L. Fu et al., ANALYTIC APPROACH TO THE INTERFACIAL POLARIZATION OF HETEROGENEOUS SYSTEMS, Physical review. B, Condensed matter, 47(20), 1993, pp. 13818-13829
We have obtained an analytical solution of Maxwell's equations for a d
ielectric system of spherical particles in a medium. The system is pla
ced between two parallel electrode plates, subject to a low-frequency
alternating potential, and the solution is obtained from the correspon
ding boundary-value problem for the Green function. All the multipole
moments and the electric field are expressed in terms of the applied p
otential at the electrodes and a matrix which depends on the system co
nfiguration. The effective dielectric function is then obtained as an
average over the whole sample. For disordered systems, we solve exactl
y the case of two-particle distributions with short-range correlations
and find that the form of the distribution plays a crucial role. In p
articular, we prove that for spherically symmetric two-particle distri
butions all multipole moments except dipoles are exactly zero, and the
Maxwell-Garnett result, or, equivalently, the Clausius-Mossotti relat
ion for spherical particles, is valid regardless of the particle conce
ntration. Within the two-particle distribution, corrections to the Max
well-Garnett result can only derive from nonsphericity in the distribu
tion: in such a case, higher multipole moments are generally nonzero a
nd may strongly affect the effective dielectric function. We provide t
he explicit expressions for all the multipole moments and the effectiv
e dielectric function, which can be computed straightforwardly for any
given distribution. We show that an iterative unsymmetrical procedure
proposed originally by Bruggeman is inconsistent with our results.