## 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 *g*T = 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.

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Schulmann, N., Xu, H., Meyer, H. *et al.* Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited.
*Eur. Phys. J. E* **35**, 93 (2012). https://doi.org/10.1140/epje/i2012-12093-x

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DOI: https://doi.org/10.1140/epje/i2012-12093-x

### Keywords

- Soft Matter: Polymers and Polyelectrolytes