Free energy calculations by molecular simulations of deformed polymer glasses

A rigorous thermodynamic framework is developed for performing free energy calculations of polymer glasses described by classical molecular forcefields. The proper free energy connected to all combinations of imposed external conditions (strain, stress) is derived from a well defined Helmholtz energy calculated from the detailed atomistic configurations. The quasi-harmonic approximation (QHA) is employed around local minima of the system on its potential energy landscape. The ingredients of the methodology, i.e. the derivatives of the free energy with respect to atomic positions (forces, elements of the Hessian) and the relevant derivatives with respect to strain (stresses and elastic constants), are calculated through tractable analytic expressions which are thoroughly presented and discussed. The derivation is general and readily applicable to any system described by classical molecular forcefields. As a proof of concept, we study the mechanical response of long-chain glassy atactic polystyrene, in the elastic and the plastic regime (compressive strain up to 100%). The macroscopic stress–strain curve for polystyrene is obtained and the evolution of the microscopic polymer configurations in the course of deformation is studied