Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: an effective-medium approach

TL;DR

This paper explains the bimodal distribution of transverse fluctuations in a grafted semiflexible polymer using an effective-medium approach, drawing analogies with shear-driven random walks, and predicts the effect of relaxing inextensibility.

Contribution

It introduces an effective-medium approximation to analytically describe bimodality in polymer fluctuations, linking it to shear flow behavior and suggesting effects of inextensibility relaxation.

Findings

Effective-medium approach captures bimodality in fluctuations.

Analogy between polymer fluctuations and shear-driven random walks.

Relaxing inextensibility may eliminate bimodality.

Abstract

Recent Monte Carlo simulations of a grafted semiflexible polymer in 1+1 dimensions have revealed a pronounced bimodal structure in the probability distribution of the transverse (bending) fluctuations of the free end, when the total contour length is of the order of the persistence length [G. Lattanzi et al., Phys. Rev E 69, 021801 (2004)]. In this paper, we show that the emergence of bimodality is related to a similar behavior observed when a random walker is driven in the transverse direction by a certain type of shear flow. We adapt an effective-medium argument, which was first introduced in the context of the sheared random-walk problem [E. Ben-Naim et al., Phys. Rev. A 45, 7207 (1992)], in order to obtain a simple analytic approximation of the probability distribution of the free-end fluctuations. We show that this approximation captures the bimodality and most of the qualitative features of the free-end fluctuations. We also predict that relaxing the local inextensibility constraint of the wormlike chain could lead to the disappearence of bimodality.