Elastic steric stabilization

Theories of elastic steric stabilization Dolan and Edwards (1974) have calculated the elastic free energy of repulsion for isolated polymer chains attached terminally to parallel flat plates. It was shown in Section 11.4.1.1. that probability distribution function for a random flight chain obeys the diffusion equation... 

In elastic steric stabilization, the elastic repulsion must exceed the attractive van der Waals interaction for stabiUty to be observed. Dolan and Edwards showed that two types of aggregation occur. The first, corresponding to close adhesion of the particles, occurs if... 

Experimental evidence for elastic steric stabilization There is a paucity of experimental studies of elastic steric stabilization. Smitham and Napper (1976a,b) have shown that it is possible to prepare polystyrene latex particles stabilized by poIy(oxyethylene) and dispersed in molten poly(oxyethylene). These experiments suggested that the maximum particle size that could be elastically stabilized was dependent upon the molecular weight of the stabilizing moieties, as would be expected intuitively. Everett and Stageman (1978a) have also reported the elastic stabilization of poly(methyl methacrylate) particles stabilized by poly(dimethylsiloxane) in liquid poly(dimethylsiloxane). 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

From a technical standpoint, it is also important to note that colloids display a wide range of rheological behavior. Charged dispersions (even at very low volume fractions) and sterically stabilized colloids show elastic behavior like solids. When the interparticle interactions are not important, they behave like ordinary liquids (i.e., they flow easily when subjected to even small shear forces) this is known as viscous behavior. Very often, the behavior falls somewhere between these two extremes the dispersion is then said to be viscoelastic. Therefore, it becomes important to understand how the interaction forces and fluid mechanics of the dispersions affect the flow behavior of dispersions. 

In the final section, we build on the thermodynamic theories of polymer solutions developed in Chapter 3, Section 3.4, to provide an illustration of how a thermodynamic picture of steric stabilization can be built when excluded-volume and elastic contributions determine the interaction between polymer layers. 

One of the first theoretical attempts to understand steric stabilization of dispersions was based on an entropic mechanism that resembles the elastic contribution to AGR. We consider this mechanism in Example 13.3. 

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

Figure 38 shows the shear moduli variation with solid volume fraction for sterically stabilized polystyrene latex suspensions at an oscillating frequency of 1 Hz. One can observe that the particle size does not have a significant effect on the shear moduli when the particles are relatively large, say d > 0.5 pm. For small particles, the size effect becomes noticeable. In all these cases, the shear moduli depict a gradual change from a more viscous (G > G ) behavior to a more elastic (G" < G ) behavior with increasing solid volume fraction. 

It is further remarked that compression, involving as it does the exclusion of the segments from complete volume elements in space, is unlikely to be preferred to interpenetration wherein the segments have access to most (usually more than 70%) of those volume elements. If there is an elastic contribution to steric stabilization, it must surely arise, not directly from a high segment density, but from the loss of flexibihty concomitant with multipoint anchoring at the surface. 

It is possible that an elastic contribution to steric stabilization could have a kinetic, rather than a thermodynamic, origin. The polymer segments in the stabilizing moieties may relax too slowly to allow interpenetration to proceed in the time span of a Brownian collision. A denting mechanism would then be operative in order to transmit the repulsive stress to the particles. This kinetic mechanism for the introduction of an elastic repulsion would predict that the enhancement should be strongly dependent upon the particle size which determines the duration of a Brownian encounter. No experimental evidence for such a particle size dependence has apparently been published. 

The preceding division of the region of close approach of two sterically stabilized particles into three domains leads quite naturally to a discussion of the steric interaction in terms of two basic components the mixing free energy and the elastic free energy. 

The results of Clayfield and Lumb relate entirely to the loss of configurational entropy of the polymer chains on close approach of the particles, due either to the presence of the impenetrable surface of the opposite particle or the polymer chains that are attached to that particle. In the early papers, the effect of the solvent on the conformation of the macromolecules was ignored but an attempt was made to include the role of solvency in some of the later publications. Notwithstanding this, essentially what Clayfield and Lumb calculated was the elastic contribution to Ae repulsive free energy of interaction between sterically stabilized particles. As such, their results are manifestly unable to explain the observed flocculation of sterically stabilized particles that is induced by decreasing the solvency of the dispersion medium. Even if only for this reason, the assertion by Osmond et al. (1975) that the Clayfield and Lumb theory was the best available at that time is clearly untenable. 

Fig. 10.5. The distance dependence of the potential energy of interaction of latex particles sterically stabilized by poly(vinyl alcohol) in water. The different particle radii were (1) 500 nm, (2) 100 nm and (3) 10 nm. The left-hand ordinate corresponds to an elastic modulus of l-4x lO Nm" whereas that of the right-hand side corresponds to l-2x 10 Nm (after Sonntag, 1974).

Hesselink et al. have also evaluated the distance dependence function V(d) [see equation (11.26)] for the elastic free energy contribution to steric stabilization. The result obtained for tails is the same as that published by Meier (1967)... 

Comparison of theory with experiment. It will be shown in Section 13.3.2.1 that the flat plate potentials can be used to calculate the osmotic disjoining pressures in concentrated monodisperse sterically stabilized dispersions. Evans and Napper (1977) have compared the theoretical predictions using the above equations with those measured by Homola and Robertson (1976) for polystyrene latex particles stabilized by poly(oxyethylene) of molecular weight ca 2 000 in aqueous dispersion media. The elastic repulsion in the interpenetrational-plus-compressional domain was estimated from the following expression for the constant segment density model... 

Fig. 12.5. The disjoining pressure as a function of the interparticle distance of separation for spheres sterically stabilized by poly(oxyethylene) curve 1, the experimental results of Homola and Robertson (1976) curve 2, constant segment density model. The crosses (x) show the theoretical results for a softened elastic potential (after Evans and Napper, 1977).

Notwithstanding these criticisms, it remains an experimental fact that the theories of steric stabilization which consider the sole origin of repulsion in worse than 0-solvents to be the elastic repulsion, predict a rise in the repulsion that is seemingly nowhere near sufficiently steep to explain Klein s results. This strongly suggests the operation of another source of repulsive interaction, of which that suggested by Flory is the most soundly based. 

Nonionic surfactants stabilize colloidal systems not by electrostatics but basically by osmotic forces. If two sterically stabilized particles approach each other, the soluble parts of the adsorbed chains causes a higher concentration in the interstitials when compared to the average continuous phase. This will cause a flux of continuous phase into the interstitials, which subsequently leads again to drop separation. As nonionic stabilizers are mainly polymeric in nature (for instance, poly(ethylene glycol) chains), elastic forces may contribute to the stability as well. The elastic force per... 

Evans, R. and Napper, D.H., Theoretical prediction of the elastic contribution to steric stabilization, J. Chem. Soc. Faraday Trans. I, 73, 390, 1977. 

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