Radial distribution function: Difference between revisions

Revision as of 17:06, 14 February 2007

Revision as of 17:11, 14 February 2007

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If <math>\phi(r)</math> would be zero for all r - i.e. if the molecules did not exert any influence on each other g(r) = 1 for all r. Then from (1) the mean local density would be equal to the mean density <math>\rho</math>: the presence of a molecule at O would not influence on the presence or absence of any other molecule and the gas would be ideal. As long as there is a <math>\phi(r)</math> the mean local density will always be different from the mean density <math>\rho</math> due to the interactions between molecules.

When the density of the gas gets higher the so called low-density limit (2) is not applicable anymore due to the fact that the molecules attratcedattracted to and reppeled by the molecule at O also reppel and attract eaceach other. The correctuioncorrection terms needed to correctly describe g(r) resemble the [[virial equation]], it is an expansion in the density:

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in which additional functions <math>g_{1}(r), \, g_{2}(r)</math> appear which may depend on temperature <math>T</math> and distance <math>r</math> but not on density, <math>\rho</math>.

Given a [[potential energy]] function, the radial distribution function can be found via computer simulation methods like the [[Mote Carlo method]]. It could also be calculated numerically using rigourous methods obtained from [[statistical mechanics]] like the [[Perckus-Yevick approximation]].