Thermodynamic behaviour of two-dimensional vesicles revisited

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 $\tilde{p}$ , where $\tilde{p}$ = Np/4$\pi$ , with the number of monomers N $\rightarrow$ ∞ and the pressure p $\rightarrow$ 0 , keeping $\tilde{p}$ 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.