Elastic Lattice Polymers

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.

10 pages

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• Kremer-Grest models for commodity polymer melts: Linking theory, experiment and simulation at the Kuhn scale
• Universal properties of knotted polymer rings
• The entropic cost to tie a knot
• Topological signatures of globular polymers
• Unwinding dynamics of double-stranded polymers
• Equilibrium winding angle of a polymer around a bar
• Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings