Eur. Phys. J. E (2012) 35: 30
https://doi.org/10.1140/epje/i2012-12030-1

Regular Article

Thermodynamic behaviour of two-dimensional vesicles revisited

¹ S. N. Bose National Centre for Basic Sciences, 700098, Salt Lake, Kolkata, India
² The Institute of Mathematical Sciences, C.I.T. Campus, 600113, Taramani, Chennai, India

^* e-mail: mithun@bose.res.in

Received: 11 May 2011
Accepted: 17 April 2012
Published online: 24 April 2012

Abstract

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher (Phys. Rev. Lett. 59, 1989 (1987)). We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure , where = Np/4 , with the number of monomers N ∞ and the pressure p 0 , keeping constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N -gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. Away from these limits, we argue that the transition is replaced by a sharp crossover. The area, however, scales with N² for all positive p in all such models, consistent with earlier scaling theories.