FEA Simulation on Dielectric Composite and Semi-Crystalline Composite, and Analytical Computations and Approximations for the Charge, Force and Chemical Potential for a Prolate Spheroid Aligned with an Electric Field

Date of Completion

January 2011

Keywords

Engineering, Electronics and Electrical|Physics, Condensed Matter|Engineering, Materials Science

Degree

Ph.D.

Abstract

A finite element study has been carried out to determine the effective dielectric constant of composite materials containing linear or nonlinear fillers. In the linear systems, spherical particles with field-independent dielectric constant are distributed randomly in a linear matrix. The effective dielectric constant is studied as a function of volume fraction and particle size. In the nonlinear system, a Landau thermodynamic model is employed to describe the field-dependent dielectric properties for both ferroelectric and antiferroelectric material. For the 2D ferroelectric-dielectric composite, the effective dielectric constant and dielectric tunability are examined based on filler volume fraction, size and shape, and then compared to classical effective medium theories. For the 3D antiferroelectric-dielectric composite, both the "hard" sphere and "soft" sphere models are examined at a volume fraction of 40%, which is above percolation for spherical filler. ^ The finite element method is then adapted to determine the relaxation time constant, effective conductivity and electric field distribution of semi-crystalline composite. The simulated results show that both the effective conductivity of the composite and field distribution in the composite strongly depend on the crystalline volume fraction and the shape of the crystalline region. To achieve lower average electric field in the amorphous region, crystallites with larger length/thickness ratio are preferred. ^ The charge and force on a conducting particle standing on a ground plane in a uniform background field are important to a range of technical areas, such as particle motion in gas-insulated substations. The charge, force and lifting field for such a particle is normally evaluated using approximate formulas in an obscure paper published over 40 years ago. Software technology now facilitates the solution of many such problems exactly, which allows evaluation of (i) the published approximation and (ii) the range of parameters over which the approximation is accurate. In the present contribution, we provide an exact solution to the charge and field-induced force for semi-spheroid standing on a ground plane, derive the commonly used approximation from the exact solution, and find that the commonly used approximate solution for the force on a rodlike particle agrees poorly with finite element computations of the force. We provide both "exact" and approximated formulas which agree well with finite element computations of the force on a rod-like particle for asperities from 2 to 100. ^ An analytical expression is derived for the chemical potential of a water-filled spheroid in a dielectric medium based on Zeller's hypothesis for the chemical potential, against which Zeller's approximations for chemical potential could be compared for the same system. In doing so, we found that Zeller's approximation for DC component of the chemical potential is very good, although his expression for the conductivity at which the peak DC component occurs is not accurate at low spheroid asperities. However Zeller's approximation does not provide a very good approximation for the AC component of the chemical potential. Following Zeller's approach but with corrections, we have developed a much more accurate approximation for the AC component of the chemical potential which was compared with both the exact analytical solution and FEA computations. ^

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