Dielectric constant of polarizable, nonpolar fluids and suspensions

Dielectric function of aggregates of small metallic particles embedded in host insulating matrix

“…Generalizing the method of cluster expansion [8][9][10][11] in this case, we can develop the following expression for the calculation of the system effective dielectric permittivity:…”

“…The main purpose of [4][5][6][7][8][9][10][11][12][13] consists of accounting for the multipole interaction between inclusions. We shall consider here the method of cluster expansion developed in works.…”

“…A general expression for and its imaginary part as functions of the composite parameters containing inclusions of two different radii of the same material is considered using this approximation. We shall consider a system that consists of the continuous dielec- Generalizing the method of cluster expansion [8][9][10][11] in this case, we can develop the following expression for the calculation of the system effective dielectric permittivity:…”

“…The total number of particles is Nϭ⌺ ␣ N ␣ . The system is located in the external field proportional to e Ϫit with a wavelength ϭ2c/, which is much larger than the sphere radius and mean distance between particles; n a ϭN a /V, n b ϭN b /V,... are the concentrations of particles of the kinds a,b,... .Generalizing the method of cluster expansion [8][9][10][11] in this case, we can develop the following expression for the calculation of the system effective dielectric permittivity:whereis a usual dipole polarizability of the particle of kind a, ⌽ a,b (R ab ) is the two-particle distribution function of particles in the matrix, and R ab ϭ͉r a Ϫr b ͉, where r a and r b are the origins of spheres a and b, respectively. Equation ͑1͒ is a generalization of the relation ͑5.8͒ 12 for the case of a system with inclusions of different kinds.…”

Self-consistent electric field-induced dipole interaction of colloidal spheres, cubes, rods, and dumbbells

“…We note here that this analytical expression used in the SSCD approach, though it follows naturally from the CDM, has been derived before by Buckingham and Pople when examining the first-order correction to the ClausiusMossotti relation for an imperfect gas. 36 Further research in this direction seems to have focused on atomic and molecular gases and crystals; [37][38][39][40][41][42][43][44][45][46][47] in this paper, we wish to concentrate on interactions between colloidal particles and compare various methods for calculating their pair interactions.…”