Modes of polymer adsorption with excluded volume on parallel colloidal plates and their interaction

Abstract

By using a lattice model in which excluded volume and nearest-neighbour interactions are taken into account in the self-consistent mean-field approximation, a study is made of polymer adsorption on two parallel flat plates, which represent interacting colloidal particles. The segment density profile and free energy of polymers adsorbed on the two plates are derived from a recurrence relation for the distribution of the last segment of a polymer chain. Various modes of adsorption of the polymers on the plates (tails, loops, bridges) are conveniently treated by formulating the recurrence relations in terms of matrices similar to those of Rubin and DiMarzio. In its linear form the recurrence relation is equivalent to a one-dimensional self-consistent field equation of Dolan and Edwards. The interaction free energy between the adsorbed polymers is calculated in a range of plate separations for athermal and theta mixtures and for two adsorption energies of segments on the plates.