Double layer capacitance and relaxation in electrolytes and solids

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Abstract
After a review of the idealizations usually made in theories of space-charge polarization in liquids and solids, published theoretical and experimental work dealing with the a.c. response of two-electrode systems is discussed and various corrections pointed out. A calculation of the equilibrium space charge capacitance of two blocking electrodes separated by material containing mobile positive and negative charge of arbitrary valences is presented for the limit of vanishingly small applied static potential. The result of this calculation may be used to obtain the frequency dependence of diffuse layer parallel capacitance and conductance in the Debye dispersion frequency range, where the motion of charges in space charge regions leads to an admittance involving only a single time constant. Expression given previously by Baker and Buckle for this time constant and for the low-frequency limiting capacitance are corrected, along with their conditions for the extent of the Debye dispersion range. The relaxation time constant is G∞(r–1)τD/G0, where G0 and G∞ are the low-and high-frequency limiting values of the series conductance, τD is the dielectric relaxation time of the material containing mobile charges, rM cotanh M, and M is the ratio of the separation between electrodes to twice the Debye length. Finally, deviations from Debye dispersion behaviour for various 1 : 1 valence theories are calculated and compared; for the two-blocking-electrodes situation, Debye behaviour and a simple equivalent circuit of frequency-independent elements extend up to nearly ωτD 1. Beyond this range, the parallel space-charge capacitance shows ω– limiting behaviour, similar to that previously found only with partly blocking electrodes, and the equivalent series space-charge capacitance eventually decreases as ω–½.

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