Advances in Colloid and Interface Science 122 (2006) 3 – 33
www.elsevier.com/locate/cis
Thermodynamic and kinetic aspects of fat crystallization
C. Himawan, V.M. Starov, A.G.F. Stapley ⁎
Department of Chemical Engineering, Loughborough University, Ashby Road, Loughborough, Leicestershire, LE11 3TU, United Kingdom
Available online 14 August 2006
Abstract
Naturally occurring fats are multi-component mixtures of triacylglycerols (TAGs), which are triesters of fatty acids with glycerol, and of which
there are many chemically distinct compounds. Due to the importance of fats to the food and consumer products industries, fat crystallization has
been studied for many years and many intricate features of TAG interactions, complicated by polymorphism, have been identified. The melting
and crystallization properties of triacylglycerols are very sensitive to even small differences in fatty acid composition and position within the TAG
molecule which cause steric hindrance. Differences of fatty acid chain length within a TAG lead to packing imperfections, and differences in chain
lengths between different TAG molecules lead to a loss of intersolubility in the solid phase. The degree of saturation is hugely important as the
presence of a double bond in a fatty acid chain causes rigid kinks in the fatty acid chains that produce huge disruption to packing structures with
the result that TAGs containing double bonds have much lower melting points than completely saturated TAGs. All of these effects are more
pronounced in the most stable polymorphic forms, which require the most efficient molecular packing. The crystallization of fats is complicated
not just by polymorphism, but also because it usually occurs from a multi-component melt rather than from a solvent which is more common in
other industrial crystallizations. This renders the conventional treatment of crystallization as a result of supersaturation somewhat meaningless.
Most studies in the literature consequently quantify crystallization driving forces using the concept of supercooling below a distinct melting point.
However whilst this is theoretically valid for a single component system, it can only at best represent a rough approximation for natural fat
systems, which display a range of melting points. This paper reviews the latest attempts to describe the sometimes complex phase equilibria of fats
using fundamental relationships for chemical potential that have so far been applied to individual species in melts of unary, binary and ternary
systems. These can then be used to provide a framework for quantifying the true crystallization driving forces of individual components within a
multi-component melt. These are directly related to nucleation and growth rates, and are also important in the prediction of polymorphic
occurrence, crystal morphology and surface roughness. The methods currently used to evaluate induction time, nucleation rate and overall
crystallization rate data are also briefly described. However, mechanistic explanations for much of the observed crystallization behaviour of TAG
mixtures remain unresolved.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Nucleation; Crystal growth; Triacylglycerol; Melts; Polymorphism; Crystal morphology
Contents
1.
2.
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1. Molecular structure and composition of fats. . . . . . . . . . . . . . . . . . .
1.2. Basic polymorphism of TAGs . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Scope of this review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamic aspects of the melt crystallization of fats . . . . . . . . . . . . . . .
2.1. Free energy diagrams and polymorph stability . . . . . . . . . . . . . . . . .
2.2. Correlating and predicting the melting temperature and enthalpy of pure TAGs
2.3. The polymorphic behaviour of pure TAGs . . . . . . . . . . . . . . . . . . .
2.3.1. Monoacid saturated TAGs . . . . . . . . . . . . . . . . . . . . . . .
⁎ Corresponding author. Tel.: +44 1509 222525; fax: +44 1509 223923.
E-mail address: [email protected] (A.G.F. Stapley).
0001-8686/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.cis.2006.06.016
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C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
2.3.2. Mixed-acid saturated TAGs . . . . . . . . . . . . . .
2.3.3. Mixed-acid saturated/unsaturated TAGs . . . . . . . .
2.4. Phase behaviour of binary mixtures of TAGs . . . . . . . . .
2.4.1. Phase diagrams . . . . . . . . . . . . . . . . . . . .
2.4.2. Modelling the solid–liquid equilibria of TAGs . . . .
3. Kinetic aspects of the melt crystallization of fats . . . . . . . . . . .
3.1. Nucleation and crystal growth rates — theoretical aspects. . .
3.1.1. Thermodynamic driving force. . . . . . . . . . . . .
3.1.2. Nucleation thermodynamics, kinetics and mechanisms
3.1.3. Polymorphic-dependent nucleation . . . . . . . . . .
3.1.4. Induction time. . . . . . . . . . . . . . . . . . . . .
3.1.5. Growth rate and mechanisms . . . . . . . . . . . . .
3.1.6. Morphology of TAG crystals . . . . . . . . . . . . .
3.1.7. Spherulitic growth. . . . . . . . . . . . . . . . . . .
3.1.8. Polymorphic transformation . . . . . . . . . . . . . .
3.2. Measurement of fat crystallization kinetics. . . . . . . . . . .
3.2.1. Induction time and nucleation rate . . . . . . . . . .
3.2.2. Overall crystallization rates . . . . . . . . . . . . . .
4. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . .
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Fats are highly abundant compounds in nature and are
widely used in food and other consumer products [1]. Their
behaviour heavily influences the microstructure and physical
properties of these products. The development of solid fat
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12
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31
31
microstructure from a liquid melt to create commercial fat
products such as margarine or chocolate is schematically
presented in Fig. 1 [2], which illustrates how both the
initial processing (within the factory) and subsequent
storage conditions (in the warehouse, shop or home)
ultimately affect final product structure, texture and quality.
Fig. 1. Schematic presentation of processes involved in crystallization and storage of fats (adapted from [2]).
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
A number of factors, including crystallization conditions,
are important.
Crystallization occurs in the initial processing stage, and
the relative rates of nucleation and growth determine the initial
crystal size distribution. This is a key parameter for texture as
crystals greater than a few tens of microns in size are
detectable on the tongue, and are thus undesirable in products
which require a smooth texture. As the solid fraction
increases, individual crystals begin to touch each other
which slows crystal growth (growth impingement). Interactions between crystals then start to dominate the process.
Depending on the nature of the fat substances, gel formation
may also occur [3].
During storage, a number of post crystallization processes
occur, which can affect properties such as hardness, which often
noticeably increases [4]. This is due to sintering, i.e. the
formation of solid bridges between crystals to form a network
[2,4,5]. Polymorphic transformation (see Section 1.2) towards
more stable phases and changes in size distribution via Ostwald
ripening may occur [6].
The above events are not necessarily chronological once
nucleation occurs. It is possible, even usual, in processing fats,
that after primary nucleation and subsequent growth that
secondary nucleation, defined as nucleation occurring due to
the presence of the growing crystals [7], can take place
simultaneously along with crystal growth and ripening.
Furthermore, polymorphic transformations may occur in the
processing stage. Transformation into the desirable polymorphic forms that deliver favourable properties is often forced
via manipulating conditions. For example, shearing and
tempering have been applied in cocoa butter crystallization
for controlling its polymorphism [8–12].
The characterization of microstructure and the relation to the
mechanical properties of the final product is a difficult (and still
largely unresolved) field of study in its own right, and readers
are suggested to consult the reviews by Walstra et al. [2],
5
Narine and Marangoni [13,14], and Marangoni [15]. It can be
seen, however, that control of the initial crystallization of the fat
is crucially important to the final quality of any fat based
product.
The crystallization of fats also determines the behaviour of
fractionation processes in which fat fractions with different
melting ranges are separated by crystallizing the higher
melting fats and filtering the slurry that is formed. The
resulting fractions are used as ingredients in food formulations and the main reason for fractionation is to tailor these
fats to improve their functionality. The crystallization
conditions in fractionation are different to those in other
food processes as growth impingement generally does not
occur and larger crystals are required to promote easy filtering
[16,17].
The study of fat crystallization is thus a valuable activity
as a greater understanding of fat crystallization enables
fractionation and food processes to operate more efficiently
and the functional effectiveness of fats in food products to
be optimised. However, before reviewing fat crystallization
in detail, it is necessary to first cover two complicating
aspects of fats — their multi-component nature and
polymorphism.
1.1. Molecular structure and composition of fats
Edible oils and fats mainly consist of a multi-component mix
of triacylglycerols (TAGs) with a small amount of other minor
components. An edible oil or fat can typically contain more than
a hundred different TAGs. A TAG is a triester of glycerol with
three fatty acid molecules, and the general chemical structure is
depicted in Fig. 2. Fatty acids consist of a hydrocarbon chain
terminated by a carboxylic acid group. The hydrocarbon chain
length ranges from 4 to 30 carbons (between 12 and 24 are the
most common). The chain usually has an even number of
carbons and is linear unless double bonds are present in which
Fig. 2. (a) A general molecular structure of triacylglycerol (R1, R2, and R3 are individual fatty acid moieties). (b) The chemical structures of a saturated and a nonsaturated fatty acid [5].
6
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Table 1
Nomenclature of commonly occurring fatty acids
Code Fatty acid
2
4
6
8
C
L
M
Chain length Double bonds Code Fatty acid
acetic acid (ethanoic acid)
2
butyric acid (butanoic acid)
4
caproic acid (hexanoic acid)
6
caprilic acid (octanoic acid)
8
capric acid (decanoic acid)
10
lauric acid (dodecanoic acid)
12
myristic acid (tetradecanoic acid) 14
none
none
none
none
none
none
none
P
S
O
E
l
R
A
B
case the chain becomes kinked. The carbon atoms of these
“linear” chains are arranged in a zigzag fashion, which has
implications for crystal packing (see next section). The physical
properties of TAGs heavily depend upon the fatty acid
composition [18].
For convenience, TAGs are usually identified by a 3-letter
code. Each of the characters in the code represents a fatty acid
with the middle character always indicating the fatty acid that is
on the 2-position of the glycerol. For example, PSP represents
glycerol-1,3-dipalmitate-2-stearate. If the three fatty acids are
the same, the TAG is monoacid; otherwise it is called mixedacid. A TAG is unsaturated if a CfC double bond is present in at
least one of the fatty acid moieties, otherwise it is referred to as
saturated. The characters used to represent fatty acids are given
in Table 1 and will be used throughout this paper.
1.2. Basic polymorphism of TAGs
TAG molecules are inherently able to pack in different
crystalline arrangements or polymorphs, which exhibit significantly different melting temperatures [19,20]. The polymorphism of most fats is based around three main forms: α, β′,
and β; the nomenclature scheme following Larsson [21] as
reviewed in Hagemann [20], Hernqvist [22], Wesdorp [23],
Sato [24], and Gothra [5]. However, some fats display more
polymorphs than this.
TAG molecules are “three legged” molecules that can pack
with the acyl chains (“legs”) in one of two configurations,
neither of which involves all three chains packing alongside
each other. They can pack in a “chair” configuration where the
acyl chain in the 2 position is alongside the chain on either the 1
or 3 positions. Alternatively, a “tuning fork” configuration can
palmitic acid (hexadecanoic acid)
stearic acid (octadecanoic acid)
oleic acid (cis-9-octadecanoic acid)
elaidic acid (trans-9-octadecanoic acid)
linoleic acid (cis-cis-9,12-octadecadienoic acid)
ricinoleic acid (12-hydroxy-9-octadecenoic acid)
arachidic acid (eicosanoic acid)
behenic acid (docosanoic acid)
Chain length Double bonds
16
18
18
18
18
18
20
22
none
none
1
1
2
1
none
none
be adopted where the acyl chain in the 2 position is alone and
the chains in the 1 and 3 positions pack alongside each other.
Either configuration naturally packs in a chair-like manner. The
stacking of these chairs can be in either a double of triple chain
length structure (see Fig. 3a), and these stack side by side in
crystal planes, sometimes at an angle. The differences between
polymorphs are most apparent from a top view of these planes
which shows the subcell structure (Fig. 3b). These structures
can be identified by powder X-ray diffraction patterns [22,24],
where long spacings give information on the repeat distance
between crystal planes (chain length packing) and short
spacings give information on subcell structure (interchain
distances). These interchain distances depend on how the
chains pack together and this is complicated by the “zigzag”
arrangement of successive carbon atoms in aliphatic chains.
Closer packing is achieved when the zigzags of adjacent chains
are in step with each other (“parallel”) as opposed to out of step
(“perpendicular”).
• The α-form is characterized by one strong short spacing line
in the XRD pattern near 0.42 nm. The chains are arranged in
a hexagonal structure (H), with no angle of tilt and are far
enough apart for the zigzag nature of the chains to not
influence packing.
• The β′-form is characterized by two strong short spacing
lines at 0.37–0.40 nm and at 0.42–0.43 nm. The chain
packing is orthorhombic and perpendicular (O⊥), that is
adjacent chains are out of step with each other so they cannot
pack closely. The chains have an angle of tilt between 50°
and 70°.
• The β-form is characterized by a strong lattice spacing line at
near 0.46 nm and a number of other strong lines around
Fig. 3. (a) Chain-length packing structures in TAGs, and (b) the subcell structures of the three most common polymorphs in TAGs (viewed from above the crystal
planes) [24]. Reprinted with permission.
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
0.36–0.39 nm. This is the densest polymorphic form having
a triclinic chain packing, in which adjacent chains are in step
(“parallel”), and thus pack snugly together. The chains also
have an angle of tilt between 50° and 70°.
The β and β′ polymorphs can exist as either double chainlength or triple chain length structures. A double chain length
structure normally occurs when the chemical nature of the three
fatty acid moieties are the same or very similar. Conversely, if
the moieties are quite different to each other (for instance in a
mixed saturated-unsaturated TAG), a triple chain-length
structure is formed. The α form is normally only found to
exist in a double chain length structure.
1.3. Scope of this review
Many efforts have been performed to unravel the complex
behaviour of fat systems. Crystallization studies are regularly
carried out for natural fats and these are classified by their
origins, e.g. palm oil and related oils [11,12,25–33], milk fats
[11,34–43] and cocoa butter [11,12,44–49]; just to mention a
few of the most recent contributions. Further reviews can be
7
found in Smith [50] for palm oil, in Hartel and Kaylegian [51]
for milk fat, and in Sato and Koyano [52] for cocoa butter. Many
other studies have investigated the blending of natural fats as
means of tailoring the physical and thermal properties of fats
[53–58].
The disadvantage of the above approach is the empirical and
case by case nature of the information obtained. This can cause
difficulties when coping with the compositional variations in
natural fats that originate from geographical, climatic, or
seasonal factors. A more fundamental approach is to study the
crystallization of fats by considering them as multi-component
systems. This is a huge challenge but has already given
extended insights on the behaviour observed in natural fats as
excellently reviewed by Sato [24,59]. This is necessarily a
bottom-up exercise, whereby an understanding of pure TAG
and binary systems must first be obtained.
This review seeks to provide an overview of the current
fundamental understanding of fat crystallization approached
from the thermodynamic and kinetic behaviour of pure TAGs
and binary mixtures of pure TAGs. Fat crystallization differs
from most industrial crystallization processes in that crystallization is seldom from a “solvent”, and thus traditional
Table 2
Literature on polymorphic and phase behaviour of pure and binary mixtures of TAGs
Author
Systems
Measurement techniques
Remarks
(A) Polymorphic occurrence and transformation of pure TAGs
Miura et al. [168]
PPP, SSS, POP, SOS, POS, POS/SOS mixtures
Ueno et al. [167]
PPP, LLL
Higaki et al. [48]
Pure and impure PPP
Smith et al. [213]
Different TAGs
Sprunt et al. [214]
SOS
Boubekri et al. [111]
SRS
Ueno et al. [110]
SOS
Dibildox-Alvarado et al. [215] PPP in sesame oil
Toro-Vazquez et al. [216]
PPP in sesame oil
Ueno et al. [66]
SOS
Rousset et al. [197]
POP, POS, SOS
Yano et al. [109]
SOS, POP, POS
Kellens et al. [95]
PPP
Arishima et al. [107]
POS
Kellens et al. [94]
PPP, SSS
Kellens et al. [93]
PPP
Arishima et al. [97]
POP, SOS
Koyano et al. [105]
POP, SOS
DSC, XRD
DSC, SR XRD
DSC, XRD
Light microscopy, DSC, XRD
FT Raman spectroscopy, DSC
FTIR, SR XRD
SR XRD
DSC, light microscopy, XRD
DSC, light microscopy, XRD
DSC, SR XRD
Light microscopy, DSC
FTIR
Light microscopy, DSC
DSC, XRD
SR XRD
SRXRD
DSC, XRD
DSC, light microscopy, XRD
Effect of
Effect of
Effect of
Effect of
(B) Phase behaviour and polymorphic transformation of binary TAG mixtures
Miura et al. [168]
POS/SOS
Takeuchi et al. [125]
LLL/MMM, LLL/PPP, LLL/SSS
Takeuchi et al. [124]
SOS/SLS
Takeuchi et al. [123]
SOS/SSO
Rousset et al. [146]
SOS/POS
Minato et al. [121]
POP/PPO
Minato et al. [122]
POP/OPO
Minato et al. [120]
PPP/POP
Engstrom et al. [128]
SOS/SSO
Kellens et al. [181]
PPP/SSS
Koyano et al. [119]
SOS/OSO
Kellens et al. [192]
PPP/SSS
Wesdorp [23]
Binary TAGs
Cebula and Smith [194]
PPP/SSS
DSC, XRD
SR XRD
DSC, SR XRD
DSC, SR XRD
DSC, SR XRD
DSC, SR XRD
DSC, SR XRD
DSC, SR XRD
DSC, XRD
DSC, XRD
DSC, XRD
DSC, SR XRD
DSC
SR XRD
Effect of ultrasound
Effect of the difference of molecule length
DSC = Differential scanning calorimetry. SR XRD = synchrotron radiation X-ray diffraction.
ultrasound
ultrasound
magnetic fields
phospholipids additives
Intermediate structured liquids
Molecular structure and interactions
Variability of morphology
Existence of molecular compounds
Phase diagram of metastable phases
Existence of molecular compounds
Existence of molecular compounds
Immiscibility of the least unstable polymorph
Existence of molecular compounds
Existence of molecular compounds
Mixing properties
Confirmation of the intermediate phase (β′)
8
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Table 3
Literature on crystallization kinetics of pure and binary mixtures of TAGs
Reference
Systems
(A) Crystallization kinetics of pure TAGs
Hollander et al. [178]
Different TAGs
Meekes et al. [217]
Different TAGs
Hollander et al. [149]
Different TAGs
Higaki et al. [48]
Pure PPP, impure PPP
Smith et al. [213]
Different TAGs
Dibildox-Alvarado et al. [215]
PPP in sesame oil
Toro-Vazquez et al. [216]
PPP in sesame oil
Rousset et al. [146]
POP, POS, SOS
Kellens et al. [95]
PPP
Kellens et al. [218]
SSS
Koyano et al. [199]
POS
Koyano et al. [106]
POP, SOS
Sato and Kuroda [92]
PPP
Zhao et al. [219]
PPP, LLL, SSS
(B) Crystallization kinetics of binary TAG mixtures
Rousset et al. [146]
SOS/POS
MacNaughtan et al. [127]
PPP/SSS
Himawan et al. [150,182,193]
PPP/SSS
Measurement techniques
Kinetic aspects
Light microscopy
Light microscopy
DSC, XRD
Light microscopy, SEM and DSC
DSC, XRD
DSC, XRD
DSC, light microscopy
DSC, light microscopy, XRD
DSC, light microscopy, XRD
Light microscopy
Light microscopy
DSC, light microscopy
DSC
Crystal growth rate and morphology
Simulation of morphology
Crystal growth rate and morphology
Induction time, effect of ultrasound
Crystal growth rate and morphology (effect of additives)
Using Avrami model for kinetic analysis
Using Avrami model for kinetic analysis
Nucleation and growth rates. Mapping of crystal morphology
Induction time, nucleation, and growth rate
Induction time and nucleation
Induction time. Direct melt and melt mediated crystallization
Induction time. Direct melt and melt mediated crystallization
Induction time
Bulk and emulsified samples
DSC, light microscopy
DSC
DSC, light microscopy
Nucleation and growth rates. Mapping of crystal morphology
Induction time and half time of crystallization
Nucleation and growth rates. Spherulite morphology
concepts of supersaturation are not helpful. A more detailed
examination of thermodynamic driving forces based upon
chemical potential relationships is needed. The thermodynamics of fats systems are thus first discussed in Section 2,
and subsequently extended in Section 3 to quantify crystallization driving forces and to examine the kinetic aspects of
fat crystallization. Tables 2 and 3 list the current literature on
the polymorphic and kinetic behaviour of pure and binary
mixtures of TAGs, on which much of this review is based.
2. Thermodynamic aspects of the melt crystallization of fats
Traditionally, a solid fat mixture is characterized by its solid
fraction content (SFC), i.e. the mass fraction of solid present at a
certain temperature. The SFC is then normally used as a basis to
predict and determine the many physical properties of the
material [60].
The typical melting temperature (i.e. normally defined as the
temperature at which the SFC is zero) and SFC characteristics
of some natural fats are shown in Table 4 [61–63]. These are
determined most importantly by the composition of the fat. For
instance, the main TAGs in palm oil are POP (22%), POO
(22%), PPO (5%), PPP (5%), POS (5%), PlP (7%), PlO (7%),
OOO (5%), and POl (3%) [50]; meanwhile those in coconut
butter are POS (46%), SOS (29%), POP (13%), PlS (3%), SOO
(2%), and SlS (2%) [52].
In this section the thermodynamic aspects of fat systems are
addressed. This begins with a general outline of polymorphism,
before focussing on individual systems. The inherently complex
nature of fats dictates that the discussion of phase equilibria is
best tackled starting with the simplest systems first, namely pure
TAGs of a single saturated fatty acid moiety (e.g. PPP, see Table
1 for the nomenclature). Increasing complexity can then be
added by the presence of double bonds and mixing different
fatty acid moieties within a TAG molecule whilst still
maintaining a single component system. Finally, the phase
behaviour of binary mixtures of different TAG molecules is
introduced.
2.1. Free energy diagrams and polymorph stability
Two types of polymorphism generally exist in lipids and
organic compounds [20,23,64]. Enantiotropic polymorphism
occurs when each polymorphic form is thermodynamically the
most stable in a particular range of temperature and pressure.
Changing the temperature or pressure to outside this range will
Table 4
Melting temperatures and SFC values of natural fats in their most stable polymorph
Fat
Butter
Cocoa butter
Lard
Palm oil
Palm kernel oil
Tallow
Melting
temperature (°C)
SFC (%) at temperature
10 °C
15 °C
20 °C
25 °C
30 °C
35 °C
Data sources
36
34
42
40
28
50
55
–
27
54
68
58
37
–
–
40
56
–
19
76
20
26
40
45
11
70
–
16
17
–
5
45
3
11
–
25
1
1
–
8
–
15
Bockisch [61]
Gunstone [62]
Bockisch [61]
Gunstone [63]
Gunstone [63]
Bockisch [61]
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
favour the transformation into a different polymorph (that which
is most stable under the new conditions) [6,65]. Long chain odd
carbon number alkanes exhibit such behaviour [23]. In
monotropic polymorphism, on the other hand, one polymorphic
form is always the most thermodynamically stable. Transformations occur from the less stable polymorphs to the more stable
ones given sufficient time [6,65].
The relative stability of two polymorphs and the driving
force for transformations between them at constant temperature
and pressure are determined by their respective Gibbs free
energies (G) — the polymorph which has the lowest Gibbs free
energy is the most stable. Gibbs free energy–temperature
diagrams are utilised to map the thermodynamic stability of the
polymorphs. Fig. 4a shows the G–T diagram for the three basic
polymorphs in TAGs from which ΔG values between phases
can be deduced. The form of the plots follows the defining
equation for Gibbs free energy as a function of enthalpy (H),
entropy (S) and temperature (T) which is:
G ¼ H−TS
ð1Þ
Due to its monotropic nature, the Gibbs free energy values
are largest for the α-form (least dense crystal packing),
intermediate for the β′-form, and smallest for the β-form
(most dense crystal packing). This is mainly a consequence of
the higher heats of fusion of polymorphs with higher melting
temperature. Each polymorphic form has its own melting
temperature, Tm, shown as the intersection points of the G–T
curves of the polymorphs and the liquid phase (Fig. 4a).
The transformation pathways among the three main polymorphs are shown in Fig. 4b and can be summarised as follows:
• The three polymorphic forms can all be directly crystallized
from the melt.
• Although any polymorph can be returned to the liquid phase
by raising the temperature above the melting point,
interpolymorphic transformations are always irreversible
(i.e. β cannot transform to β′ and β′ cannot transform to α).
• Two different modes of transformation are possible: (i)
transformations within the solid state, and (ii) a recrystallization of the more stable forms after the less stable forms have
9
melted. The latter is normally called “melt-mediated
transformation”.
• It has been found in some fat systems that a thermotropic
liquid crystalline phase exists (not shown in the G–T
diagram) as a mesophase or intermediate phase which occurs
before the crystallization of the polymorphic crystals or
during melt-mediated transformation [66–68]. In such cases,
the transformation pathway diagram becomes more complicated (Fig. 4b).
The transformations between liquid and crystalline states and
between crystalline states are all first order transitions where
there is a discontinuity in the first derivative of the free energy
[69].
2.2. Correlating and predicting the melting temperature and
enthalpy of pure TAGs
The melting temperature and the melting enthalpy of pure
TAGs are central to a thermodynamic description of solid liquid
phase equilibria in multi-component fat systems as they can be
accurately measured and can be used to construct basic free
energy diagrams assuming constant ΔH and ΔS. Here
correlations between these thermal properties and the chemical
structure of the compounds are described.
Fig. 4a shows that each polymorph in a pure TAG has its
own distinct melting temperature. As at equilibrium ΔG = 0, the
melting temperature can be written as the ratio of the enthalpy to
the entropy of melting (ΔHm and ΔSm) given by:
Tm ¼
DHm
DSm
ð2Þ
Thus one strategy for correlating melting points is to
combine separate correlations for melting enthalpy and entropy.
However, enthalpy and entropy are also difficult to correlate.
The values of ΔHm and ΔSm are governed by several factors
such as hydrogen bonding, the molecular packing in crystals
(influenced by molecular shape, size and symmetry), and other
intermolecular interactions such as charge transfer and dipoledipole interactions in the solid phase [70]. These interactions are
Fig. 4. (a) The relation between Gibbs free energy and temperature for the three main polymorphic forms of TAGs (monotropic polymorphism). (b) The polymorphic
transformation pathways in fats involving liquid crystals. Adapted from [59].
10
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
complex and it is difficult to predict them (and thus ΔH and ΔS)
with confidence. Due to such complex interactions, only limited
guidelines exist for describing the relationship between the
melting temperature of an organic compound and its chemical
structure despite the enormous amount of available melting
temperature data.
Several recent studies on the estimation of the melting
temperature and melting enthalpy of organic compounds have
been reported covering a wide variety of classes of organic
compounds. A review on this subject was given by Katritzky
[70] who classified existing correlations into three categories:
• Models utilising physicochemical and structural parameters,
such as bulkiness, cohesiveness, hydrogen-bonding parameters, and geometric factors [71–73].
• Group contribution methods in which a molecular breakdown scheme is generally employed and multiple regression
analysis is performed to determine the contribution of a large
number of molecular groups to the melting temperature [74–
78]. Usually, melting enthalpy is calculated from group
contribution methods while melting entropy consists of a
group contribution value as well as non-additive molecular
parameters. The latter represents rotational and conformational entropies [77,78].
• Estimations from Monte Carlo or molecular dynamics
computer simulations for the phase transitions and related
properties of compounds including the melting temperature
[79–82].
In the case of TAGs, saturated fatty acids are relatively linear
molecules (Fig. 2b) and thus TAGs containing only saturated
fatty acids can easily align themselves to form a compact mass.
On the other hand, unsaturated fatty acids in TAGs have kinks
in their aliphatic chains (Fig. 2b). The disrupted packing of the
unsaturated TAGs hinders the formation of crystals and causes
unsaturated TAGs to have a lower melting temperature than
saturated TAGs with the same chain length.
Molecular symmetry [83,84] and crystal packing [70,74] are
considered to be the most influential factors governing the
thermal properties of TAGs. The many different combinations
of arranging fatty acid moieties in TAGs, along with
polymorphism, means that the estimation of melting temperature of TAGs is more difficult compared to that of most organic
compounds.
The methods used for general organic compounds can,
nevertheless, be applied to TAGs. Normally, the melting
enthalpy and entropy are expressed as the sum of a contribution
of the hydrocarbon chains (depending linearly on the chain
length) and a contribution of the end and head groups
(independent of chain length) [23].
DHm ¼ hn þ h0
ð3Þ
DSm ¼ sn þ s0
ð4Þ
Here, n is the length of hydrocarbon chains, h and s are
constants that do not depend on the nature of the compound but
only on the way hydrocarbon chains are packed, thus they are
universal constants that only depend on the polymorphic form.
The other constants h0 and s0 that account for the end-group
contributions (the structure of fatty acid moieties) are specific to
each class of lipid.
Combining Eqs. (2)–(4), gives:
DHm hn þ h0
A
Tm ¼
¼
¼ Tl 1 þ
ð5aÞ
nþB
DSm
sn þ s0
with:
h
Tl ¼ ;
s
A¼
h0 s 0
− ;
h s
B¼
s0
s
ð5bÞ
This implies that if the melting temperatures of a class of
lipids have been correlated, only one data point for the enthalpy
of fusion is in principle sufficient to obtain a correlation for the
enthalpy of fusion of the complete class of lipids. However, this
is an oversimplification, as differences in chain lengths of
individual moieties need to be accounted for.
Timms [85] compiled Tm and ΔHm data of β′- and β-forms
of selected TAGs and gave regressed correlations for each
polymorphic form. Zacharis [86] used Eq. (3) to represent the
thermal data of monoacid TAGs. Perron [87,88] updated the
work of Timms [85] and published correlations for the three
polymorphic forms for saturated TAGs. Furthermore, Perron
modelled the lower melting enthalpy of unsaturated TAGs
(ΔHm,unsat) by comparing them with the corresponding
saturated TAG (ΔHm,sat) and then making an adjustment
according to the following equation:
DHm;unsat ¼ DHm;sat −115ð1−e−0:706d Þ
ð6Þ
where d is the number of double bonds in the unsaturated TAG.
Won [89] followed the approach of Zacharis [86] but applied the
equations to saturated TAGs with mono and mixed acyl groups.
However, data were only correlated with the total number of
carbon atoms and the effects of position were not considered.
Thus the fitted values were identical for different TAGs with the
same total number of carbon atoms.
Zeberg-Mikkelsen and Stenby [90] developed empirical
correlations based upon a group-contribution method which
took into account the position of the acyl groups. The
correlations were only valid for saturated TAGs which had an
even number of carbon atoms (between 10 and 22) in each acyl
group. Chickos and Nichols [74] developed simple relationships for homologous series and showed that they were
applicable to the three polymorphic forms of symmetrically
substituted TAGs. Anomalous behaviour, which was revealed in
some cases, was argued to be caused by different packing
between members of a series. Molecular modelling has also
recently been applied to estimate the thermal and transport
properties of TAGs with reasonable predictive capability [91].
Wesdorp [23] developed a model to estimate Tm and ΔHm
for different polymorphic forms of saturated and unsaturated
TAGs from a large database. He improved the method of Eqs.
(5a) and (5b) to account for the effect of position and chain
length of the three acyl groups in TAGs (symbolised by pqr).
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Two parameters were introduced x = q − p and y = r − p, where q
is the chain length of the acyl group in position 2 of the TAG
and p is the shortest chain length of the acyl group in positions 1
or 3. From many regression trials, Wesdorp [23] identified
several factors to be important in order to successfully estimate
Tm and ΔHm values of TAGs. These were (1) the length of each
chain, (2) whether the chain has an even or odd number of
carbon atoms, (3) whether the chain is saturated or unsaturated,
and (4) the molecular symmetry. It was also found that the
melting enthalpy of the β-form depended on whether it was
double chain length or triple chain length packed. Correlations
obtained for unsaturated TAGs in the study were found to be
less reliable due to the limited data available compared to those
for saturated TAGs. Although aimed at the development of an
empirical model, the work of Wesdorp [23] indicated that the
thermal behaviour of TAGs directly follows from their
molecular structure.
2.3. The polymorphic behaviour of pure TAGs
The polymorphic nature of TAGs is well established. It is
also well known that mixing different fatty acid moieties in a
TAG produces more complex polymorphic behaviour (principally the number of observable polymorphs). Thus saturated
monoacid TAGs are simplest, followed by mixed acid saturated,
with mixed acid saturated/unsaturated being the most complex
[18,59].
2.3.1. Monoacid saturated TAGs
This group of TAGs has been examined by thermal
techniques (such as DTA and DSC) more than any other
group and shows the basic α, β′, and β polymorphic forms [20].
Melting temperature and enthalpy data for the three polymorphic forms with fatty acid chain lengths ranging from 8 to
11
30 have been compiled by Hagemann [20], Wesdorp [23], and
by Zelberg-Mikkelsen and Stenby [90].
Generally, the polymorphic behaviour of TAGs with an even
carbon number are well represented by the behaviour of PPP
[67,92–95] and SSS [20,94,96] and summarised as follows (see
Fig. 5 for the SSS thermal behaviour and the structural model of
the molecular packing of each polymorph):
• The α-form is crystallized upon cooling from the melt at
moderate to high cooling rates. Remelting the α-form
induces an endotherm at a slightly higher temperature than
the cooling exotherm, but this is soon followed by an
exotherm associated with the formation of the stable β-form
[20,94].
• The β′-form crystallizes if the temperature is maintained
slightly above the melting temperature of the α-form (about
30 min induction time for SSS). Several endotherms may be
observed upon remelting caused by submodifications of the
β′-form [20,94].
• The β-form can be crystallized directly using a solvent
[20,97] or by tempering/holding (about 60 min induction
time for SSS) slightly above the melting temperature of β′form [94]. Only CCC (tricaprin) was reported to reveal
multiple β-forms [98].
The chain length of fatty acid moieties has a significant
influence on the polymorphic behaviour. Of particular note is
that the crystal packing of β′ and β forms also depends on
whether the number of carbons in the chain is even or odd
[22].
• For TAGs of C22 and longer, rapid cooling exhibits a single
exotherm associated with the formation of the α-form.
However, Hagemann [20] showed that tempering can lead to
Fig. 5. (a) Typical thermograms of monoacid saturated TAGs represented by tristearin. Adapted from [20]: cooling from the melt at 20 °C/min (dashed line), followed
by heating at 2.5 °C/min (solid line). Intermediate forms (β1′ and β2′) are observed after holding 30 min slightly above the melting point of the α-form. (b) Side-view
structural model of molecular packing of the α, β′ and β; the different between the structure of the β′- and the β-form is in their subcell structure (see Fig. 2). Adapted
from [22].
12
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
structure due to steric hindrance of the molecular structure of
odd number TAGs and the more precise packing of the β
polymorph.
Fig. 6. Melting temperatures plotted against fatty acid chain lengths of α-, β′-,
and β-forms of monoacid saturated TAGs [99]. Reprinted with permission from
the American Oil Chemists' Society.
two submodifications of the α-form with greater separation
between the two peaks as the chain length increases.
• Three different submodifications of the β′-form were
reported in even carbon numbers shorter than C16. The
third modification melted close to the β-form, the difference
in melting points decreasing wth increasing chain length
[20].
• The β′-form of odd carbon number monoacid TAGs is more
stable compared to even number TAGs [20]. X-ray
diffraction analysis indicates this is due to a closer similarity
of the crystal structure of the β′- and β-forms with odd TAGs
than is the case with even TAGs [98].
• The melting points of the α-form increase monotonically
with fatty acid chain length but those of the β′- and β-forms
show fluctuations due to the odd–even chain length effect
(see Fig. 6) as reported in hydrocarbon type materials
[20,23,99]. The trend of melting temperature versus chain
length for odd numbered TAGs is generally lower than that
for even numbered TAGs. The effect is most pronounced at
lower chain lengths and is maintained for the β polymorph at
higher chain lengths. This reflects the less packed crystal
2.3.2. Mixed-acid saturated TAGs
Mixed-acid saturated TAGs, mainly those with acids with
even carbon number chain lengths in the range 12–20, are
widely prevalent in natural fats. Modifications of polymorphic
behaviour from that of monoacid saturated TAGs result from
differences in chain length between the fatty acid moieties, and
this is also influenced by their relative positions [20,59]. This
was best described by Sato [59] when analysing the
polymorphic and thermal behaviour of the asymmetric PPn
TAGs [24,100–102] the symmetric CnCn + 2Cn TAGs [103,104].
Here n represents even chain lengths varying from 0 to 16 in
PPn and from 10 to 16 in CnCn+2Cn.
Sato and Ueno [59] observed that heterogeneity in the chain
lengths of the three acyl groups tends to reduce the gap in
stability of the β′-form and β-form such that the β-form is not
observed. This is illustrated by the behaviour of asymmetric
PPn TAGs, where β′ was the most stable form of PP6, PP8, and
PPM, while β was most stable in PP2, PP4, and PPC. The
chain-length structure of the most stable forms also varied with
increasing n from double (PP2, PP4) to triple (PP6, PP8, PPC)
and back to double again (PPL, PPM). The irregular trend of the
melting temperatures of the PPn, shown in Fig. 7a, reflects the
variation in the chain length structures.
In CnCn+2Cn TAGs, β′ was always found to be the most
stable form as no β form was observed [103]. The melting
temperatures and long spacings of the CnCn+2Cn series
increased monotonically with increasing n (Fig. 7b) as would
be expected.
The complexity of polymorphs of mixed acid TAGs is
illustrated by Fig. 8 which shows the polymorph structures of
PPC [101]. The most notable aspect is that there are various
submodifications of the β′-form of this molecule. The α-form
occurs by rapid cooling from the melt which further transforms
to β3′ (O⊥ subcell). Upon remelting, the β3′-form transforms to
the β2′-form with the same subcell type. All α-, β2′- and β3′forms are double chain length structures. A transformation from
Fig. 7. Long spacing values (open squares) and melting temperatures (closed circles) of (a) PPn TAGs [100] and (b) CnCn+2Cn TAGs [103]. Adapted from Sato and
Ueno [59].
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Fig. 8. Polymorphic transformations in PP10 [59,101,220].
the β2′-form to the triple chain length β-form proceeds at higher
temperatures. Additionally, rapid melting of the α-form induces
another β′-form showing a hexa-layered structure (β1′-6).
Many issues regarding the polymorphic behaviour in
asymmetric mixed-acid saturated TAGs remain unresolved
[59], due to the various interchain interactions of the methyl end
groups, aliphatic chains and glycerol groups [24].
2.3.3. Mixed-acid saturated/unsaturated TAGs
TAGs with unsaturated fatty acids at the sn-2 position and
saturated acids at the other positions (Sat-U-Sat) are the main
components of a number of widely used vegetable fats such as
palm oil and cocoa butter. These will be considered here to
illustrate the complexities of unsaturated systems. Particularly
commonplace are those containing oleic acid at the sn-2
position. The presence of the double bond (with the inflexible
“kink”) gives greater steric hindrance than found in completely
saturated TAGs, which forces specific structures to be formed to
enable the saturated and unsaturated fatty acid moieties to be
13
packed together in the same lamella leaflet. Consequently, this
TAG group exhibits still more complicated polymorphic
behaviour as observed in the systems of SOS, POP, POS,
SRS, and SlS [66,105–112].
Kaneko et al. [113] and Sato [24] expressed this complexity
by highlighting the importance of olefinic conformations (see
Fig. 9) in addition to the molecular chain packing (subcell
packing) and the chain-length structure. These relate to how the
aliphatic chains on either side of the double bond are twisted
with respect to the plane of the double bond. Information on
these structures can be obtained from XRD, Fourier Transform
Infra Red (FTIR) [109,114,115] and Nuclear Magnetic
Resonance (NMR) [116,117].
The polymorphic structures of all Sat-O-Sat TAGs (with Sat
being saturated fatty acid and O being oleic acid) are similar,
with the exception of POP [24,59]. Fig. 10 shows the structures
of both POP and SOS (which can be taken to be representative
of the other Sat-O-Sat TAGs) [109]. Particularly noteworthy for
this TAG group are:
• Another intermediate phase, γ can occur which has a triple
chain-length structure. The saturated and oleic acid chains of
this form are disordered with oleic acid chains packing in a
hexagonal subcell (as in the α-form) whilst the saturated
chain leaflet shows a parallel packing.
• The β′-form is a triple chain-length structure, whereby the
saturated chain leaflets form an ordered O⊥ subcell whilst the
oleic acid chain leaflets remain in a disordered hexagonal
subcell.
• In the case of the two β-forms the saturated and oleic acid
leaflets both pack in an ordered manner. There is a slight
difference in the length of the triple chain-length structure of
these two forms, and a small difference in melting
temperature of 1.5–2.0 °C.
The presence of a double bond in Sat-O-Sat TAGs generally
forces the β′- and β-forms to adopt a triple chain-length
Fig. 9. Representation of the olefinic conformations of fatty acids in TAGs containing oleic acid moieties; S–C–S′ when ω- and Δ-chains are placed in the same plane
and S–C–S when the two chains are normal to each other [113].
14
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Fig. 10. A structural model of the polymorphic behaviour in Sat-O-Sat TAGs
represented by the behaviour of POP and SOS [109]. Reprinted with permission
from The Journal of Physical Chemistry. Copyright (1993) American Chemical
Society.
structure so that the oleic acid chains are packed together and
separately from the saturated chains. The exception is the β′form of POP which forms a double chain-length structure
(Fig. 10)). This is probably because the palmitic and oleic acid
chains pack to a similar length once the kink in the longer
oleic acid chain is taken into account. This would result in a
weaker steric hindrance to the formation of a double chain
length structure than would be the case with the other Sat-OSat TAGs.
The long spacings (representing the chain-length structure)
and melting temperatures of Sat-O-Sat TAGs are presented in
Fig. 11. In general, a smooth increase of the long spacing and
melting temperature with increasing length of the saturated acid
chains is observed except for the more stable polymorphs which
show rather jagged profiles. The long spacing of the β′-form of
POP is much shorter than for the other TAGs as it forms a
double rather than triple chain-length structure (Fig. 10). An
exception to the general pattern is POS, which does not show a
γ-form and only shows a single β-form. Sato and Ueno [59]
have suggested that this might be due to the racemic nature of
POS (although the similarly racemic SOA does not show the
same behaviour).
Boubekri et al. [111] and Takeuchi et al. [112] in turn
reported that SRS and SlS exhibit similar polymorphism to the
other Sat-U-Sat TAGs, except that their polymorph stability and
thermal properties are modified significantly. In SRS, hydrogen
bonding in the ricinoleoyl chains of the β′-form is much tighter
than that in the case of SOS so that the β′-form is much more
stable. Evidence for the greater hydrogen bonding comes from
the much higher melting enthalpy and entropy of the β′-form of
SRS than in SOS and SSS [59]. In SlS, the γ-form is stabilised
due to interactions among the linoleoyl chains at the sn-2
position. Accordingly, the enthalpy and the entropy values for
the melting of γ of SlS are much larger than those of SOS and
SRS.
We have discussed here only the Sat-U-Sat TAGs to give an
impression of the complex polymorphism that can occur in fats.
Other mixed acid saturated–unsaturated TAGs also exist such as
Sat-Sat-U and Sat-U-U. For information on these systems the
reader is recommended to consult the review by Sato and Ueno
[59].
2.4. Phase behaviour of binary mixtures of TAGs
The next step up in complexity of systems is to consider
binary mixtures of TAGs. The equilibrium behaviour of a binary
mixture is best illustrated using phase diagrams.
2.4.1. Phase diagrams
Timms [118] identified four main types of phase diagram
that are commonly observed in binary mixtures of TAGs
(Fig. 12):
• Monotectic continuous solid solutions, which are formed
when the TAGs, are very similar in melting temperature,
molecular volume and polymorphism (e.g. SSS/SSE, POS/
SOS).
• Eutectic systems, which are the most commonly found, tend
to occur when the components differ in molecular volume,
Fig. 11. Long spacing values (left) and melting temperatures (right) of polymorphs of Sat-O-Sat TAGs [108]. Adapted from [59].
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
15
Fig. 12. The four main types of phase diagram in binary mixtures of TAGs (a) monotectic, continuous solid solution, (b) eutectic, (c) monotectic, partial solid solution,
(d) peritectic [118].
shape, and polymorph but not greatly in melting temperature
(e.g. PPP/SSS, POS/POP, SOS/SSO).
• Monotectic partial solid solutions form in preference to a
eutectic system if the difference in melting temperature of the
TAG components is increased (e.g. PPP/POP).
• Peritectic systems (2 solid solutions and 1 liquid) have only
been found to occur in mixed saturated/unsaturated systems
where at least one TAG has two unsaturated acids (e.g. SOS/
SOO, POP/POO).
An extensive compilation of phase diagrams of binary TAG
mixtures from the literature has been made by Wesdorp [23]
who identified three critical issues when considering such
diagrams: (i) the purity of materials used in experiments, (ii) the
stabilisation procedure for producing the most stable phase
(which must be standardised to reduce error), and (iii)
difficulties in the determination of the solidus resulting from
kinetic effects (discussed in Section 3).
Recently, binary phase diagrams have been constructed via
the use of synchrotron radiation (SR) XRD [119–125]. The
high intensity of this X-ray technique provides richer
information about the polymorphic phases and it is also
gained in real time which allows metastable polymorphs to be
characterized distinctly, in contrast to traditional methods
[125].
For binary TAG mixtures, the primary factors determining
phase behaviour are differences between the TAGs in chain
length, the degree of saturation and position of the fatty acid
moieties, and which polymorphs are involved. Different phase
behaviour is frequently observed for different polymorphs,
e.g. PPP/SSS shows complete miscibility of the less stable
forms (α and β′) but a eutectic system for the β-form
[126,127].
The effect of the differences in chain length is illustrated by
the behaviour of mixtures of two monosaturated TAGs.
Takeuchi et al. [125] studied the phase diagrams of LLL/
MMM, LLL/PPP, and LLL/SSS and after also considering that
of PPP/SSS, came to the following conclusions for binary
monosaturated TAG mixtures:
• The metastable α- and β′-forms are miscible when the
carbon numbers for the fatty acid chains of the three TAGs
differ by 2 or less. This is the case, for example, with PPP/
SSS and LLL/MMM (see Fig. 13a).
• Immiscibility of the metastable phases appears when
differences in carbon chain lengths of 4 or 6 are present
16
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Fig. 13. The effect of the difference of carbon numbers in binary saturated TAG mixtures on phase behaviour: (a) miscible metastable phases in LLL/MMM, (b)
immiscible metastable phases in LLL/SSS [125]. The melting temperatures reported are slightly higher than the onset temperatures of melting. Reprinted with
permission from Crystal Growth and Design. Copyright (2003) American Chemical Society.
such as with LLL/PPP and LLL/SSS (see Fig. 13b). Eutectic
and monotectic behaviour are observed in the β-form for the
LLL/PPP and LLL/SSS systems, respectively, with the α
form of SSS co-existing with the β form of LLL under
certain conditions.
As already mentioned, increasing the difference between the
melting temperatures of the pure TAG's shifts the phase
behaviour from eutectic to monotectic. The reasons for this are
largely unexplored [125].
In mixtures where monosaturated and mixed-acid saturatedunsaturated TAGs are combined, such as the PPP/POP system
(see Fig. 14), there is a pronounced steric effect. It is difficult for
the oleic acid chain to pack directly with PPP and this results in
Fig. 14. The effect of steric hindrance in the PPP/POP system, an example of a
mixture of a monosaturated and a mixed-acid saturated–unsaturated TAG. All
three polymorphs show eutectic behaviour [120]. Reprinted with permission
from the American Oil Chemists' Society.
limited miscibility and is reflected by eutectic behaviour for all
three polymorphic forms α, β′ and β [120].
Combining two TAGs which both contain an unsaturated
fatty acid is less problematic as like chains from either TAG can
arrange themselves together. Indeed it is sometimes the case that
two TAGs can display a synergistic compatibility and pack
more easily together than on their own. These form so-called
“molecular compounds” with a 50:50 ratio of the two
components. This is observed in systems such as SOS/OSO
[119], SOS/SSO [123,128], POP/PPO [121], and POP/OPO
[122]. As an example, the phase behaviour of the POP/PPO
system is presented in Fig. 15. The three polymorphs α, β′ and
β form eutectic phases at the 50:50 molar composition.
The properties of molecular compounds have been investigated using FT-IR and XRD, and show significant deviations
from those of the component molecules [113]. Molecular
compounds also consistently form double chain length
structures in the metastable and stable phases in contrast to
the triple chain length structures that are found in the stable
polymorphs of the pure TAG components. These molecular
compounds also crystallize faster than the pure components of
the same polymorph [59,123].
The formation of molecular compounds impacts upon the
performance of fractionation processes, as only limited
separation is thus experienced. On the other hand this can be
useful for blending purposes [59,119].
2.4.2. Modelling the solid–liquid equilibria of TAGs
With the plethora of binary phase diagrams in existence for
TAGs, it is useful to be able to condense this information into a
(relatively) small number of parameters by the use of modelling.
This also potentially enables extensions to be made to describe
ternary and higher systems.
The equilibrium condition for a multi-component system
with a liquid phase and at least one solid phase can be described
as the point where the chemical potential of each component (i)
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
17
Fig. 15. Formation of molecular compounds in the mixture of unsaturated TAGs (PPO/POP): (a) the most stable phase and (b) metastable phases; C represents
molecular compounds [121]. Reprinted with permission from The Journal of Physical Chemistry B. Copyright (1997) American Chemical Society.
in each phase is equal to that in any other phases present [129],
i.e.:
lLi ¼ lSj
i
ð7Þ
where μiL and μiSj are the chemical potentials of each component
i in the liquid and the jth solid phase, respectively. The chemical
potential of component i in a mixed phase p (solid or liquid) is
given by:
lpi ¼ lpi;0 þ RT lnðgpi xpi Þ
ð8Þ
p
is the chemical potential of the pure component i in
where μi,0
the respective phase, xip is the mole fraction of component i and
γip is the activity coefficient for component i.
Substitution of Eq. (8) into Eq. (7) results in the equilibrium
condition for component i:
!
Sj
lLi;0 −lSj
gSj
i;0
i xi
ð9Þ
ln L L ¼
RT
gi xi
p
p
To evaluate the right hand side of Eq. (9), let dμi,0
= − Si,0
dT
p
p
p
+ Vi,0dP (where Si,0 and Vi,0 are the pure component molar
entropy and molar volume of the p phase for component i,
respectively, P is pressure) and ΔSi,0 = ΔHi,0/T (where ΔHi,0 is
the change of molar enthalpy upon melting of pure component
i). Using these definitions we obtain:
d Dli;0 ¼ −DSi;0 dT þ DVi;0 dP
DHi;0
dT þ DVi;0 dP
¼−
ð10aÞ
T
or
dðDli;0 Þ
DHi;0
DVi;0
¼−
dP
dT þ
RT
RT 2
RT
ð10bÞ
A simplification of Eq. (10b) can be made by assuming the
following:
• The reference temperature is the melting temperature of the
pure component i at the system pressure, Tm,i(P). Thus the
effect of pressure does not need to be considered further
(dP = 0).
• The change in molar enthalpy can be represented by
ΔHi,0 ≅ ΔHm,i,0 + ΔCpi,0(T − Tm,i), where ΔHm,i,0 is the
molar enthalpy of melting of pure component i at the
reference temperature Tm,i and ΔCpi,0 is the molar heat
capacity difference between the liquid and solid for the pure
component i (assumed to be independent of temperature).
Integration of Eq. (10b) and substitution into Eq. (9) results
in [60,130]:
!
Sj
Dli;0 DHm;i;0 DT DCpi;0 DT
gSj
i xi
ln L L ¼
¼
−
RTm;i;0 T
RT
RT
gi xi
DCpi;0
Tm;i;0
þ
ln
ð11Þ
R
T
where ΔT = Tm,i − T.
Eq. (11) relates the equilibrium compositions in the two
phases (left hand side) to the system temperature (right hand
side). These equilibrium compositions are heavily dependent on
the activity coefficients, and to describe the equilibrium
conditions, the effect of composition and temperature on the
activity coefficients (in Eq. (11)) must be appropriately
modelled. This is usually only required for the solid phase
activity coefficients as the liquid phase can generally be
assumed to be ideal. Prausnitz [129] elaborately describes the
existing thermodynamic models for such a purpose.
The simplest case is where there is a large difference in
melting points. The high melting component essentially forms a
pure crystal (xiS = 1). Both liquid and solid activity coefficients
are unity and Eq. (11) is rearranged and reduced to the so-called
Hildebrand equation (where xi in Eq. (12) is the mole fraction
of the high melting component in the liquid phase):
DHm DT DHm 1 1
¼
−
lnxi ¼
ð12Þ
RTm T
Tm T
R
Of course, the activity coefficients also dictate the mixing
behaviour of the system in both the liquid and solid phases. If it
is possible for the overall system Gibbs free energy to be
18
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Fig. 16. Modelling of the phase diagram of the stable phases in binary TAG mixtures [23]. Examples are shown for PSP/SPS which forms a eutectic (left) and for PPP/
POP without a eutectic point (right) [60].
reduced by splitting the solid into two different solid fractions of
different compositions then immiscibility will occur. This
generally requires activity coefficients to be greater than unity.
The thermodynamic modelling of binary solid liquid
equilibria involving solid solutions has been applied to many
different areas of application. An example is the long chain
hydrocarbons (waxes), which exhibit non-ideal mixing (activity
coefficients deviate from unity) in both liquid and solid phases.
Investigations have thus focused on finding the appropriate
model to describe activity coefficients for liquid and solid
phases and then assessing the capability of binary parameters to
describe the multicomponent mixtures [131–137]. Equations of
state have also been applied in this particular case [138]. The
use of thermodynamic models in the food area has also recently
been reported [139–142], and Tao [143] has reviewed their
application in material science.
Despite the usefulness of thermodynamic modelling in many
other areas of application, there has been relatively little work
on modelling the solid–liquid equilibria of TAG mixtures [60].
Wesdorp [23] studied the mixing behaviour of TAG mixtures in
the liquid phase and three different polymorphic forms. He
found that melts of TAG mixtures and solid solutions of αpolymorphs behave as ideal mixtures (as long as the difference
of chain length does not exceed 15 carbon atoms) while β′- and
β-forms exhibit significantly non-ideal behaviour. Based on
those findings, a thermodynamic model to describe the phase
behaviour of multi-component fats was proposed.
The excess Gibbs energy for all solid phases, ΔGES, was
successfully fitted using a 3-suffix Margules equation (see Eqs.
(13) and (14) for binary systems). A drawback of this equation
is the lack of a rational base for its extension to multicomponent systems. It is generally assumed that the contributions of the binary parameters (A12 and A21 in Eqs. (13) and
(14)) to the excess Gibbs energy in the multi-component
mixture are the same as in the binary mixture at the same
relative concentrations.
DGE ¼ ðA21 x1 þ A12 x2 Þx1 x2
RT lng1 ¼ x22 ½A12 þ 2ðA21 −A12 Þx1 ð13Þ
RT lng2 ¼ x21 ½A21 þ 2ðA12 −A21 Þx2 ð14Þ
All 4 types of binary TAG phase diagram [118] have been well
simulated by the 3-suffix Margules equation. Examples are shown
in Fig. 16 for eutectic and non-eutectic binary TAG mixtures [60].
Binary interactions parameters of various TAG combinations have
been documented [23] and have been used to simulate the SFC of
fats containing many TAG components; showing reasonably good
agreement with experimental data [23,60,144,145]. A similar
approach was employed by Rousset et al. [146] to characterise the
equilibrium states of binary mixtures of the POS/SOS system
which was then used to define the crystallization driving forces for
a kinetic study (see Section 3.1.1).
Having demonstrated the ability of the 3-suffix Margules
equation to simulate phase diagrams of TAG mixtures, Wesdorp
[23] attempted to theoretically estimate the binary interaction
coefficients needed in the Margules equation by evaluating the
degree of isomorphism [147] and lattice distortion and thus
produce a predictive model. However, reliable correlations were
not achieved.
Ideally, thermodynamics should give a firm foundation for
predictive models of SFC provided the compositions of the fat
mixture are known. By extracting binary interaction coefficients
between the triacylglycerol components in the mixture, it is
possible to extrapolate to ternary and more complex mixtures
[23,60,146]. In practice, however, kinetics cannot be neglected
due to the often slow process of fat crystallization [144,145] and
the presence of metastable regions. Yet thermodynamic aspects
are critical since equilibrium information of a fat mixture will
enable the driving force of crystallization to be quantified and
establish a benchmark for the kinetic behaviour. The kinetic
aspects will now be addressed.
3. Kinetic aspects of the melt crystallization of fats
Although a solid becomes the thermodynamically stable
phase when a melt is cooled down below its melting
temperature, this liquid–solid transition does not occur spontaneously. The occurrence of a solid phase in its early stages
requires two distinct events: (1) the formation of nuclei in the
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
mother phase followed by (2) the advancement of the faces of the
nuclei resulting in crystal growth. In fat systems, it has been
proposed that an ordering process of molecules into lamellae
acts as a precursor to the formation of a crystalline solid phase
[24,51] (see Fig. 17a). This process follows a path through
transitory states that requires energy barriers to be overcome as
shown in Fig. 17b for different polymorphic forms [148].
The finite diffusion rates of molecules in the liquid and solid
phases and the arrangement and subsequent attachment of
molecules onto the surface of growing crystals all contribute to
the kinetics of the overall process [149]. Consequently, kinetic
factors are as important as thermodynamic ones in determining
which polymorph will form from the melt and the amount,
composition and properties of the crystalline phase. Examples
of these kinetic effects are described below.
(a) Polymorphic occurrence
Usually fats crystallize first in the least stable polymorph
with the lowest energy barrier (α) and later transform or
recrystallize to more stable polymorphs (β′ or β). Direct
crystallization of β′- or β-forms from melts tends to occur only
when no supercooling, or sometimes little, of the less stable
forms is present. Fig. 18 shows the kinetic phase diagram of
PPP/SSS [150] upon linear cooling at different cooling rates.
Depending on the cooling rates applied, either α- or β′-forms
crystallize. This illustrates the strong influence of kinetics on
polymorphic occurrence in fats.
(b) Composition gradients within crystals
Differences in composition between the outer and inner
regions of a crystal are thought to occur during a slow cooling
crystallization as described in Wesdorp [23] and Los et al.
[144,145]. This would be due to the higher melting components
preferentially solidifying during the early stages of crystal
growth which are then depleted from the liquid melt. The low
19
Fig. 18. Effect of kinetics on the polymorphic occurrence in the binary PPP/SSS
system at a number of cooling rates [150]. Tm,α is the equilibrium temperature of
the α-form. The β′-form crystallised at 0.5 and 1 K min− 1 in PPP-rich mixtures
(shown as open symbols).
diffusion rate in the solid phase hampers the inner part of the
growing crystals to reach equilibrium with the liquid phase as
the composition of the liquid phase changes, whereas the
surface composition is much closer to equilibrium. The crystals
are ultimately inhomogeneous in composition having a
concentration gradient between the centre and the surface of
the crystal. However, although the concept of a composition
gradient within crystals is plausible, as far as we know no
experimental proof has been published.
(c) Crystal perfection
Fig. 17. (a) Simplified schematic representation of ordering in the liquid state of TAGs preceding the formation of a crystalline solid phase [24,51] (reprinted with
permission). (b) Energy barrier diagrams for the three main polymorphic forms of a TAG at a given conditions below their melting temperatures. Adapted from [148].
20
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Poorly packed crystals can result from rapid crystallization
[67,151,152]. The thermal properties of such imperfect crystals
deviate significantly from those of well-ordered ones. Imperfect
crystals may persist for years in the absence of a liquid phase
[20] but can easily recrystallize into well packed crystals via the
liquid phase if a liquid phase is present [22].
Los et al. [130,144,145] extended the work of Wesdorp [23]
by implementing a simple kinetic expression into the “flash”
calculation of multi-component TAG mixtures. They showed,
via simulation using thermodynamic parameters from Wesdorp
[23], that the effect of kinetics on the prediction of the SFC of
fat mixtures is substantial. However, comparisons with experimental data were not presented.
It is clear that kinetic factors should be considered in order to
describe properly the crystallization behaviour of fats. In the
following sections aspects characterising the dynamics of fats
crystallization are examined.
3.1. Nucleation and crystal growth rates — theoretical aspects
3.1.1. Thermodynamic driving force
The fundamental thermodynamic driving force for the crystallization of a component i is the difference in chemical potential of i (Δμi) between the liquid (μiL ) and solid (μiS) phases.
The chemical potentials are formulated as in Eq. (8), and thus:
Dli ¼ lLi −lSi ¼ Dli;0 þ RT ln
gLi xLi
gSi xSi
ð14aÞ
Substituting in the expression for (Δμi,0) from Eq. (11)
yields:
Dli DHm;i ðTm;i −T Þ DCpi ðTm;i −T Þ
¼
−
RTm;i T
RT RT
DCpi
Tm;i
gL xL
ln
þ
þ ln iS iS
R
T
gi xi
ð14bÞ
However, in almost all cases in the literature, one of two
simplified approaches is used [148,153].
(a) Liquid-solution approach
The first approach represents the fat blend as a mixture of
two pseudo-components that are immiscible in the solid state.
The pseudo-component with the higher melting temperature is
considered to be the solute, while the one with lower melting
temperature is the solvent. This is normally applied when fats
contain two families of distinctly different TAGs [2,31,154].
The approach is similar to most studies of industrial
crystallization, where the crystallization driving force is
modelled as the result of supersaturation. Thus for a liquid
phase of a defined concentration of solute, the difference
between the saturation concentration is evaluated (at the same
temperature). The saturation composition (xiL,eq) is that which is
in equilibrium with the forming solid phase (xiS), which can
related by Eq. (9) thus:
ln
gSi xSi
gL;eq
xL;eq
i
i
!
¼
Dli;0
RT
ð15Þ
Combining Eqs. (14a) and (15) and eliminating (Δμi,0)
results in:
!
!
gSi xSi
gLi xLi
gLi xLi
Dli ¼ RT ln L;eq L;eq þ RT ln S S ¼ RT ln L;eq L;eq
gi xi
gi xi
gi xi
ð16Þ
In many cases, the liquid phase of multi-component fats is
nearly ideal due to the relatively similar size and structure of the
component molecules [23], i.e. γiL,eq ≈ γiL ≈ 1. Eq. (16) is thus
further simplified to:
Dli iRT ln
xLi
xL;eq
i
ð17Þ
L
For small supersaturations (xiL/xi,eq
< 1.1) a further approximation via a Taylor expansion yields Δμi ≅ RT[(xiL − xiL,eq)/ xiL,eq].
Frequently, s ≡ (xiL − xiL,eq)/xiL,eq is used as an approximation to the
crystallization driving force, particularly at low supersaturations,
considering that concentrations are relatively easy to measure.
Sometimes, (xiL − xiL,eq) is also used [155,156]. For high supersaturations (xiL/xiL,eq > 1.1), Eq. (16) should be used.
A limitation of this method is that it is reliant on the
availability of an equilibrium liquid concentration for the solid
phase. This cannot be evaluated if the sample temperature is
below the solidus, in which case a different approach is called
for.
(b) Liquid-melt approach
When fats are composed of relatively similar component
TAGs, it is often assumed that crystallization can be described
as occurring from a pure melt. Thus the last term in Eq. (14b) is
neglected. A further simplication can also be made by
neglecting the second and third terms on the right-hand side
of Eq. (14b), which for fats are at least two orders of magnitude
smaller than the first term, where ΔT = Tm,i − T is not larger than
10 K [130]. This gives:
Tm;i −T
Dli iDHm;i
ð18Þ
Tm;i
According to the latter equation, the driving force is thus
proportional to the difference between the actual temperature
and the melting temperature.
Note, however, that for very complex systems such as natural
fats which have many different TAG components, the definition
of the above crystallization driving force becomes ambiguous as
melting typically occurs over a broad range [51] and a single
representative melting point is difficult to establish in a way that
can be consistently reliable under different conditions. Different
polymorphic forms can also crystallize concomitantly to
hamper accurate melting temperature identification. A reasonable strategy in some circumstances is to apply a global
supercooling approximation [5]. The global melting temperature of the complex melt mixture is defined to be the highest
temperature at which solid phases can exist and are about to
disappear. The difference between the crystallization temperature and this global melting temperature is regarded as the
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
driving force of crystallization [28]. If this does not appear to
work satisfactorily then recourse should be made to Eq. (14b).
3.1.2. Nucleation thermodynamics, kinetics and mechanisms
The formation of nuclei is an early stage of solid phase
formation. Theoretical models are well known for nucleation
from a solution [157,158], and from a melt [159,160]. Classical
nucleation theory visualises the event as bimolecular reactions
of growth units. The Gibbs free energy of the system, ΔGhom,
changes due to the decrease of free energy per unit volume
arising from the enthalpy of fusion, − ΔGV, and the increase of
the surface energy due to the surface tension, ΔGS. For
spherical nuclei of isotropic pure substances undergoing
homogeneous nucleation this yields the familiar equation:
4
DGhom ¼ −DGV V þ DGS S ¼ − pr3 DGV þ 4pr2 r
3
ð19Þ
where V, S and r are the volume, surface and radius of the
cluster respectively; σ is the surface energy. ΔGhom increases
with r until a critical (maximum) value ΔGhom⁎ is reached at a
critical size r⁎, i.e. when dΔGhom/dr = 0. Any clusters larger
than r⁎ = − 2σ/ΔGV decrease the free energy when they grow
and hence become more stable. Eq. (17) gives for ΔGV ≅ − ΔH
(ΔT/TmVm), where Vm is the molar volume of the clusters, and
ΔT = Tm − T is the supercooling. The critical free energy, the
activation energy barrier, of nucleation can thus be written as:
DGhom ⁎ ¼
16 pr3 Vm2 Tm2
3 ðDHm DT Þ2
ð20Þ
Thermodynamic considerations yield the energy barrier for
nucleation and the critical nucleus size, but not the nucleation
rate (the number of nuclei formed per unit volume per unit
time). It is normally postulated that for a particular value of
Δμ (= ΔGhom) a cluster size distribution arises which follows
the Boltzmann distribution and thus the density of the critical
size clusters (Chom⁎) can be expressed as Chom⁎ = Noexp
(− ΔGhom⁎/kT), where No is the number of molecules per
unit volume, and k is the Boltzmann constant [6,153]. As
only clusters greater than the critical size are able to grow
into a stable crystal, the frequency of nuclei formation (Jhom)
turns out to be proportional to Chom⁎, as well as the maximum
molecular frequency of collision, given by kT/h where h is
Planck's constant:
Jhom ¼
NA kT
−DGhom ⁎
exp
h
kT
ð21Þ
and where NA is the Avogadro number.
Note, however, that there are other barriers to nucleation as
molecules must diffuse to the nucleus site and adopt the
appropriate configuration to the surface of the growing nuclei.
These barriers lead to additional diffusive and entropy terms
[159]. The diffusive term reflects the fact that as the
temperature is lowered the diffusion rate falls caused by an
increase in the viscosity of the melt or solution. The entropy
term can be significant for long and flexible TAG molecules.
21
The loss of entropy due to the incorporation of molecules into
a nucleus is given by ΔSm = ΔHm/Tm. The probability of the
fraction, αS, of molecules in the melt with suitable conformation
to incorporate to the surface of nuclei is exp(− αSΔS/R).
However, one often assumes this conformation barrier is
⁎ ),
included in the expression for the diffusion barrier (− ΔGdiff
hence Eq. (21) becomes:
NkT
−DGdiff ⁎
−DGhom ⁎
exp
exp
ð22Þ
Jhom ¼
h
kT
kT
In real solutions, nucleation is substantially accelerated due
to the presence of impurities which act as catalytic nucleation
sites [6,148,153]. In fat processes these can be the vessel wall,
impellers, mono- or diglycerides and other minor lipids, as well
as dust particles.
TAGs thus almost always undergo heterogeneous nucleation
since they are normally impure [5]. The activation energy is
lower than that of homogeneous type (a result of the catalytic
action of foreign substances). Consequently, the supercooling
required is also reduced. The activation energy for heterogeneous nucleation can be related to that for homogeneous
nucleation as ΔGhet⁎ = ΔGhom⁎f(θ), with θ represents the wetting
characteristics of foreign solid impurities by the supercooled
melts [6]; thus a similar expression to Eq. (22) applies.
Another nucleation mechanism is secondary nucleation
which is caused from (1) fragments of growing crystals that
are mechanically chipped off and which act as new nuclei, (2)
the generation of small crystals due to collisions of crystals with
other crystals as well as with parts of the crystallizer, and (3) the
disturbance of the (pseudo) static condition of the liquid
lamellae by the presence of crystal lattices leading to a lamellae
alignment which enhances the nucleation event [7,151,161].
These mechanisms are more likely to be important in industrial
scale crystallizers.
A potential tool to control the polymorphic crystallization
of fats is to provide “ready made” crystal nuclei via the
addition of crystal seeding. The polymorphic forms of the
seeds must be in the same forms of the targeted forms to
nucleate from the mother phase which are mostly the β′- or βforms [24]. Additionally, at molecular level, the chemical
structure of the seed TAGs is also of paramount importance.
Takiguchi et al. [162] suggested, postulating from the template
effects of fatty acid thin films on the crystallization of long
chain n-alcohols, that the chain length of the fatty acid
moieties should not differ by more than 4 carbon numbers.
Sato [24] found that in order to crystallize TAGs which
contain unsaturated fatty acids, the seed material should also
have an unsaturated fatty acid moiety to be effective. This
reflects the immiscibility of those TAGs which are fully
saturated with those which contain unsaturated fatty acid
moieties, as discussed in Section 2.4.1 (Fig. 14). Lastly, and
perhaps this is obvious, the melting temperature of the seed
material must be such that it does not itself melt when added
to the liquid phase of the crystallizing material. BOB and SOS
have been shown to be quite effective for controlling the
polymorphic nucleation of cocoa butter [163–166].
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C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
3.1.3. Polymorphic-dependent nucleation
In monotropic polymorphism, as is the case with TAGs, there
is only one truly stable solid polymorph below the melting
temperature, the others being only meta-stable. However, if
more than one polymorph possesses a positive driving force for
crystallization then nucleation and growth rates are decisive in
determining polymorphic occurrence (see Fig. 18). Empirically,
this is described by Ostwald's rule of stages [6], which states
that the thermodynamically less stable phase is always formed
first and a step-by-step phase change may then occur towards
the most stable one.
Three main factors influence the polymorphic-dependent
nucleation of TAGs:
• Supercooling (ΔT), which if increased leads to higher
nucleation rates (Eq. (20))
• The interfacial free energy of the crystals (σ) which is
normally smaller for the less stable forms (α < β′ < β)
• The ordering dynamics from a random conformation of
liquid TAG molecules to a densely packed conformation of
the crystalline state [6,123].
ΔT must be positive for a polymorph to form but of those
polymorphs which possess a positive ΔT it is the interfacial free
energy term that is usually decisive. Lower melting polymorphs
have lower values of σ and so they will form if they can.
Ostwald's rule of stages is thus explained by the competition to
nucleate among the polymorphic forms; the phase with the
highest nucleation rate will form preferentially [6].
The Ostwald rule of stages in TAGs, however, can be
overridden if external influences are present such as local
pressure and temperature fluctuations (e.g. by ultrasonic
stimulation), template and seeding [24]. These are used in
industry to manipulate the crystallization of fats.
Tempering, which applies certain temperature-time protocols
and frequently involves shear, is often employed in order to
induce the nucleation of the more stable polymorphs. As the
more stable phases are too slow to crystallize from the melt
directly, a tempering protocol (e.g. thermal annealing) allows
the formation of the less stable form followed by its
transformation to the desired form either by direct transformation or via melting of the less stable phase. Additionally, if a
mixture of unstable and stable polymorphs occurs, then raising
the temperature will melt out unstable polymorphs and leave
seed crystals of the stable polymorph. This procedure is the
most common technique for controlling polymorphic fat
crystallization in chocolate confectionery.
The introduction of shearing has been found to significantly
accelerate the formation of certain polymorphic forms
[8,9,10,11,12,45]. Mazzanti et al. [11] argued that macroscopic
shearing can provoke the alignment of less stable polymorph
crystals that in turn will induce a higher transformation rate into
a more stable phase. Mazzanti et al. [12] then reported that
increasing the shearing rate does not influence the nucleation
rate of the less stable phase but it does affect the rate of the
formation of the more stable phase which is transformed from
the less stable phase. So far, only limited explanations have
been made of the effect of shearing on fat crystallization kinetics
[24]. Most studies on the effect of shearing have been conducted
on natural fats. A better understanding might be obtained by
conducting a systematic study on pure or well-defined TAG
mixtures.
Recently, ultrasound and magnetic fields have been
examined as other potential candidates to control the polymorphic nucleation of fats [48,167,168]. The creation of local
pressure and thus higher local supersaturation may induce faster
nucleation rates.
3.1.4. Induction time
According to nucleation theory (see Section 3.1.2), a critical
cluster size distribution must be established before nucleation
starts. It can be imagined that when the melt is cooled down
rapidly from well above its melting temperature, the number of
clusters will barely have exceeded zero by the time the
crystallization temperature is reached [169]. An induction or
incubation time, tind, is required to develop such a cluster size
distribution [170]. This induction time can be long (hours) for
relatively large TAG molecules [148]. In many nucleation
studies, including those involving TAGs, researchers have
tended to correlate tind as inversely proportional to the
theoretical homogeneous/heterogeneous nucleation rate
[7,171], although induction time and nucleation rate represent
distinctly different physical phenomena. From Eq. (22), this
yields:
h
−DGdiff ⁎
−DGhom ⁎f ðhÞ
tind i1=J ¼
exp
exp
:
NA kT
kT
kT
ð23Þ
3.1.5. Growth rate and mechanisms
The growth rate from melts can be controlled by either the
attachment rate of growing units at the crystal surface (surface
kinetics) or by the transport of mass to or heat from the growing
surface [161].
The factors affecting the growth of TAGs can be grouped
into two main categories, namely factors that are governed by
the bulk crystal structure and those which are dictated by the
nature of the mother phase [6]. Fig. 19 shows these relationships
schematically.
In fat systems it is regularly presumed that surface kinetics
are rate controlling [2]. The primary evidence for this is that
dissolution or melting rates (which are heat and mass transfer
limited, but not surface kinetics limited) can often be orders
of magnitude faster than the growth rate for the same driving
force. There are also mechanistic arguments that surface
kinetics are important as a great number of conformational
changes are needed before a molecule can properly fit into the
crystal lattice, and this also allows a chance for detachment to
occur in the meantime. This conformational hindrance of
TAG molecules causes relatively slow crystal growth rates of
the order of 0.01–0.1 μm/s at Δμ/RT values between 0.5 and
1.5 [2]. It has been observed using AFM that the
advancement of a smooth crystal front in TAGs progresses
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
23
Fig. 19. Flow chart showing the interrelationships of factors affecting the morphology and growth rate of TAG crystals.
via the creation of two-dimensional nuclei on the surface
[172].
The effect of chain length on the growth rate of TAGs is
significant. Fig. 20 shows that the linear growth rates of
monosaturated TAGs (CCC, LLL, PPP, and SSS) reduce as the
chain length increases. This might be attributed to the time
needed for the ordering of the methyl chains — the longer the
chain, the longer the ordering time.
The crystallization of fats does also release a considerable
quantity of latent heat (as much as 200 kJ kg− 1) [2]. At a
microscopic level, the transport of this heat away from the
crystal surface into the bulk liquid can be of importance. Los
and Mitovic [173] recently showed from computer simulations
that heat transport in molecular systems, such as in fat mixtures,
may be more important than mass transport, as opposed to
atomic systems such as the solidification of alloys. Kloek et al.
[31] roughly estimated that heat transfer may increase the
interfacial temperature by about 1 K at the half crystallization
time (i.e. when the solid content has reached 0.5), which is a
significant amount.
Mass transport can reduce the overall growth rate if, for
instance, a significant increase in viscosity occurs leading to a
decrease in diffusivity [5,174]. Walstra et al. [2] argued that this
is unlikely in fat system as only moderate supercoolings are
normally applied in fat crystallization. Hollander et al. [149],
however, showed that at high supercooling, the solution and
melt crystallization of pure and binary mixtures of TAGs is
transport limited. An interesting example is shown in Fig. 21.
The growth of pure CLC at low Δμ shows a non-linear
Fig. 20. Growth rates of monosaturated TAGs with different chain lengths. The
growth rates of tricaprin (CCC) and trilaurin (LLL) were collected from [212]
and those of tripalmitin (PPP) and tristearin (SSS) (β′-form) from [182]. The
growth rate of 30% SSS in PPP/SSS system is also shown [182].
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C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
Fig. 21. Growth rate versus crystallization driving force curves of pure CLC and
with 10%-w addition of LLL [149].
dependency on the driving force, which suggests that surface
kinetics are dominant [6]. The growth rate is thus proportional
to the surface nucleation rate on the crystal surface [5,175].
This explains the non-linear growth rates at low Δμ (in Fig. 21)
as nucleation rates, as a rule, vary exponentially with driving
force.
This trend changes to a linear relationship at high Δμ.
Furthermore the addition of a small amount (10%) of trilaurin
has a significant effect on reducing the growth rate at high Δμ,
but not at low Δμ. These are both evidence for mass transfer
control. It is argued that because a trilaurin molecule is too large
to fit into CLC crystals it does not affect surface integration.
However, trilaurin does build up a layer surrounding the
growing crystals and this is important when mass transport
becomes controlling at higher driving forces. It is not clear yet
whether this behaviour applies generally for all TAGs as
Hollander et al. [149], on the other hand, also found that the
growth rate of PSP showed a linear dependency on Δμ even at
reasonably low driving forces. The reason for these apparently
contradictory findings is unclear.
The solid–liquid interface, being dependent on both the
crystal structure (internal) and the nature of the mother phase
(external), plays a critical role in crystal growth. Two distinct
interfaces are recognised: (i) smooth or faceted surfaces and
(ii) rough interfaces. The former are characterised by an
atomically immediate change in the degree of crystalline order
across the solid–liquid boundary. On the other hand, the rough
interface can be described as being structurally diffuse, with a
degree of crystalline order that varies continuously over the
scale of a few atomic planes across the solid–liquid boundary
[176].
An entropy factor, defined as ΔHm/kTm, can be used as an
internal parameter to indicate the likely smoothness of a
growing surface [177]. Highly anisotropic materials with high
entropy factors such as TAGs (with ΔHm/kTm ∼ 60) exhibit
smooth surfaces if the planes are densely packed, but planes
which are much less densely packed can easily experience
roughening [5]. Hollander et al. [172] showed using AFM that
different surfaces of a TAG under the same crystallization
conditions can grow by different mechanisms. The highly
asymmetric shape of TAG molecules causes different packing
densities in different crystal planes [178]. Accordingly, different
surfaces of a TAG crystal can exhibit significantly different
surface roughnesses so that the growth rates of different planes
at the same conditions can differ greatly, resulting in needle
shape crystals [179]. This is in contrast to other materials which
have a relatively low entropy factor, and generally possess
rough surfaces. The attachment of growth units is relatively
easy in such cases and results in fast and unstable growth, for
example dendritic growth.
Two distinctly different mechanisms for roughening have
been observed. “Thermal roughening” occurs when a surface is
exposed above a particular temperature called the “roughening
temperature” [161]. Above this temperature, growth units attach
to the surface very quickly as they are more easily able to
overcome the attachment energy. Alternatively, rough surfaces
can be created at high crystallization driving forces, where mass
transport is controlling, and growth units will easily attach onto
the crystal surface wherever they come into contact. This is well
known as “kinetic roughening” [180]. As rough surfaces grow
much faster than smooth ones, in the frame of morphology
development, the rough surfaces ultimately disappear and are
not observed in the final habit.
In multi-component systems there is competition between
similar TAG molecules for vacant sites, and thus the growth
rates are generally slower than that of pure TAGs. Kellens et
al. [181] observed that PPP/SSS mixtures with an equal
composition of PPP and SSS had a half-time of crystallization
of the β′ solid solution in between those of pure PPP and pure
SSS. Himawan et al. [182] confirmed this behaviour after
measuring growth rates using light microscopy (see Fig. 20).
The exception to this rule is when molecular compounds are
formed [2]. Takeuchi et al. [123], and Sato and Ueno [59]
showed that the crystallization rate of molecular compounds in
binary TAG mixtures is significantly faster than the rates for
pure components, presumably because steric hindrances are
much reduced.
As mentioned previously, solid solutions of TAG molecules
are frequently formed especially in metastable polymorphs. The
composition can vary between the inner and outer regions of a
crystal as higher melting TAGs preferentially deposit first and
diffusion rates in the solid phase are low, so that such
composition gradients persist. There is a further issue of
segregation kinetics of TAG components during the growth of
TAG solid solutions. Kirwan and Pigford [183] presented an
approach to estimate the composition of a growing solid
solution from multi-component melts. They assumed spiral
growth to be the growth mechanism and derived the segregation
kinetics accordingly. Los and Floter [130] proposed a method to
obtain kinetic phase diagrams for multi-component TAG
systems. The model was derived for growth at rough surfaces,
thus using linear supersaturation dependency on crystal growth
(linear kinetic segregation). Los et al. [144,145] showed
significance differences between simulated equilibrium solid
solution compositions and those estimated when also including
kinetic factors. Subsequently, Los and Matovic [173] also
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
25
included the transport mechanisms into the kinetic expressions
and estimated the importance of mass and heat transfer on
different systems. However, experimental validation of this
procedure has not been carried out.
The segregation issue, however, has been tackled in
metallurgy regarding the solidification of alloys. The definition
of thermodynamic driving forces and the segregation kinetics
have been well developed in this field [184–186]. The challenge
to apply such approaches to fat systems is still open.
3.1.6. Morphology of TAG crystals
The overall morphology (shape) of a crystal is fundamentally determined by the relative growth rates of different
crystal surfaces. The slower the advancement rate of a
crystal surface, the higher the probability that the surface
will have a large surface area in the final crystal habit. As
mentioned in the previous section, the anisotropic nature of
TAG crystals results in large differences in growth rate
between surfaces.
TAG crystals of different polymorphs, as the term suggests,
exhibit various morphologies. Under the microscope the α-form
produces an amorphous mass of very tiny crystals, the β′-form
is generally a bulky shape or spherulitic, while the β-form is
usually a needle shape [59]. Although it is often found that fat
crystals grow as spherulites, enormous variations can occur
depending on the crystallization conditions, even for the same
TAG system [95]. Fig. 22 shows morphology-maps depicting
the habit variations during the isothermal crystallization of
binary TAG mixtures (POS/SOS) as functions of TAG
composition and temperature [146].
Traditionally, the morphology of a crystal is estimated by
employing surface energy theories such as the Bravais-FriedelDonnay-Harker (BFDH) theory [161,180], which assume that
the crystal faces advance at rates proportional to their surface
energies. The equilibrium shape of a crystal is ultimately
achieved when the total surface free energy of existing crystal
surfaces is minimised. The free energy of a surface can thus be
related to the distance between the face and the central point of
the crystal body [6,187].
Alternatively, morphology can be predicted using the
attachment energy as the growth-controlling parameter, as in
the Hartman-Perdok (HP) theory [180,188]. The attachment
energy here represents the amount of energy that is lost when a
crystal is cut along the plane of a crystallographic orientation.
The growth rate of the plane of that orientation is assumed to be
proportional to its attachment energy.
However, the surface energy and the attachment energy
methods, which are solely based on thermodynamics (knowledge of crystal structure), have not been able to completely
explain experimentally observed TAG crystal morphologies
[178,189]. Hollander et al. [149,178] showed that the aspect
ratio of the needle β- and β′-forms of different saturated TAGs
model systems was underestimated by the morphology
estimation procedure using the attachment energy.
Therefore in order to reproduce the experimentally observed
morphology of TAG crystals, the growth mechanism (kinetics)
and roughness of each crystal surface must be taken into
Fig. 22. A map of volume fractions of the various crystal morphologies upon
isothermal crystallization of the POS/SOS system with different compositions
(a) 75/25, (b) 50/50, (c) 25/75 [146]. Reprinted with permission from the
American Oil Chemists' Society.
account [149,178–180,190]. Fig. 23 shows a comparison
between experimental TAG morphologies and those estimated
from the surface energy theory (BFDH), the attachment energy
algorithm (HP), and the attachment energy algorithm combined
with the Burton-Cabrera-Frank screw dislocation theory (HPBCF) [161] for the β′-form of PSP and for the β-form of PPP.
Clearly, kinetic factors are predominant since the experimental
morphologies are much better predicted by the latest methods.
The application of this approach for multi-component fats,
however, is a challenge.
3.1.7. Spherulitic growth
In most cases, pure TAGs and mixtures of TAGs grow as
spherulites. A spherulite is an aggregate made up of many
crystalline ribbons that grow radially from the same central
nucleus (Fig. 24) [148,149]. The ribbons that build up the
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C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
surfaces where the completion of a layer is not necessary, thus
secondary nucleation can occur simultaneously in different
layers resulting in more diffuse structures (Fig. 24b).
The spherulitic growth of TAGs can be described by the
Hoffman-Lauritsen or surface nucleation theory that has been
widely applied to polymer crystallization [191]. The model
assumes that the progression of the spherulite front is controlled
by secondary nucleation at the frontal surfaces of the
spherulites. The relation between the spherulitic growth rate
and the driving force is given by:
Rspherulite ¼ R0 exp −
Fig. 23. Morphology of the β-form of PPP and the β′-form of PSP as (i)
calculated using the surface energy theory (BFDH), (ii) calculated using the
attachment energy theory (HP), (iii) calculated by means of the attachment
energy combined with screw dislocation growth mechanism (HP-BCF), and (iv)
observed from experiments [172].
spherulite are in many cases needle-like (Fig. 24a). The reasons
for this morphology to exist in TAGs have been discussed
earlier. Often irregular structures are observed where some
distortions are possible and the interface with the liquid may be
diffuse (see Fig. 24b).
The difference between the morphologies of the TAG
spherulites shown in Fig. 24 is due to differences in the
magnitude of the driving force, which causes changes to the
mechanism of the secondary nucleation of crystal layers. At low
to moderate driving force the progression of the front is layer by
layer. This means secondary nucleation is slow enough to
ensure that one layer is completed before the next layer is
created (Fig. 24a). Higher driving forces can induce rougher
U⁎
KR
exp −
RðT −Tl Þ
T ðTm −T Þ
ð24Þ
where Rspherulite is the linear growth rate of the spherulite, R0
is the pre-exponential factor, U⁎ is the activation energy
related to entropy and diffusion barriers (equivalent to ΔGdiff
in Fisher-Turnbull equation, see Eq. (22)), T∞ is a hypothetical
temperature where the motion associated with viscous flow
ceases, and KR is the kinetic parameter. A linear correlation is
obtained when plotting lnRspherulite versus 1/T(Tm − T), which
assumes a relatively constant value of [lnRo − U⁎/R(T − T∞)].
Both Rousset et al. [146,148] and Himawan et al. [182] have
used this equation to model TAG spherulitic growth. Fig. 25
shows the equation applied to the PPP/SSS system showing
two different correlating fits arising from the different
nucleation mechanisms (and morphologies) at different driving
forces.
3.1.8. Polymorphic transformation
Transformations between phases (liquid, α, β′, and β) are an
important factor in the processing and storage of fats (see
Introduction). As fats exhibit monotropic polymorphism, the
transformation among polymorphs is irreversible in the
direction of less stable to more stable phases. This can proceed
via a solid–solid or a melt-mediated transformation.
The solid–solid transformation mechanism in fat systems is
still poorly understood. Hagemman [20] suggested that the
change from the vertical α-form to the tilted β′-form is
suspected to occur via a collapse of hydrocarbon chains or from
Fig. 24. Spherulites of β′-polymorph crystallized from 30%-w SSS of PPP/SSS binary mixture at (a) 52.5 °C, (b) 49 °C. The field of view of the pictures is 200 μm
across [182].
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
27
in SOS significantly increased the complexity of the transformation. Of particular interest was that:
• During the transformation from the α-form into the γ- or β′forms, the SR-XRD long spacing spectra occurred earlier
than the short spacing spectra. This indicated that the
formation of lamellar ordering occurred more rapidly than
that of subcell packing. The time lags between the spectra
became shorter for the less stable polymorphs (for instance
for the γ-form compared to the β′-form).
• Liquid crystal phases were observed if a very rapid meltmediated transformation occurred from the α-form to the
β′-form.
Fig. 25. The application of the Hoffman-Lauritzen theory to model spherulite
growth in 30/70 PPP/SSS mixtures. The units of Rspherulite are 10− 3 μm s− 1
[182]. Two different fits are possible depending on morphology, resulting from
different nucleation mechanisms at different driving forces.
a bending of each molecule in the glycerol region. Dafler [152]
interpreted his DSC data to suggest a two step mechanism
during the β′- to β-form transformation. The first part, which is
fast, may be regarded as a thermally activated process; the
second, slower, process is speculated to be dependent on the
concentration of the β-form already present. Due to the more
restricted molecular arrangement in the solid state the rate of
this transformation mode is much slower than that of meltmediated transformations.
Melt-mediated crystallization can be viewed as the melting
of the less stable form followed by the subsequent nucleation
and growth of the more stable forms. Mass transfer occurs in the
liquid formed by the melting of the less stable form [24]. These
events most probably occur concurrently within a sample which
makes it difficult to measure them separately.
Traditionally, DSC is used for characterising polymorphic
transformations, but recently synchrotron radiation (SR) XRD
has been applied to pure TAG systems [66,93,94,110], binary
TAG mixtures [120–122,192], and natural fats [12,44–46].
This has been able to provide molecular-level insights of the
polymorphic transformation of fats. A review on this subject
can be found in Sato and Ueno [59].
Kellens et al. [93,192] presented SR-XRD spectra of the melt
mediated polymorphic transformation from the α-form into the
β-form in a pure PPP system. During the α→β transformation,
the β′-form could be seen for a very short time. This is barely
detectable by DSC, although this is more obvious in mixtures of
PPP and SSS [181,193]. SR-XRD was also able to show the
sequential ordering in the β-form subcell arrangement from
time lags between the appearance of the three XRD spacings
associated with the β-form.
Ueno et al. [66,110] studied the melt-mediated transformation of SOS, and found out that the presence of the double bond
It is implied from observations in the PPP and SOS systems
that there are potentially enormous variations of mechanism
during the melt-mediated polymorphic transformation of fats.
A number of researchers have reported that the crystallization rate, for instance, of the β′-form, from the melt of the
α-form (the α-melt) is much faster than that from the
supercooled melt. The explanations, however, vary. Some
workers argued that this is due to a molecular arrangement in
the liquid phase [20,194]. Hagemman [20] reported that the
tuning-fork conformation of TAGs associated with the lamellar
arrangement already exists above the melting temperature.
Relaxation data on primary glycerol carbons of a rapidly
heated α-form were different from those from an undercooled
liquid at the same temperature. Another possibility is that nonmelted high melting TAGs may act as seed materials,
accelerating the crystallization rate of the more stable phase
[195]. For some fats involving unsaturated moieties, it has also
been suggested that liquid crystalline phases might be involved
[66–68,110,196].
3.2. Measurement of fat crystallization kinetics
In order to characterise crystallization kinetics, nucleation
and crystal growth rates should ideally be measured
separately. Neither nucleation nor growth rate measurements
are straightforward in TAGs. Only a few attempts to directly
measure nucleation and growth rates have been reported
[31,146,154,197]. Inadequate resolution of existing instruments to identify solid particles at the length scale of nuclei
limits nucleation rate measurements, whilst the irregularity
and aggregative form of TAG crystal morphologies hampers
accurate crystal growth rate characterization. This remains a
major challenge in the characterization of lipid crystallization
[198].
3.2.1. Induction time and nucleation rate
The induction time, tind, has been regularly chosen as a
mean of characterising the crystallization kinetics of TAGs and
fats in general [55,92,198–200]. A diverse range of measurement techniques have been employed to measure tind ranging
from DSC [28], light transmittance [201], turbidimetry [198],
pulsed nuclear magnetic resonance [198], laser-polarised light
turbidimetry [33,202], polarised light microscopy (PLM)
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[171,200,203], viscometry [27], PLM supplemented by a CdS
photo sensor [106,199], and diffusive light scattering (DLS)
[30]. PLM and DLS are considered to be the most sensitive.
This does not guarantee, however, that the measured tind
reflects the real induction time since, for instance, the smallest
identifiable crystal by PLM is approximately 0.2 μm [200],
while Timms [151] has estimated that the nuclei critical size is
about 0.01 and 0.001 μm at 3 and 7 °C supercooling,
respectively.
Measured tind values thus depend on the instrument
employed. They have also been interpreted in one of two
ways. Some investigators regard tind to contain both nucleation
and growth information: tind ≅ tnucl + tgrowth. In this sense, tind is
the total time needed to form the nuclei and then to grow to a
size, which is observable by the instruments used, and as such
is often used as a representative measure of the overall
crystallization kinetics. Example data are shown in Fig. 26
from Sato and Kuroda [92] who used PLM with a CdS sensor
to measure induction times for PPP at various isothermal
temperatures. This shows fast, intermediate, and slow kinetics
for α, β′, and β polymorphs, respectively, and reflects
Ostwald's rule whereby nucleation favours the least stable
polymorphs. Similar findings were obtained for POP and SOS
[106], and in POS [199]. The induction time has also been
utilized for comparing the rates of melt and melt-mediated
crystallizations.
Other researchers assume that tind predominantly represents
the nucleation rate. Takeuchi et al. [123] for instance interpreted
tind as nucleation dominated and used it to qualitatively show
the faster nucleation of the α-form of the SOS/SSO molecular
compound compared to pure αSOS and αSSO. Frequently, tind is
correlated inversely with the expression for nucleation rate, J,
from the Fisher-Turnbull relation (see Eq. (22)). Combining
Eqs. (20) and (23) results in:
!
h
DGdiff ⁎
16 pr3 Vm2 Tm2
tind ¼
exp
f ð hÞ
exp
NA kT
kT
3 kT ðDHm DT Þ2
ð25Þ
A further assumption for TAG systems is that the main barrier
to diffusion is entropic and arises from molecular conformation
issues (i.e. ΔT is moderate or even low, but the flexibility of the
three fatty acid chains is enormous) leading to ΔGdiff⁎/kT = αSΔS/R. Rearranging Eq. (25) results in:
Ttind
!
h
aS DS
16 pr3 Vm2 Tm2
exp
¼
f ð hÞ
exp
NA k
R
3 kT ðDHm DT Þ2
ð26Þ
Thus from a plot of ln(Ttind) against 1/T(ΔT)2, a slope, sind,
can be obtained which allows the estimation of the activation
energy of nucleation from ΔGnucl = ΔGhom⁎ f (θ) = simdk/(ΔT)2.
However, this approach has weak theoretical and practical
foundations when considering that (i) the Fisher-Turnbull
equation was derived for pure systems and (ii) the induction
time is a physically distinct phenomenon from nucleation rate.
Nevertheless, it is commonly applied to characterize the
Fig. 26. Inverse induction times for the crystallization of PPP polymorphs. The
melting temperatures of the polymorphs are indicated (αm, βm′, βm) [92].
Reprinted with permission from the American Oil Chemists' Society.
nucleation kinetics of natural fats such as palm and other
vegetable oils [26–30,171,203], cocoa butter [46,49], and milk
fat [37,39,40,43,53]. Using this approach, ΔGnucl values were
estimated and used to illuminate the significant differences in
nucleation energy barriers between polymorphic forms. Surprisingly, there have been few attempts to apply such a method
to pure TAGs or well-defined TAG mixtures. We recently
performed such an attempt for the PPP/SSS mixtures as shown
in Fig. 27, which resulted in a much larger value of energy
barrier for the β form compared to the β′ form [127].
It should be noted that the use of t ind for kinetic
characterization is also limited to a certain range of isothermal
crystallization temperatures, as below a certain temperature the
tind value becomes so short that isothermal conditions cannot be
established in the sample before nucleation begins [200]. This is
especially true for the α-form crystallization [127]. Nonisothermal crystallization methods have been introduced to try
to characterize the crystallization kinetics of this polymorph
[150,193,204].
3.2.2. Overall crystallization rates
A plot of total solid content versus time during an isothermal
crystallization of fats exhibits a sigmoidal shape [205]. This is a
result of simultaneous nucleation, growth and the so-called
impingement effect, i.e. the colliding of growing crystal faces of
neighbouring crystals that slows down growth and thus the
overall crystallization process. Nucleation is the predominant
event at the initial stage, growth in the following stage, but
impingement is the predominant factor towards the end of the
crystallization process [155].
In order to describe properly the whole crystallization
process, each event must be well-characterised. However, it is
difficult to measure these overlapping events separately. The
overall sigmoidal curve is reasonably quantifiable using various
measurement techniques such as DSC, pulsed NMR, turbidity,
time resolved XRD, viscosity change, and ultrasound velocity
measurements (see reviews in Foubert et al. [205] and
Marangoni [15]). Hence, the characterisation of crystallization
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
29
crystal volume can be calculated. A correction is finally made to
allow for impingement effects assuming that volume increases
are proportional to the liquid volume fraction still remaining.
After some mathematical arrangements, a simple equation can
be derived as follows:
Xsolid ¼ 1−expð−kt n Þ
Fig. 27. Linear correlation between ln(Ttind) and 1/T(ΔT)2 for β′ and β
polymorphs in PPP/SSS mixtures [127]. Reprinted with permission from the
American Oil Chemists' Society.
kinetics of fats is routinely carried out via the analysis of the
experimental sigmoid curve.
The interpretation of the sigmoid curve has been performed
using various models. Rousset [148] and Foubert et al. [205]
have compiled a review of the existing models used in fat
crystallization. The existing models can be divided into
deterministic, numerical, and stochastic approaches, Rousset
[148]. The deterministic approach incorporates nucleation,
growth, and impingement events with some assumptions
leading to a simple equation to fit the time evolution of the
solid fraction. The Avrami model (also known as the JohnsonMehl-Avrami-Kolmogorov equation), the Gompertz model, and
the aggregation-flocculation model are examples of this
approach [205]. An analytical model that incorporates the
evolution of size distribution along the melt crystallization is
also available [155,156]. The numerical approach is theoretically similar to the deterministic one but uses more complicated
expressions for nucleation and growth rates. The resulting
equations cannot be solved analytically and thus numerical
integration must be applied [148]. Stochastic models visualise
nucleation and growth as statistical/probabilistic events. A 2- or
3-dimensional space is defined in which the evolution of the
solid/liquid interface, and thus the evolution of solid content,
can be obtained as time progresses [148].
The Avrami model [206,207] is frequently used to describe
the isothermal crystallization kinetics of fats [205]. This model
is based upon a geometrical framework which mimics the actual
crystallization process of nucleation, crystal growth and
impingement. Nucleation is modelled by the number of nuclei
per unit volume (NJ), and this is assumed to be either “sporadic”
where NJ linearly increases with time or “instantaneous” where
NJ is fixed number created at time zero (equivalent to a “seeded”
crystallization). Once formed, nuclei grow at a constant rate in
one, two, or three dimensions from which an unimpinged
ð27Þ
where Xsolid is the solid fraction, k is a constant depending
on the nucleation rate, nucleation mode (instantaneous/
sporadic) and on the growth rate, while n depends on the
nucleation mode and the growth morphology (see Foubert et
al. [205]).
Violations of the assumptions made in the Avrami model are
likely to occur in fat crystallization. For instance, the growth
velocities are assumed to be constant throughout the transformation which is not the case in multi-component systems where
the crystallization driving force can vary substantially. Fitting
the sigmoidal crystallization curve with the Avrami model often
gives a non-integer n parameter which is difficult to explain
physically. A mathematical model mimicking reversible reaction kinetics has also been proposed by Foubert et al. [47]. This
generally provides acceptable fits to data but the fitted
parameters do not have as much physical meaning as those of
the Avrami model. The challenge thus remains to develop more
realistic models which will undoubtedly require numerical
rather than algebraic integration. This must be obviously in
accordance with the development of reliable measurement
techniques.
In many multi-component fat systems, it is frequently
observed that the sigmoid curve appears to exhibit a two-step
transformation [12,15,44]. It has been proposed that the
isothermal crystallization of multi-component fats is initiated
by the formation of the α-form followed by a subsequent
transformation to a more stable phase β′-form. Modifications of
the Avrami model to fit this crystallization curve have been
proposed [12,15].
4. Concluding remarks
TAGs are not only commercially useful materials but their
crystallization behaviour is also academically interesting.
TAG systems can be made to be very simple (such as a pure
TAG system where all the fatty acid moieties are identical
and saturated, such as PPP) to very complex, naturally
derived fats containing hundreds of TAGs with seemingly
limitless combinations of fatty acid moieties. The behaviour
of TAGs is ultimately dictated by the molecular structures of
the TAGs in the system (the fatty acid mix) and how they are
able to pack together in crystals in the various polymorphic
forms available. Heterogeneity of fatty acid moieties in a
TAG results in more complicated behaviour, in particular
different lengths of fatty acids in a mixed-acid TAGs, and
TAGs containing both saturated and unsaturated fatty acid
moieties. Incompatibility of TAGs due to differences in chain
length and degree of saturation leads to immiscibility in the
solid state. However, in special cases where the molecular
30
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
shape of TAG components is compatible to each other, chainchain interactions can provoke the formation of molecular
compounds at a composition of 50/50.
Both thermodynamic and kinetic aspects need to be
considered to gain a full understanding of fat crystallization
behaviour, and it is useful to be able to classify behaviour
according to whether they are caused by thermodynamics,
kinetics or both.
Thermodynamics is able to establish the stability (or metastability) of different polymorphs, and the miscibility or
immiscibility of different TAGs in mixed crystals. It also
enables the driving force for crystallization to be quantified,
which provides a benchmark for the modelling of nucleation
and growth rates and the surface roughness of crystals. To date
either supersaturation or supercooling has generally been used
for this purpose, but for fat systems which display an almost
continuous spectrum of melting points a definition based upon
the rigorous expression for chemical potential differences
(using pure component melting data and activity coefficients)
is required to model individual driving forces for each
component. Only a very limited number of studies can be
found regarding the description of solid–liquid equilibria of
polymorphic systems via activity coefficient expressions. This
is largely also due to the lack of reliable experimental data for
the estimation of thermodynamic parameters.
Kinetics is however required to explain many other
phenomena, apart from the obvious practical consideration of
the timescale over which crystallization proceeds. Polymorphic
occurrence, for example, cannot be explained by thermodynamics which would always predict the most stable polymorph
to be formed. Instead it is governed by the kinetics of the
polymorph which is able to nucleate first. Kinetics factors also
dictate the relative advancement rates of different crystal
surfaces and thus the overall crystal morphology.
Although our understanding of fat crystallization is extensive
there remain many gaps in our knowledge. Much of this is due
to our inability of make precise measurements of the nucleation
and crystal growth rates of TAGs. This is partially solved by the
determination of overall crystallization kinetics and the use of
models such as the Avrami equation, but the assumption that the
driving force, nucleation and crystal growth rates do not vary is
often too simplistic. It is additionally worth stating that in a
number of industrial applications fat crystallization occurs in
dispersions (emulsions) which introduces its own complications
[208–211].
In nucleation studies, induction time measurements are
commonly made, whereas nucleation rates (the number of
nuclei appearing per unit time and per unit volume) are seldom
measured. It is often assumed that induction times represent the
reciprocal of the nucleation rate despite the fact that they are
distinctly different physical phenomena.
Spherulitic growth is common in TAGs but crystal growth
mechanisms are not well understood. Most of the work in the
past has assumed that surface integration kinetics are
dominant, yet more recent data have shown the importance
of transport processes. A general theory is not yet currently
available.
The segregation of components during the growth of
TAGs solid solutions needs to be investigated in order to
describe properly the growth and overall crystallization
kinetics of TAGs. This requires some method of following
the crystallization of individual components in fats. This is
difficult as TAGs are chemically very similar to one another.
Other than retrospective analyses of fractionation experiments few studies have investigated this aspect of fat
crystallization.
A great deal has been learned about the crystallization
behaviour of fats in the past half century, but it is clear that much
remains to be achieved. For example, food engineers do not
have access to the sort of simulation software which designers
of distillation columns are now routinely able to turn to,
whereby merely entering the composition of an input stream
and a choice of processing parameters allows a complete
simulation of a process to be made via vapour–liquid
equilibrium calculations. A similar tool to predict solid–liquid
equilibria in fat crystallization processes, in which TAG
composition of a fat blend is entered in a similar fashion
along with process conditions, is still a long way off. Although,
the theoretical framework for the equilibrium phase behaviour
of binary systems is now well established, this still needs to be
extended and properly validated for multi-component systems.
These solid–liquid equilibria can (in theory) be handled in an
analogous manner to vapour–liquid equilibria in distillation
column simulators, and it is quite feasible (again, in theory) to
extend the database to cover the various different fat interaction
parameters required.
However, as already mentioned, a proper model of fat
crystallization will need to extend beyond that of solely
predicting phase equilibria if it is to be a truly useful tool, as
the kinetic aspects of nucleation and growth also need to be
taken into account. An additional consideration is how many
of the hundreds of different TAG and non-TAG components
present in natural fats need to be included in a working
model, or can one make do with grouping many of the less
abundant components into “pseudo-components” without
causing problems? Trace components can cause problems in
nucleation, for example, which is liable to be heavily
influenced by small quantities of high melting fats which
act as seed crystals and it may be difficult to establish their
presence by analytical techniques. The surface integration of
molecules into growing crystals can similarly be upset by
small quantities of impurities. Add to that the need to predict
polymorphic occurrence, inter-polymorphic transformations (if
any), crystal morphology and size distribution and one can
readily conclude that such a model would need to be highly
sophisticated.
Nomenclature
Abbreviations
AFM Atomic Force Microscopy
BCF
Burton-Cabrera-Frank
BFDH Bravais-Friedel-Donnay-Harker
DLS
Diffusive Light Scattering
C. Himawan et al. / Advances in Colloid and Interface Science 122 (2006) 3–33
DSC
Differential Scanning Calorimetry
FTIR Fourier Transform Infra Red
HP
Hartman-Perdok
NMR Nuclear Magnetic Resonance
PLM
Polarised Light Microscopy
SFC
Solid Fraction Content
SR-XRD Synchrotron Radiation X-ray Diffraction
TAGs Triacylglycerols
XRD
X-ray diffraction
Acknowledgements
The authors wish to acknowledge and thank the BBSRC
(UK) for funding this work (grant reference D20450).
References
Symbols
Aij
G
H
h
Jhom
k
KR
NA
NJ
P
R
r
r⁎
Ro
Rspherulite
S
sind
T
tind
Tm
U⁎
V
Vm
xpi
Xsolid
Binary parameters in the 3-suffix Margules equation
Gibbs free energy
Enthalpy
Planck constant
Homogeneous nucleation rate
Boltzmann constant
Kinetic parameter in the Lauritsen-Hoffman
equation of spherulite growth rate
Avogadro number
Number of nuclei per unit volume
Pressure
Universal gas constant, (8.314 J mol− 1K− 1)
Cluster radius
Critical radius
Pre-exponential factor in Lauritsen-Hoffman
equation of spherulite growth rate
Linear growth rate of spherulite
Entropy
Slope in the determination of ΔGnucl
Temperature
Induction time
Melting temperature
Activation energy related to entropy and diffusion
barriers in the Lauritsen-Hoffman equation
Volume
Molar volume of clusters in the nucleation theory
Mole fraction of component i in phase p
Solid fraction
–
J mol− 1
J mol− 1
Js
# m− 3 s− 1
J K− 1
J mol− 1
# mol− 1
# m− 3
kPa
J mol− 1 K− 1
m
m
–
m s− 1
J mol− 1 K− 1
K
s
K
J mol− 1
m3
m3
–
–
Greeks
αS
γpi
μpi
σ
θ
ΔCpi
ΔG
ΔGdiff
ΔGE
ΔGhet⁎
ΔGhom⁎
ΔGnucl
ΔGS
ΔGV
ΔH
ΔHm
ΔS
ΔSm
ΔT
Fraction of molecules in the melt with
suitable conformation to incorporate to the surface
of a growing nuclei
Activity coefficient of component i in phase p
Chemical potential of component i in phase p
Surface energy
Wetting characteristics of foreign solid impurities
by the supercooled melts
Molar heat capacity difference between liquid and
solid for component i
Free energy difference
Activation energy related to diffusion barriers
Excess free energy difference
The critical free energy (the activation free energy)
of heterogeneous nucleation
The critical free energy (the activation free energy)
of homogeneous nucleation
The activation energy of nucleation
The surface free energy
The volume free energy
Enthalpy difference
Melting enthalpy
Entropy difference
Melting entropy
Supercooling, Tm − T
31
–
–
J mol− 1
J mol− 1 m− 2
–
J mol− 1 K− 1
J mol− 1
J
J mol− 1
J
J
J mol− 1
J m− 2
J m− 3
J mol− 1
J mol− 1
J mol− 1 K− 1
J mol− 1 K− 1
K
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