A method for describing the local structure of a liquid

Abstract

The study, begun by Bernal [i], of the geometry of the immediate environment in a model disordered system imitating a liquid is based on the construction of Voronoi polyhedra and the study of their statistics. In a real liquid, where there is attraction between the particles, it is possible to analyze the structure of the immediate environment using another method, based on the separation of bonded (by an interaction) g~oups of particles and the determination of the geometric and topological properties of each such group. This second method has been found to be more useful in the study of the topological properties of a system. Comparison of a liquid and a crystal shows that the difference in their topological properties is more fundamental than the difference in their geometric properties. In fact, the geometric properties of a crystal (the instantaneous distances and angles between the particles) change continuously in the thermal motion of the particles, and their comparison with the analogous properties of a liquid close to the phase equilibrium line does not make it possible, without special treatment (averaging over a certain time interval), to distinguish the properties of one phase from those of another. The topological properties of a crystal (in the terms of graph theory these are the powers of the vertices, the lengths of the rings, etc. [2]) are independent of the thermal motion of the particles, and, as follows from [I], differ qualitatively from the topological properties of a liquid. It is for this reason that in the present work the main attention will be paid to the description of the topological structure of a system. At the present time there is no generally accepted viewpoint regarding the understanding of the term "structure of a liquid." In statistical physics it is the set of the partial distribution functions [3], and in crystallography and computer modeling it is the list of the coordinates of all the particles. Naberukhin [4] refined the last definition, by introducing into it, in addition to the list of coordinates, the laws given above this list. We shall examine below the local structure, that is, the properties of configurations made up of a small number of particles. In this case it is appropriate that the concept being examined should be independent of the choice of the system of coordinates. We shall therefore use the following definition: The structure of a given set of particles is the set of geometric or topological relationships between the coordinates of the particles. Naturally, the structure defined in this way characterizes to some extent the relative arrangement of the particles.