NEW STATISTICAL-MECHANICAL TREATMENT OF SYSTEMS NEAR SURFACES .3. POLYDISPERSE LINEAR AND BRANCHED POLYMERS IN AN INTERACTING SOLUTION

We apply a recently developed analytical but approximate method to stu dy the behavior of polydisperse linear and branched polymers in a solu tion with interaction and near various kinds of surfaces. We consider equilibrium polydispersity controlled by a set of activities. The meth od allows us to account for polymer connectivity and excluded-volume e ffects and goes beyond the random mixing approximation. The method als o allows us to probe the entire density range, which is not possible i n a Monte Carlo simulation. The density profiles show oscillations for bulk densities phi(mb) larger than some threshold value phi(mt), the amplitudes of those oscillations being a strong function of the solven t-monomer interaction parameter w. The behavior of linear and branched polymers is almost identical for the same bulk densities phi(mb), exc ept when the solvent-monomer interaction is repulsive and the surface- monomer interaction is not attractive. In this case, the effect of bra nching is to increase the correlation length xi describing the approac h of a density profile to its bulk value. We also compute the surface thermodynamic functions (the entropy and the free energy). While the s urface free energies are identical for linear and branched polymers, t he surface entropies are very different. (C) 1997 American Institute o f Physics.