Finite-N effects for ideal polymer chains near a flat impenetrable wall

Abstract

This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function, G(N)(z), for a chain of N discrete monomers with one end fixed a distance z from the wall. It is well accepted that in the limit of infinite N, G(N)(z) satisfies the diffusion equation with the Dirichlet boundary condition, G(N)(0) = 0, unless the wall possesses a sufficient attraction, in which case the Robin boundary condition, G(N)(0) = -xi G'(N)(0), applies with a positive coefficient, xi. Here we investigate the leading N(-1/2) correction, G(N)(z). Prior to the adsorption threshold, Delta G(N)(z) is found to involve two distinct parts: a Gaussian correction (for z less than or similar to aN(1/2)) with a model-dependent amplitude, A, and a proximal-layer correction (for z less than or similar to a) described by a model-dependent function, B(z).