A theory of percolation in liquids

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Abstract
Problems involving percolation in liquids (i.e., involving connectivity of some sort) range from the metal–insulator transition in liquid metals to the properties of supercooled water. A common theme, however, is that connectivity can be distinguished from interaction and that one should not be slighted in order to describe the other. In this paper we suggest a model for percolation in liquids—the model of extended spheres—which permits connectivity to be studied in the context of, but independently from, liquid structure. This model is solved exactly in the Percus–Yevick approximation, revealing the existence of an optimum liquid structure for percolation. We analyze this behavior by first deriving an explicit diagrammatic representation of the Percus–Yevick theory for connectivity and then studying how the various diagrams contribute. The predictions are in excellent qualitative agreement with recent Monte Carlo calculations.

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