Percolation in ionic fluids and formation of a fractal structure.
The size of a dense region in the nonuniform distribution of particles generated in an ionic fluid can develop under certain conditions, as the charge on each particle increases. To derive this result, it is assumed that such a dense region is an ensemble of particles linked to each other as particle pairs that satisfy the condition E(ij)+u(ij)(r)< or =0, where E(ij) is the relative kinetic energy for i and j particles and u(ij)(r) the Coulomb potential. The percolation of the ensemble can be estimated analytically. The result described above has been derived from this estimation. According to the pair connectedness function derived for analytic estimation of the percolation, the dense region resulting from the contribution of the Coulomb attractive force between positive and negative particles can produce a fractal structure with a fractal dimension of 1.5. Furthermore, a configuration of charged particles, which can be approximately drawn from a characteristic of the pair connectedness function, agrees with that of the Bjerrum theory.
Kaneko
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Kurakenchikuzokeisha Company, Ltd., Shimo 1-27-22, Kita-ku, Tokyo 115-0042, Japan. kanekous@ppp.bekkoame.ne.jp