Electromagnetic properties of composites containing elongated conducting inclusions

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Abstract
We present a detailed theoretical study of the dielectric and magnetic response of composites containing elongated conducting inclusions—sticks. These composites are widely used as engineering materials. They can be also considered as a model to describe many processes occurring in nature, e.g., dielectric enhancement in grain-saturated porous rocks. An approach is proposed that is based on the idea of a scale-dependent local dielectric constant. We develop an effective-medium approximation and derive an equation to calculate an effective dielectric constant of the composites in the quasistatic case and for the high frequency when there is a strong skin effect in the conducting sticks. Our theory predicts very large values of the effective dielectric constant in a wide range of the stick concentration. We find that the dielectric constant can exhibit various dispersive behaviors. It can have relaxation behavior, power-law scaling behavior, or resonance dependence on the frequency. The resonance dependence occurs when the skin effect is strong and wavelength is comparable to the stick length. Then the real part of the dielectric constant has negative values in some frequency ranges. The possibility of a wave localization is discussed in that case. We consider effective magnetic properties of the conducting stick composites. We propose that the composites with nonmagnetic components will have a giant paramagnetic response as a result of a collective interaction of the sticks with an external magnetic field. © 1996 The American Physical Society.