A Monte Carlo Study of Distribution Function P(S) of a Polymer Chain

Abstract

The distribution function P(S) of the radius of gyration of linear polyethylene (PE) is studied by use of Monte Carlo method in tetrahedral lattice. Three different cases, according to different interactions between polymer chain molecules, are investigated. The P(S)s of three different cases are compared with the exact distribution function P0(S) for random flight chain obtained by Yamakawa. At θ-state, the P(S) of N=260 (N is the length of polymer chain) is similar to P0(S), but that of N=20 deviates largely from P0(S). When the chain perturbed by an excluded volume, the difference between P(S) and P0(S) becomes large, but when we introduce long-range interaction (Van der Waals potential) at the same time, the difference becomes smaller. The results show that not only can short chain effect affect the distribution function P(S), excluded volume and long-range interaction can also affect P(S) of the chain.