Stress tensor in model polymer systems with periodic boundaries

Abstract

SUMMARY: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.

Viscosity of heavy n -alkanes and diffusion of gases therein based on molecular dynamics simulations and empirical correlations

“…The instantaneous pressure P int was calculated during the simulation according to the molecular virial expression proposed by Theodorou et al [40]. The tail contributions to the internal energy and to the pressure were taken into account [12].…”

Relaxation time, diffusion, and viscosity analysis of model asphalt systems using molecular simulation

“…20 We calculated the stress tensor using the molecular virial. 56 The diffusion coefficient of each molecule type was calculated based on center of mass displacement…”

Nature of Stress on the Atomic Level in Dense Polymer Systems

“…For the case of freely jointed chains, in which both the bonded interaction potential, ub(r), and the nonbonded potential, u,,~(T), are two-body, the virial formula is where n is the number of atoms in volume v; ra is the vector displacement between a pair, a, of interacting atoms; r" = 1r"l; rp are the components of r" with respect to the coordinate system x,; the notations a E b and a E nb indicate that these sums range over all pairs of atoms interacting by way of the potential, ub or u,,,,, respectively; uhf and unht denote derivatives of these potentials; and brackets denote long-time averages in equilibrium systems or ensemble averages in nonequilibrium studies. Further details regarding the use of the virial stress formula and its generalization to cases in which three-body angle potentials and four-body rotational potentials are present may be found in ( 1 [1][2][3][4][5][6][7][8][9][10][11][12][13].…”