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On the structure of generalized Poisson–Boltzmann equations

Published online by Cambridge University Press:  20 November 2015

N. GAVISH  and
K. PROMISLOW
N. GAVISH
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, Haifa, Israel email: ngavish@tx.technion.ac.il
K. PROMISLOW
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI, USA email: kpromisl@math.msu.edu
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Abstract

In this work, we analyse a broad class of generalized Poisson–Boltzmann equations and reveal a common mathematical structure. In the limit of a wide electrode, we show that a broad class of generalized Poisson–Boltzmann equations admits a reduction that affords an explicit connection between the functional form of the corresponding free energy and the associated differential capacitance data. We exploit the relation to we show that differential capacitance curves generically undergo an inflection transition with increasing salt concentration, shifting from a local minimum near the point of zero charge for dilute solutions to a local maximum point near the point of zero charge for concentrated solutions. In addition, we develop a robust numerical method for solving generalized Poisson–Boltzmann equations which is easily applicable to the broad class of generalized Poisson–Boltzmann equations with very few code adjustments required for each model

Keywords

Poisson-Boltzmanndifferential capacitanceconcentrated electrolyte solutions

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 4 , August 2016 , pp. 667 - 685
Copyright
Copyright © Cambridge University Press 2015 

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