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

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) = - G N ′ (0) , applies with a positive coefficient, . Here we investigate the leading N -1/2 correction, G N ( z ) . Prior to the adsorption threshold, G N ( z ) is found to involve two distinct parts: a Gaussian correction (for z aN 1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z a described by a model-dependent function, B ( z ) .