Savescu, S. B. (2009) Dielectric properties of heterogeneous materials. (MSc(R) thesis), Kingston University, .

Abstract

This dissertation is concerned with the passive electrical phenomena (phenomena of dielectric relaxation) which occur due to the interaction of the electric field with heterogeneous systems. Heterogeneous dielectrics are materials with multiple layers or shells, whose permittivities and conductivities have different values. The relaxation mechanism and its time-dependence gives information about the structure of a dielectric. The frequency-dependent components of the real and complex permittivity and conductivity for heterogeneous dielectrics are obtained using Debye equations and the electric parameters of compartments (electric parameters of phase) are correlated with the overall properties of a heterogeneous particle. To the best of our knowledge, the calculations of the field distribution in a double layer dielectric do not feature in the previous literature. It is shown that at periodic voltage, the electric field distribution in a double layer dielectric with losses is similar to the field distribution at a constant voltage in an ideal dielectric. Debye equations as studied by Frohlich in [33] enable comparison with their role in the Maxwell-Wagner two-layer model. The distinct term appearing in the latter is attributed by Hippel to interfacial polarization, arising due to compositional fluctuations and is shape-size dependent. These compositional fluctuations are often caused by chemical reactions within the dielectric, e.g. oxygen diffusion. A time-dependent semilinear singularly perturbed problem which can describe this phenomenon is numerically analysed. The term singularly perturbed refers to a small parameter multiplying a term which changes the character of the equation. This is inversely proportional to the reaction constant and, being very small for fast diffusion reactions, causes high stiffness of the differentiation matrix and makes these types of problems very difficult to compute with usual numerical methods, if not impossible. Thus layer-adapted meshes of Shishkin and Bakhvalov type are used and also the computational errors are estimated. The electrical properties of cells can be determined with two different techniques, the micro electrode and the inclusion (suspension) technique. The first one has the disadvantages of being invasive (the electrode has to be inserted in a living organism), a limited frequency range and being affected by electrode polarization problems, whereas the latter does not have these disadvantages. A theoretical model capable of describing the dielectric behaviour of inclusions is formulated through an algorithm (not explicitly formulated in the previous literature) which gives a relation between structural properties of the inclusion phases (e.g. membranes, shells) and the electric parameters of these phases.

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