Radial distribution function: Difference between revisions

Revision as of 12:30, 13 September 2017

Revision as of 20:33, 14 March 2018

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In simplest terms it is a measure of the probability of finding a particle at a distance of <math>r</math> away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of <math>r</math> and <math>r+dr</math> away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those which are within the circular shell, dotted in orange.

The RDFradial distribution function is usually determined by calculating the distance between all particle pairs and binning them into a histogram. The histogram is then normalized with respect to an ideal gas, where particle histograms are completely uncorrelated. For three dimensions, this normalization is the number density of the system <math>( \rho )</math> multiplied by the volume of the spherical shell, which mathematicallysymbolically can be expressed as <math>g(r)_I = \rho \, 4\pi r^2\rho dr</math>, where <math>\rho</math> is the number density.

Given a [[potential energy]] function, the radial distribution function can be computed either via computer simulation methods like the [[Monte Carlo method]], or via the [[Ornstein-Zernike equation]], using approximative closure relations like the [[Percus-Yevick approximation]] or the [[Hypernetted-chain equation|Hypernetted Chain Theory]]. It can also be determined experimentally, by radiation scattering techniques or by direct visualization for large enough (micrometer-sized) particles via traditional or confocal microscopy.