Radial distribution function: Difference between revisions

Revision as of 10:45, 16 August 2018

Revision as of 22:40, 14 November 2018

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{{NumBlk|:| <math>g(r) = \exp \left [ -\frac{u(r)}{kT} \right ] </math>.|{{EquationRef|11}}}}

If <math>u(r)</math> were zero for all <math>r</math> &ndash; i.e., if the particles did not exert any influence on each other, then <math>g(r) = 1 </math> for all <math>\boldmathbf{r}</math> and the mean local density would be equal to the mean density <math>\rho</math>: the presence of a particle at O would not influence the particle distribution around it and the gas would be ideal. For distances <math>r</math> such that <math>u(r)</math> is significant, the mean local density will differ from the mean density <math>\rho</math>, depending on the sign of <math>u(r)</math> (higher for negative interaction energy and lower for positive <math>u(r)</math>).

As the density of the gas increases, the low-density limit becomes less and less accurate since a particle situated in <math>\mathbf{r}</math> experiences not only the interaction with the particle in O but also with the other neighbours, themselves influenced by the reference particle. This mediated interaction increases with the density, since there are more neighbours to interact with: it makes physical sense to write a density expansion of <math>g(r)</math>, which resembles the [[virial equation]]: