218 HYDROGEN ION CONCENTRATION 



membranes msiy give rise to electric phenomena bj^ an entirely different 

 mechanism. 



61. Polarization phenomena at phase boundaries 



All of the above considerations of phase boundary potentials 

 relate to the conditions where chemical equihbrium prevails, at least 

 at the contiguous boundary layers. These potential differences 

 are comparable to the E.M.F. of an open galvanic chain without 

 a current. When such a galvanic chain is closed, the resulting 

 current produces a greater or lesser change, according to the con- 

 ditions, in the concentrations of the solutions, and along with it a 

 change in the E.M.F. which is designated as polarization. This 

 polarization may result either from the current produced by the 

 E.M.F. of the chain itself or from a current sent out by an external 

 E.M.F. through the chain. In the same way polarization, and 

 hence a change in the phase boundary potential, may occur in phase 

 boundary chains either when they are short circuited for a longer 

 period of tune, or when an external current is sent through them. 

 Nernst and Riesenfeld" furnished the theory and the discussion of 

 these polarization phenomena: 



The arrangement, from left to right is as follows: (1) water 

 saturated with phenol, (2) phenol saturated with water, (3) water 

 saturated with phenol again; an electrolyte is distributed among 

 these phases in a state of equilibrium, and, furthermore, for the 

 sake of simphcity it is assumed that the phase boundary potential 

 is zero. An electric current is sent through this system from left 

 to right for a period of time, until one faraday (96,500 coulombs) 

 has flowed through every cross section. The dissolved electrol5^e 

 consists of two univalent ions whose relative speeds are u for the 

 cation and v for the anion. In general the value of u in water will 

 not be the same as in phenol, hence let us designate it as Ui in water 

 and U2 in phenol; and hkewise we shall differentiate Vi from V2. 

 Let us consider any given cross section of the path of the current 

 in the water. We find that the fraction of cations concerned in the 



Ui 



transport of one faraday is — y — - = ni. This fraction is known as 



. . . . Vi 



the transference number of the cation. Likewise the fraction , 



Ui 4- Vi 



" Nernst and Riesenfeld, Ann. d. Physik [4] 8, 600 (1902). 



