Note: Perturbation theory of polymer chains revisited. I. Corrected C1 and C2 parameters for excluded volume chains

Abstract

Random walks (RWs) and self-avoiding random walks (SAWs) embedded in the cubic lattice are evaluated with respect to the number of i-tuples of overlaps within incompatible pairs leading to the parameters Ck of the perturbation theory of the excluded volume u. These parameters are strongly dependent on chain length N never before realized by theory. Extrapolated to infinite chain length C1 and C2 are fairly well recovered for RWs while markedly larger values appear for SAWs. The Kurata-Yamakawa approach recovers the simulation results with high accuracy if self-consistent C1 and C2 values are applied thus representing an easy to use well-performing method for the prediction of u in athermal solution.