Polymer chain stiffness vs. excluded volume: A Monte Carlo study of the crossover towards the worm-like chain model

Abstract

When the local intrinsic stiffness of a polymer chain varies over a wide\nrange, one can observe both a crossover from rigid-rod-like behavior to\n(almost) Gaussian random coils and a further crossover towards self-avoiding\nwalks in good solvents. Using the pruned-enriched Rosenbluth method (PERM) to\nstudy self-avoiding walks of up to $N_b=50000$ steps and variable flexibility,\nthe applicability of the Kratky-Porod model is tested. Evidence for\nnon-exponential decay of the bond-orientational correlations $<\\cos \\theta (s)\n>$ for large distances $s$ along the chain contour is presented, irrespective\nof chain stiffness. For bottle-brush polymers on the other hand, where\nexperimentally stiffness is varied via the length of side-chains, it is shown\nthat these cylindrical brushes (with flexible backbones) are not described by\nthe Kratky-Porod wormlike chain model, since their persistence length is\n(roughly) proportional to their cross-sectional radius, for all conditions of\npractical interest.\n