806 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



1)01' of operations required to make contacts active and relative humidity 

 has no clear interpretation in our present state of knowledge. 



6.2 Diffusion of Activating Vapor 



In Ivisliuk's vacuum experiments the amount of carbon formed and 

 the degree of activation attained was independent of benzene vapor 

 pressure. This is not at all the case when activation is produced by op- 

 erating contacts in air. In fact, one of the earliest observations was a 

 minimum vapor pressure below which contacts could not be activated 

 (Reference 2, Table I). In more careful later tests it was found that the 

 minimum vapor pressure is a function of rate of operation of the con- 

 tacts, the minimum pressure being actually proportional to the rate of 

 operation over a factor of 100 which was the range tested (Reference 8, 

 Fig. 2). Obstruction offered by air supplies the explanation of this rate 

 effect. Activation cannot occur if electrodes are separated between one 

 arc and the next for a time which is short in comparison with the time 

 required to cover the surface with one monolayer of organic molecules. 

 A rough order of magnitude calculation confirms this conclusion. 



As an approximation, one assumes one dimensional diffusion to an 

 electrode surface from the space in front of it, with all molecules reaching 

 the surface sticking to it. Boundary conditions for the solution of the 

 diffusion equation, dC/dt = Dd-C/dx^, are then: 



C = Co at t = ioY X > 



C = at a; = for all values of t 



The concentration of activating molecules in the space in front of the 

 electrode is then C = Co erf [x/2 (Dt)^'-]. The total number of molecules 

 to have reached the surface at any time ti is, 



dt = 2Co{D/Ty'W 



expressed in molecules/cm-, when Co is given in molecules/cm^. We 

 are interested in the value of ^i for which 7W is the number of molecules 

 in a monolayer, and the maximum rate of operation of contacts for ac- 

 tivation to occur can be expected to be comparable with 



n = i^i = 2Co^ D/Tm'- = 8.1 X 10^^ D(p/mY, (2) 



where p is the partial pressure of activating vapor in mm Hg. The factor 

 I in n = ^ti appears because diffusion to the surface can occur only when 

 the electrodes are separated, and it is assumed that they are separated 

 for half of the time. 



The best data we have for testing this relation are represented by ex- 



