568 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



05 1.0 1.5 20 2.5 3.0 3.5 4.0 



r IN CENTIMETERS 



4.5 



5.0 



5.5 



6.0 

 X10~^ 



Fig. 12 — Distribution of nearest neighbors in a random assembly of particles 

 for a concentration of 10^^ cm~^. 



That (7.4) solves (7.3) is easily demonstrated by substitution of the 

 latter into the former. 



If there were no forces of attraction between ions then c{r) would 

 equal N, and if a is take equal to zero (7.4) reduces to 



g{r) = 47rr'A^exp(-47rr'A^/3) (7.5) 



This function is plotted in Fig. 12 for the case N = 10^^ cm~^ Note that 

 the position of the maximum, the most probable distance of location of a 

 nearest neighbor, occurs near the value of r equal to (3/47rA^)^'^ This is 

 the radius of the average volume per particle when the concentration is 

 N, i.e. the volume, 1/A^. 



In order to write g{r) for the case of coulombic interaction it is neces- 

 sary to compute c(r) under these conditions. Fuoss (after Bjerrum) rea- 

 soned as follows. If a theory can be constructed which depends only upon 

 the characteristics of near nearest neighbors (nearest neighbors at small 

 values of r) then the force of interaction experienced by the nearest 

 neighbor can be assumed to originate completely in the coulomb field of 

 the negative ion at the origin. This is predicated on the argument that 

 both positive and negative ions develop atmospheres of opposite sign 

 which are superposed when the two ions are close to one another. The 

 result is a cancellation of the net atmosphere leaving nothing for the two 



