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Introduction to Aggregation Phenomena in Food Colloids
Introduction to Aggregation Phenomena in Food Colloids By Pieter Walstra DEPARTMENT OF FOOD SCIENCE, WAGENINGEN AGRICULTURAL UNIVERSITY, PO BOX 8129,6700 EV WAGENINGEN, THE NETHERLANDS
1 Intmduction Many foods are colloidal systems, containing particles of various kinds. The particles may aggregate, i.e. stay very close to each other for a much longer time than would be the case in the absence of attractive forces between them. Such aggregation may determine the rheological properties and the appearance of the product, as well as its physical instability, as reflected in a change in consistency or a loss of homogeneity. Many foods also contain macromolecules (polymers) which may affect aggregation and its rate in various ways. Whether aggregation occurs depends primarily on the interaction forces between the particles, the classical subject of colloid science. One should, however, be cautious in applying colloid theory to foods. Colloid science typically considers the interaction between two identical, homogeneous, hard spheres, whereas most foods contain many particles, varying in size, shape, heterogeneity, and deformability, and making up a considerable volume fraction. In most studies on the effects of polymers, fairly simple molecules are considered, e.g. uncharged block copolymers, whereas foods typically contain proteins. Moreover, hydrodynamic forces are often prominent during food processing, and many phenomena may occur simultaneously. Finally, the food may show chemical changes, for instance due to enzyme action. Nevertheless, the application of colloid science maybe very useful. Ever more complicated situations are being studied and the increasing possibilities for the application of intricate model calculations is tending to bridge the gap between simple model systems and actual foods. It is essential, however, to first know what system the food is, what particles it contains, and in what manner they aggregate, before applying colloid theory.
4
Introduction to Aggregation Phenomena in Food Colloids
2 Interaction Forces DLVO Theory The Deryagin-Landau-Verwey-Overbeek (DLVO) theory considers the free energy G needed to bring two particles from infinite distance apart to a close distance between their surfaces h.'-3 There are two terms which are additive. One describes the electrostatic repulsion between the particles, perhaps better explained as being due to the local increase in osmotic pressure where the ion clouds around the charged particles overlap. The attractive term is due to the ubiquitous van der Waals attractions between identical molecules, and hence particles. For two identical homogeneous spheres of radius a , we have for conditions as are common in food colloids (e.g. in water at room temperature)
and
if expressed in SI units. Here vo is the surface potential of the particles, often taken as the more experimentally accessible, electrokinetic potential. K is the Debye-Huckel parameter, or the inverse of the thickness of the electric double layer; in the present case it equals about 3.3 fi in nm, where I is the total ionic strength (molar). A is the Hamaker constant, which depends on the material of the particles and that of the interstitial liquid; tabulated values are available. One may thus calculate the interaction free energy from known or determinable parameters. An example is given in Figure la. If the minimum near C is deep compared to the average kinetic energy involved in the encounter of two particles, k T , the particles tend to aggregate, i.e. stay together at the corresponding value of h (aggregation in the secondary minimum). If the maximum near B is not large compared to k T , two particles may occasionally move over this energy barrier and become aggregated near A (in the primary minimum). Lowering the surface potential-e.g. by altering the pH-or increasing the ionic strength diminishes the electrostatic repulsion and thereby promotes aggregation. The Hamaker constant can usually not be manipulated. The DLVO theory has been fairly successful in predicting the aggregation stability of inorganic colloids, except for the prediction of a considerable effect of particle size, which is mostly not observed. Moreover, the theory rarely holds at very small distances, say h < 3 nm, because of surface unevenness and because the presence of adsorbed material cannot easily be accounted for: it may cause additional repulsion (see below) and it interferes with the determination of the surface potential. Consequently, the DLVO theory is rarely exact for food colloids, although it often predicts trends fairly well.
P. Walstra
5
G/k T
+zoo
0
-200 m Figure 1 Calculated examples of the repulsive ( G R ) , attractive ( G A ) , and total interaction free energy ( G T ) as a function of surface separation distance h of two identical spheres: ( a ) electrostatic repulsion and van der Waals attraction ( D L V O ) ; ( b ) steric repulsion and van der Waals attraction
Roles of Macromolecules Polymers present in the continuous (usually aqueous) phase may adsorb onto the particles. If not, the polymers mostly cause the viscosity of the liquid to be higher, thereby slowing down any aggregation, or even causing a weak gel to be formed, thus preventing aggregation. Dissolved polymers may also, on the other hand, cause aggregation by depletion flocculation; see below. Adsorbed polymers may either prevent aggregation: steric stabilization; or cause it: bridging flocculation. The theory has now been fairly well developed and has been proved to be useful. We refer to a recent review by Fleer and S ~ h e u t j e n s . ~ Figure 2 schematically shows how macromolecules may adsorb (or be grafted) onto surfaces. Whether adsorption occurs greatly depends on the solubility of the polymer. In this respect, it is enlightening to consider the osmotic pressure Il of a polymer solution. It can be expressed by
n
=
RT (c,
+ B c; + . . .)
(3)
where R is the gas constant, c , is the molar concentration, and B is the second virial coefficient, which can be fairly easily determined. Schematic
Introduction to Aggregation Phenomena in Food Colloids
6
homo polymer fairly soluble
,
//////A///////////////
grafted very soluble
homopolymer poorly soluble/charged
block copolymer
Figure 2 Types of protruding macromolecules (highly schematic)
examples are shown in Figure 3. For a good solvent (the upper curve refers to xanthan in water), adsorption is very unlikely; for so called theta conditions, it is likely; and for poor solvents, it is all but certain. To assure adsorption, on the one hand, and a considerable protrusion of the macromolecule into the solvent, on the other hand, (block) copolymers are often used: part of the macromolecule is poorly soluble and adsorbs, and another part is highly soluble and sticks out. For charged macromolecules the relations are more complicated.’ Proteins may adsorb in many ways: almost unchanged, with some change in conformation, or almost fully unfolded.
Steric Stabilization Figure 4 attempts to explain the two mechanisms involved in steric stabilization. When a surface approaches protruding macromolecules, the latter become restricted in their freedom of motion; hence, a decrease in entropy; hence, a repulsive free energy. This volume restriction free energy term is always positive, i.e. it causes strong repulsion (unless the
7
P. Walstra TT/C,
o!
0
I
1 c ( kgm-3)
Figure 3 Osmotic pressure divided by molar concentration n/c, versus mass concentration c of polymer solutions for various kinds of solvent quality. (6 denotes a theta solvent.)
Figure 4 Mechanisms of steric repulsion by protruding macromolecules (highly schematic): volume restriction (left) and mixing (right)
8
Introduction to Aggregation Phenomena in Food Colloids
macromolecule adsorbs onto the other surface; see below. Mere volume restriction, however, will rarely occur, since the other surface mostly bears macromolecules as well. Now the concentration of macromolecular matter increases as the polymer layers overlap and this may induce a local increase in osmotic pressure, causing repulsion (this is called the mixing term). Whether or not repulsion occurs primarily depends on the second virial coefficient in equation (3); see also Figure 3. If ll/c increases with concentration, there will be strong repulsion; if it markedly decreases, attraction may occur. (NB This treatment of the effect of the solubility of the polymer is to some extent an oversimplification, but it serves to illustrate the salient points.) An example of the interaction free energy as a function of separation distance is given in Figure l b . Mostly, repulsion increases very steeply with decreasing h , almost as a step function. Whether the secondary minimum is deep enough to allow aggregation primarily depends on the ratio of particle size to protrusion distance: large particles (strong van der Waals attraction) and fairly small macromolecules are associated with a deeper minimum, and hence with lower stability. Also a decrease in solvent quality, for instance by the addition of ethanol to an aqueous system, may lead to aggregation. Steric stabilization is often of considerable importance in food colloids. Calculation of the interaction free energy is rarely possible, but a reasonable estimate of the protrusion distance of the macromolecules can often be made, thereby allowing one to roughly predict whether steric stabilization may be possible. Adsorbed proteins mostly provide stability against aggregation by the combined effect of both electrostatic and steric repulsion.
Bridging Flocculation Adsorbed homopolymers between closely approaching particles will always make bridges (i. e. single molecules become adsorbed simultaneously onto two surfaces) if equilibrium is attained.4 Equilibrium is, however, mostly not attained, because the time needed for reaching that conformation is much longer than the time during which particles in Brownian motion are close to each other. Nevertheless, one would theoretically expect bridging to occur when particles are close together for a long time, as in a sedimented layer. Even this is not widely observed in practice, presumably because copolymers are often used. Bridging flocculation does occur if particles covered with adsorbed polymer are mixed with uncovered particles.6 A prerequisite is that the concentration of the polymer in the solvent is very low, a condition that can be fulfilled because of the very high surface activity of many polymers. Consequently, the method of processing may determine, along with composition, whether bridging flocculation will actually occur.
P . Walstra
9
Depletion Flocculation As depicted in Figure 5, non-adsorbing macromolecules with a radius of gyration R , leave a layer of approximate thickness R , around any particle depleted of macromolecules. This causes the osmotic pressure of the system to be higher than it would be in the absence of particles. If now the particles come close to each other, the volume of solvent depleted is decreased; hence, a lower osmotic pressure; hence, a decrease in free energy; hence, a driving mechanism for flocculating the particles. For two hard spheres of radius a , the interaction free energy is given by'
Gdep= -
T
R i (2a
+ 4R,/3) n f(h)
(4)
where Il is given by equation ( 3 ) and the function f(h) decreases from 1 at zero separation distance to 0 for h > 2R,. Depletion flocculation may thus occur, especially if R , is large (high molar mass, good solvent) and if ll is high; the latter implies that, because of the high molar mass, the second virial coefficient B must be high-ie. there is, again, a good solvent. The free energy minimum may become much deeper if the particles slightly flatten on close contact.8 Xanthan can in fairly low concentrations cause depletion flocculation,9~'0 for instance inducing rapid creaming in emulsions, but at somewhat higher concentration it may slow down creaming (and possibly aggregation), because of the increased apparent viscosity, especially at very low velocity gradients." For several polysaccharides added to foods, it may be very difficult to determine whether they cause aggregation by (weak) bridging or by depletion. l1
Figure 5 Schematic explanation of the depletion of macromolecules, radius of gyration R,, from the solution near spherical particles, radius a, and of the resulting depletion flocculation
10
Introduction to Aggregation Phenomena in Food Colloids
Other Aggregation Mechanisms Figure 6 summarizes the interparticle region in various kinds of aggregates. Besides those already mentioned, one may distinguish the following mechanisms. (i) Bridging by particles, e.g. casein micelles between emulsion droplets ('homogenization cluster'), l2 fat crystals between emulsion droplets ('partial coalescence'), 12,13 and milk fat globules between air bubbles (whipped cream). l2 (ii) Liquid necks, e.g. tiny aqueous droplets between cocoa particles in cocoa mass (melted chocolate), which considerably enhance its consistency. Partial coalescence can also be envisaged as aggregation due to liquid necks, at least in some systems. (iii) Cross-linking of adsorbed macromolecules. Steric repulsion caused by the latter does not imply that the macromolecules cannot touch each other. If protein-covered particles are touching under conditions favouring cross-linking reactions (for instance during intensive heating), aggregation of the particles may readily occur. This happens, for instance, during the heat coagulation of homogenized cream. l4 The diversity of this list conveys a warning: when aggregation phenomena occur in a food system, one should always try to find out first what the mechanism is before applying the theory. It also follows that the simple classical division of aggregation phenomena into flocculation (caused by polymers) and coagulation (caused by salt) makes little sense for food colloids.
colloidal or depletion flocculation
[
1
-1
bridging flocculation
crossIinking
Figure 6 Various kinds of particle aggregation (highly schematic)
bridging by particles
P. Walstra
11
3 Consequences of Aggregation The unhindered aggregation of particles in Brownian motion leads to the formation of fractal flocs. Such a floc is characterized by a relation between the number of particles n in the floc and its radius R ,
where a is the radius of the primary particles. The fractal dimensionality D is always < 3 (mostly 1.7-2.4), implying that the flocs become ever more tenuous as they grow. Consequently, at a certain stage, the flocs take up the whole system volume and a gel forms. This has been discussed before? The aggregation leads to a gel (even if weak) rather than to a coagulate, making the system more stable to sedimentation, rather than less so. This has also been discussed before. l6 If a rearrangement of aggregated particles occurs as depicted in Figure 7 (top), a coagulate is formed. Very subtle differences may determine which structure is the result of aggregation in a quiescent system, and, although some determinant conditions have been identified, l7 this aspect needs more study, especially because of its great practical importance. If the liquid is stirred during aggregation, as is often the case when aggregation proceeds very fast, a coagulate is commonly formed; the fractal dimensionality then is almost 3. If the particles coalesce directly after aggregation, we have D = 3. Figure 7 depicts some other forms of rearrangement that may occur after aggregation. Local repositioning is common for irregularly shaped particles, - particle rear-
ra ngement
- local scale
rearrangement
- flattening
( f l u i d part cles
>c -3(
- local sintering
Figure 7 Examples of bond strengthening mechanisms of aggregated particles (highly schematic)
12
Introduction to Aggregation Phenomena in Food Colloids
local flattening occurs with deformable ones, and sintering especially occurs with particles consisting of a material having a finite solubility in the continuous phase, i.e. with most crystals. All of these rearrangements lead to bond strengthening, implying that it becomes more difficult to redisperse the aggregates, or that the gel formed becomes stiffer and, mostly, stronger and shorter. To the examples shown in Figure 7, we may add slow polymer bridging and chemical cross-linking (Figure 6). All of these changes may also occur with particles residing in a sedimented layer, irrespective of any previous aggregation.
4 Aggregation Kinetics Smoluchowski Theory According to Smoluchowski the encounter frequency J (m-3 s-l) of equal sized spherical particles due to Brownian motion is given by" J = 4 kTN2/3
(6)
where N is the particle concentration and q is the solvent viscosity. (Note that the particle radius is not involved in the equation: its effects on collision radius and diffusion rate cancel.) Assuming that any aggregate of particles is counted as one particle (of the same original radius), the so-called perikinetic aggregation rate is given
- dN/dt = J/W
(7)
The time needed to halve the number of particles then turns out to be ca. d3/10 @ seconds if the particle diameter d is measured in pm. For a volume fraction @ = 0.1 and d = 1 pm, this yields a value of 1 s, provided that all encounters lead to aggregation (W = 1). In many cases aggregation is much slower. The stability factor W may be larger than unity for any of the following reasons. (i) There is a free energy barrier for aggregation, as depicted in Figure l a , near separation B. This is typical for particles stabilized by electrostatic repulsion. (ii) Only a limited part of the surface of the particles is reactive (i.e. there are 'hot spots'). This may be the case for emulsion droplets containing a few protruding crystals that can induce partial coalescence, or for particles partly covered with protein, and partly with other surfactants. (iii) Besides aggregation, some disaggregation occurs. This may be the case if the free energy minimum of two particles is only a few times k T , e.g. for flocculation in the secondary minimum (see Figure 1) or for depletion flocculation. This aspect has been insufficiently studied.
P. Walstra
13
Complications Smoluchowski’s theory for perikinetic aggregation, equations (6) and (7), has been observed to be reasonably valid in several fairly simple model systems, albeit merely for the first few aggregation steps. In practice, large deviations are often observed. Possible causes for deviations have been extensively studied by Bremer,” and some highlights of his results will be mentioned here. The first question to be asked is to what stage aggregation has to proceed to induce a perceptible change, since that is the crucial point in practice. It is often (tacitly) assumed that the time needed for such a change is a few times that needed to halve the number of particles, i.e.
for perikinetic aggregation. Often, to.5 is even designated as the coagulation time. This is very misleading. Let us assume that the first perceptible change is the emergence of visible particles, as may occur when the aggregated particles immediately coalesce or rearrange into compact flocs. We define a radius Rvis at which these flocs can be seen, say 0.2 mm, and obtain the corresponding time
If fractal aggregation occurs, the first perceptible change is usually the formation of a gel. Now we obtain for perikinetic aggregation a gelation time
which may be smaller than tvis by several orders of magnitude (see Figure 8). Under some conditions (large primary particles, large density difference, small @) the first perceptible change may be a visible separation into layers due to sedimentation of the growing aggregates. There are more complications in the case of fractal aggregates. (i) The particles, and certainly the aggregates, are polydisperse , implying that aggregation proceeds faster than predicted. (ii) The collision radius of the aggregates may become markedly larger than the hydrodynamic (or diffusion) radius, thereby, again, causing faster aggregation. (iii) The volume fraction of the effective particles (i.e. fractal aggregates) may not any more be neglected (as was done by Smoluchowski) since it always becomes large; this may reduce the gel time by at least an order of magnitude. Last but not least, the effects of velocity gradients in the system must be taken into account. Smoluchowski derived for the encounter frequency at a shear rate S:
14
Introduction to Aggregation Phenomena in Food Colloids
10 d t,,,
5
D
3
s=o
0
-2
-1
Figure8 Calculated examples of aggregation times t, (either t,, or t,,) of spherical particles, radius 0.1 pm, in water at various volume fractions @. Other variables: fractal dimensionaliq D = 3 (particles coalesce) or 2.0 (fractal flocculation); velocity gradient S . Sedimentation is neglected. (See text for further details. )
This implies that, in water at room temperature, the ratio of this orthokinetic aggregation rate over that for perikinetic aggregation is 0.2 d 3 S , where d is in pm. Consequently, for shear-rates as small as 0.1 s-l, which easily develop due to slight temperature fluctuations, orthokinetic aggregation becomes the determining factor for aggregates larger than about 4 p m . This will tend to occur quite often in practice; some results are shown in Figure 8. There is much more to be said about these various aspects, and a full discussion is given elsewhere. l7
5 Some Conclusions (i) Aggregation phenomena largely determine the consistency, the appearance, and the physical stability of several types of food colloids. (ii) Most food systems are too complicated for the direct application of the theories of elementary colloid science, although trends are often predicted correctly. The use of advanced numerical methods may greatly extend the applicability of colloid theory. However, one should first establish what is the actual aggregation mechanism. (iii) Changes occurring after the primary formation of aggregates such as deflocculation, rearrangement of aggregate structure, and ‘sintering’ need more study. These changes may determine whether either a coagulate or a gel is formed, and the nature of their mechanical properties.
P . Walstra
15
(Iv) The theory of fractal aggregation is a powerful tool for describing aggregation and its consequences. (v) Aggregation kinetics is far more intricate than suggested by simple perikinetic Smoluchowski theory. In particular, the formation of fractal aggregates and the presence of small velocity gradients may affect (by some orders of magnitude) the time needed for aggregation to become perceptible.
References 1. ‘Colloid Science. Vol. I. Irreversible Systems’, ed. H. R. Kruyt, Elsevier, Amsterdam, 1952. 2. E. Dickinson and G . Stainsby, ‘Colloids in Foods’, Applied Science, London, 1982. 3. J. Lyklema, ‘Fundamentals of Interface and Colloid Science. Vol. I. Fundamentals’, Academic Press, London, 1991. 4. G. J. Fleer and J. M. H. M. Scheutjens, in ‘Coagulation and Flocculation: Theory and Applications’, ed. B. Dobias, Dekker, New York, 1992. 5 . G. J. Fleer, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 34. 6. G. J. Fleer and J. Lyklema, J. Colloid Interface Sci., 1974, 46, 1. 7. A. Vrij, Pure Appl. Chem., 1976, 48, 471. 8. I. D. Evans and A. Lips, this volume, p. 214. 9. A. Lips, I. J. Campbell, and E. G. Pelan, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 1. 10. H. Luyten, M. Jonkman, W. Kloek, and T. van Vliet, this volume, p. 224. 11. B. Bergensthhl, in ‘Gums and Stabilizers for the Food Industry’, eds. G. 0. Phillips. P. A. Williams, and D. J. Wedlock, IRL Press, Oxford, 1988, Vol.4, p. 363. 12. H. Mulder and P. Walstra, ‘The Milk Fat Globule. Emulsion Science as Applied to Milk Products and Comparable Foods’, Pudoc, Wageningen, 1974. 13. K. Boode and P. Walstra, this volume, p. 23. 14. P. Walstra, J. Dairy Sci., 1990, 7 3 , 1965. 15. P. Walstra, T. van Vliet, and L. G. B. Bremer, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 369. 16. T. van Vliet and P. Walstra, in ‘Food Colloids’, eds. R. D. Bee, P. Richmond, and J. Mingins, Special Publication No. 75, Royal Society of Chemistry, Cambridge, 1989, p. 206. 17. L. G. B. Bremer, ‘Fractal Aggregation in Relation to Formation and Properties of Particle Gels’, Ph.D. Thesis, Wageningen Agricultural University, 1992. 18. J. T. G. Overbeek, in ‘Colloid Science, Vol. I. Irreversible Systems’, ed. H. R. Kruyt, Elsevier, Amsterdam, 1952, p. 278.
1 Intmduction Many foods are colloidal systems, containing particles of various kinds. The particles may aggregate, i.e. stay very close to each other for a much longer time than would be the case in the absence of attractive forces between them. Such aggregation may determine the rheological properties and the appearance of the product, as well as its physical instability, as reflected in a change in consistency or a loss of homogeneity. Many foods also contain macromolecules (polymers) which may affect aggregation and its rate in various ways. Whether aggregation occurs depends primarily on the interaction forces between the particles, the classical subject of colloid science. One should, however, be cautious in applying colloid theory to foods. Colloid science typically considers the interaction between two identical, homogeneous, hard spheres, whereas most foods contain many particles, varying in size, shape, heterogeneity, and deformability, and making up a considerable volume fraction. In most studies on the effects of polymers, fairly simple molecules are considered, e.g. uncharged block copolymers, whereas foods typically contain proteins. Moreover, hydrodynamic forces are often prominent during food processing, and many phenomena may occur simultaneously. Finally, the food may show chemical changes, for instance due to enzyme action. Nevertheless, the application of colloid science maybe very useful. Ever more complicated situations are being studied and the increasing possibilities for the application of intricate model calculations is tending to bridge the gap between simple model systems and actual foods. It is essential, however, to first know what system the food is, what particles it contains, and in what manner they aggregate, before applying colloid theory.
4
Introduction to Aggregation Phenomena in Food Colloids
2 Interaction Forces DLVO Theory The Deryagin-Landau-Verwey-Overbeek (DLVO) theory considers the free energy G needed to bring two particles from infinite distance apart to a close distance between their surfaces h.'-3 There are two terms which are additive. One describes the electrostatic repulsion between the particles, perhaps better explained as being due to the local increase in osmotic pressure where the ion clouds around the charged particles overlap. The attractive term is due to the ubiquitous van der Waals attractions between identical molecules, and hence particles. For two identical homogeneous spheres of radius a , we have for conditions as are common in food colloids (e.g. in water at room temperature)
and
if expressed in SI units. Here vo is the surface potential of the particles, often taken as the more experimentally accessible, electrokinetic potential. K is the Debye-Huckel parameter, or the inverse of the thickness of the electric double layer; in the present case it equals about 3.3 fi in nm, where I is the total ionic strength (molar). A is the Hamaker constant, which depends on the material of the particles and that of the interstitial liquid; tabulated values are available. One may thus calculate the interaction free energy from known or determinable parameters. An example is given in Figure la. If the minimum near C is deep compared to the average kinetic energy involved in the encounter of two particles, k T , the particles tend to aggregate, i.e. stay together at the corresponding value of h (aggregation in the secondary minimum). If the maximum near B is not large compared to k T , two particles may occasionally move over this energy barrier and become aggregated near A (in the primary minimum). Lowering the surface potential-e.g. by altering the pH-or increasing the ionic strength diminishes the electrostatic repulsion and thereby promotes aggregation. The Hamaker constant can usually not be manipulated. The DLVO theory has been fairly successful in predicting the aggregation stability of inorganic colloids, except for the prediction of a considerable effect of particle size, which is mostly not observed. Moreover, the theory rarely holds at very small distances, say h < 3 nm, because of surface unevenness and because the presence of adsorbed material cannot easily be accounted for: it may cause additional repulsion (see below) and it interferes with the determination of the surface potential. Consequently, the DLVO theory is rarely exact for food colloids, although it often predicts trends fairly well.
P. Walstra
5
G/k T
+zoo
0
-200 m Figure 1 Calculated examples of the repulsive ( G R ) , attractive ( G A ) , and total interaction free energy ( G T ) as a function of surface separation distance h of two identical spheres: ( a ) electrostatic repulsion and van der Waals attraction ( D L V O ) ; ( b ) steric repulsion and van der Waals attraction
Roles of Macromolecules Polymers present in the continuous (usually aqueous) phase may adsorb onto the particles. If not, the polymers mostly cause the viscosity of the liquid to be higher, thereby slowing down any aggregation, or even causing a weak gel to be formed, thus preventing aggregation. Dissolved polymers may also, on the other hand, cause aggregation by depletion flocculation; see below. Adsorbed polymers may either prevent aggregation: steric stabilization; or cause it: bridging flocculation. The theory has now been fairly well developed and has been proved to be useful. We refer to a recent review by Fleer and S ~ h e u t j e n s . ~ Figure 2 schematically shows how macromolecules may adsorb (or be grafted) onto surfaces. Whether adsorption occurs greatly depends on the solubility of the polymer. In this respect, it is enlightening to consider the osmotic pressure Il of a polymer solution. It can be expressed by
n
=
RT (c,
+ B c; + . . .)
(3)
where R is the gas constant, c , is the molar concentration, and B is the second virial coefficient, which can be fairly easily determined. Schematic
Introduction to Aggregation Phenomena in Food Colloids
6
homo polymer fairly soluble
,
//////A///////////////
grafted very soluble
homopolymer poorly soluble/charged
block copolymer
Figure 2 Types of protruding macromolecules (highly schematic)
examples are shown in Figure 3. For a good solvent (the upper curve refers to xanthan in water), adsorption is very unlikely; for so called theta conditions, it is likely; and for poor solvents, it is all but certain. To assure adsorption, on the one hand, and a considerable protrusion of the macromolecule into the solvent, on the other hand, (block) copolymers are often used: part of the macromolecule is poorly soluble and adsorbs, and another part is highly soluble and sticks out. For charged macromolecules the relations are more complicated.’ Proteins may adsorb in many ways: almost unchanged, with some change in conformation, or almost fully unfolded.
Steric Stabilization Figure 4 attempts to explain the two mechanisms involved in steric stabilization. When a surface approaches protruding macromolecules, the latter become restricted in their freedom of motion; hence, a decrease in entropy; hence, a repulsive free energy. This volume restriction free energy term is always positive, i.e. it causes strong repulsion (unless the
7
P. Walstra TT/C,
o!
0
I
1 c ( kgm-3)
Figure 3 Osmotic pressure divided by molar concentration n/c, versus mass concentration c of polymer solutions for various kinds of solvent quality. (6 denotes a theta solvent.)
Figure 4 Mechanisms of steric repulsion by protruding macromolecules (highly schematic): volume restriction (left) and mixing (right)
8
Introduction to Aggregation Phenomena in Food Colloids
macromolecule adsorbs onto the other surface; see below. Mere volume restriction, however, will rarely occur, since the other surface mostly bears macromolecules as well. Now the concentration of macromolecular matter increases as the polymer layers overlap and this may induce a local increase in osmotic pressure, causing repulsion (this is called the mixing term). Whether or not repulsion occurs primarily depends on the second virial coefficient in equation (3); see also Figure 3. If ll/c increases with concentration, there will be strong repulsion; if it markedly decreases, attraction may occur. (NB This treatment of the effect of the solubility of the polymer is to some extent an oversimplification, but it serves to illustrate the salient points.) An example of the interaction free energy as a function of separation distance is given in Figure l b . Mostly, repulsion increases very steeply with decreasing h , almost as a step function. Whether the secondary minimum is deep enough to allow aggregation primarily depends on the ratio of particle size to protrusion distance: large particles (strong van der Waals attraction) and fairly small macromolecules are associated with a deeper minimum, and hence with lower stability. Also a decrease in solvent quality, for instance by the addition of ethanol to an aqueous system, may lead to aggregation. Steric stabilization is often of considerable importance in food colloids. Calculation of the interaction free energy is rarely possible, but a reasonable estimate of the protrusion distance of the macromolecules can often be made, thereby allowing one to roughly predict whether steric stabilization may be possible. Adsorbed proteins mostly provide stability against aggregation by the combined effect of both electrostatic and steric repulsion.
Bridging Flocculation Adsorbed homopolymers between closely approaching particles will always make bridges (i. e. single molecules become adsorbed simultaneously onto two surfaces) if equilibrium is attained.4 Equilibrium is, however, mostly not attained, because the time needed for reaching that conformation is much longer than the time during which particles in Brownian motion are close to each other. Nevertheless, one would theoretically expect bridging to occur when particles are close together for a long time, as in a sedimented layer. Even this is not widely observed in practice, presumably because copolymers are often used. Bridging flocculation does occur if particles covered with adsorbed polymer are mixed with uncovered particles.6 A prerequisite is that the concentration of the polymer in the solvent is very low, a condition that can be fulfilled because of the very high surface activity of many polymers. Consequently, the method of processing may determine, along with composition, whether bridging flocculation will actually occur.
P . Walstra
9
Depletion Flocculation As depicted in Figure 5, non-adsorbing macromolecules with a radius of gyration R , leave a layer of approximate thickness R , around any particle depleted of macromolecules. This causes the osmotic pressure of the system to be higher than it would be in the absence of particles. If now the particles come close to each other, the volume of solvent depleted is decreased; hence, a lower osmotic pressure; hence, a decrease in free energy; hence, a driving mechanism for flocculating the particles. For two hard spheres of radius a , the interaction free energy is given by'
Gdep= -
T
R i (2a
+ 4R,/3) n f(h)
(4)
where Il is given by equation ( 3 ) and the function f(h) decreases from 1 at zero separation distance to 0 for h > 2R,. Depletion flocculation may thus occur, especially if R , is large (high molar mass, good solvent) and if ll is high; the latter implies that, because of the high molar mass, the second virial coefficient B must be high-ie. there is, again, a good solvent. The free energy minimum may become much deeper if the particles slightly flatten on close contact.8 Xanthan can in fairly low concentrations cause depletion flocculation,9~'0 for instance inducing rapid creaming in emulsions, but at somewhat higher concentration it may slow down creaming (and possibly aggregation), because of the increased apparent viscosity, especially at very low velocity gradients." For several polysaccharides added to foods, it may be very difficult to determine whether they cause aggregation by (weak) bridging or by depletion. l1
Figure 5 Schematic explanation of the depletion of macromolecules, radius of gyration R,, from the solution near spherical particles, radius a, and of the resulting depletion flocculation
10
Introduction to Aggregation Phenomena in Food Colloids
Other Aggregation Mechanisms Figure 6 summarizes the interparticle region in various kinds of aggregates. Besides those already mentioned, one may distinguish the following mechanisms. (i) Bridging by particles, e.g. casein micelles between emulsion droplets ('homogenization cluster'), l2 fat crystals between emulsion droplets ('partial coalescence'), 12,13 and milk fat globules between air bubbles (whipped cream). l2 (ii) Liquid necks, e.g. tiny aqueous droplets between cocoa particles in cocoa mass (melted chocolate), which considerably enhance its consistency. Partial coalescence can also be envisaged as aggregation due to liquid necks, at least in some systems. (iii) Cross-linking of adsorbed macromolecules. Steric repulsion caused by the latter does not imply that the macromolecules cannot touch each other. If protein-covered particles are touching under conditions favouring cross-linking reactions (for instance during intensive heating), aggregation of the particles may readily occur. This happens, for instance, during the heat coagulation of homogenized cream. l4 The diversity of this list conveys a warning: when aggregation phenomena occur in a food system, one should always try to find out first what the mechanism is before applying the theory. It also follows that the simple classical division of aggregation phenomena into flocculation (caused by polymers) and coagulation (caused by salt) makes little sense for food colloids.
colloidal or depletion flocculation
[
1
-1
bridging flocculation
crossIinking
Figure 6 Various kinds of particle aggregation (highly schematic)
bridging by particles
P. Walstra
11
3 Consequences of Aggregation The unhindered aggregation of particles in Brownian motion leads to the formation of fractal flocs. Such a floc is characterized by a relation between the number of particles n in the floc and its radius R ,
where a is the radius of the primary particles. The fractal dimensionality D is always < 3 (mostly 1.7-2.4), implying that the flocs become ever more tenuous as they grow. Consequently, at a certain stage, the flocs take up the whole system volume and a gel forms. This has been discussed before? The aggregation leads to a gel (even if weak) rather than to a coagulate, making the system more stable to sedimentation, rather than less so. This has also been discussed before. l6 If a rearrangement of aggregated particles occurs as depicted in Figure 7 (top), a coagulate is formed. Very subtle differences may determine which structure is the result of aggregation in a quiescent system, and, although some determinant conditions have been identified, l7 this aspect needs more study, especially because of its great practical importance. If the liquid is stirred during aggregation, as is often the case when aggregation proceeds very fast, a coagulate is commonly formed; the fractal dimensionality then is almost 3. If the particles coalesce directly after aggregation, we have D = 3. Figure 7 depicts some other forms of rearrangement that may occur after aggregation. Local repositioning is common for irregularly shaped particles, - particle rear-
ra ngement
- local scale
rearrangement
- flattening
( f l u i d part cles
>c -3(
- local sintering
Figure 7 Examples of bond strengthening mechanisms of aggregated particles (highly schematic)
12
Introduction to Aggregation Phenomena in Food Colloids
local flattening occurs with deformable ones, and sintering especially occurs with particles consisting of a material having a finite solubility in the continuous phase, i.e. with most crystals. All of these rearrangements lead to bond strengthening, implying that it becomes more difficult to redisperse the aggregates, or that the gel formed becomes stiffer and, mostly, stronger and shorter. To the examples shown in Figure 7, we may add slow polymer bridging and chemical cross-linking (Figure 6). All of these changes may also occur with particles residing in a sedimented layer, irrespective of any previous aggregation.
4 Aggregation Kinetics Smoluchowski Theory According to Smoluchowski the encounter frequency J (m-3 s-l) of equal sized spherical particles due to Brownian motion is given by" J = 4 kTN2/3
(6)
where N is the particle concentration and q is the solvent viscosity. (Note that the particle radius is not involved in the equation: its effects on collision radius and diffusion rate cancel.) Assuming that any aggregate of particles is counted as one particle (of the same original radius), the so-called perikinetic aggregation rate is given
- dN/dt = J/W
(7)
The time needed to halve the number of particles then turns out to be ca. d3/10 @ seconds if the particle diameter d is measured in pm. For a volume fraction @ = 0.1 and d = 1 pm, this yields a value of 1 s, provided that all encounters lead to aggregation (W = 1). In many cases aggregation is much slower. The stability factor W may be larger than unity for any of the following reasons. (i) There is a free energy barrier for aggregation, as depicted in Figure l a , near separation B. This is typical for particles stabilized by electrostatic repulsion. (ii) Only a limited part of the surface of the particles is reactive (i.e. there are 'hot spots'). This may be the case for emulsion droplets containing a few protruding crystals that can induce partial coalescence, or for particles partly covered with protein, and partly with other surfactants. (iii) Besides aggregation, some disaggregation occurs. This may be the case if the free energy minimum of two particles is only a few times k T , e.g. for flocculation in the secondary minimum (see Figure 1) or for depletion flocculation. This aspect has been insufficiently studied.
P. Walstra
13
Complications Smoluchowski’s theory for perikinetic aggregation, equations (6) and (7), has been observed to be reasonably valid in several fairly simple model systems, albeit merely for the first few aggregation steps. In practice, large deviations are often observed. Possible causes for deviations have been extensively studied by Bremer,” and some highlights of his results will be mentioned here. The first question to be asked is to what stage aggregation has to proceed to induce a perceptible change, since that is the crucial point in practice. It is often (tacitly) assumed that the time needed for such a change is a few times that needed to halve the number of particles, i.e.
for perikinetic aggregation. Often, to.5 is even designated as the coagulation time. This is very misleading. Let us assume that the first perceptible change is the emergence of visible particles, as may occur when the aggregated particles immediately coalesce or rearrange into compact flocs. We define a radius Rvis at which these flocs can be seen, say 0.2 mm, and obtain the corresponding time
If fractal aggregation occurs, the first perceptible change is usually the formation of a gel. Now we obtain for perikinetic aggregation a gelation time
which may be smaller than tvis by several orders of magnitude (see Figure 8). Under some conditions (large primary particles, large density difference, small @) the first perceptible change may be a visible separation into layers due to sedimentation of the growing aggregates. There are more complications in the case of fractal aggregates. (i) The particles, and certainly the aggregates, are polydisperse , implying that aggregation proceeds faster than predicted. (ii) The collision radius of the aggregates may become markedly larger than the hydrodynamic (or diffusion) radius, thereby, again, causing faster aggregation. (iii) The volume fraction of the effective particles (i.e. fractal aggregates) may not any more be neglected (as was done by Smoluchowski) since it always becomes large; this may reduce the gel time by at least an order of magnitude. Last but not least, the effects of velocity gradients in the system must be taken into account. Smoluchowski derived for the encounter frequency at a shear rate S:
14
Introduction to Aggregation Phenomena in Food Colloids
10 d t,,,
5
D
3
s=o
0
-2
-1
Figure8 Calculated examples of aggregation times t, (either t,, or t,,) of spherical particles, radius 0.1 pm, in water at various volume fractions @. Other variables: fractal dimensionaliq D = 3 (particles coalesce) or 2.0 (fractal flocculation); velocity gradient S . Sedimentation is neglected. (See text for further details. )
This implies that, in water at room temperature, the ratio of this orthokinetic aggregation rate over that for perikinetic aggregation is 0.2 d 3 S , where d is in pm. Consequently, for shear-rates as small as 0.1 s-l, which easily develop due to slight temperature fluctuations, orthokinetic aggregation becomes the determining factor for aggregates larger than about 4 p m . This will tend to occur quite often in practice; some results are shown in Figure 8. There is much more to be said about these various aspects, and a full discussion is given elsewhere. l7
5 Some Conclusions (i) Aggregation phenomena largely determine the consistency, the appearance, and the physical stability of several types of food colloids. (ii) Most food systems are too complicated for the direct application of the theories of elementary colloid science, although trends are often predicted correctly. The use of advanced numerical methods may greatly extend the applicability of colloid theory. However, one should first establish what is the actual aggregation mechanism. (iii) Changes occurring after the primary formation of aggregates such as deflocculation, rearrangement of aggregate structure, and ‘sintering’ need more study. These changes may determine whether either a coagulate or a gel is formed, and the nature of their mechanical properties.
P . Walstra
15
(Iv) The theory of fractal aggregation is a powerful tool for describing aggregation and its consequences. (v) Aggregation kinetics is far more intricate than suggested by simple perikinetic Smoluchowski theory. In particular, the formation of fractal aggregates and the presence of small velocity gradients may affect (by some orders of magnitude) the time needed for aggregation to become perceptible.
References 1. ‘Colloid Science. Vol. I. Irreversible Systems’, ed. H. R. Kruyt, Elsevier, Amsterdam, 1952. 2. E. Dickinson and G . Stainsby, ‘Colloids in Foods’, Applied Science, London, 1982. 3. J. Lyklema, ‘Fundamentals of Interface and Colloid Science. Vol. I. Fundamentals’, Academic Press, London, 1991. 4. G. J. Fleer and J. M. H. M. Scheutjens, in ‘Coagulation and Flocculation: Theory and Applications’, ed. B. Dobias, Dekker, New York, 1992. 5 . G. J. Fleer, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 34. 6. G. J. Fleer and J. Lyklema, J. Colloid Interface Sci., 1974, 46, 1. 7. A. Vrij, Pure Appl. Chem., 1976, 48, 471. 8. I. D. Evans and A. Lips, this volume, p. 214. 9. A. Lips, I. J. Campbell, and E. G. Pelan, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 1. 10. H. Luyten, M. Jonkman, W. Kloek, and T. van Vliet, this volume, p. 224. 11. B. Bergensthhl, in ‘Gums and Stabilizers for the Food Industry’, eds. G. 0. Phillips. P. A. Williams, and D. J. Wedlock, IRL Press, Oxford, 1988, Vol.4, p. 363. 12. H. Mulder and P. Walstra, ‘The Milk Fat Globule. Emulsion Science as Applied to Milk Products and Comparable Foods’, Pudoc, Wageningen, 1974. 13. K. Boode and P. Walstra, this volume, p. 23. 14. P. Walstra, J. Dairy Sci., 1990, 7 3 , 1965. 15. P. Walstra, T. van Vliet, and L. G. B. Bremer, in ‘Food Polymers, Gels and Colloids’, ed. E. Dickinson, Special Publication No. 82, Royal Society of Chemistry, Cambridge, 1991, p. 369. 16. T. van Vliet and P. Walstra, in ‘Food Colloids’, eds. R. D. Bee, P. Richmond, and J. Mingins, Special Publication No. 75, Royal Society of Chemistry, Cambridge, 1989, p. 206. 17. L. G. B. Bremer, ‘Fractal Aggregation in Relation to Formation and Properties of Particle Gels’, Ph.D. Thesis, Wageningen Agricultural University, 1992. 18. J. T. G. Overbeek, in ‘Colloid Science, Vol. I. Irreversible Systems’, ed. H. R. Kruyt, Elsevier, Amsterdam, 1952, p. 278.