Collapsed 2-Dimensional Polymers on a Cylinder

TL;DR

This study investigates the behavior of collapsed 2D polymers confined on a cylindrical surface, analyzing their free energy, surface tension, and density near the theta temperature using advanced simulation methods.

Contribution

It extends previous models of polymers by examining their properties on a cylindrical surface, revealing how free energy, surface tension, and density scale near the theta point.

Findings

Free energy minimum at a finite cylinder radius diverges as temperature approaches T_theta.

Surface tension vanishes as (T_theta - T)^1.7 near T_theta.

Interior density scales as (T_theta - T)^0.32 near T_theta.

Abstract

Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM). The same model had previously been studied for free polymers (infinite lattice, no boundaries) and for polymers on finite lattices with periodic boundary conditions. We verify the previous estimates of bulk densities, bulk free energies, and surface tensions. We find that the free energy of a polymer with fixed length $N$ has, for $N\to \infty$, a minimum at a finite cylinder radius $R^*$ which diverges as $T\to T_\theta$. Furthermore, the surface tension vanishes roughly as $(T_\theta-T)^\alpha$ for $T\to T_\theta$ with $\alpha\approx 1.7$. The density in the interior of a globule scales as $(T_\theta-T)^\beta$ with $\beta \approx 0.32$.