Mathematics of Anisotropic Electrical and Dielectric Properties of Nanocomposites

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ZhengDMS-08-7954 The investigator studies two important areas innanocomposites: (1) homogenized effective dielectric constant ofnanocomposites; and (2) percolation-dominated electricalconductivity of nanocomposites. This project is focused onanisotropic systems with orientationally ordered nanoparticles,and is based on an accurate description of the nanoparticleorientational probability distribution function fromflow-processing databases, which we then map to effectiveproperties through volume averaging and percolation phenomena. In the first part, the effective dielectric tensor is consideredin two explicit systems of current interests: high dielectricconstant nanoparticles dispersed in polymers, and conductingnanoparticles dispersed in polymers. Both systems are observedto lead to enhanced effective dielectric properties. Thisrequires careful preparation, because the properties areextremely sensitive to details of composition and processing. Inthe second part, key aspects of salient electric properties areconsidered, such as percolation threshold modification bymechanical loading, multiscale homogenization method, and amolecular-scale electron hopping model. Numerical andmathematical homogenization and non-equilibrium percolationtechniques need to be developed to address these challenges. Theproposed projects modify, apply, test, and extend existingmathematical theory and numerical approaches for two-phase (orthree phase, if interphase is considered) composites, where thenumber of particles and new surface area simply overwhelmexisting tools. The aspirations for extreme property enhancements throughdesigner nanoparticles mixed into traditional materials are basedon prototype experiments. However, there are new challengesunique to nanocomposites for which there are no predictivemathematical or computational tools. This project is a responseto these needs, through a coordinated combination of mathematicalanalysis and scientific computation, ranging in scale fromindividual particles to bulk properties. Today, limitationsimposed by particle numbers only allow low moments of thenanoparticle distributions to be measured, and the inherentmaterial sensitivity to the details of the distribution observedin experiments is unknown. This project gives insight into themechanism underlying extreme property gains, and thus provideskey input into design and control strategies.