Steric stabilization

Steric Stabilization D. H. N A P P E R Department of PhysicaZ Chemistry, University of Sydney, N.S.W. 2006, Australia Received April 12, 1976; accepted August 4, 1976 Steric stabilization is a generic term that embraces all aspects of the stabilization of colloidal particles by nonionic macromolecules. The technological exploitation of steric stabilization dates back at least 4000 years to the preparation in ancient Egypt of fresco paints and inks. Despite this long history, the mechanisms whereby polymers impart stability have only been recognized in the past two decades. Three types of experiment have proved useful in discriminating between the various competing theories of steric stabilization. These are studies of incipient flocculation, measurements of the repulsive interactions between stable particles, and stability in polymer melts. Experiments suggest that two separate regions of close approach must be distinguished : the interpenetration domain (characterized by an interparticle separation of between one and two contour lengths of the stabilizer chains) and the interpenetration plus compression domain, which is entered on even closer approach. Particle interactions in the interpenetrational region arise primarily from the mixing of segments and solvent ; the elastic interactions are negligible. This mixing term is evaluated in the first generation theories via the Flory-Huggins theory. It may be positive or negative. As compression occurs on closer approach, the elastic contributions also become significant. These may be evaluated by statistical thermodynamics and are always positive. The foregoing concepts correctly predict the observed practical limit to stability, which is the attainment of theta-conditions for the stabilizing chains. Except for very short chains, the van der Waals attraction is rarely important in determining stabilization by polymers. Stabilization in polymer melts, however, arises primarily from elastic effects so that for these systems van der Waals forces become the major source of attraction. Elastic contributions increase abruptly, even under incipient flocculation conditions; consequently, Brownian collisions sample primarily the interpenetrationaI domain. The distance dependence of the repulsion between stable particles can be wedicted with a fair degree of success.

water using natural steric stabilizers, such as gum arabic, egg albumin, or casein (from milk) (1). Traditionally colloid scientists have referred to stabilization by natural macromolecules as "protection." There is presumably an electrostatic component to stability imparted by natural macromolecules because they are usually charged. Heller and Pugh (2) appear to have been the first to use the term "steric stabilization" which may be differentiated from protective action by the absence of any electrostatic component. The word "steric" in this context is perhaps somewhat misleading

INTRODUCTION Steric stabilization is a generic t e r m t h a t encompasses all aspects of the stabilization of colloidal particles b y n o n i o n i c m a c r o m o l e c u l e s . T h e p h e n o m e n o n has h a d an especially long h i s t o r y of technological exploitation. I t d a t e s b a c k s o m e five m i l l e n n i a to the d y n a s t i e s of such p h a r a o h s as Cheops and C h e p h r e n , whose p y r a m i d s can still be v i s i t e d today. I t was d u r i n g those alchemical times t h a t inks (and p a p y r u s ) were first d e v e l o p e d to solve an early p r o b l e m in c o m m u n i c a t i o n . A n c i e n t E g y p t i a n inks were p r e p a r e d b y dispersing c a r b o n b l a c k (formed b y c o m b u s t i o n ) in 390

Journal of Colloid and Interface Science, Vol. 58, No. 2, February 1977 I S S N 0021-9797

Copyright © i977 by Academic Press, Inc. All rights of reproduction in any form reserved.

STERIC STABILIZATION

because the phenomenon is not closely related to the more familiar steric effects betweert nonbonded atoms or groups that are beloved by organic chemists. The latter arise from electron-electron and electron-nuclei interactions and are usually repulsive. Clearly steric stabilization embraces a significantly wider range of fundamental thermodynamic causes. It seems conceivable that classical steric effects could impart colloid stability; indeed, they may well be operative in stabilizing some lipid bilayers that contain few or no solvent molecules. Steric stabilization has been exploited through, the ages in the preparation of both water-based and, since Roman times, oil-based paints and inks. It is especially useful in nonaqueous media where electrostatic stabilization is less successful. It can also be effective in media of high. ionic strengths. Indeed, because steric stabilizers are often relatively insensitive to the presence of eIectrolytes, it is scarcely surprising that the phenomenon is important in biological systems (e.g., in the stabilization of blood, milk, etc.). Stabilization by nonionic macromolecules has also become of increasing technological significance (e.g., in pharmaceutical emulsions, in the dispersal of oil spills, in the domestic use of nonionic surfactants, in dry cleaning, etc). Steric stabilization is likely to be even more widely exploited because of its versatility in being equally effective in aqueous and nonaqueous dispersion media. Despite the long history of technological exploitation of steric stabilization, it is only in the past two decades that some understanding of the mechanisms by which polymers can impart colloid stability has emerged. T H E P R E P A R A T I O N OF S T E R I C A L L Y STABILIZED DISPERSIONS

A comprehensive monograph (3) has appeared recently that describes in detail most of the various methods of preparation of sterically stabilized latices that have been developed to date. The patent literature is especially well covered. For our purposes all

391

that need be noted is that there are two general procedures presently available. The first method (3, 4) generates the latex particles in the presence of a steric stabilizer. This may be considered to be an in situ method of particle formation. The stabilizer may also be generated in situ by the addition of a suitable precursor; alternatively, it may be fully preformed before addition to the reaction mixture. The second general method (5) consists of adding the stabilizer to an already formed colloidal dispersion (or vice versa). In the latter case a significant electrostatic component to stability may be present because the first-formed particles are usually electrostatically stabilized. A critically important question, both from the practical and theoretical viewpoints, is the types of polymers that constitute the best steric stabilizers. Considerable experience (3) shows that the stabilizers that provide best stability are amphipathic block or graft copolymers. The most effective stabilizers consist of both anchor groups and stabilizing moieties. The stabilizing moieties must be soluble in the dispersion medium to be effective whereas the anchor groups function most efficiently if nominally insoluble in the dispersion medium (3). The purpose of the anchor polymer is to prevent the stabilizing moieties attached to one particle from moving away from the interaction zone on the approach of a second particle (3). The stabilizing moieties could in principle escape from the stress of the interaction zone by two different mechanisms (6): first, the stabilizer molecules could move laterally around the surface of the particle while remaining attached to the particle; or secondly, the stabilizers may in some circumstances be desorbed from the particle surface. Lateral movement can usually be prevented by ensuring that the surfaces are fully coated. Desorption can be eliminated by attaching the stabilizing moieties to suitably insoluble polymer chains that anchor, either chemically or

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D. H. NAPPER

physically, the moieties to the particles. Of course, the manufacturers of nonionic detergents have long recognized the need for anchor groups, without necessarily being aware of all the physicochemical principles involved so far as stability is concerned. Stabilizing moieties that are unanchored or not strongly anchored can, in fact, impart some stability to colloidal dispersions (7). Such dispersions will, however, flocculate before the thermodynamic limit to stability is reached, as a result of stabilizer displacement or desorption. The pioneering studies of steric stabilization by Heller and co-workers (2, 8, 9) were performed on such unanchored macromolecules. Unfortunately, quantitative theoretical description of such complex behavior seems to be out of the question at present. For this reason, we shall confine our discussion to systems that are stabilized by strongly anchored moieties. EXPERIMENTAL STUDIES OF INCIPIENT INSTABILITY As with electrostatically stabilized dispersions, there are two general aspects of the stability of sterically stabilized dispersions that can usefully be investigated. These two domains cover long-term stability and incipient instability. Studies of the incipient instability of model dispersions appear to have ontpaced

/

1.0

0.6

@ W

I

290

The Critical Flocc~dation Point

Most of the studies on incipient instability have been performed on model polymer latices. These latices are reasonably mon0disperse and can be prepared, even in aqueous media, in an apparently uncharged state (4). The particles can be regarded as being fully coated by stabilizing moieties that are strongly anchored to the particle surface. When these conditions are fulfilled, patterns of behavior emerge that are common to both aqueous and nonaqueous dispersion media (6). The simplest way to induce instability in sterically stabilized dispersions is to reduce the solvency of the dispersion medium for the stabilizing moieties. This may be achieved through temperature changes (4, 5, 10-12), pressure changes (13), or a combination of both (14). Another method is to add nonsolvent for the stabilizing moieties to the dispersion medium (10). When the solvency is reduced, the dispersions often exhibit a very sharp transition from long-term stability to catastrophic instability (4, 10). An example of this is displayed in Fig. 1 (4). This shows that the transition from long-term stability to fast flocculation occurs over only a few degrees Celsius when poly(ethylene oxide) stabilized latices are heated in aqueous electrolyte. Note that such flocculation is commonly reversible (4, 10). If the solvency of the dispersion medium for the stabilizing chains is significantly improved (e.g., by cooling), spontaneous redispersion of the latex particles usually occurs.

0.2 286

studies on stable dispersions. These will therefore be discussed first.

294

J/K

I

298

Fio. 1. Characteristic increase in turbidity of a poly(vinyl acetate) dispersion, stabilized by poly(ethylene oxide), on reaching the cft in an aqueous electrolyte solution.

The critical flocculation point (cfpt) at which flocculation first becomes observable is referred to as a critical flocculation temperature (cft) or a critical flocculation pressure (cfp), according to which intensive variable is used to induce flocculation. If flocculation results from the addition of nonsolvent, the corresponding terms are the critical flocculation volume (cfv) (for a liquid nonsolvent)

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STERIC STABILIZATION and the critical flocculation concentration (cfc) (for a solid nonsolvent). The strong temperature dependence of the stability of many sterically stabilized dispersions contrasts markedly with the relative insensitivity of electrostatically stabilized dispersions to changes in temperature. The temperature dependence of stability provides a clue to the thermodynamic processes that govern stabilization (15, 16). One very characteristic feature of sterically stabilized systems is the diversity of their responses to temperature changes. Some dispersions flocculate on heating (4, 16) whereas others flocculate on cooling (10, 16). Still others cannot, at least in principle, be flocculated at any accessible temperature (12). To date, only one system has been prepared (polyacrylonitrile latex particles stabilized by polystyrene in methyl acetate) that flocculates both on heating and cooling (17). Dispersions that flocculate either on heating or on cooling can be prepared in both aqueous and nonaqueous dispersion media. Ottewill (18) has rightly noted that entropic stabilization is more common in nonaqueous media whereas enthalpic stabilization is more frequently encountered in aqueous media. The temperature dependence of the Gibbs free energy of close approach (AGR) for two sterically stabilized particles is given by

393 TABLE

I

T y p e s of S t e r i c S t a b i l i z a t i o n AHR

ASII

i AHR I / I'i ,aSRI

AGP~

Type

Flocculation

~-+

-~---

>1 < 1 ~ t

~@ @

Enthalpic Entropic Combined enthalpicentropic

On heating On cooling Not accessible

cause the enthalpic contribution to the free energy of close approach is dominant, this is referred to as enthalpic stabilization. The dominance of the enthalpic contribution to the free-energy changes over that of the entropic contribution will clearly be reduced if the temperature is increased. Accordingly enthalpically stabilized dispersions are characterized by flocculation on heating. A contrasting situation to enthalpic stabilization occurs if both zXHa~ and zXSRare negative and [2xH•l < T IAS~[. In this case, the entropy term opposes flocculation whereas the enthalpy term favors it. The dominance of the entropic contribution to the free energy of close approach suggests that this possibility be termed entropic stabilization. It is clearly characterized by flocculation on cooling. The third category is characterized by AHR being positive and AS~ being negative so that both the enthalpy and entropy terms contribute to stability. Dispersions stabilized by combined enthalpic-entropic stabilization, where AS~ is the corresponding entropy as this case is called, cannot in principle be change. Since AG~ must change from being flocculated at any accessible temperature. positive to being negative in passing from the Flocculation may, however, be induced on stability to the instability domain, the sign of changing the temperature because a transition AS~ may be inferred by whether flocculation to enthalpic or entropic stabilization may conis induced by heating or cooling. The various ceivabIy occur. Three important points must, however, be combinations of signs for AS~ and AH~ (the corresponding enthalpy change) that lead to noted with regard to the foregoing discussion. a positive value for 2xGm and thus to stability, First, the signs of AS~ and AH~ are determined unequivocally only in the vicinity of are summarized in Table I. The simplest way to discuss the different the cfpt because AG~ necessarily changes sign possibilities is in terms of the relationship only on passing through the cfpt. How far 2~G~ = 2~HR -- TzSS~. If both £xH~ and ASa from the cfpt these inferences remain valid is are positive but AH~ > T A S m the enthalpy critically dependent upon the nature of the change on close approach opposes flocculation stabilizing moieties and the dispersion medium ; whereas the entropy change promotes it. Be- for some systems the signs of AHR and 2xSa Journal of Colloid and Interface Science, VoI. 58, No. 2, F e b r u a r y 1977

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are unchanged even several hundred degrees from the cfpt. The need for caution, however, is brought home forcibly by recalling the behavior of the latex cited above that flocculates both on heating and on cooling. The second important point to note is that AG~ refers to the free-energy change associated with that part of the steric barrier that is sampled during Brownian collisions. As shall be seen, incipient flocculation appears to be associated primarily with the interpenetrational domain of close approach. The domain characterized by interpenetration plus compression is not ordinarily accessible to any significant extent in the course of a Brownian collision because of the rapid rise in the elastic repulsion on compression. The final point to note is that the preceding thermodynamic discussion is model independent. Osmond et al. (19) have claimed that the classification of dispersions as outlined above depends upon the assumption of some specific model (in actual fact that due to Fischer (20)). This assertion is clearly incorrect. The only bases needed to specify the general thermo-

dynamic origin of stability near to the cfpt is Eq. [-11,plus some elementary classical thermodynamic notions. No model-dependent assumptions are required to establish the signs of zXSR and &Hu. Of course, any physical interpretation of the signs of zXSu and zXHu must necessarily be associated with modeldependent concepts. Table II lists the sterically stabilized dispersions that have been prepared and whose classification near to the cfpt seems reasonably well assured (13). Note that both entropic and enthalpic stabilization have been observed in both aqueous and nonaqueous media. Several other points deserve comment. First, it is clear that a polymer may be a n enthalpic stabilizer in one dispersion medium and an entropic stabilizer in another. For example, PEO is an enthalpic stabilizer in water (4) and an entropic stabilizer in methanol (5). Likewise polyisobutylene is an enthalpic stabilizer in isopentane (14) and an entropic stabilizer in n-pentane (21). In the latter case, the difference between the two dispersion media is the rather subtle chemical difference

TABLE II Classification of Sterically Stabilized Dispersions Near to the Critical Flocculation Point Stabilizer Type

Dispersion medium Example

Classification

Poly (laurylmethacrylate) Poly ( 12-hydroxystearic acid) Polystyrene Polyisobutylene Poly (ethylene oxide) Polystyrene

Nonaqueous Nonaqueous Nonaqueous Nonaqueous Nonaqueous Nonaqueous

n-Heptane n-Heptane Toluene n-Heptane Methanol Methyl acetate

Entropic Entropic Entropic Entropic Entropic Entropic

Polystyrene Polyisobutylene

Nonaqueous Nonaqueous

Methyl acetate 2-Methylbutane

Enthalpic Enthalpic

Poly(ethytene oxide) Poly(vinyl alcohol) Poly(methacrylic acid)

Aqueous Aqueous Aqueous

0.48 M MgSO4 2 M NaC1 0.02 M HC1

Enthalpic Enthalpic Enthalpic

Poly(acrylic acid) Polyacrylamide

Aqueous Aqueous

0.2 M HCI 2.1 M (NI-I4)~SO4

Entropic Entropic

Poly(vinyl alcohol) Poly (ethylene oxide)

Mixed Mixed

Dioxan/water Methanol/water

Combined Combined

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STERIC STABILIZATION TABLE III Comparison of Theta-Temperature with Critical Flocculation Temperature Stabilizer

MoIecular weight

Poly(ethylene oxide) Poly(ethylene oxide) Poly(ethylene oxide)

10,000 96,000 1,000,000

Cfpt/°K

0/°K

0.39 M MgSQ 0.39 M MgSO4 0.39 M MgSO4

318 4- 2 316 4- 2 317 4- 2

315 :t= 3 315 4- 3 315 4- 3

9,800 51,900 89,700

0.2 M HCI 0.2 M HC1 0.2 M HCI

287 4- 2 283 4- 2 281 4- 1

287 4- 5 287 4- 5 287 4- 5

Poly(vinyl alcohoI) Poly(vinyl alcohol) Poly(vinyl alcohol)

26,000 57,000 270,000

2 M NaC1 2 M NaC1 2 M NaC1

302 -4- 3 301 4- 3 312 4- 3

300 4-4-3 300 4- 3 300 =t=3

Polyacrylamide Polyacrylamide Polyacrylamide

18,000 60,000 180,000

2.1 M (NH4)2SO4 2.1 M (NH4)2SO4 2.1 M (NI-I4)2SO4

292 4- 3 295 4- 5 280 4- 7

Polyisobutylene Polyisobutylene

23,000 150,000

2-methylbutane 2-methylbutane

325 4- 1 325 4- i

Poly(acrylic acid) Poly(acrylic acid) Poly(acrylic acid)

Disl)ersion medium

between two positional isomers; yet it leads to a reversal of the roles of the enthalpy and entropy contributions to stabilization. Secondly, the evidence to support the classification of dispersions as combined enthalpic-entropic stabilization is necessarily indirect because it is not possible to approach the cfpt directly. Finally, note that although only one dispersion has been demonstrated to date to exhibit flocculation both on heating and on cooling, all dispersions in principle should display similar behavior, if only a sufficiently wide range of temperature and pressure could be scanned. The next question that must be resolved is whether the critical flocculation point can be identified in some general way. The answer is found experimentally to be the same irrespective of whether we are considering aqueous or nonaqueous systems; or whether flocculation is induced by a change in temperature or by a change in pressure, or by the addition of nonsolvent. The critical flocculation point correlates strongly with the corresponding theta (0)-point of the stabilizing moieties in free solution (4, 10-16). The 0-point is variously defined from both the conformational

325 4- 2 325 4- 2

and the thermodynamic viewpoint. The different definitions are not always equivalent. For our purposes the definition of a 0-point that is most germane is a thermodynamic one. A 0-point will be defined as one where the second viral coefficient of the polymer chains vanishes (22). Experimental methods for the absolute determination of 0-points include light scattering and osmometry (22). Quicker, but perhaps less soundly based methods have been developed by Elias (23, 24) and Cornet and van Ballegooijen (25). Nevertheless, these quicker methods give good agreement with the absolute methods (22) and they can be shown to have a thermodynamic basis (25). Shown in Table I I I is a comparison of some 0-temperatures and critical flocculation temperatures. The 0-point is a measure of the magnitude of the segment-solvent interaction. As such the 0-point ought to be essentially independent of the molecular weight of the polymer. The PEO data provide good evidence to support this assertion. Changes in the molecular weight of the stabilizing moieties of three orders of magnitude scarcely altered the measured 0-temperature. Neither were the cfts of P E O stabilized latices significantly influ-

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D. H. NAPPER

enced by comparable changes in molecular weight. The strong correlation between the 0-temperatures and the cfts is apparent from Table III. Similar strong correlations have been observed between 0-pressures and cfps (13), and 0-volumes and cfvs (10). Note that the data are not sufficiently precise to allow any statement to be made with regard to stability under 0-conditions. All that can be concluded is that 0-conditions represent a practical thermodynamic limit to the stability of some model sterically stabilized dispersions. From the experiments (4, 10) that have been conducted thus far, it would appear that the critical flocculation point is essentially independent of the size of the core particles, the nature of the disperse phase (if polymeric), and the nature of the anchor polymer (if insoluble in the dispersion medium). Such independence would be expected if the cfpt correlated with the 0-point. The cfpt, however, does depend upon the extent of the coverage of the surface. The correlation between the cfpt and the 0-point is only observed (4, 10) if the surface is fully covered (i.e., the plateau of the adsorption isotherm has been attained), At lower surface coverages, flocculation occurs in dispersion media that are better solvents than 0-solvents. This may be a consequence of lateral movement of the stabilizer, of desorption or even, perhaps, of bridging flocculation by the stabilizing chains.

Enhanced Steric SlabilisaEon

We have noted in the foregoing description that the general pattern of incipient flocculation behavior is disrupted if the stabilizing moieties are only weakly attached to the surface. A different pattern of behavior may also result if the stabilizing chains interact too strongly with the surface (27). Strong interactions between the chains and the surface can produce anchoring at many points along the stabilizing chain. This is termed multipoint anchoring. One consequence of multipoint anchoring is that the free-solution thermodynamics may no longer be relevant. No correlation between the cfpt and the 0-point for the chains in free solution would then be expected. So far only one system exhibiting this type of behavior has been investigated in any detail (27). The strong interactions in that case were those between stabilizing poly(ethylene oxide) chains and carboxylic acid groups. The carboxylic acid groups were at the surfaces of polystyrene latex particles. It was found that at suitably low pH valueS, such latices were stabilized by poly(ethylene oxide) in dispersion media that were significantly worse solvents than 0-solvents. The low pH values were apparently necessary to ensure that H-bonding was possible between the protonated carboxylic acid groups and the ether oxygens of the stabilizing moieties. Figure 2 displays the cft of such latices as 340 a function of the solution concentration of the 330 stabilizer. The cft exceeded the 0-temperature significantly at solution concentrations corresponding to incomplete surface coverage. 310 This was interpreted as resulting from multipoint anchoring. At higher solution concentraI I ] I 29C --K t ~ O.O 0.2 0.4 0.6 0.8 1.0 2.0 tions, the adsorption of more stabilizer resulted WT. OF SURFACTANT/ WT. OF PARTICLES in a reduction in multipoint anchoring. The FIG. 2. Plots of the cft versus concentration of frequently encountered correlation between the stabilizer for latex particles stabilized by poly (ethylene cfpt and the free solution 0-point reappeared oxide) of molecular weight 10,000 at pH = 4.65. Curve a t the higher solution concentrations. 1, poly(vinyl acetate) lattices (no carboxylic acid Stability in worse than 0-solvents is termed groups) ; curves 2 and 3, low carboxyland high carboxyl enhanced steric stabilization. The magnitude polystyrene lattices, respectively; curve 4, polyof the enhancement (i.e., the penetration into (styrene-co-acryllc acid) latex particles.

3o032°

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STERIC STABILIZATION

the worse than 0-solvent domain) was found to depend upon such factors as the pH, the molecular weight of the stabilizing moieties, and the density of surface groupings. The enhancement decreased with increasing pH, increasing molecular weight, and fewer surface carboxylic acid groupings. These trends are just those expected for a reduction in multipoint anchoring. Experiments on enhanced steric stabilization provide some clues as to the range of vaiidity of the assumption that the thermodynamic properties of the stabilizing moieties in free solution are relevant to stabilizing chains attached to an interface. STABILIZATION IN POLYMER MELTS Recent experiments have shown that it is p3ssible to prepare stable latices in polymer melts (28). The pattern of flocculation behavior is again different from that observed near to the 0-point. It was found that there was apparently an upper limit to the size of the latex particles that could be stabilized by a given molecular weight stabilizer. Some results are shown in Table IV for stabilization in poly(ethylene oxide) melts. The molecular weight of the stabilizer was the same as that of the melt polymer. The higher this molecular weight, the larger was the maximum particle size that could be stabilized. Thus, in the melt, incipient instability appears to depend critically upon the stabilizer molecular weight and the particle radius. As discussed above, neither of these factors was found to be important in studies on incipient instability near to the 0-point. Different patterns of behavior suggest fundamental differences in the primary origins of stability in the two types of dispersions. F L O C C U L A T I O N BY H I G H C O N C E N T R A T I O N OF P O L Y M E R

In the foregoing presentation of the experimentally observed phenomenology associated with stericalty stabilized dispersions, it was noted that latices stabilized by PEO could be prepared in pure water and also in pure

39 7 T A B L E IV

Apparent Maximum Latex Particle Sizes in PEO Melts at 70°C Molecular weight

600 1500 6000

Maximum particle size/nm Experimental

Flory theory + Monte Cmlo

Dolan and Edwards

30-60 100-150 300-500

50 100 500

92 145 290

PEO melt. It is surprising to find, therefore, that the addition of PEO to the aqueous dispersion medium of a PEO stabilized latex in water may induce flocculation. This was first demonstrated by Li-in-on et al. (29), who showed that the stability of such latices exhibited a minimum as the volume fraction of added PEO increased. The position of the minimum depended critically upon the molecular weight of the added PEO but typically occurred at volume fractions in the range 0.3-0.8. The lower molecular weight polymers were less effective in inducing flocculation. It should be noted that the instability domain was quite broad. Moreover, if water is added to polymer latices prepared in a PEO melt, flocculation is also observed (28). Whether such phenomena are exhibited by all sterically stabilized systems remains to be established. However, Li-in-on el al. (29) reported qualitatively similar results for polystyrene latices stabilized by polyisoprene. THEORIES OF STERIC STABILIZATION There does not appear, at least to date, to be significant disagreement about the experimental aspects of incipient instability. However, formulation of a physically realistic theoretical framework within which these data may be interpreted is decidedly controversial. The Unimporlance of the London-vau der Waals Forces

In the DLVO theory for electrostatic stabilization, the London-van der Waals dispersion forces play a central role as the primary

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D. H. N A P P E R

driving force towards coagulation. It is tempting to assume, by analogy, that dispersion forces are also very important in determining the incipient instability of sterically stabilized latices. This may well be true, e.g., for very low molecular weight chains; for very large particles; for incompletely covered surfaces; or for poorly anchored stabilizers. Moreover, it seems likely that the stability of latices prepared in polymer melts is probably determined primarily by the van der Waals interactions between the core particles (28). It appears to be extremely unlikely, however, that the incipient instability behavior of model systems, which was discussed above is a consequence of dispersion forces. Any realistic calculation of the magnitude of the London forces between particles stabilized by chains of molecular weight greater than say, 10 000, strongly suggests that the dispersion interactions are negligibly small. This conclusion holds at the ordinary distances of close approach sampled in a Brownian collision but may break down if the particles are forced by compression to approach more closely. It should be noted that Meier (30), Hesselink et al. (31), and Edwards and co-workers (32; 33) ascribe central importance to the dispersion interactions between the core particles. In our view, their assumed values (of order 10-19-10-2° J) for the Hamaker "constant" (which may, in electrolyte-free systems, be variable) are at least an order of magnitude too large for polymer latex particles (34). If the London dispersion forces are not responsible for incipient instability then alternative attractive interactions must be invoked to account for flocculation. It is well known (35) that polymer segments become self-attracting in worse than 0-solvents. Thus segmental interactions appear to be responsible not only for stability but also for incipient flocculation near to the 0-point.

The Two Domains of Close Approach In order to understand flocculation behavior, it seems to be imperative to distinguish between two domains of close approach o f two

sterically stabilized colloidal particles. Let L represent the contour length in solution of the highest molecular weight stabilizing moiety and d be the minimum distance of close approach of the surfaces of the core particles. If d/> 2L, then no direct interaction is seemingly possible between the polymer chains attached to the different particles. If, however, L ~< d < 2L then the polymer chains on the opposing surfaces may, in principle at least, undergo segmental interpenetration. Not until d < L can there be compression of the chains attached to one surface by the impenetrable surface of the other particle; in principle, therefore, both interpenetration and compression may occur in this domain. It is convenient in what follows to refer to the L ~< d < 2L region of close approach as the interpenetration domain and to the inner region, d < L, as the interpenetration plus compression domain. Note that L may often be conveniently regarded as the barrier layer thickness rather than the contour length, without altering the foregoing arguments. Of course, whether interpenetration occurs exclusively (or even at all) in the interpenetration domain will depend critically upon both the kinetic and thermodynamic parameters that govern any specific act of close approach. The approaching macromolecules may have insufficient time to undergo interpenetrational relaxation and if so, some compression may occur. Interpenetration is clearly one extreme possibility in this domain; it seems likely to correspond to the lowest free-energy state because any compressional interactions result from the exclusion of the segments completely from some elemental volume rather than from part thereof. T H E G E N E R A L P H Y S I C A L BASES F O R STERIC STABILIZATION

For our purposes, the simplest way to view the behavior of polymers in solution is to regard them as occupying two different spaces. The first is a thermodynamic space in which the polymer segments occupy an excluded volume that may be positive, negative, or zero. In

Journal of Colloid and Interface Science, Vol. 58, No. 2, February 1977

STER!rC ST,~,B[I~IZATION addition, the segments exist in real space in which their real volumes are necessarily always positive. The first space gives rise to what Flory (35) termed "mixing" effects, whereas the second space gives rise to "elastic" contributions. These two spaces are at least weakly coupled because the coordinates of the centers of mass of the segments in real space are determined by excluded volume effects. Flory (35) used these bases in his classic treatment of the excluded volume effect. The mixing free energy on interpenetration or compression can be positive or negative according to the sign of the segmental excluded volume. On the other hand, the elastic freeenergy term is always positive for movements away from the mean equilibrium conformation. The total free-energy change is obtained by simply summing the mixing and elastic terms. The propriety of separating these two effects has been called into question (33). Nevertheless, the Flory theory for the intramolecular expansion factor a has proved (36) to be fairly accurate when compared with experiment; it has not greatly been improved upon over the years, despite the expenditure of significant effort (36). In our view, the application of this approach to steric stabilization ought to provide a realistic first-order theory. Note, however, that Osmond et al. (19) have put forward the contrary view without apparently providing compelling substantiating arguments. The Interpenetration Domain In what follows, we will assume that the stabilizing macromolecules have sufficient time to interpenetrate if the core particles approach one another. As the polymer chains interpenetrate, solvent molecules will be forced out of the interpenetration volume. There will clearly be a free energy associated with this solvent exclusion. Whether there is a significant elastic contribution in this domain is still an open question. Undoubtedly, given sufficient time, the interpenetrated chains will relax into new conformations different from those in the absence of interpenetrations. Consequently, it

oO

seems indisputable that there will be an elastic contribution. But the volume fraction of real space occupied by the segments of a polymer molecule is quite small on average (usually ~<0.1) and will be even smaller in the peripheral regions of the chains that are involved in interpenetration. It seems unlikely, therefore, that there is a significant elastic contribution to stabilization in the interpenetration domain. Osmond et al. have, however, contended in a recent review that there is a significant elastic contribution (19). The problem of the interpenetration of two polymer molecules in solution has been treated by Flory and Krigbaum (37), using the FloryHuggins theory for polymer solutions. Their theory assumes that the segment density distribution funct{ons of the chains are the same before and after interpenetration. Strictly speaking, this cannot be correct, if the macromolecules have sufficient time to relax to their equilibrium conformations. Because the density of polymer segments is likely to be quite small and to be symmetrically displaced about the interpenetration zone, it seems probable that this effect is quite small. Recent calculations by Dolan and Edwards (33) support this viewpoint. They found relatively small perturbations of one chain by the presence of another. It is our opinion that this effect is likely to be insignificant compared with the gross inadequacies of the Flory-Huggins theory. It seems pointless to include these relaxation effects without introducing more sophisticated theories of polymer solutions, such as the FloryPrigogine free-volume theory. According to the Flory-Krigbaum theory, the free energy of interpenetration of two chains brought from infinite separation to a separation d may be written as

where V~ = volume of segment, V1 = volume of a solvent molecule, xl = interaction parameter, pa and pa' are the segment density distribution functions of the two chains, respec-

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D. H. NAPPER

tively. The integration is taken over the entire volume of interpenetration. The adaptation of Eq. [-2] to steric stabilization is almost, but not quite, trivial. Consider two parallel flat plates to which stabilizing chains are irreversibly attached. The problem is dramatically simplified if we assume that the segment density parallel to the surface is constant. This is an intuitively satisfying assumption but it is an approximation at best. The free energy of interpenetration per unit area (zXGIp) then becomes

AGUe = 2kT(V~2/V~)v2i2(½ -- xl) X

d~dtdx d d--L

,

~3"~

I

where d is now the distance of separation of the flat plates. The segment density distribution functions have been normalized so that

fo L ~adx = 1 and ~i is the total number of segments in the volume normal to unit surface area of one flat plate at infinite separation. The x-direction is chosen normal to the surface. The evaluation of the integral in Eq. [-3] can be achieved, either numerically or analytically, once the nature of the segment density distribution functions has been specified. Both the constant segment density (38) and a Gaussian type of distribution (39) function have been evaluated analytically. A flat-plate potential (FP) can be transformed into a sphere (S) potential for thin layers and large particles by using the Deryagin integration (40) procedure:

o

where a = particle radius and do = minimum distance of separation between the surfaces of the particles. Thus, for the interpenetration of two constant segment densities, we find that ~ a s ~ 2~'N.o,~(v~V¢~)(½ -- X~)C*Skr.

[5]

Here S = 2 ( 1 - do/2Lfi, w = weight of stabilizing moieties per unit surface area, and v2 = partial specific volume of the moieties (38). One virtue of Eq. ['5] is that it predicts the observed flocculation near to the 0-point. For solvents better than 0-solvents, xl < ½ and the free energy of close approach is positive. On the other hand, for worse than 0-solvents, Xl > ½ and the free energy of close approach in the interpenetration domain becomes negative. If sufficiently large, this attraction between the attached chains can lead to flocculation. Thus the foregoing approach would predict flocculation in somewhat worse than 0-solvents. Numerical calculations suggest that in many systems flocculation should occur within a few degrees of the 0-temperature (39). This would explain the observed correlation between the cfpt and the 0-point. The foregoing theory is also able to explain the observed temperature dependence of stability. The thermodynamic parameter (½ - xl) may be rewritten in terms of the classical entropy (~bl) and enthalpy (K1) parameters through the relationship: 1

-- x~ = ¢~ -- K1 = ¢1(1 -- O/T),

[6]

where 0 = theta-temperature. All the evidence currently available suggests that for model dispersions, the signs of zXS~ and zXH~ may be equated to those of -~b~ and -K1, respectively. Since the signs of both ¢1 and K1may assume both positive and negative values, the whole gamut of behavior summarized in Tables I and II becomes readily explicable. Of course, at this point, our discussion of zXHa and zXS~has become model-dependent. The values of ~1 and K1 that are relevant here are those determined experimentally. Any attempt to explain the signs and magnitude of ¢~1 and KI will demand a more elaborate theory than the Flory-Huggins theory. It is stressed yet again that the signs of 2XHR and ASR are determined near to the cfpt in a rigorous thermodynamic and model-independent fashion by the temperature dependence of stability. The strong correlations observed between the cfpt and the O-point provides comforting

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STERIC STABILIZATION reassurance of the insignificance of elastic effects in the interpenetration domain. Elastic interactions are independent of the solvency of the dispersion medium and if strong, would demand significantly worse solvency than 0-solvents to induce flocculation. This is not found experimentalIy. Osmond el al. (19) have argued that the correlation between the cfpt and the 0-point is rather fortuitous, being an artefact of the method of determining 0. This claim overlooks the fact that the correlation is observed irrespective of the method used to determine 0. Perhaps the most precisely determined 0-temperature is that for polystyrene in cyclohexane. The value 0 = 307 4- I°K is generally agreed upon. March (41) has shown that the reversible cft for water-in-cyclohexane emulsions sterically stabilized by well-anchored polystyrene is 308 4- 3°K. This type of experiment suggests that the correlation between the cfpt and 0 is far from being a consequence of artefactual serendipity. The Inlerpenelration Plus Compression D o m a i n

If two spheres approach such that do < L, then both compression and interpenetration of the stabilizing chains may occur. Intermolecular interpenetration gives rise to a mixing term as described above. Compression of the chains attached to one surface by the impenetrable opposing surface produces two effects: the first is an intramolecular self-interpenetration, which is accompanied by a corresponding mixing term; the second effect is the configurationaI compression, which results in an elastic term. Of course, the aforementioned intermolecular interpenetration term must be calculated for compressed chains. The total free-energy change in this domain may, therefore, be split up into three terms : A G ~+c

sight from Eq. [-2]. Thus, for fiat plates, ~ G F p ~ x (inter) = 2k T (V~2/' V~) (½ -- Xl) ~i 2 )4

d~d;dx \JO

, ¢

Moreover, AGF~Mix (in tra) = 2k T (V~2/VI) (½ -- X~)~2i2 X

(/0 / ; ) ~j-

~Vx

[-7]

where ~ = compression ratio

(=d/L

in this

case). The theory for spheres is once again developed through Deryagin integrations. A typical formula for spheres, if we assume a symmetrical Gaussian distribution function for polymer chains between two flat plates, is A G s I+C ~

27ryAw2(v22/?Q (½ -- xl)aZ/{T

where S = 0.5 + 2.3484 in (/./'do)

The first two terms may be written down on

,

where the factor of 2 now allows for the presence of two surfaces. Note that the intramolecular interpenetration term is derived from the intermolecular term simply by setting /~d = /~d t since it is self-interpenetration. Of course, allowance must be made in this case for the mixing term due to self-interpenetration at infinite separation. The importance of an eIastic contribution to steric stabilization was probably first stressed by JEckel (42), although he appears to have used the term in a somewhat different sense from that employed here. The simplest method by which to calculate the elastic contribution seems to be that developed by Flory (35) in the theory of rubber elasticity. This allows different types of segment density distribution functions to be studied. For a Gaussian distribution function, the Flory approach yields:

+ 2 7 r c m k r ( ~ -- go/2 -- 6o'/6 + ao In go),

= 5 GS~IX(inter) + AGM~X(intra) + AGELAs'nO.

401

--0.498(L --do)/(r2)t

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D. H: NAPPER

rately the maximum particle that can be stabilized in polymer melts. The Edwards theory (33), however, to be discussed below, will 3 probably prove in the long run to be a more 4O powerful and physically satisfying approach. 20 10 aOs The elastic contribution to the free energy J of close approach rises quite abruptly once the 20 1 \\NN\ particles are sufficiently close for elastic effects to become significant (39). Three important \\.< consequences follow from this. First, the repulsive elastic term is dominant in very close 10 20 3 approach, even in worse than 0-solvents. For do/n m this reason, most sterically stabilized particles appear unlikely to exhibit the primary miniFIG. 3. The distance dependence of the repulsion between polyacrylonitrile latex particles stabilized by mum so important to the understanding of the polystyrene in toluene. Curve 1, data of Doroszkowski stability of electrostatically stabilized disperand Lambourne; curves 2 and 3, theory of Smitham, sions. Accordingly, the ubiquitous statements Evans, and Napper with mixing term only (2) and in textbooks of colloid science that all diswith mixing plus elastic term (3). persions of colloidal particles are thermodyNote that in Eq. [-9], 60 = do/L and (r2){ = rms namically unstable may require qualification. end.to-end length in free solution. Sterically stabilized latices in dispersion media A comparison of the predictions of Eqs. [-5] that are good solvents for the stabilizer may and [9] with the experimental results of well be thermodynamically stable. If that is Doroszkowski and Lambourne (43) is pre- so, the classical textbook statement must be sented in Fig. 3. These refer to polyacrylonitrite restricted in its application to electrostatically particles stabilized by polystyrene in toluene. stabilized dispersions. There are no major adjustable parameters in The second point to be made in this context this model. The agreement seems reasonable follows from the first. Because the elastic conat larger distances of separation. On close ap- tribution exceeds thermal energy so abruptly, proach, however, the theory predicts much the predominant region of close approach stronger interactions than were observed sampled during a Brownian collision will be the interpenetration domain, together with experimentally. Note that in polymer melts the large values that part of the interpenetration plus comfor 171 render the mixing terms very small. pression domain that admits of negligible Stability in those systems appears to derive elastic contributions (39). This implies that primarily from elastic interactions (28). This only mixing terms will be important in deteraccounts very well for the different phenome- mining incipient flocculation. The body of nology observed. The above mentioned theory experimental data available to date supports predicts, that there is a maximum particle size this inference overwhelmingly. It is for this that canbe stabilized by a given low molecular reason that elastic contributions to steric staweight polymer. Of course, it is necessary in bilization prove experimentally to be somewhat these systems to include the London-van der elusive. They are perhaps most easily perceived Waals dispersion attraction between the core experimentally in melt systems or in tile comparticles, for these interactions constitute the pression of flocculated latices. dominant constraint on stability. Provided Finally, it should be noted that incipient that a realistic, Monte Carlo predicted value for the "elastic thickness" of the steric barrier flocculation near to the 0-point appears to take is adopted, the theory predicts fairly accu- place in a potential energy minimmn that is Journal of Colloid and Interface Science,

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S T E R I C STABILIZATIION

403

analogous to the secondary minimum in electrostatically stabilized systems. It must be regarded as a pseudo-secondary minimum, however, because, as discussed above there is no apparent primary minimum (see Fig. 3). Therefore the pseudo-secondary minimum is determined primarily by the mixing parameters. The rheologicat data of Hunter et al. (44) on latices flocculated near to the 0-point provides strong support for this viewpoint.

dictions of theory with the results of experiment. The merit of any theory, however, must surely be directly related to its ability to comprehend the results of a wide range of experiments. Space permits but a brief review of these theories, all of which have contributed, to a greater or lesser extent, to the development of the subject.

O T H E R T H E O R I E S OF S T E R I C STABILIZATION

Mackor (45, 46) was perhaps the first to attempt to calculate the repulsive energy barrier in steric stabilization. His primitive, yet germinal, theory estimated the loss of configurational entropy of a rigid rod, freely jointed to one fiat plate, on the approach of a second parallel flat plate. The free-energy change was calculated directly from the decrease in entropy for it was assumed that enthalpy effects could be ignored. Of course, such calculations, which ignore the solvent completely, are unlikely to possess any quantitative predictive value. In addition, most steric stabilizers are synthetic macromolecules that exhibit a high degree of external flexibility. Note that Bagchi and Vold (47) have extended Mackor's theory to spheres. Clayfield and Lumb (48-52) in a series of papers have elaborated upon the approach of Mackor. They have allowed for the flexibility of the stabilizing chains by computer simulation, using Monte Carlo methods. A cubic lattice was adopted and it was claimed that the excluded volume effect was incorporated into the models by not allowing more than one segment to occupy any given lattice site. Osmond el al. (19) have asserted that this approach is the best that has been developed thus far. We would contest the assertion of Osmond el al. (19). First, it is by no means clear physically to what process the loss of entropy calculated by Clayfield and Lumb actually refers. The claim that the excluded volume effect was allowed for might suggest that it was part of the entropy of compression associated with the mixing term. Yet the solvent was virtually

Many of the theoretical concepts discussed above were developed by Evans, Smitham, and the author. This approach provides the only theory that has been compared with experiment in at least three different stability regions: these are incipient flocculation near to the 0-point; long-term (thermodynamic?) stability; and stability and incipient flocculation in polymer melts. The predictions of this theory of steric stabilization are in excellent qualitative agreement with the results of experiment in all three areas. The quantitative predictions of the theory are also in fair agreement with experiment. Only one type of experiment is not easily encompassed by the foregoing approach. This is the flocculation that is induced by the addition of moderate to high concentrations of polymer to the dispersion medium. This phenomenon is, however, brought within the ambit of our approach if it results from the concentration dependence of the interaction parameter, which may well become greater than or equal to ½. The phenomenon would then fall into the category of flocculation near to the 0-point. Certainly this interesting observation requires more detailed study. Other theories of steric stabilization, which differ either in matters of detail or in general approach, have been proposed. They all appear, with perhaps one notable exception, to fail in some important respect when compared with experiment. We note that in the area of steric stabilization, there seems to have been some degree of reluctance to compare the pre-

Enlropy Theories

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D. H. NAPPER

ignored. There is absolutely no doubt, therefore, that the approach fails to predict the observed incipient flocculation near to the 0-point. Further, the Monte Carlo method is a notoriously ineffectual procedure for treating problems in the thermodynamics of polymer solutions. In our conceptual framework, it seems that what Clayfield and Lumb actually calculated is an elastic contribution to the free energy of close approach. Fischer' s Soh'ency Theory

Fischer (20) was perhaps the first to stress the importance of the molecules of the dispersion medium in steric stabilization. He recognized that in the interaction zone, the molecules of the dispersion medium (hereafter termed the solvent) may have a chemical potential different from that in the external bulk phase. If this chemical potential is less than that in the bulk phase, solvent molecules from the bulk phase flow into the interaction zone and force the particles apart. The key role of the solvent in steric stabilization thus becomes apparent. Fischer, however, only considered the interpenetration of two layers of constant segment density. His simple theory makes no allowance for compressional interactions and ignores elastic effects completely. But, because elastic effects are so repulsive, interpenetration is the main effect apparent in Brownian collisions. Accordingly, the Fischer theory predicts the observed incipient flocculation near to the 0-point. It does not, however, comprehend stability in polymer melts. Entropy Plus Soh ency Theories

Meier (30) proposed that the entropy and solvency concepts should be added to obtain the total interaction. He regarded the mixing contribution as an osmotic effect and the elastic term as one deriving from volume restriction. Hesselink et al. (31) subsequently adopted Meier's terminology. In our view, this terminology is confusing. There are contributions to the mixing term that result from the

restriction of the available volume by the approaching impenetrable surface. The GibbsDuhem relationship, moreover, assures that elastic contributions may give rise to differences in the chemical potential of the solvent in the interaction zone, i.e., to osmotic effects. The terms "mixing" and "elastic," as cited by Flory, seem to be more appropriate. Meier (30) estimated the elastic term by application of the diffusion equation and the mixing term by using Flory-Krigbaum theory. His results, however, are in error because the polymer chains were, in fact, allowed to penetrate the impenetrable barriers. Subsequently, Hesselink et al. (31) corrected this mistake. Their calculations predicted (a) that the boundary between stability and instability should be very sensitive to the molecular weight of the stabilizing moieties, (b) that stability should be observed in significantly worse than 0-solvents, and (c) that no correlation should be evident between the cfpt and the 0-point. None of these predictions appears to be realized in incipient instability studies. In attempting to trace the source of this discrepancy between theory and experiment, Evans and the author (53) tentatively attributed it to an erroneous adoption of standard states. Osmond et al. (19) have argued against this ascription of the discrepancy. We now accept that our tentative proposal is incorrect, although not for the reasons adduced by Osmond et al. As noted by the latter authors, both Meier (30) and Hesselink et al. (31) invoke London dispersion forces to explain incipient instability. They assume values for the Hamaker constant that are at least an order of magnitude too large for latex particles. If the value of the Hamaker constant is reduced to a more realistic figure, the predictions of Hesselink et al. become even more discordant when compared with experiment. We now believe that the discrepancies can be traced to the use of segment density distribution functions that extend to infinity, rather than being truncated at the contour length. As a result, any distinction between the inter-

Journal of Colloid and Interface Science, Vol. 58. No. 2, February 1977

STERIC STABILIZATION penetration and the interpenetration plus compression domains becomes blurred. There results a significant elastic contribution at all separational distances of interest. Such an elastic term would destroy any correlation between the 0-point and the cfpt, and would be strongly molecular weight dependent, as is predicted by the calculations of Hesselink et al.

Bagchi (54-58) has extended the earlier ideas that he published with R. D. Vold (47, 59, 60) on what he has termed a "denting" model. This model assumes that when the stabilizing chains attached to one particle come in contact with those attached to another particle, the chains are compressed as if they had come in contact with an inlpenetrable surface. Such an assumption is intuitively disquieting in the light of the small segment densities involved, at least in the peripheral zones. The incipient flocculation results seem to be quite decisive in eliminating the denting models for that case at least. A strong elastic contribution would again be implicit in the denting model, obscuring any correlation between the cfpt and the 0-point. Note, too, that Bagchi applies the Flory-ttuggins theory in a self-inconsistent fashion. He retains the logarithmic form for the entropy of mixing term; yet he uses experimental data derived on the assumption that the logarithmic term is truncated after the second power of the volume fraction. This is not a pedantic objection, for such an inconsistency demands that x1 be ca. 0.6 for incipient flocculation. As a result, any correlation between the cfpt and the 0-point is totally obscured. I)olan and Edwards (32, 33) have recently provided an important signpost to how the second generation of entropy plus solvency theories will be developed. All the theories described in this section have demanded significant digital computation. Simple analytical formulas were missing. Of course, the theory developed in the present author's laboratory is essentially of an entropy plus solvency type; this study, moreover, has been directed toward the generation of analytical formulas. It is a

405

first-generation theory, however, for it uses the now obsolete Flory-Huggins theory (albeit in an updated, pragmatic fashion) and separately calculates the elastic and mixing terms. Dolan and Edwards (32, 33) have shown how it is possible to solve the diffusion equation for a polymer attached at one end to an impenetrable flat surface by exploiting either the method of images or an eigenfunction expansion method. Approximate analytic expressions can then be generated for the loss of entropy on approach of a second flat surface. The original theory was developed in the absence of excluded volume effects but subsequently these were incorporated into the theory by a powerful self-consistent field device. Unfortunately, to date no comparison between theory and experiment has been published for the case where excluded volume effects are important. As analytical formulas are still lacking for that case, resort to digital computation is mandatory. The method does appear, however, to offer significant potential for calculating, without artificial separation, the mixing and elastic terms. In addition, the theory developed for the elastic contributions can be expressed approximately in closed form ; when due allowance is made for the curvature of the particles, these formulas provide a realistic basis for estimating the maximum particle size that can be sterically stabilized in polymer melts (61). CONFORMATION OF MACROMOLECULES AT AN INTERFACE The conformation of macromolecules at an interface is important in the theory of steric stabilization because it determines the segment density distribution function. This in turn controls the distance dependence of the steric repulsion in stable systems. Note that incipient flocculation is apparently insensitive to the segment density distribution function. The theories (62, 63) developed for the adsorption of a homopolymer at an interface could well lead to the inference that adsorption at various points along the chain would produce a flattened stabilizer conformation at the

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particle surface. This inference is almost surely incorrect. All the experimental evidence available thus far for sterically stabilized latices suggests that the macromolecules are in an extended conformation normal to the interface (64-68). This extension exceeds significantly that predicted for a 1-D random walk normal to an impenetrable barrier (69). The foregoing experimental observation may be rationalized if we recall that block and graft copolymers are the most effective steric stabilizers. Hence the free energy of adsorption is made up of contributions from both the anchor polymer and the stabilizing moieties: AG ads = AG anchor _[_ AG stab. Clearly, AG ads may be negative, even if AG stab is positive. It requires only that AG anch°r be sufficiently negative. That will be true if the chains are suitably well anchored, as is required for steric stabilization. This is not to argue that the stabilizing moieties adopt, in all cases, a thermodynamically unfavorable conformation. Rather it is a cautionary warning of the difficulty of trying to predict, by minimization of its free energy, the conformation of a stabilizing moiety. The presence of the anchor polymer may well vitiate this approach. We originally ascribed the additional extension at an interface to the compression of the stabilizing moieties by close packed contiguous chains (38). Monte Carlo calculations on the problem of a polymer-in-a-box fail, however, to substantiate this hypothesis, at least at the normal packing densities observed experimentally (70). The extension normal to the interface appears to be a consequence of excluded volume effects. This conclusion is also supported by the self-consistent field approach of Dolan and Edwards (33). If this conclusion is correct, previous theories of macromolecular conformations at interfaces, which ignore excluded volume effects, are likely to be substantially in error (71, 72).

CONCLUSIONS This review of the present status of steric stabilization is intended to convey some sense of the dramatic improvement in our understanding of the principles governing steric stabilization. Hopefully, such primitive notions as ascribing steric stabilization to "hydration effects" have been swept away and replaced by more precise physical concepts. That is not to say that much does not remain to be done. Incipient instability near to the 0-point is now fairly well characterized experimentally. The distance dependence of the repulsive barrier for stable dispersion needs further experimental characterization. This should allow the now emerging theories of steric stabilization to be tested in more detail. In this process, the first generation theories will undoubtedly be superseded by more complete descriptions of steric stabilization. ACKNOWLEDGMENTS It is a pleasure to express my gratitude to my coworkers, Messrs. R. Evans, J. B. Smitham, R. Feigin, and G. March, each of whom has contributed significantly to my understanding of the subject. I am grateful to the ARGC for financial support of our studies. I thank the Australian-American Educational Foundation for the award of a Fulbright-Hays Senior Scholar's Travel Grant. REFERENCES 1. "Encyclopaedia Brittanica," Vol. 12, p. 257, 1968; Vol. 17, p. 38, 1968. 2. HEELER, W., AND PUGS, T. L., J. Chem. Phys. 22, 1778 (1954). 3. BARRETT, K. E. J., "Dispersion Polymerization in Organic Media." Wiley, London, 1975. 4. NAPeER, D. H., J. Colloid Interface Sci. 32, 106 (1970). 5. NAPPER, D. H., AND NETSCHEY, A., J. Colloid Interface Sci. 37, 528 (1971). 6. NAPPER, D. H., AND HUNTEI~, R. J., M T P Int. Rev. Sci. Set. 1 7, 280 (1972). 7. FLEER, G. J., AND LYKLEMA,J., J. Colloid Interface Sci. 46, 1 (1974). 8. HELLER, W., AND PUGH, T. L., J. Chem. Phys. 24, 1107 (1956). 9. HEELER, W., Pure Appl. Chem. 12, 249 (1966). 10. NAPPER, D. H., Trans. Faraday Soc. 64, 1701 (1968).

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Journal of Colloid and Interface Science, Vol. 58, No. 2, February 1977