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Numerical Solution of the Coupled Nernst-Planck and Poisson Equations for Ion-Selective Membrane Potentials

Published online by Cambridge University Press:  11 February 2011

Peter Lingenfelter ,
Tomasz Sokalski  and
Andrzej Lewenstam
Peter Lingenfelter*
Affiliation:
Process Chemistry Group (www.abo.fi/instut/pcg/), c/o Centre for Process Analytical Chemistry and Sensor Technology (ProSens; www.abo.fi/fak/ktf/prosens/), Åbo Akademi University, Biskopsgatan 8, FIN-20500 Åbo/Turku, Finland
Tomasz Sokalski
Affiliation:
Process Chemistry Group (www.abo.fi/instut/pcg/), c/o Centre for Process Analytical Chemistry and Sensor Technology (ProSens; www.abo.fi/fak/ktf/prosens/), Åbo Akademi University, Biskopsgatan 8, FIN-20500 Åbo/Turku, Finland
Andrzej Lewenstam
Affiliation:
Process Chemistry Group (www.abo.fi/instut/pcg/), c/o Centre for Process Analytical Chemistry and Sensor Technology (ProSens; www.abo.fi/fak/ktf/prosens/), Åbo Akademi University, Biskopsgatan 8, FIN-20500 Åbo/Turku, Finland
*
* Corresponding author: Peter Lingenfelter, Tel: +358 2 215 3247, Fax: +358 2 215 4479, email: [email protected]
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Abstract

A numerical model is presented for analyzing the propagation of ionic concentrations and electrical potential in space and time in the solution ion-exchanging membrane system. Diffusion and migration according to the Nernst-Planck (NP) flux equation govern the transport of ions, and the electrical interaction of the species is described by the Poisson (P) equation. These two equations and the continuity equation form a system of partial non-linear differential equations that is solved numerically. As a result of the physicochemical properties of the system, both the contact/boundary potential and the diffusion potential contribute to the overall membrane potential. It is shown that interpreting the electrical potential of ion-exchanging membranes exclusively in terms of boundary potential at steady-state is incorrect. The Nernst-Planck-Poisson (NPP) model is general and applies to ions of any charge in space and time domains.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 752: Symposium AA – Membranes–Preparation, Properties and Applications , 2002 , AA8.11
Copyright
Copyright © Materials Research Society 2003

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References

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