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On the Bergman-Milton bounds for the homogenization of dielectric composite materials
Authors:Andrew J Duncan  Tom G Mackay  Akhlesh Lakhtakia
Institution:a School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3JZ, United Kingdom
b CATMAS - Computational and Theoretical Materials Sciences Group, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802-6812, United States
Abstract:The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter regimes for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.
Keywords:Bergman-Milton bounds  Maxwell Garnett estimates  Hashin-Shtrikman bounds  Metamaterials
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