206 THE PHYSICS of viruses 



So 



and therefore 





dW dW dW _ ^Tnim''eW 

 dx'' + dy'- ^ dz-' ~ KIT 



Now for a plane surface which accumulates an ionic atmos- 

 phere, we need only consider the a-coordinatc and, if we put 

 p^ = ^irnrn'^e'^/KkT, we have the very simple equation 



for which the general solution is 



where f i and Co are constants determined by the physical 

 conditions present. Since, V = for .r = co we have Ci = 0. 

 And since T^ = Vq, the potential at the surface, for x =0, we 

 have 



The double-layer potential has then dropped to 37% (or 1 /e) 

 of its original value in a distance of 1 //) cm, or a distance 



1 I KJ'T 



— \ -^ This depends sharplv on m, the valence of the ions, 



me \ Sth I I . ■> 



and somewhat on n, the average concentration of the ions. 



Now if two double-layers are formed at a distance ^d apart, 

 there will be an interaction between them which will result in a 

 repulsive force and hence a net ])otential energy which is a 

 function of 2f/, their separation. It is possible to calculate this 

 re])idsive i)otential, Fyj, in several ways (see Verwey and Over- 

 beek, 1948, ]). (j()), and an approximate value for this is 



' V Lf'" + iJ 



