Swelling of two-dimensional polymer rings by trapped particles

Details Swelling of two-dimensional polymer rings by trapped particles Swelling of two-dimensional polymer rings by trapped particles

2006-07-25

arxiv.org/abs/cond-mat/0607646v3

Eur. Phys. J. E 21, 33 (2006); Eur. Phys. J. E 25, 223(E) (2008)

Physics

Condensed Matter

Soft Condensed Matter

8 pages

Scientific paper

10.1140/epje/i2006-10041-1

The mean area of a two-dimensional Gaussian ring of $N$ monomers is known to diverge when the ring is subject to a critical pressure differential, $p_c \sim N^{-1}$. In a recent publication [Eur. Phys. J. E 19, 461 (2006)] we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as $ \sim N$, to a smooth state with $ \sim N^2$. In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For fixed number $Q$ of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, $ \sim NQ$, that the pressure exerted by the particles is at $p_c$ for any $Q$. In the freely jointed model the mean area is such that the particle pressure is always higher than $p_c$, and $$ consequently follows a single scaling law, $ \sim N^2 f(Q/N)$, for any $Q$. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems.

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