Statistical mechanical theory electrical double layer

The simplest, self-consistent model of the diffuse-ion swarm near a planar, charged surface like that of a smectite is modified Gouy-Chapman (MGQ theory [23,24]. The basic tenets of this and other electrical double layer models have been reviewed exhaustively by Carnie and Torrie [25] and Attard [26], who also have made detailed comparisons of model results with those of direct Monte Carlo simulations based in statistical mechanics. The postulates of MGC theory will only be summarized in the present chapter [23] ... 

S. L. Carnie, G.M. Torrie, The Statistical Mechanics of the Electrical Double Layer, Advan. Chem. Phys. 56 (1984) 141 253. (Gouy-Chapman and more advanced models, including integral equation theories, discrete charges, simulations.)... 

Levine, S., C. W. Outhwaite, and L. B. Bhuiyan. 1981. Statistical mechanical theories of the electric double layer. Journal ofElectroanalytical Chemistry 123, no. 1 105-119. 

The modified Poisson-Boltzmann (MPB) approximation is the product of many theoretical investigations into improvements of the PB approach of Gouy and Chapman based on classical statistical mechanics [22, 23] for the description of the electric double layer at a charged plane interface. These extensions originated in a work of Kirkwood [24] who used the Giintelberg charging process to examine the fluctuation terms neglected in the DH theory of electrolytes. 

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