Local fields in random dielectrics: Distribution characteristics and the effects of microstructure

A generalized Onsager approach is developed for the calculation of local fields in random dielectrics. The distribution of local fields obtained is shown to display a double-peak character in general. This unexpected behavior is explained in terms of two types of local environment defined relative to the applied field. We find the characteristics of the local-field distribution to be sensitive to the microstructure of a random medium. Two types of random structures, characterized by uniform or percolative spatial correlations, were considered. The standard deviation of the distribution is shown to be directly proportional to the product of the polarizability and a parameter that measures the local anisotropy of the medium. The mean of the distribution is found to be bounded below by the Lorentz local-field value, with the fractional deviation, S, from the lower bound proportional to the variance σ². The same quantity S is identified as the correction factor to the Clausius-Mossotti relation. We demonstrate that the extended spatial correlation has a significant effect on the values of S. Implications of our results, for effective-medium theories and optical properties of random small-particle systems, are discussed.