Curvature Distribution of Worm-like Chains in Two and Three Dimensions

TL;DR

This paper investigates the curvature distribution of worm-like polymers, revealing that in two dimensions the most probable curvature is zero, while in three dimensions the probability of zero curvature vanishes, challenging previous assumptions.

Contribution

It demonstrates through geometric arguments and simulations that zero curvature is not the most probable in 3D, contrasting with 2D behavior.

Findings

Zero curvature is most probable in 2D polymers.

In 3D, zero curvature occurs with zero probability.

Monte Carlo simulations support the theoretical results.

Abstract

Bending of worm-like polymers carries an energy penalty which results in the appearance of a persistence length l such that the polymer is straight on length scales smaller than l and bends only on length scales larger than this length. Intuitively, this leads us to expect that the most probable value of the local curvature of a worm-like polymer undergoing thermal fluctuations in a solvent, is zero. We use simple geometric arguments and Monte Carlo simulations to show that while this expectation is indeed true for polymers on surfaces (in two dimensions), in three dimensions the probability of observing zero curvature anywhere along the worm-like chain, vanishes.