Heterogeneous materials are inherently dielectric, and charge distribution and transport in such materials involves complex local fields and polarizations that are remarkably sensitive to morphology and the interaction of conduction and permittivity. Trial and error design of such material systems is time consuming and expensive, and often ineffectual. However, heterogeneous materials are essential for energy conversion and storage, and they have become the foundation for major advances in the performance of devices such as batteries, fuel cells, separation membranes, and solar cells. The present paper presents some relationships in support of rational design based on an extensive experimental validation of the concepts and analysis that form a foundation for that design. Salient results include the prediction and confirmation of volume fraction effects (including nondilute mixtures), and the prediction and direct measurement of surface charge effects at internal interfaces as a function of constituent morphology and orientation.

Abstract. The present paper is concerned with heterogeneous materials in which the

Many of the advanced composite materials used in aerospace, energy storage and conversion, and electrical devices are multifunctional, i.e., they operate on (or in the presence of) some combination of mechanical, thermal, electrical, chemical, and magnetic fields. Designing composite materials for airplanes, for example, must include not only structural, but also thermal and electrical considerations. Most energy storage and conversion devices are made from advanced composite materials, and they must be designed to interact and sustain their functions in multiple fields, often mechanical, electrical, electrochemical, and thermal. The functional characteristics of such materials are not only controlled by the constituent properties, but are highly dependent on the size, shape, geometry, arrangement, and interfaces between the constituent materials, the extrinsic factors controlled by processing. That is the subject of the present paper. In particular, we will focus on the design of microstructure in heterogeneous materials to manage the dielectric properties and character of such materials.

Background: Essentially all heterogeneous materials are dielectric, i.e., they are imperfect conductors that generally display internal charge displacements that create dissipation and local charge accumulation at interfaces. Over the last few years, the authors have focused on the development of an understanding of such behaviour in heterogeneous functional materials for energy conversion and storage, called HeteroFoaM (www.HeteroFoaM.com). Using paradigm problems, this work will indicate major directions for developing generally applicable methods for the multiphysics, multi-scale design of heterogeneous functional materials. Methods: The present paper outlines the foundation for developing validated predictive computational methods that can be used in the design of multi-phase heterogeneous functional materials, or HeteroFoaM, as a genre of materials. Such methods will be capable of designing not only the constituent materials and their interactions, but also the morphology of the shape, size, surfaces and interfaces that define the heterogeneity and the resulting functional response of the material system. Results: Relationships to applications which drive this development are identified. A paradigm problem based on dielectric response is formulated and discussed in context.

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