Stress tensor in model polymer systems with periodic boundaries

The calculation of the stress tensor from molecular simulations of atomistic model polymer systems employing periodic boundary conditions is discussed. Starting from the dynamical equations governing the motion of sites, correct double summation forms of the atomic and the molecular virial equations are derived, which are valid for flexible, infinitely stiff and rigid chain models even in the presence of interactions between different images of the same parent macromolecule. A new expression for the true instantaneous stress (flux of momentum through the faces of the simulation box) is derived and shown to exhibit large fluctuations when applied in molecular dynamics simulations. A new equation for the thermodynamic stress, cast exclusively in terms of intermolecular forces on interaction sites, is also derived. Application to Monte Carlo simulations shows that the molecular virial expression exhibits the smallest fluctuations among all stress expressions discussed, and thus allows computation of the thermodynamic stress with least uncertainty. A scheme is developed for the calculation of surface tension from intermolecular forces only.