Collaborative Research: Collaborative Proposal for Mathematics & Computation of Nano-Composite Flows & Properties

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ZhouDMS-0604912ForestDMS-0604891 This collaborative project targets mathematics andcomputation for a technologically important class of materialscalled polymer nano-composites (PNCs). The investigators studytwo topics: the hydrodynamics of processing, and effectiveproperty characterization (e.g., conductive and mechanicalproperties). PNCs consist of ensembles of thin rods orplatelets (millions in a cubic micron, generating football fieldsof surface contact with the solvent), whose orientationaldistribution and superior properties relative to the matrix haveexhibited huge enhancements of materials properties in testsystems. However, success in Nature and industry with fibers,which uniformly align the load bearing or conductingnano-elements, has not been duplicated for films and molds,thereby dramatically limiting the range of applications. Thedifficulties are widely documented in benchmark experiments: shear dominated, confined steady processing yields complexdynamics and heterogeneity in the rod or platelet ensemble. Resultant film properties are highly anisotropic, non-uniform,and sensitive to nano-particle geometry, volume fraction, andprocessing conditions. Theory, models, analysis, and numericalalgorithms are undertaken to explain these phenomena, to explorethe most perplexing observations, to map out parameter domains ofrobust film flows, and to characterize the conductivity andmechanical effective property tensors. The key object acrossall projects is the orientational probability distributionfunction (PDF) of the nano-particle ensemble. The PDF isdescribed by the Doi kinetic theory and its extension toviscoelastic solvents, which the investigators and theircollaborators merge into homogenized averaging andpercolation-dominated effective property characterization. The promises of nano-composite materials are profound. Nano-scale "designer" molecules are added at very low percentagesto traditional materials, with the result of huge gains inperformance properties of the composite relative to the originalmaterial. The nano-elements are much stronger, conductelectricity or heat significantly better, or are impermeable togases and liquids that contaminate traditional materials. Thereis an engineering price, however, in that the smart engineeringmodels and numerical codes that perform effectively fortraditional composites simply do not apply to nano-composites. There are millions of nano-particles per cubic micron, withfootball fields of new surface area per raindrop of volume. Thus, nano-composite flows cannot be simulated with existingsimulation tools. The principal investigators are designing newnumerical simulation tools, based on new theoretical models,which extend the traditional flow processing models and codes byaddition of new physics specific to nano-composites. Thepredictions are tested in conjunction with nano-engineeringexperimentalists. The goal of this effort is a platform fordesign and control of nano-composite materials, with the abilityto steer the processing phase to achieve targeted propertyspecifications.