Simulations of Polymer Crystals: New Methods and Applications

The major difficulties in carrying out polymer simulations are: (a) Accurate calculation of the lattice sums for the nonbond interactions, i.e., electrostatic and dispersion, which converge very slowly, (b) Computational time for systems large enough to simulate real materials (1 million atoms), (c) Procedures for calculating the properties of interest such as energy, force, stress, curvature, phonons, elastic constants, dielectric constants, and piezoelectric constants. We describe herein progress on each of these three issues. Concerning (a) we developed Accuracy-Bounded Convergence Acceleration (ABCA) procedure which finds the optimal Ewald parameters to achieve a given accuracy in minimum computation time. Concerning (b) the critical bottleneck in atomic level simulations of the structure and dynamics of very large molecules is the calculation of N^2 non-bond interactions, where N is the number of atoms. Here a major advance is the development of the Cell Multipole Method (CMM) which involves no steps scaling higher order than N. A major issue in carrying out simulations for materials is the force field. We have developed general procedures for obtaining empirical force fields and have applied this to systematic development of parameters for polyethylene and poly(vinylidene fluoride) crystals. For polyethylene, valence terms are determined by a biased -Hessian method for n-butane, and yield stress and surface energy are obtained from calculations of stress-strain relations in directions perpendicular to polymer chains. For poly(vinylidene fluoride) crystals a shell model is introduced to include atomic polarizabilities into the simulation. Properties of five different forms, including a new one suggested by Lovinger, are computed using the same parameter sets. We find that the shell model leads to significant improvement in the agreement between calculated and experimental piezoelectric and dielectric constants. In addition we find that the new form, although not yet observed experimentally, is mechanically stable and has similar energy with other forms.