Elastic Lattice Polymers

Details Elastic Lattice Polymers Elastic Lattice Polymers

2010-06-15

arxiv.org/abs/1006.2976v1

Phys. Rev. E 81, 061801 (2010)

Physics

Condensed Matter

Statistical Mechanics

10 pages

Scientific paper

10.1103/PhysRevE.81.061801

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 $\rho_m = 1 - /m$ 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.

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