Time‐dependent step–step correlations in a self‐avoiding random walk

Abstract

The space–time step–step correlations of a polymer chain, described by a self‐avoiding random walk on a cubic lattice, are studied by simulating its behavior on a computer. Chains of N = 16 and N = 32 beads are studied. The short‐time behavior of the correlations is characterized by peaks, which become depressed and broadened with increasing interstep distance. The long‐time behavior is characterized by extremely slow decay, which goes to zero in about the same time for all interstep distances. The short‐time behavior is a consequence of the rotation of parts of the chain smaller than or equal to the static coherence length ζ. These short‐time processes also seem to be responsible for the relaxation of the square of the end‐to‐end distance, since in both cases the relaxation is of the order of 6N2. The long‐time behavior of the correlations is a consequence of the rotations of parts of the chain greater than the coherence length. The correlations vanish when the entire chain has had time to rotate in space. Our results suggest that this corresponds to the relaxation of the end‐to‐end vector.