574 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



1.0 



0.8 



0.6 



o 



li 



0.4 



0.2 



10 20 30 40 



r IN CM X (08 



50 



60 



Fig. 14 — Average mobility (calculated from the refined theory of pairing) of 

 a mobile ion in a pair as a function of the distance from its immobile neighbor. 

 The example shown corresponds to a substance having a = 2.5 X 10~* cm k = 16 

 at a temperature of 400°K. 



at r = £/2 = 6, ju/juo is near 0.5 which is the average value of Fuoss's 

 /i/)Uo for ions taken from either side of r = h. Therefore a certain sym- 

 metry with respect to r = 6 does exist, tending to justify Fuoss's model. 

 According to (7.24) ju/juo is 0.8 by the time r = 3£/2 = 36, independent 

 of the value of a. In other words an ion located a short distance beyond 

 h does have practically complete mobility as the Bjerrum-Fuoss theory 

 assumes. 



The refinement of (7.15) which occurs can be written as follows 



+ 2f(^ - A exp (£/r) 



(7.25) 



exp (- 4t/N/3) dr\ 



Mo 



Comparison of ju/mo computed from (7.25) with 1 — (P/N) appearing 

 in (7.15) over wide ranges of conditions again reveals an excellent cor- 

 respondence and further substantiates the Bjerrum-Fuoss theory. Since 

 calculations employing the latter are so much simpler it is expedient to 

 regard the cruder theory as an accurate approximation to the more re- 

 fined one. This practice will be followed from now on. 



