Concentration profiles in the space charge zones

The solution of Eq. (5.220) for semiinfinite boundary conditions leads to the Gouy-Chapman profile [247]. Let us follow the treatment in Ref. [248] and change to the concentration as the variable. First, let us consider the case that only two equivalently (but oppositely) charged defects (subscripts + and -) are relevant (z+ = (z j = z). The bulk concentrations are equal for reasons of electroneutrality (c+oo = c oo = Coo). Oo combination with Eq. (5.215) we obtain the differential equation for the concentration enhancement ( + or C ) 

If both defects are mobile and there is electrochemical equilibrium, it follows because C+ = C- (see Eq. (5.215)) that  

This differential equation can be integrated using the boundary conditions 

Before we give the general solution, let us consider a helpful approximation (Fig. 5.74). If the splitting effect is very marked, the depleted defect (defect 2) very rapidly 

The subscript 1 now applies to the enriched positive or negative defect. Using 

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