(161f) A Software Module for Calculation of Virial Coefficients of Macromolecules

ZENO is a software tool developed at NIST, with capabilities for calculation of properties of polymer and particle suspensions. The latest implementation can compute capacitance, electric polarizability tensor, intrinsic conductivity, volume, gyration tensor, and several more related quantities. Results are obtained by performing appropriate calculations on a single particle instance of the dispersed material, which then enters as the leading order (in concentration φ) estimate of the bulk material properties. The dispersed particles may be modeled as arbitrarily shaped objects, including those formed as fused assemblies of smaller objects, such as polyhedra or spheres. The actual particle dispersions modeled this way may be quite complex, with examples including geological systems, food, and blood, as well as engineered systems formulated to improve the mechanical and electrical properties of polymeric materials. A large array of dispersants is of interest, including carbon nanotubes, metal nanoparticles, graphene sheets, polypeptides, and polynucleotides. Significant advances in methods for synthesizing nanoparticles of arbitrary shape open up new possibilities for materials engineering and applications, further driving interest in improving our ability to predict properties for complex suspensions and blends.

Presently, ZENO’s capabilities are restricted to single-particle calculations, so its utility can be significantly enhanced by adding features to compute properties using multi-particle metrics. These quantities enter into bulk-property models at second order in concentration, extending the range of conditions where the models are effective. The quantity of interest to this project is the second virial coefficient B2, or more generally the set of coefficients Bn. For particles in solution, these appear in an expansion of the osmotic pressure in terms of the concentration. We consider coefficients with effective interactions mediated by the solvent, so no explicit solvent is considered; rather its effect is manifested by the form chosen for the solute-solute interactions. In principle these interactions are multibody, but often they are treated using pairwise-additive forms. The osmotic virial coefficients can then be effectively given in terms of expressions for the conventional (gas-phase) virial coefficients.

We describe our efforts to implement capabilities within ZENO to compute virial coefficients of arbitrary macromolecules composed of hard spheres. We implement Mayer-sampling Monte Carlo with overlap sampling to reduce the likelihood of bias. The capability builds upon the ZENO framework, and thus may be used with the same input file formats that have already been established by ZENO. Several example applications are demonstrated.