Novel and Efficient Methods for Calculating Pressure in Polymer Lattice Models

Pressure calculation in polymer lattice models is an important but nontrivial subject. The three existing methods -- thermodynamic integration, repulsive wall, and sedimentation equilibrium methods -- all have their limitations and cannot be used to \textit{accurately} calculate the pressure at \textit{all} polymer volume fractions $\varphi $. Here we propose two novel methods. In the first method, we combine Monte Carlo simulation in an expanded grand-canonical ensemble with the Wang-Landau -- Optimized Ensemble (WL-OE) simulation to calculate the pressure as a function of polymer volume fraction, which is very efficient at low to intermediate $\varphi $ and exhibits negligible finite-size effects. In the second method, we introduce a repulsive plane with bridging bonds, which is similar to the repulsive wall method but eliminates its confinement effects, and estimate the two-dimensional density of states (in terms of the number of bridging bonds and the contact number) using the 1/$t$ version of Wang-Landau algorithm. This works well at all $\varphi $, especially at \textit{high} $\varphi $ where all the methods involving chain insertion trial moves fail.