Elastic Lattice Polymers

TL;DR

This paper introduces a model of elastic lattice polymers with fluctuating length, demonstrating how the entropic exponent relates to knot complexity and providing simulation results that reveal the influence of knots on polymer scaling behavior.

Contribution

The study presents a new elastic lattice polymer model and shows that the entropic exponent depends only on the number of prime knots, not their type, supported by simulation data.

Findings

The stored length density scales with polymer size as predicted.

The entropic exponent is determined solely by the number of prime knots.

Knots induce significant corrections to scaling, affecting entropic competition.

Abstract

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $\rho_m = 1 - <l>/m$ scales asymptotically for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of $\rho_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $\rho_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.