TY - JOUR

T1 - Swelling of two-dimensional polymer rings by trapped particles

AU - Haleva, E.

AU - Diamant, H.

PY - 2006/9

Y1 - 2006/9

N2 - 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 ∼ 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 ∼ N, to a smooth state with ∼ 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 a 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, ∼ 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, ∼ 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.

AB - 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 ∼ 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 ∼ N, to a smooth state with ∼ 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 a 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, ∼ 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, ∼ 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.

UR - http://www.scopus.com/inward/record.url?scp=33751007570&partnerID=8YFLogxK

U2 - 10.1140/epje/i2006-10041-1

DO - 10.1140/epje/i2006-10041-1

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AN - SCOPUS:33751007570

SN - 1292-8941

VL - 21

SP - 33

EP - 40

JO - European Physical Journal E

JF - European Physical Journal E

IS - 1

ER -