New statistical mechanical treatment of systems near surfaces. V. Incompressible blend of interacting polydisperse linear polymers

Abstract

We consider a lattice model of an incompressible blend of interacting (repulsive, attractive, or neutral) polydisperse polymers of two species, A and B. The blend is next to an infinite plane surface whose interaction with A can be attractive, repulsive, or neutral. This is the only parameter required to completely specify the effect of the surface on both components of the blend. We numerically study various density profiles and surface functions, as we move away from the surface, by using the method of Chhajer and Gujrati that has already been successfully applied to study a polymer solution next to a surface. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations (but with magnitude enhanced and range diminished due to the presence of free volume in simulations), and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a PC, even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations usually take a few seconds to a minute.