Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited

TL;DR

This study investigates the thermodynamic properties and scaling behaviors of strictly two-dimensional self-avoiding polymer chains using simulations, confirming theoretical power-law relations and analyzing elastic responses and structure factors.

Contribution

It provides detailed simulation-based confirmation of scaling laws for thermodynamic and elastic properties of 2D self-avoiding polymers, and discusses experimental determination of the semidilute blob size.

Findings

Confirmed power-law scaling of interaction energy, pressure, and compressibility with density.

Analyzed elastic contributions and their dependence on density and sampling time.

Showed how to determine the semidilute blob size from structure factor measurements.

Abstract

The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density rho the expected power-law scaling for the interaction energy between different chains e_inter\sim\rho^(21/8), the total pressure P\sim\rho^3 and the dimensionless compressibility gT=lim(q->0)(S(q)\sim1/\rho^2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size xi(rho) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wavevector q. We comment briefly on finite persistence length effects.