Approximate Solutions of the PB Equation

A number of approximate analytical solutions to the PB equation have been proposed as summarized by Ohshima, Healy, and White (1982). These authors introduced quite accurate expressions for the potential profile and the surface charge-potential 

Other expressions are mentioned in the study by Ohshima, Healy, and White 

The origin of the surface charge has not been deal with as yet. The charge is due to adsorption of ionic species and/or surface reactions these matters will be analyzed in the next chapters. 

Atkins, R, and J. de Paula. 2009. Physical Chemistry. 9th ed. New York W. H. Freeman. Baldelli, S. 2008. Surface structure at the ionic liquid-electrified metal interface. Accounts of Chemical Research Al, no. 3 421-431. doi 10.1021/ar700185h. 

Faulkner. 2000. Electrochemical Methods Fundamentals and Applications. 2nd ed. New York John Wiley Sons. 

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To obtain a useful approximate solution of the PB equation (S8.6-4), we consider the dilute limit in which the electric potential O is weak compared with the ambient thermal energy kT. In this limit, the Boltzmann exponential can be linearized by retaining only the leading term in the power series expansion... 

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