The effect of chain length on the mean value of the end-to-end distance of a random-flight polymer chain adsorbed on a surface

Abstract

A general solution of the one-dimensional random-walk problem with an adsorbing barrier has been developed. For a given adsorption energy, θ, as the chain length is increased, the mean position of the free end of the molecule with respect to the surface, z, approaches the asymptotic values predicted by Rubin. The attainment of the asymptote is found to become more rapid as θ increases. For a given chain length, N, as θ is varied, there is a smooth transition in the value of z at θ_c even for as high a value of N = 250 in contrast to the sharp transition predicted by the asymptotic solution.