Dielectric metal/metal oxide nanocomposites: modeling response properties at multiple scales

Nanocomposites with metallic inclusions show great promise as tunable functional materials, particularly for applications where high permittivities are desirable, such as charge-storage. These applications strain quantum mechanical computational approaches, as any representative sample of the material includes hundreds if not thousands of atoms. Many continuum methods offer some predictive power for matrix-inclusion composites, but cannot be directly applied to composites with small inclusions, for which quantum and interfacial effects dominate. Here, we develop an adjustable finite element approach to calculate the permittivities of composites consisting of a metal-oxide matrix with nanometer-scale silver inclusions, by introducing an interfacial layer in the model. The approach involves solving the Laplace equation with Dirichlet and Neumann boundary conditions. We demonstrate that such a continuum model, when appropriately informed using quantum mechanical results, can capture many of the relevant polarization effects in a metal/metal oxide nanocomposite, including those that contain arbitrarily-small inclusions, at a fraction of the computational cost of performing the full quantum mechanics.