Theory of space-charge polarization and electrode-discharge effects

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Abstract
A combined, general treatment of intrinsic and extrinsic conduction in a liquid or solid is presented. Positive and negative species of mobile charge of arbitary valences and mobilities are assumed present, together with homogeneous immobile charge in the extrinsic case. The general equations are specialized to a one‐dimensional situation and then to that where both position‐dependent static and much smaller sinusoidally time‐varying components of charge, field, and current are simultaneously present. Sufficiently general boundary conditions are used that any condition from complete blocking to free discharge of positive and negative mobile carriers separately can occur at the electrodes. For the flat‐band condition (zero static field; in the binary electrolyte case, coincidence of the zero charge potential and the equilibrium potential) exact equivalent circuits and an exact expression for the small‐signal impedance are obtained. Relatively simple, closed‐form expressions for the zero‐frequency limiting values, Ci0 and Ri0, of the two frequency‐dependent elements which appear in the equivalent circuit, Ci and Ri, are derived even in general cases. The dependence of the normalized quantitities CiN0 and RiN0 on detailed boundary conditions, mobility ratio, valence ratio, temperature, and impurity doping level is examined in detail, reserving examination of frequency and temperature dependence of CiN and RiN themselves for later publication. Even for complete blocking of charges of both sign, Ci0 and Ri0 are not both intensive (interface) quantities unless the electrode separation contains many Debye lengths and the mobility and valence ratios are equal. When charges of one sign are completely blocked and those of the other partially or completely free to discharge, neither Ci0 nor Ri0 is generally intensive, and Ci0 may be many orders of magnitude larger than the completely blocking, diffuse‐double‐layer value. The dependence of CiN0 and RiN0 on all the above parameters is quite different in the extrinsic conduction case depending upon whether the discharging species involves majority or minority carriers.