On the existence of exact conditions in the theory of electrical double layers

It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of ...

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Veröffentlicht in:The Journal of chemical physics 1992-03, Vol.96 (5), p.3767-3771
Hauptverfasser: ATTARD, P, WEI, D, PATEY, G. N
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WEI, D
PATEY, G. N
description It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out.
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General and physical chemistry
Properties of electrolytes: conductivity
title On the existence of exact conditions in the theory of electrical double layers
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