Phase transitions in pressurized semiflexible polymer rings.

We propose and study a model for the equilibrium statistical mechanics of a pressurized semiflexible polymer ring in two dimensions. The Hamiltonian has a term which couples to the algebraic or signed 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 behavior of the area is calculated for both continuum and lattice versions of the model. For small pressures, the area is obtained through a known 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.