Simulations of polymer crystals : new methods and applications

Citation

Karasawa, Naoki (1992) Simulations of polymer crystals : new methods and applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/mjj7-qt65. https://resolver.caltech.edu/CaltechETD:etd-08062007-104316

Abstract

The most important applications for simulations of polymers involve composites or blends with extensive, amorphous regions. To simulate such materials we use a very large unit cell, so that the polymer can have random behavior within the cell, but periodic boundary conditions to keep the problem tractable. The major difficulties in carrying out such calculations are: (a) accurate calculation of the lattice sums for the nonbond interactions (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 (energy, force, stress, curvature, phonons, elastic constants, dielectric constants, and piezoelectric constants).

We describe herein significant progress on each of these three issues. Concerning (a) we developed the 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 N2 nonbond interactions. Here a major advance is the development of the Cell Multipole Method (CMM), which involves no steps scaling a higher order than N. CMM treats the interactions in terms of a far field (which is evaluated in terms of multipole expansions) and a near field (which involves only approximately 50 near neighbors). The far field can be evaluated infrequently so that the full calculation for a million-atom system involves only the effort of calculation to interactions of each atom with about 50 near neighbors. This leads to a dramatic increase in efficiency, and systematic calculations have been carried out in realistic polymers with up to 1 million atoms (on a workstation). The CMM is 1500 times faster than the exact method for 1 million atoms. For periodic systems the cell multipole method is extended, using a reduced set that reproduces low-order multipoles of an original unit cell (CMMX). For a polymer with 1 million atoms, the C calculation is 1000 times faster than either the Ewald or Minimum Image Methods (the standards currently in use).

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 force-field parameters for polyethylene and poly (vinylidene fluoride) crystals. Van der Waals parameters for carbon and hydrogen are empirically determined from experimental lattice constants, elastic constants and lattice frequencies utilizing Ewald/ABCA procedures. Various mechanical properties are calculated and compared with experimental data. 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 form suggested by Lovinger) are computed using the same parameter sets. We find that using 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 (not yet observed form) is mechanically stable with comparable energy with other forms.

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