Liquid Structure and Self-Diffusion

The method of molecular dynamics has been used to study the structure of a liquid and its relation with the process of self-diffusion. The particles around a given particle are separated into shells of primary, secondary, etc., neighbors by a precise geometrical procedure. Each shell of neighbors of a particle generates a closed convex polyhedron surrounding the polyhedron of the previous shell. The faces of the polyhedra are the bisector planes of lines joining the particle to its neighbors. The primary polyhedron is the smallest closed convex polyhedron around the particle. The primary polyhedra of a random system of points, of a liquid, and of a solid are compared; the average number f̄ of faces are found to be 15.67, 14.45, and 14.26, respectively. The average number p̄ of sides to the polygons forming the faces is obtained through the relation p̄=6—(12/f̄). The pair correlation function g(r) is decomposed into a sum Σig(i)(r), where g(i)(r), arises out of neighbors forming the ith-order polyhedra. The distributions up to i=5 have been calculated. g(1) and g(2) give the first two maxima in g(r). For higher values of i the g(i)(r) do not correspond to maxima in g(r). For the liquid and for the random set of points the average number of faces f̄i of the ith-order polyhedra increases linearly with i; the departure from the linear law is significant only for i=1 and 2 in the case of the liquid. It is found that the shape of the primary polyhedra is related to the direction of displacement, in time τ, of the central particle; and the correlation is maximum when τ=0.5×10−12 sec. The positions of the neighbors are analyzed with respect to this displacement direction and expressed as a distribution g(r, μ; τ), which, in addition to the dependence on the distance, contains the angular correlation between the position of a neighbor and the displacement direction in time τ of the central particle. The nearest neighbors are found to be preferably situated in a direction away from the displacement direction. As the distance increases, the forward direction becomes more favorable. In the region of the secondary neighbors the same behavior is repeated but is less in magnitude. This local fluctuation in the distribution of neighbors disappears beyond the secondary neighbors. The velocity autocorrelation function and its spectrum f(ω) are found to have characteristics related to these local fluctuations. f(ω) is found to have a solidlike part having the same Debye ω as that in the solid before melting. The diffusive part of the velocity autocorrelation function arises out of the particle's taking advantage of the local fluctuation in the configuration of its neighbors to move in the ``easy'' direction afforded to it by the fluctuation.