Use of Dielectric Mixture Equations for Estimating Permittivities of Solids from Data on Pulverized Samples
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USE OF DIELECTRIC MIXTURE EQUATIONS FOR ESTIMATING PERMITTIVITIES OF SOLIDS FROM DATA ON PULVERIZED SAMPLES STUART 0. NELSON* AND TIAN-SU YOU** *U. S. Department of Agriculture, Agricultural Research Service, Richard B. Russell Agricultural Research Center, P. 0. Box 5677, Athens, GA 30613 of Radio Electronics, Zhejiang University, Hangzhou, China; Formerly visiting scientist with the USDA, ARS, Richard B. Russell Agricultural Research Center
"**Department
ABSTRACT The complex permittivities of solid and pulverized samples of two plastics, Rexolite 1422 and Kynar, were measured at frequencies of 2.45, 11.5, and 22.0 GHz at 25"C by the short-circuited waveguide technique. Several dielectric mixture equations and extrapolation of functions of the real and imaginary parts of the permittivity that are linear with bulk density were then used to estimate the permittivities at solid-material densities from measurements on the pulverized samples. For these materials, the best estimates of the permittivities were provided by extrapolations that are consistent with the Complex Refractive Index and Landau and Lifshitz, Looyenga mixture equations. The Bottcher mixture equation often gave values very close to the Landau and Lifshitz, Looyenga equation, and the Bruggeman-Hanai, Rayleigh, and Lichtenecker mixture equations gave increasingly larger permittivity estimates in that order.
INTRODUCTION Relationships between the permittivities of pulverized or granular samples of materials and those of the solid materials have long been of interest for use in determining the permittivities of the solids from measured permittivities of the particulate samples. Dielectric mixture equations have been developed and investigated for this purpose [1]-[4]. An extrapolation procedure, based on the linearity with density of functions of the real and imaginary parts of the permittivity of pulverized and granular materials, has also been used to obtain estimates of the permittivity of the solid material [5],[6]. Often the true values of the permittivities of the solid materials were unknown, so the reliability of the procedures for determining those properties from measured permittivities of particulate samples could not be properly assessed. This paper reports the microwave permittivities measured on two plastic materials in both the solid and pulverized forms. Permittivity values for the solid materials predicted by several dielectric mixture equations and those obtained by the linear extrapolation technique are compared with the values measured on solid material samples. Here we are considering the complex permittivity relative to free space, =-'--je". The real part is referred to as the dielectric constant, and the imaginary part is the dielectric loss factor. The loss tangent or dissipation factor of the dielectric is tan6=0'/•', and the conductivity in siemens/m is Y=wcac", where w=2irf is the angular frequency and Co is the permittivity of free space, 8.854 x 10-12 farad/rn.
PERMITTIVITY RELATIONSHIPS FOR SOLID AND PULVERIZED MATERIALS
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