Steric layer theory

Fig. 15.4. Schematic representation of the steric layer theory (after Vincent et al., 1980).

The steric layer theory of Vincent, Luckham and Waite (1980) also provides reasonable semi-quantitative predictions of the onset of flocculation. According to this theory, the onset of flocculation marks the entrance into the semi-dilute polymer concentration regime (i.e. V2 = C2 ). Flocculation arises because there is a net decrease in free energy when two particles come together and displace into the bulk solution some of the free polymer molecules that are interpenetrating the stabilizing moieties. Restabilization is said to be associated with the onset of the so-called concentrated polymer regime (i.e. 

It was claimed by. Vincent et al. (1980) that a more quantitative indication of the predictions of the steric layer theory could be ascertained as follows. The free energy of interaction in the presence of free polymer is given by... 

Comparison of the predictions of the steric layer theory with experiment for polystyrene latices flocculated by poly(oxyethylene)... 

In addition to the molecular weight of the free polymer, there axe other variables, such as the nature of the solvent, particle size, temperature, and thickness of adsorbed layer which have a major influence on the amount of polymer required to cause destabilization in mixtures of sterically stabilized dispersions and free polymer in solution. Using the second-order perturbation theory and a simple model for the pair potential, phase diagrams relat mg the compositions of the disordered (dilute) and ordered (concentrated) phases to the concentration of the free polymer in solution have been presented which can be used for dilute as well as concentrated dispersions. Qualitative arguments show that, if the adsorbed and free polymer are chemically different, it is advisable to have a solvent which is good for the adsorbed polymer but is poor for the free polymer, for increased stability of such dispersions. Larger particles, higher temperatures, thinner steric layers and better solvents for the free polymer are shown to lead to decreased stability, i.e. require smaller amounts of free polymer for the onset of phase separation. These trends are in accordance with the experimental observations. 

The first theory to recognize clearly the prime importance of the solvency of the dispersion medium in steric stabilization was that published by Fischer (1958). Fischer considered the overlap of the steric layers attached to two spheres (see Fig. 10.4). The mixing free energy change S A G ) in the small volume element dV for one of the steric layers is given by... 

One disadvantage of the approach of Fischer (1958) and Ottewill and Walker (1968) is that, as noted above, the formulae proposed by these authors are only valid for the mixing of constant segment density steric layers in the interpenetrational domain. Once the interpenetrational-plus-compressional domain is entered, no allowance is made for the elastic contribution to the free energy. The elastic interactions can become important, even paramount, when the minimum distance of separation between the surfaces of the particles (Hq) is less than the barrier layer thickness. An additional defect of the Fischer approach is apparent in this domain the overlap volume is decreased below that given by equation (12.8) because part of it is occupied by the cores of the particles. Both the Fischer and the Ottewill and Walker theories disregard this decrease in volume. Implicit in their formulae is the notion that the solid cores become equivalent to the steric barriers. This is, of course, quite unphysical. 

A radically different theory for the origin of the flocculation of colloidal dispersions by dissolved polymers has been proposed by Vincent, Luckham and Waite (1980). This involves the presence of a steric layer at the particle/dispersion medium interface, and its interactions with the free... 

The essence of this theory can be grasped from Fig. 15.4. In the semidilute region, the free polymer molecules can be assumed to overlap the polymer in the steric layers. However, these unattached interpenetrated chains are displaced into the bulk phase on the close approach of two sterically stabilized particles. The free energy change that accompanies this displacement is simply... 

It should further be noted that any agreement between theory and experiment presented in this section may be somewhat fortuitous in that the dispersions studied experimentally were sterically stabilized. Steric layers, unless very thin, can influence profoundly the quantitative effects of free polymer. This is vividly illustrated by the exponents reported by de Hek and... 

The data presented in Table 17.2 were obtained by the entropy maximization procedure. Recalculation adopting the free energy minimization approach yielded the results shown in Table 17.3. This leads to somewhat better agreement between theory and experiment but there is still a strong tendency for the theoretical values of both V2 and V2 to lie below the experimentally observed values. This suggests that the steric layers, which were present in the experiment but ignored in the calculations to date, may have an effect on the observed values of V2 and V2. Such an effect could be... 

Feigin and Napper (1980b) predicted quite different behaviour with respect to the solvency of the system the better is the solvent for the free polymer, the larger are the free energy changes involved and thus the smaller are the values of V2 and V2. These predictions, however, only apply to naked surfaces. The situation is much more complicated when steric barriers are present, as they would be in the theory of Scheutjens and Fleer and in many practical situations. In that case, the steric repulsion is greater in the absence of free polymer in a better solvent. It is the subtle interplay of the effects of solvency change on both steric stabilization and depletion stabilization that determines the overall trend observed. At present there does not appear to be any data in the literature that permit a clear cut statement to be made of the effects of solvency on depletion stabilization in the presence of steric layers. 

This theory has been applied to a range of dispersions, both aqueous (Vincent et ai, 1980) and nonaqueous (Clarke and Vincent, 1981a,b) in character. The precise results depend upon the nature of the segment density distribution function assumed for the steric layer but semi-quantitative agreement could be achieved between theory and experiment in tliis fashion. The results obtained will not be presented in detail because they span the values of c and C2 tabulated in Table 17.5. Accordingly, these more detailed calculations really provide no better prediction of the values of vz and V2 " than do Ci and Cz if account is taken of the number of adjustable parameters necessary to perform the calculations. 

Surface energies of sohds, surface and interfadal tensions and the interfacial region, thermodynamics of colloidal systems, improved electrical double layer theory, adsorbed pol)mer layers and steric stabilization, relationships between surface energies and bulk properties... 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

Parkinson, E.L., Ettelaie, R., Dickinson, E. (2005). Using self-consistent-field theory to understand enhanced steric stabilization by casein-like copolymers at low surface coverage in mixed protein layers. Biomacromolecules, 6, 3018-3029. 

---