Space Charge Profiles and Capacitances

For two oppositely charged majority carriers with zq = z. s z the Gouy-Chapman-profile (see textbooks on electrochemistry) results which we write ( = x/A) here as 

The parameter 9 varies between -1 and 0 for depletion and between 0 and +1 for accumulation, and plays the role of a degree of influence of the interface.94 

Two extreme cases are worth mentioning the first if the concentration variation is small (9 - 0), then we end up with the exponential solution [ CiQ = Cj (x = 0) ] 

Unlike the Debye length the effective width X depends on the space charge potential  

From Eqs. (73) and (74) which describe accumulation and depletion for strong effects, the concentrations of the other mobile species are simply accessible through Eq. (68). In liquid electrochemistry these profiles have been used to evaluate electrode/liquid electrolyte capacitances.79 

---