interacties (zoutbruggen)spelen iniedergeval een belangrijke rol. De interne structuur van de deeltjes
lijkt in hoofdzaak het karakter en het aantal bindingen tussen
205
naburige deeltjes te bepalen, waarbij bovengenoemde interactiekrachten, Vander Waals-attractie, sterische interacties (o.m.
viadeconformatievandecaseïnemoleculen)enmogelijkwaterstofbruggen een rol zullen spelen. Een kleine verschuiving in het
evenwicht tussen deze krachten kan daardoor een groot effectop
de structuurvan dedeeltjes en daarmee op dereologische eigenschappenvanhetgelnetwerkhebben.
Een aanzienlijk deel van debindingen heefteen relaxatietijd
indeordevan 0,6 tot6000s.Terkarakteriseringvandebindingen is deverliestangens tan ô (=G"/G')een geschikteparameter,
omdatdezevrijwelonafhankelijk isvanheteffectieveaantalbindingen. Indetijdschaal van 0,6 tot60sistanôvoorallezure
caseïnegelen gelijk en isevenmin afhankelijk van de temperatuur
(0°C<T<50°C).In de tijdschaal van 60tot 6000 s istanô (en
dus het visceuze karakter) groter bij lagere meettemperatuur.
Blijkbaar worden bij lagere temperatuur relatief veel bindingen
3
gevormd met een relaxatietijd in de orde van 10 s, want beide
dynamischemodulizijndangroter.
Hoewel zure caseïnegelen bij langere tijdschaal eenmeervisceus karakter krijgen, bleken ze toch bij tijdschalen van 10 s
en langer nog steeds duidelijke elastische eigenschappen tehebben. Ditbleek uitmetingenvandeschijnbarespanningsrelaxatiemodulusbijlangdurigevervorming;hoewelveelbindingenrelaxeer3 10 s,5
den in 10 tot
bleek dat een wezenlijk aantal zelfseen
nog langere levensduur heeft.Hetverloopvanderelaxatiemodulus
bleek inovereenstemming methetrelaxatiespectrum,zoalsdatuit
dedynamischemoduliberekendkanworden.
Wanneer na aanzuren stremsel aan koude ondermelk wordttoegevoegd (hoofdstuk 5),kunnen caseïnegelen gemaaktworden overeen
veel brederpH- entemperatuurgebied. Hetglycomacropeptide,d.i.
het deel van de K-caseïne dat door stremsel wordt afgesplitst,
bleek bij pH=4,6 nog eenbelangrijke bijdrage aande stabiliteit
van de caseïnedeeltjes tegen vlokking te leveren. Rond pH=5,2
treedt een scherpe overgang op in de reologische eigenschappen
van de aldusbereide gelen.Beneden dezepHhebben demetstremsel en zuurbereide gelenhetzelfdekarakteralsalleanderezure
gelen, terwijl ze boven deze pH globaal hetkarakter hebbenvan
gelenmet stremselbij depHvanmelkgemaakt.Erbleekeengoede
4
206
correlatietezijntussentanôenhetoptredenvanmicrosynerese.
Inhoofdstuk6wordtdespin-spinrelaxatietijd (T2)vanwaterprotonen incaseïne-oplossingen als functie vanpHentemperatuur
besproken. De resultaten bevestigen de sterke verandering in de
interne structuur van decaseïnedeeltjest.g.v.aanzuren.DegemetenT~ isvrijwel uitsluitend afhankelijkvandeinteractievan
dewatermoleculenmetdecaseïnemoleculenindecaseïnedeeltjes.
De belangrijkste resultaten en conclusies zijn samengevat en
aaneendiscussieonderworpeninhoofdstuk7.
207
CURRICULUMVITAE
Op 9 maart 1956 aanschouwde BasRoefs het eerste levenslicht
op de ouderlijke boerderij in het Brabantse Erp. Aldaarbezocht
hij de R.K. lagere jongensschool St.Josef. In de periode19681974doorliephijhetgymnasium-ß aanhetCollegevanhetH.Kruis
te Uden. Aansluitend begon hij zijn studie aan deLandbouwhogeschool teWageningen inde studierichtingMoleculaireWetenschappen. In april1982 slaagde hijmet lofvoor hetdoctoraalexamen,
met als hoofdvakken Kolloïdchemie en Moleculaire Fysica, en als
bijvakkenBodemscheikunde enWiskunde.Depraktijktijdbrachthij
door aan de Ruhruniversität te Bochum (BRD) in de periode meioktober1980.
Per 1februari1982 trad hijvoor eenperiodevandriejaarin
dienst van de Landbouwhogeschool als wetenschappelijk assistent
bij de sectie Zuivel enLevensmiddelennatuurkunde vandevakgroep
Levensmiddelentechnologie. Gedurende deze tijd verrichtte hijhet
onderzoekwaaruitditproefschriftisvoortgekomen.
Sinds 1juni1985 is hij werkzaam bij de afdeling winningsprocessen vanhetKoninklijke/Shell Exploratie enProduktieLaboratoriumteRijswijk(ZH).
208
NAWOORD
Een proefschrift schrijven en het verrichten van de vereiste
experimentele arbeid is zelden het werk van een enkel persoon.
Ook aanhettot stand komenvanditproefschrifthebbenvelemenseneenpraktischedanwelmorelebijdragegeleverd.Opdezelaatste bladzijde wil ik iedereen daarvoor oprecht bedanken. Enkele
mensenwilikmetnamenoemen.
Allereerstwil ikmijn ouders bedanken,diemijdegelegenheid
gavenomtegaanstuderen.
MijnpromotorAlbertPrinsbenikerkentelijkvoordevrijheid,
die hij mij gaf bij deuitvoeringvan hetonderzoek, envoorde
prettige samenwerking bij de afronding van het proefschrift. De
dagelijksebegeleidingvanco-promotorTonvanVlietisonontbeerlijk geweest voor het welslagen van dit onderzoek. Zelfs ophet
ziekbed zette Ton de begeleiding voort. De meestal korte,maar
zeer nuttige discussies met PieterWalstra zullenmij nog lang
heugen.. De morele en experimentele ondersteuning van Alizade
Groot-Mostertlatenzichnietinéénzinbeschrijven.
InhetkadervanhundoctoraalonderzoekhebbenFransdenOuden,
FransDuurland, HarryHabets, JanOlde Heuvel, EricTimmermans,
JennekeNetjes,MartinWarmerdamenJanKuileenaanzienlijkebijdragegeleverd.
Hetbereidwillig terbeschikking stellenvandeNMRapparatuur
door de vakgroep Moleculaire Fysica en de hulp van HenkvanAs
bij de interpretatie van de NMR metingen zijn zeer opprijsgesteld.
De elektronenmicroscopische foto's zijn totstand gekomenmet
dehulpvanElBouw,HermanElerie enBramBroekesteinvandeafdelingElektronenmicroscopievandeTFDL.
Aan de vormgeving van het proefschrift is bijgedragen door
dhr.C.Rijpmavandetekenkamer,dhr.A.vanBaarenenW.vanHof
van de afdeling fotografie van het Biotechnion en door mevr.
R.Treffers van de afdeling tekstverwerking van deLandbouwhogeschool.
209
DavidHome van het "Hannah Research Institute" te Ayr in
SchotlandcorrigeerdedeEngelsetekstopwerkelijkvoortreffelijkewijze.
Zonder de Brabantse gastvrijheid van Jeanne enHarrievanden
Bijgaart zouhetveelmoeilijker zijngeweestomdeafrondingvan
het proefschrift tecombinerenmeteennieuwebaanelders inden
lande.
Aan decollega's en doctoraalstudenten vandesectieZuivelen
Levensmiddelennatuurkunde heb ik goede herinneringen vanwege de
gezelligesfeerendegoedeonderlingecontacten.
Entenslotte eenwoord van dankaanallevrienden,vriendinnen
en familieleden in Wageningen en in Brabant, wier namen ikhier
niet hoef te noemen, maar die ieder voor zich weten hoezeer ik
hunbetrokkenheidbijditproefschriftwaardeer.