Eur. Phys. J. E (2012) 35: 93
https://doi.org/10.1140/epje/i2012-12093-x

Regular Article

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

¹ Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, BP 84047, 67034, Strasbourg Cedex 2, France
² LCP-A2MC, Institut Jean Barriol, Université de Lorraine & CNRS, 1 bd Arago, 57078, Metz Cedex 03, France

^* e-mail: joachim.wittmer@ics-cnrs.unistra.fr

Received: 26 June 2012
Revised: 25 August 2012
Accepted: 27 August 2012
Published online: 27 September 2012

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 ρ the expected power law scaling for the interaction energy between different chains e _int ∼ ρ ^21/8, the total pressure P ∼ ρ ³ and the dimensionless compressibility gT = lim _q→0 S(q) ∼ 1/ρ 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 ξ(ρ) 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 wave vector q . We comment briefly on finite persistence length effects.