Crumpled-to-tubule transition and shape transformations of a model of self-avoiding spherical meshwork

Abstract

This paper analyzes a new self-avoiding (SA) meshwork model using the canonical Monte Carlo simulation technique on lattices that consist of connection-fixed triangles. The Hamiltonian of this model includes a self-avoiding potential and a pressure term. The model identifies a crumpled-to-tubule (CT) transition between the crumpled and tubular phases. This is a second-order transition, which occurs when the pressure difference between the inner and outer sides of the surface is close to zero. We obtain the Flory swelling exponents $\nu_{{\rm R}^2}(=\!D_f/2)$ and $\bar{\nu}_{\rm v}$ corresponding to the mean square radius of gyration $R_g^2$ and enclosed volume $V$, where $D_f$ is the fractal dimension. The analysis shows that $\bar{\nu}_{\rm v}$ at the transition is almost identical to the one of the smooth phase of previously reported SA model which has no crumpled phase.