Pseudocapacitance Effects and the Concentration of Intermediate Species

Reaction paths of the type found for the discharge of divalent species, involving univalent intermediates, must exhibit pseudocapacitance effects in transient or ac phenomena. This is due to the fact that a change in potential 

Conversely, the appearance of pseudocapacitance can be taken as another proof of the correctness of the assumed mechanism and a way of finding out the concentration of the intermediate. 

Two cases may arise. If the intermediate species is a surface species, i.e., strongly adsorbed and at a negligible concentration in solution, the change is limited practically to the surface concentration only, which can vary from surface coverage zero to unity. Hence, the maximum amount of the intermediate that can be formed or removed will be of the order of 10 molcm . However, when the intermediate has a finite stability in solution, as is the case with copper, the steady state can in theory be reached only after the concentration has been appropriately adjusted throughout the bulk of the solution. Hence, the amount of charge for charging the pseudocapacitance 

Suppose that, at any given potential, E, equilibrium between the univalent intermediate M and one of the states, initial-M or final-M, is established instantaneously by transfer of charge. The relationship between the equilibrium concentration of at that potential, Cm, and that at the reversible potential, Cm. o, is given by 

At the very beginning of any perturbation (e.g., in a galvanostatic pulse) ry - 0, and hence 

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