Statistical mechanics and distribution functions

Most of the modern developments in electrolyte theory rest on the use of statistical mechanical arguments, with the computational details carried out by computer simulation methods, 

1 The simplest situation the radial distribution function of the Debye-Huckeltheory 

The physical meaning of this equation can alternately be expressed in terms of probabilities, such that  

This gives the probability of finding an ion of the ionic atmosphere in a given small region lying at a distance r from the central reference j ion at the origin. It is often written in the more explicit form g r 12). Here the superscript represents the number of species involved, here the central reference ion, ion 1, and the ion in the ionic atmosphere, ion 2, and the bracket lists the distances on which the probability depends. Since only two ions are considered explicitly, then there can only be one distance to specify, i.e. the distance between the two ions, ri2- These probabilities are calculated for aU conceivable ru values of a central reference ion and an ion of the ionic atmosphere, and this allows the g to be found for each value of ri2. 

Physically, g (ri2) determines the probability of finding ion 2 in the ionic atmosphere in a given small region lying at a distance ri2 from the central reference ion, ion 1. 

---