Phase Transitions in Pressurised Semiflexible Polymer Rings

Abstract

We propose and study a model for the equilibrium statistical mechanics of a pressurised semiflexible polymer ring. The Hamiltonian has a term which couples to the algebraic area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behaviour of the area is calculated for both discrete and lattice versions of the model. For small pressures, the area is obtained through a mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.

12 pages

References in corpus (5)

• Scaling behaviour of two-dimensional polygon models
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
• Convex lattice polygons of fixed area with perimeter dependent weights
• Smoothening Transition of a Two-Dimensional Pressurized Polymer Ring

Cited by in corpus (3)

• Collapse and folding of pressurized rings in two dimensions
• Swelling of particle-encapsulating random manifolds
• Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter