Polymer chain stiffness versus excluded volume: A Monte Carlo study of the crossover towards the wormlike chain model

TL;DR

This study investigates how polymer chain stiffness influences their conformational behavior, demonstrating crossover phenomena and testing the applicability of the wormlike chain model using Monte Carlo simulations.

Contribution

It provides new insights into the limitations of the Kratky-Porod model for flexible and bottle-brush polymers through extensive Monte Carlo simulations.

Findings

Evidence of non-exponential decay of bond correlations at large distances.

Flexible bottle-brush polymers are not well-described by the wormlike chain model.

Persistence length is proportional to the cross-sectional radius in bottle-brush polymers.

Abstract

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