ABSTRACT
In the above equation, is the FloryHuggins interaction parameter, R is the universal gas constant, 2
a is the average volume fraction of polymer in the adsorbed layer, and 2
b is the bulk polymer concentration. For particles covered by an adsorbed polymer layer, it is also neces-
sary to take into account the effect on the steric repulsive forces of the structure of the adsorbed layer. For example, for the case of separations corresponding to < H < 2, the values of Ws,mix associated with linear adsorbed layer profiles may be obtained from the equation (Vincent et al., 1986):
For 0 < H < , the equation to be used for Ws,mix is the same as that for a uniform adsorbed layer profile:
a W . (3.45)
The elastic contribution to the steric potential is given by Ws,el = 2aRT 2 Sel , (3.46) where Г2 is the adsorbed amount of polymer (number of chains per unit area), and Sel is a geometric function that depends on the form of the segment concentration profile (z) in the adsorbed layer normal to the interface (Napper, 1977, 1983). Although (z) has been determined experimentally for individual particles using small-angle neutron scattering
(Fleer et al., 1993), it is necessary to know how (z) varies with particle separation in order to calculate Wsteric. For some specific systems, Wsteric may be measured directly using the surface force apparatus (Israelachvili and Adams, 1978) or atomic force microscopy (Ducker et al., 1991). It is important to be aware here that the steric repulsive force is of extremely short range, i.e., of the order of 1 nm (Leong et al., 1995). Often, the contribution from Wsteric(r) to Wtot(r) is predominant, so that particles are prevented from approaching each other close enough to experience the effect of WE arising from charges on the bare particle surface (Snowden et al., 1991). A more reliable way to calculate interparticle potentials between adsorbed polymer layers is using self-consistent-field theory, which can allow for the effects of charges on the polymer chains explicitly; the cases of adsorbed layers of s1-casein and -casein have been considered in detail (Dickinson et al., 1997).
