This collaborative project targets mathematics and computation for a technologically important class of materials called polymer nano-composites (PNCs). The investigators study two topics: the hydrodynamics of processing, and effective property characterization (e.g., conductive and mechanical properties). PNCs consist of ensembles of thin rods or platelets (millions in a cubic micron, generating football fields of surface contact with the solvent), whose orientational distribution and superior properties relative to the matrix have exhibited huge enhancements of materials properties in test systems. However, success in Nature and industry with fibers, which uniformly align the load bearing or conducting nano-elements, has not been duplicated for films and molds, thereby dramatically limiting the range of applications. The difficulties are widely documented in benchmark experiments: shear dominated, confined steady processing yields complex dynamics and heterogeneity in the rod or platelet ensemble. Resultant film properties are highly anisotropic, non-uniform, and sensitive to nano-particle geometry, volume fraction, and processing conditions. Theory, models, analysis, and numerical algorithms are undertaken to explain these phenomena, to explore the most perplexing observations, to map out parameter domains of robust film flows, and to characterize the conductivity and mechanical effective property tensors. The key object across all projects is the orientational probability distribution function (PDF) of the nano-particle ensemble. The PDF is described by the Doi kinetic theory and its extension to viscoelastic solvents, which the investigators and their collaborators merge into homogenized averaging and percolation-dominated effective property characterization.
The promises of nano-composite materials are profound. Nano-scale "designer" molecules are added at very low percentages to traditional materials, with the result of huge gains in performance properties of the composite relative to the original material. The nano-elements are much stronger, conduct electricity or heat significantly better, or are impermeable to gases and liquids that contaminate traditional materials. There is an engineering price, however, in that the smart engineering models and numerical codes that perform effectively for traditional composites simply do not apply to nano-composites. There are millions of nano-particles per cubic micron, with football fields of new surface area per raindrop of volume. Thus, nano-composite flows cannot be simulated with existing simulation tools. The principal investigators are designing new numerical simulation tools, based on new theoretical models, which extend the traditional flow processing models and codes by addition of new physics specific to nano-composites. The predictions are tested in conjunction with nano-engineering experimentalists. The goal of this effort is a platform for design and control of nano-composite materials, with the ability to steer the processing phase to achieve targeted property specifications.
