A random walk chain reptating in a network of obstacles: Monte Carlo study of diffusion and decay of correlations and a comparison with the Rouse and reptation models

Abstract

The integrated decay times for correlations of the end-to-end vector of random walk chains of length N are well known to be proportional to N2 and N3 for the Rouse and the reptation models, respectively. For subchains of length n situated in the center and at the end of a chain, respectively, these times are about nN and n2 in the Rouse model and nN2 and n2N in the reptation model if n≪N holds. For a random walk chain in a network of obstacles which moves along its contour by defect diffusion with Monte Carlo simulations, the autocorrelation time for the end-to-end vector and the disentanglement time for the primitive path are found to vary as about N3.5 and N3.7, respectively, for chain lengths varying from 15 to 63. The curvilinear diffusion coefficient varies as about N−1.2 and the center-of-mass diffusion coefficient varies as about N−2.4. The integrated autocorrelation times of small subchains vary with n/N also faster than predicted by the reptation model.