Chapter 2
Theory of Coacervation
2.1 Introduction
(Crystallization- Coacervation- Flocculation- Gelation)
If one starts from the colloidal dispersion in an appropriate solvent, then according to the
nature of the colloid, various changes (temperature, pH, addition of substance) can bring
about a reduction of solubility as a result of which a larger part of the colloid separates
out in a new phase [1- 5]. The original one phase, the sol- thus divides into two phases,
one of which is rich in colloid, the other poor. The separated colloid-rich phase can either
appear in a low dispersed state or in higher dispersed states. In the first case macroscopic
or microscopic investigation allows one to distinguish between crystallization (crystalline
individuals) are formed and coacervation, when amorphous liquid drops (charge
neutralizing individuals) are formed [1-5].
In the cases which are called flocculation, the separated colloid-rich phase is present in a
higher dispersed state and here it frequently costs a great deal of trouble or it no longer
possible by microscopic investigation of the "floccules" to determine to which category
the separated phase belongs. The case of flocculation in which at least the mass cohering
to form floccules (aggregates individuals) can be clearly distinguished macroscopically
or microscopically from the colloid-poor phase.
Flocc~lation
then takes places
immediately afterwards, in which the particles of the lyophobic sol unite with each other
with formation ofloosely constructed floccules [1-5]. The greater part of the colloid-poor
phase is thus readily obtained by spontaneous sedimentation of the floccules or by
moderate centrifuging. The floccules themselves are still always highly dispersed systems
of the colloid-rich phase, consisting of cohering "primary particles" of the lyophobic sols
[3,5]. On account of this highly dispersed state the floccules likewise again do not
represent a thermodynamic equilibrium. They will attempt to reduce still very large
boundary surface between colloid-poor and colloid-rich phase by enlarging the mutual
34
contact spots of the "primary particles". Floccules have therefore in general the tendency
to contract. Secondary processes can now also occur. When the colloid-rich phase has
coacervate nature, that is to say, is liquid- although very viscous- then the contact spots
between adjoining very small coacervate drops can transform into coalescence spots and
this process only come to an end, when all the floccules have coalesced to form a
homogeneous coacervate layer [3,5]. Finally, in the case of gelation, polymers form
network individuals [6, 7]. Various processes of phase separation and the state of
dispersion ofthe colloid-rich phase is described in the following Table 2.1.
SL.No
Name of the process
A
Crystallization
States of dispersion System obtained
of the colloid-rich
phase
Low dispersion
Colloidal crystals
+
dilute sol
B
Coacervation
Low dispersion
Coacervate +
dilute sol
c
Flocculation
High dispersion
Floccules + dilute
sol
D
Formation of
"lyphobic sols"
High dispersion
Liquid
single
system
E
apparent
colloid
(i) High dispersion
(i) Gels which are
still preferably to
be treated as twophase systems
(ii) Very high
dispersion in which
the concept phase
becomes
inappropriate
(ii) Gels which
can be
better
described as one
phase system
Gelation
Table 2.1: Various processes of phase separation and the state of dispersion of the colloid
rich phase [5].
35
2.2 Coacervate: an example of complex fluid
Let us tum on an example of complex fluid "Coacervates" which is my interest of study.
Coacervation is defined, by IUPAC, as the separation of colloidal systems into two liquid
phases. Their name derives from Latin "acervus", which means aggregation (a heap), and
the prefix "co", which means together. It was suggested by Oparin [8,9] that coacervates
might have played a significant role in the evolution of cells. In water, organic chemicals
do not necessarily remain uniformly dispersed, but may separate out into layers or
droplets. If the droplets, which contain a colloid rich in organic compounds and are
surrounded by a tight skin of water molecules then they are known as coacervates [8-11].
It is to be distinguished from precipitation, which is observed in the form of coagulum or
floes and occurs in colloidally unstable systems. The term coacervation was introduced in
1929 by Bungenberg de Jong and Kruyt [1 ], for a process in which aqueous colloidal
solutions separate, upon alteration of the thermodynamic condition of state, into two
liquid phases, one rich in colloid, i.e. the coacervate, and the other containing little colloid
[12]. "Coacervation" signifies the union of the colloidal particles. By colloidal particles,
one understands liquid droplets, called coacervates, primarily induced by demixing.
Coacervates droplets measure 0.01 to 1 micrometers across, possess osmotic properties,
and form spontaneously from certain weak organic solutions. A wide variety of solutions
can give rise to them: for example, coacervates form spontaneously when a protein, such
as gelatin, reacts with gum arabic. They are interesting not only in that they provide a
locally segregated environment but also that there boundaries allow the selective
adsorption of simple organic molecules from the surrounding medium. In Oparin's view
[9] this amounts to an elementary form of metabolism. Bernal [13] commented that they
are "the nearest we can come to cells without introducing any biological or, at any rate,
any living biological substance". However, the lack of any mechanism by which
coacervates can reproduce leaves them far short of being living systems. The earliest
commercial application of coacervation was for the development of "carbonless" carbon
copy paper by the National Cash Register Company in the late 1950s [8]. More recently,
the field of polymer coacervation has developed steadily so that a more refmed and
complete classification of coacervation systems can be proposed here (see Table 2.2).
36
Binary systems: Coacervation by partial polymer desolvation
Solvents (component 1)
Water; Organic solvents
Polymers (P; component 2)
HydrophilicPu, p+, P-; Lipophilic P
Coacervation inducing factors
Temperature, pH
Ternary systems: Coacervation induced by partial polymer desolvation
Solvents (component 1)
Water; Organic solvents
Polymers (P; component 2)
HydrophilicPu, P+, P-; Lipophilic P
Coacervating agents (component 3)
Non solvents for the polymer;
Electrolytes ("Simple Coacervation")
Ternary systems: Coacervation induced by Polymer 2-Polymer 3 repulsion
Solvents (component 1)
Water or organic solvent
Polymers (P2, component 2)
Hydrophilic P2u, P2+, PT; Lipophilic P2
Coacervating agents (component 3)
Polymer 3, P3
Ternary systems: Coacervation induced by noncovalent polymer cross-linking
Solvents (component 1)
Water
Polymers (component 2)
p+ or p-
Cross-linking agents (component 3)
p- or p+ ("Complex Coacervation"); Diand trivalent counter-cations or counteranions
Table 2.2: Classification of common aqueous and organic systems for polymer
coacervation [5].
Other
classification
schemes
and
related
principles
of
coacervation
for
microencapsulation are available in the literature with illustrated examples [8-12]. In this
contribution, we discuss coacervation as a phenomenon between one or two polymers in a
solvent, although similar phenomena may occur with ionic or highly polarized forms of
drugs such as between the anionic heparin and the cationic gentamicin or morphine, the
anionic surfactants sodium cholate or sodium dodecylsulfate and cationic antidepressants,
or anionic DNA and cationic forms of gelatin and chitosan in the presence of sulfate ions.
Further, coacervation-like phenomena are increasingly used to engineer "smart" polymers
that undergo reversible strong conformational and macroscopic changes upon small
changes in the environment, e.g., pH, temperature, ionic strength. These polymers are
essentially single or associated polyions designed for stimulus-responsive drug delivery,
37
bioseparation, biomimetic actuators, or materials with switchable hydrophilic and
hydrophobic surfaces [ 14-16].
According to the classification proposed in Table 2.2, polymer coacervation is generally
observed in binary or ternary systems, in either aqueous or organic liquids. Three main
mechanisms govern the process of coacervation in these systems: (i) Polymer desolvation,
in binary and ternary systems, (ii) Polymer 2-Polymer 3 repulsion in a common solvent of
the two dissimilar polymers, i.e., a ternary system; (iii) Poly(ion)-counterion interactions
such as between poly(cation) and poly(anion) in a common solvent, i.e., a ternary system;
similarly, a poly(H-donor)-poly(H-acceptor) interaction may also lead to polymer
coacervation. Thus, polymer coacervation is a direct consequence of changes of
molecular interactions operating between polymer-polymer (same species), polymersolvent, polymer-coacervating agent, or poly(ion)-counterion. Prior to describing the
various systems in more detail, it may be helpful to consider first some basic aspects of
polymer solution behavior, knowledge that may be useful for understanding coacervation
phenomena as well as for optimizing microencapsulation processes based on polymer
phase separation. Polymers dissolved in a solvent are encased in a sheath of solvent
molecules that solvate their functional groups, typically through hydrogen-bonding and
van der Waals forces. The envelope of solvation prevents chain segments in close
proximity from attracting one another by interchain H-bonds, van der Waals or opposite
ionic forces. Factors that lower the solvation of dissolved
polym~rs
thin out the sheath of
solvation so that, at some point, contiguous chains attract one another by secondary
valence bonds, thereby forming an entangled network or even noncovalent weak crosslinks [17].
Polymer chain desolvation is one type of mechanism leading to phase separation; under
certain conditions, gelification rather than phase separation occurs. Factors that lower
polymer solvation include temperature change, increase in molecular weight or, for
polyions, pH-change in binary systems, or the increase in polymer concentration in binary
or ternary systems. One very effective way to increase polymer solution concentration is
to lower the number of solvent molecules available for polymer solvation. This can, be
achieved practically, by adding a third component to the polymer solution (ternary
system) such as an electrolyte or a second liquid, which must be a nonsolvent for the
polymer. The term nonsolvent is used here for all poor solvents for the polymer to be
38
•
coacervated. The added electrolyte or nonsolvent will bind part of the polymer solvent.
Competitions for solvent of -solvation will desolvate the polymer molecules leading to
phase separation in the form of coacervates or precipitates [8]. When electrolytes are used
for polymer desolvation, the phenomenon is called salting-out. In aqueous systems, the
effectiveness of dehydration, i.e., a particular form of desolvation, follows the so-called
Hofmeister or lyotropic series, which arranges ions in the order of increasing salting-out
capacity for hydrocolloids: NH/ < K+ < Na+ < Ca2+ < Mg 2+ and
cr <acetate-< sol-<
tartrate2 - < HP0 42- < citrate3- (only pharmaceutically acceptable ions are indicated here).
When at least two dissimilar non-ionic, nonpolar, or only slightly polar polymers
(Polymer 2 and Polymer 3) are mixed in a common solvent, phase separation generally
occurs. This event is thermodynamically controlled and can be explained as follows . The
dissolution of a polymer in a solvent is commonly endothermic (positive enthalpy of
mixing, 1'1Hm), thus counteracting dissolution. It is indeed the entropy increase (positive
Mm) that allows a polymer to dissolve in a solvent, i.e., the entropy increases as the
arrangement (or lattice) of the solvent molecules are largely disturbed by introducing long
polymer chains, which require a relatively large molar volume inside the solution. When
a second polymeric species (Polymer 3) is mixed with a solution of Polymer 2 in a
common solvent, the two polymer species will typically interact through van der Waals
forces, and this interaction is proportional to their molecular weights. This interaction
would produce a substantial endothermic energy change whereas the entropy gain by this
intermixing is very small owing to the small number of polymer molecules involved.
Thus, because of the positive free energy change that would occur if the dissimilar
polymers would mix with one another, phase separation into two distinct phases each of
them rich in one of the two polymer species is thermodynamically more favorable.
Contrary to the aforementioned mechanism, pairs of oppositely charged poly(ions), or
highly polarizable polymers, or of poly(H-donor) and poly(H-acceptor) tend to interact
favorably with one another, i.e., their free interaction energy change is negative owing to
a negative 1'1Hm. Therefore, they may well coexist in a common solvent, or even attract
one another so strongly that the negative 1'1Hm dominates over the entropy gain in the
common solvent. In this case, the two polymers will form a polymeric complex
separating from the solvent. Depending on the strength of enthalpic interaction between
the polymeric complex and the solvent, the complex may either precipitate as solid
particles or remain partly solvated (complex coacervate).
39
A comparable mechanism operates when a poly (ion) is mixed with a low molecular
weight di- or trivalent counterion, such as Ca2.+, Mg2+, Al3+, Zn2+, tartrate2-. This type of
mechanism leads to a strong non-covalent cross-linking of the polymer chains forming a
relatively tight network. Generally, all the mechanisms of polymer coacervation involve
some sort of phase separation, thereby producing more or less dense coacervate micro
droplets. These micro droplets can either engulf an additional component, such as a
dissolved drug, or deposit on solid surfaces, which is typically used for coating solid
particles added to the system, e.g., drug particles or living cells. In the early literature
coacervation (separation into two aqueous phases) was mostly reported to occur in the
presence of colloids. These colloids are usually proteins or macromolecules, as gelatin or
casein with sulfates [18], but coacervation can also take place in ionic systems. According
to Kruyt [3-5] two types of coacervation are observed: simple coacervation and complex
coacervation.
2.2.1 Simple coacervation
Coacervation is called simple coacervation when the phase separation is induced by the
addition of salt, acetone or alcohol. This type of coacervation is a kind of segregation,
since it is characterized by a water deficit in the total system. Upon dilution the
coacervate disappears. In simple coacervation, the polymer is salted out by electrolytes,
such as sodium sulfate, or desolvated by the addition of a water miscible nonsolvent such
as ethanol, or by an increase or decrease in temperature. It is important that the solvent
and nonsolvent are mutually miscible. Low-molecular weight alcohols such as methanol,
ethanol, and !-propanol are freely miscible with water. In literature it is found that [19],
when water was added to these low molecular weight alcohols containing
macromolecules like phospholipid, coacervation, that is, phase separation, occurred in the
systems at an adequate concentration. It is also possible to add acetone and low molecular
weight alcohols to water containing single biopolymer system to reach coacervations at
different concentrations_ If the biopolymer is mixed with an incompatible or poor solvent,
phase separation can also occur [12]. The phase separations by poor solvents were studied
in this thesis. In this liquid-liquid phase separation, one phase of the mixture is
concentrated at the bottom and the diluted phase at the top contains mainly the solvent
with less concentration of polymers. Figure 2.1 represents the alcohol induced simple
coacervation and Figure 2.2 shows the principle of simple coacervation in concentrated
sol mixture of gelatin (G) and gum arabic (GA).
40
Primary
Alcohol
Complexes
Solubility
Coacervate
~
Droplets
Upper Phase
Coacervate Phase
Pbase
Separation
Figure 2.1: Schematic representation of the phase separation by simple coacervation has
shown where alcohol was used as coacervating agent.
w
Figure 2.2: Schemes showing the principle of simple coacervation in concentrated sol
mixture of gelatin (G) and gum arabic (GA). Tie lines connect liquids which are rich in G
and relatively poor on GA (on the left hand branch) with liquids which are rich in GA and
relatively poor in G (on the right-hand branch).
41
2.2.2 Complex coacervation
Complex coacervation is induced by the interactions between ionized groups. It occurs
when a second colloidal species is added to a solution of a charged colloid, which is
oppositely charged to the one being added. The charges on the macromolecules induce
the formation of salt bonds.
Voom
[20]
described complex coacervation of
polyelectrolytes in terms of electrostatic interactions and entropy. When two polymers are
oppositely charged, an electrostatic complex can be formed. The electrostatically bound
complexes can be either soluble or "insoluble". The "insoluble" complexes concentrate in
liquid coacervate droplets, that further coalesce and phase separate to form a separate
coacervate layer. As a result, one phase of the mixture is concentrated in the two
polymers and the other phase contains mainly the solvent. A schematic picture of the
complex coacervation mechanism is given in Figure 2.3.
+
Upper phase - Coacervate phase
Co solubility
Soluble I
Insoluble
complexes
Coacervate
droplets
Phase
separation
Experiimental tube with a
coacervate layer of whey
proteins and gum arabic
Figure 2.3: Schematic representation of the phase separation by complex Coacervation
[20].
Complex coacervation between oppositely charged proteins and polysaccharides was
discovered by Tiebackx in 1911 [21]. By mixing gelatin and gum arabic (GA) in an acetic
acid solution, he observed opalescence or precipitation. This type of phase separation of
gelatin I GA mixtures was extensively studied by the Dutch chemists Bungenberg de Jong
and Kruyt in the 1920's and 1940's [3-5]. Coacervation signifies the union of the
colloidal particles. By colloidal particles, one understands the liquid droplets, called
coacervates, primarily induced by demixing which is shown in Figure 2.4. Bungenberg de
Jong described the conditions under which complex coacervation of gelatin I GA
occurred, such as pH, ionic strength, polymer concentration, polymer ratio, and
temperature [3-5].
Figure 2.4: Microscopic picture of complex coacervation of bovine serum albumin and
GA (120x). The coacervate droplets have partially spread over the surface of the
microslide and so coalesced with each other. Picture reproduced from [1] with the
courtesy ofEdita KNA W.
Bungenberg de Jong gathered an impressive amount of data on which the first theoretical
model of complex coacervation was developed by Overbeek and Voom [22]. A typical
phase diagram of complex coacervation is shown in Figure 2.5. A large number of
reviews is available on the status of associative phase separation, and complex
coacervation in literature [23-26].
'"
Figure 2.5: Schematic phase diagram of a water (W) I gum arabic (GA) I gelatin (G)
system at such a pH that G is positively charged and GA is negatively charged. The
coacervates are both rich in GA and G and are to be found on the arched branch of the
curve in the plane of the triangle. The equilibrium liquid, which is poor in G and GA, lies
on a branch of the curve closes to the water comer of the triangle. Figure reproduced from
the papers by Bungenberg de Jong [3-5].
43
2.3 Theoretical description of coacervation
2.3.1 Bungenberg de Jong (1929 - 1949)
The first theoretical explanation of the coacervation phenomenon by Bungenberg de J ong
and Kruyt(1929) [1] is based on the stability of hydrophilic colloids, which is
characterized by two stability factors:
capillary electric charge and hydration.
Coacervation would be the consequence of the removal of the two stability factors, i.e.
charge and hydration. As desolvation sets in, there would be shrinkage of the solvent
layer ("solvate mantle") around the colloidal particles, which then would merge through
their "concrete solvate mantles" (concrete= after desolvation) (shown in Figure 2.6).
, ~ ~eeulation
.
, _,..,. Mino-eoa~:enration
~ M<U:ro-e~a~:enration
a
c
Figure 2.6: Schematic representation of the mechanism of phase separation by
coacervation. (a): particle with a "diffuse solvate mantle" (dotted periphery). (b): particle
with a "concrete solvate mantle". (c): fusion of the particles to a coacervate with their
"concrete solvate mantle". Figure reproduced from the papers by Bungenberg de Jong in
1949 [3-5].
Coacervates could be regarded as a liquid, which had lost its free mobility to a certain
degree. This explanation was mainly of the simple coacervation phenomenon, but when
coacervation was brought about by a decrease of charge (complex coacervation),
Bungenberg de Jong needed more research. He came up with a theory for complex
coacervation in 1949 based on a large amount of experimental data on the gelatin I GA
system [ 1]. The negative GA and the positive gelatin interact to form a complex. The role
of experimental parameters, such as salt and pH, on the coacervation highlighted that the
coacervation was a consequence of electrostatic interactions.
44
2.3.2 Voorn-Overbeek (1957)
Based on the experimental results of Bungenberg de Jong, Overbeek and Voorn
developed the first quantitative theory on complex coacervation, in which they considered
gelatin I GA coacervation as a spontaneous phenomenon [22]. They interpreted
coacervation as a competition between electrostatic forces which tend to accumulate the
charged molecules and entropic effects which tend to disperse them. The oppositely
charged molecules are associated together to form a coacervate phase entrapping solvent
molecules. The presence of solvent in the coacervate phase contributed to the increase in
entropy of the system, as it allowed a number of possible rearrangements of the
molecules. For this reason, the coacervates were liquid in nature and the coacervation is
fully reversible. The theory was based on several assumptions: (1) the molecules have a
random chain configuration, (2) solvent-solute interactions are negligible, (3) the
interactive forces are distributive in nature, with the system behaving as though the
charges are free to move, and (4) there is no site specific interaction between the
molecules. The theoretical treatment of complex coacervation was put on a quantitative
basis by using the Debye-Huckel equations for the electrical interactions and the FieryHuggins theory for the entropy term. Overbeek and Voorn set
Ftotal (T) = Fmixing (M) + Felectrostatic (e)
and then substituted the Flory-Huggins approximation for FM. Fe was calculated by
treating the polyions as the sum of single charges and approximating the total electrical
interaction free energy by the Debye-Huckel theory. Their final result was
(2.1)
where Nr =total no. of lattice sites in the system, ri =No. of sites occupied by particle i,
O"i = charge density of particle i,
~i
= volume fraction (or site fraction) of particles of type
J
.
.
.
.
e
4Jre 2]1/2( 1
.
.
.
1, a= electncal mteractwn constant = - 2[- - - , v = s1te volume, s = d1electnc
3& ck8 Tv
k8 T
constant, e = elementary charge.
The critical conditions for coacervation were derived from Eq. 2.1 for the symmetrical
two component case in which each polyion was of the same size (r2 = r3 = r, subscripts 2
45
and 3 refer to the polyions, 1 to the solvent) and charge density (cr 2 = cr 3 = cr) and both
were present in equal initial concentration
(~2
= ~3 =~).For the solvent r 1 = 1, cr = 0. The
result,
(2.2)
showed that coacervation would take place at ordinary temperatures in water only when
cr3r ~ 0.4 since ~<<1. According to this theory, for a two component system consisting of
a polyion salt and water, the critical conditions for coacervation are met when cr3r ~ 0.53,
that is to say when the charge density (cr) or the molar mass (r) are sufficiently large. This
model was extended to three or four-component systems. Overbeek and Voom explained
that the suppression of coacervation by salt excess was due to an increase of the solubility
of the polyions, a decrease of the amount of polyions in the coacervate, and a decrease of
charge density through charge screening by counterions (Figure 2. 7). It was also shown
that not only polymers but also small ions were accumulated in the coacervate. The
adaptations of various theories were developed later, since it seemed that the assumption
that the Huggins interaction parameter was negligible was insufficient.
-
0
Polymer Concentration
Figure 2. 7: Theoretical phase diagram for complex coacervation in the system solvent I
polymer PQ I univalent salt KA. The figure has been constructed for r = 1000, a= 0.15.
The dotted line is the spinodal, C is the critical point, CM is positioned at the middle of
the node lines and OE gives the equivalent polyelectrolyte I salt composition. Figure ·
reproduced from J. T. G. Overbeek and M. J. Voom [22], Phase separation in
polyelectrolyte solutions.
46
2.3.3 Veis-Aranyi (1960 - 1970)
Veis and Aranyi developed a theory at conditions where cr3r < 0.53, i.e. when the VoomOverbeek theory was not applicable [27]. This theory was based on a practical case of
coacervation upon temperature reduction between two oppositely charged gelatins. Veis
modified the Voom-verbeek theory, including the Huggins interaction parameter,
corresponding to the solvent-solute interaction; this parameter increases significantly on
temperature reduction. Flory and Huggins have shown the free energy of mixing of a nonionic polymer with solvent to be given by 11FM = !lllM -
T~M
(2.3)
n 1 and n2 are the numbers ofmolecules of solvent and solute, respectively, ~ 1 and ~ 2 their
volume fractions. X12 is a dimensionless quantity that chacterizes the solvent-solute
interaction energy per solvent molecule divide by k8 T. For a multi component system the
equation for 11FM becomes
ij
11FM
= kBTLni ln~i +kBTL:tiJni~i
(2.4)
i<j
in which
X,ij
represents the interaction per kinetic unit i-kinetic unit j pair divided by k8 T.
The modified equation obtained by Veis for the phase II, combining the Flory-Huggins
equation is given by
(2.5)
where 11FT is the free energy of mixing, and a = electrical interaction constant.
Nr =total no. of lattice sites in the system
fi
<Ji
=No. of sites occupied by particle i
= charge density of particle i
v =site volume (3.0xl0-23 cm3)
~i
=volume fraction (or site fraction) of particles of type i.
In the Veis-Aranyi theory, coacervation is considered as a two-step process rather than a
spontaneous one. First the gelatins spontaneously aggregate by electrostatic interaction to
form neutral aggregates of low configurational entropy, and then, these aggregates slowly
rearrange to form the coacervate phase. (Veis investigated complex Coacervation on a
system of water and symmetrical gelatins (polycation and polyanaion with identical
47
charge density and chain length), and he presented the following model of phase
separation,
[B-]~
[A+.B-]sAP
(2.6)
[A+.B-]sAP ~ [A+.Bl 1sAP + [A+.BliiiRC
(2.7)
[A+]+
where I and II represent the dilute and concentrated phases, A+ and B- represent the
polycataion and polyanaion, and SAP and IRC represent the symmetrical aggregate
polymer and independent random chain, respectively. The mechanism is driven by the
gain in configurational entropy resulting from the formation of a randomly mixed
coacervate phase. Veis-Aranyi considered that the molecules were not randomly
distributed in both phases, but that ion-paired aggregates are present in the dilute phase.
Moreover, the electrostatic term of the Voom-Overbeek model was replaced by a term,
which is a function of concentration and charge density of the polymers. The differences
between the Voom-Overbeek and the Veis-Aranyi theories come from the fact that they
explain different coacervation conditions: Voom-Overbeek theory was based on the
spontaneous coacervation of gelatin I GA, whereas Veis-Aranyi was developed for
coacervation between two oppositely charged gelatins.
2.3.4 Nakajima-Sato (1972)
Nakajima and Sato applied the equation of M (which was obtained by Veis for the phase
II) to both phases, and they derived the condition for phase separation. When the polymer
concentration is sufficiently high, this condition is expected to be applicable. Nakajima
and Sato studied an equivalent mixture of sulphated polyvinyl alcohol and
aminoacetalyzed polyvinyl alcohol(PVA) in microsalt aqueous solution [28]. They
adapted the Voom-Overbeek theory by including the Huggins parameter and changing
the electrostatic term. Nevertheless, they agreed with Overbeek and Voom that the
charges should be treated as uniformly distributed in both dilute and concentrated phases.
The experimental and theoretical results were in good agreement with each other, and the
study showed that for specific systems the Overbeek-Voom model could still be used.
2.3.5 Tainaka (1979 - 1980)
The Tainaka theory is the most recent model developed for complex coacervation, and is
an adaptation of the Veis-Aranyi theory. The main difference from the Veis-Aranyi
model is that the aggregates, present in both the dilute and concentrated phase, are formed
48
without specific ion pairing [29]. The biopolymer aggregates present in the initial phase
condense to form a coacervate. Tainaka obtained the condition of phase separation in low
concentration. He modified the Eq. 2.7 by Veis and considered the following model.
(2.8)
In his model, each phase is considered to be the same two-component system of water
and SAP as the phase I of the Veis model. Eq. 2.8 means that coacervate is a
condensation of SAP. In this scheme, the coacervation is a condensation phenomenon of
SAP, and the random chain has been replaced by SAP in Veis's scheme under the
consideration of weak overlapping of polymer chains. Theoretically, he applied both the
phases to the viral expansion method similar to the theory of V eis and Gates for the phase
I. Veis and Gates obtained the viral expansion method up to the second order, whereas the
second viral coefficient A 2 was obtained on the assumption that SAP is neutral. On the
other hand, he considered that A2 is directly influenced by the charges in SAP. If SAP's
overlap each other, electrostatic energy gain is produced as a result of increase of the ion
density in the overlapped domain. Therefore he took up an interaction potential between
SAP's in order to include the electrostatic energy gain and calculate the viral coefficients
up to the fifth order. This theory led the expression of osmotic pressure in SAP solution
based on the viral expansion method. He extended his theory to more complicated
phenomenon of the counterion-containing solutions. In his scheme, he deals with the
asymmetry system of polymer charges in which the charges of poly cation and polyanaion
are not identical and hence counterions exist. In this case, if the solution is salt-free, the
number of the counterions should be equal to the difference of the charges of both
polymers. The influence of counterions on the complex coacervation has been well
known from the experimental fact that the coacervation in the case of two protein species
having different isoelectric points is influenced by a pH change of the solution, that is, the
phase separation is suppressed, when the number of the counterions is increased by the
pH change. So, the effects of charge asymmetry accompanied by the existence of
counterions on the coacervation. Therefore the suffix SAP in the above Eq. 2.8 is altered
to AAP for aggregate polymer of charge asymmetry.
[A+]+ [B-]~[A+.B-]AAP
(2.9)
(2.10)
49
In the ith volume element of AAP (Asymmetric aggregated polymer) domain, the mixing
free energy !J.F'j when the number of total lattice sites is Nj may be represented with the
interaction parameter
xJJ. . , between
j and /by
where¢" ¢2 and ¢3 are the volume fraction of solvent 1, of AAP segments 2, and of
counterion 3, respectively. The suffix i denotes the ith volume element, kaT is the
Boltzmann factor, e is the elementary charge. The interaction potential U A(R) between the
two aggregated AAPs at a distance R was given by Flory's method based on Eq. 2.11 in
the following form:
(2.12)
where the four potentials U~, U2, U3 and U4 on the right hand side ofEq. 2.12 correspond
to the four terms in Eq. 2.11, respectively in turn. The potential U 1 is the Flory-Krigbaum
potential, and u2 is the electrostatic term, and u3 and u4 are the newly added terms in the
presence of counterions. The interaction potential Us between SAP is expressed by Us=
U3 + U2. IfU4 is neglected under the assumption
z 31 = 0, the necessary calculation to be
added to the previous theory is just for U 3. This U 3, which should be positive, results from
the entropy increase due to the counterion distribution. The repulsive force between
AAPs therefore appears due to this term in this system.
According to Tainaka, the driving forces for phase separation are the electrostatic and the
attractive force between the aggregates, which become stronger when the molar mass and
the charge density of the polymers increase. Charge density and molar mass of the
polymers should fall within a critical range for coacervation to occur. If the charge
density or molar mass of the polymer becomes higher than the critical range, then a
concentrated gel or a precipitate, induced by the long-range attractive forces among the
aggregates, will be formed. On the other hand, for charge densities or molar mass below
the range, short-range repulsive forces will stabilize the dilute solution and coacervation
will not occur. The Tainaka theory is more general than all the previous theories and is
applicable to both high and low charge density systems. It provides an adequate
explanation of the coacervation process for a large number of systems.
50
2.3.6 Gupta and Bohidar (2005)
The kinetics of phase separation of a homogeneous polyelectrolytic solution into a dense
polymer-rich coacervate and the dilute supernatant phase is discussed through statistical
thermodynamics [30]. In the lattice model, r is the number of sites occupied by the
polymer having a volume fraction f/Jlc, it was found that phase separation would ensue
wheno- r~(6419a )(¢2 cll-¢2 J , which reduces to (o- 3 rltp2 J~(6419a 2 )::::;0.45 at
3
2
2
20 °C for <p2c <<1. The separation kinetics mimics a spinodal decomposition process. It
has been shown that for a wide variety of experimental conditions [31-33], the onset of
complexation between complementary macro-ions conforms to an empirical relation
given by o-v I .Ji ~constant, where v is the charge density of complementary
polyelectrolyte. Odijk [34] has argued that for this empirical relation to be valid the
interactions in system must adhere to the following requirements: (i) Debye-Huckel
approximation must be valid, (ii) complexation is independent of polyelectrolyte chain
statistics and (iii) excluded volume effects are not significant. For self-charge
2
neutralization v can be replaced by cr and it follows the equation o- I .Ji ~ constant.
Gupta and Bohidar have provided a rigorous proof to the empirical condition proposed by
Dubin et al. [35] though they deal with a single polyelectrolyte undergoing self-charge
neutralization, which is comparable to the complexation between oppositely charged
polyelectrolytes described by Dubin et al. [35,36]. The system generated a simple
coacervate whereas a two-polyelectrolyte system yields a complex coacervate.
2.4 Comparison with experimental results
Burgess and co-workers described four different coacervation systems [15,37]; (i) gelatin
I GA, (ii) albumin I gelatin, (iii) gelatin I gelatin, and (iv) albumin I alginic acid.
Spontaneous coacervation as described by Overbeek and Voom was observed upon
mixing oppositely charged polymers only under specific conditions. The limiting
conditions are that the average molecular mass of the polymers and their charge densities
must fall within a specific range, the polymers should be in a random coil configuration,
Flory-Huggins type interactions should be negligible and the charge interaction between
the molecules should be distributive in nature. When deviation from these conditions
occurs, coacervation may still take place, as described by Veis-Aranyi and by Tainaka. A
large number of studies also reported the presence of primary complexes [38] prior to
51
complex coacervation, supporting the theories of Veis and Tainaka. Considering
thermodynamic parameters, knowledge is still lacking and some results are contradictory.
Some authors write and show that electrostatic complexation between biomacomolecules
is mainly enthalpically driven, due to the decrease of the electrostatic free energy of the
system [26]. Others indicate that complexation is mainly entropically driven owing to the
liberation of counterions and water molecules [39].
Current status of research
The experimental observation on simple coacervation process of gelatin studied in my
thesis was entropically driven phenomena. When a protein or a polyelectrolyte of
oppositely charged titrated with alcohol, it forms a complex through electrostatic
interaction. Various physico-chemical parameters can influence the electrostatic
interactions and thus the complex formation. Some important parameters are reported in
this section and also systematically studied in my thesis (Chapter 4). It is well known that
pH plays a key role in the strength of electrostatic interaction since it determines the
charge density of the protein. The formation of electrostatic complexes is extensively
reported in the literature for protein I synthetic polyelectrolyte systems [38-40]. These
studies revealed that the complexation appeared as a two-step process upon pH change.
Indeed, two pH-induced structural transitions (pHc and pH~) were identified. At pHc, the
formation of soluble complexes was initiated, and below
pH~,
visual phase separation
occurred. Recently, de Vries (2003) proposed a model [41] for the formation of soluble
protein-polysaccharide
complexes
incorporating
the
non-homogeneous
charge
distribution along the protein backbone. They were able to predict the complexation
above the protein pi, due to the presence of randomly charged patches on the surface of
the proteins. Furthermore, the ionic strength of the system should be carefully controlled,
since the presence of salt can suppress the complexation, depending on the nature and the
concentration of the salt. The polymer concentration is also a critical parameter, since
above a critical concentration, self suppression of the coacervation occurs as described in
the Voom-Overbeek theory. When the polymer is in excess, coacervation does not occur
because of the low energetic interest of concentrating the polymers in one phase if the
concentration is already high. Other parameters (i.e. shear, pressure, etc.) also influence
the complexation of polymers, but were not addressed in my thesis.
52
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54