Excluded volume effects in polymers attached to surfaces: Chain conformational renormalization group

Abstract

The chain conformational space renormalization group method is extended to treat polymers with one or both ends attached to a wall. The theory is illustrated for the case of reflecting boundary conditions at the wall, but the methods for treating general boundary conditions are outlined. The fixed end-vector partition functions are evaluated both in the asymptotic scaling limit and in the cross-over regime where there is an explicit dependence on the strength of the excluded volume interaction. The mean square chain sizes transverse 〈z2〉 and parallel 〈‖ρ‖2〉 to the surface are evaluated separately to illustrate the use of the theory for the direct computation of these moments (including the prefactors) and the exponents. The calculations in these cases are far simpler than those required to determine the distribution functions. The prefactors display 〈‖ρ‖2〉 to be more spread out than 〈z2〉 which, in turn, as expected, is more spread out than 〈R2〉 for a chain in free space.