Hostname: page-component-788cddb947-rnj55 Total loading time: 0 Render date: 2024-10-20T15:35:20.219Z Has data issue: false hasContentIssue false
  • English
  • Français

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: Peter.Lingenfelter@abo.fi
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1) Lewenstam, A.; Zytkow, J. M. Ion-Selective. Electrodes, 5; Pergamon Press: 1989; pp. 297–304.Google Scholar
(2) Zytkow, J. M.; Lewenstam, A. Fresenius. J. Anal. Chem. 1990, 338, 225.Google Scholar
(3) IUPAC. Pure Appl. Chem. 1976, 48, 129.Google Scholar
(4) IUPAC. Pure Appl. Chem. 1994, 66, 2527.Google Scholar
(5) Bergling, S.; Syganow, A.; Von Kitzing, E. Biophysical Journal 1999, 76, A207.Google Scholar
(6) Borry, B.; Kuyucak, S.; Chung, S. H. Biophysical Journal 2000, 78, 2364.Google Scholar
(7) Cardenas, A. E.; Coalson, R. D.; Kurnikova, M. G. Biophysical Journal 2000, 79, 80.Google Scholar
(8) Catacuzzeno, L.; Franciolini, F.; Nonner, W. Pflugers Archiv-European Journal of Physiology 2000, 440, R24.Google Scholar
(9) Chen, D.; Lear, J.; Eisenberg, B. Biophysical Journal 1997, 72, 97.Google Scholar
(10) Chen, D. P.; Eisenberg, R. S. Biophysical Journal 1994, 66, A292.Google Scholar
(11) Chen, D. P.; Eisenberg, R. Biophysical Journal 1993, 64, A22.Google Scholar
(12) Corry, B.; Kuyucak, S.; Chung, S. H. Journal of General Physiology 1999, 114, 597.Google Scholar
(13) Eisenberg, R.; Chen, D. P. Biophysical Journal 1993, 64, A22.Google Scholar
(14) Hollerbach, U.; Chen, D. P.; Busath, D. D.; Eisenberg, B. Langmuir 2000, 16, 5509.Google Scholar
(15) Hollerbach, U.; Chen, D.; Nonner, W.; Eisenberg, B. Biophysical Journal 1999, 76, A205.Google Scholar
(16) Kurnikova, M. G.; Coalson, R. D.; Graf, P.; Nitzan, A. Biophysical Journal 1999, 76, A211.Google Scholar
(17) Nonner, W.; Eisenberg, B. Biophysical Journal 1998, 75, 1287.Google Scholar
(18) Schuss, Z.; Nadler, B.; Eisenberg, R. S. Physical Review e 2001, 6403, art-036116.Google Scholar
(19) Cohen, H.; Cooley, J. W. Biophysical Journal 1965.Google Scholar
(20) Hafemann, D. R. The Journal of Physical Chemistry 1965, 69, 4226.Google Scholar
(21) Brumleve, T. R.; Buck, R. P. J. Electroanal. Chem. Interfacial Electrochem. 1978, 90, 1.Google Scholar
(22) Kontturi, A.; Kontturi, K.; Mafe, S.; Manzanares, J. A.; Niinikoski, P.; Vuoristo, M. Langmuir 1994, 10, 949.Google Scholar
(23) Kontturi, K.; Mafe, S.; Manzanares, J. A.; Pellicer, J. Journal of Electroanalytical Chemistry 1994, 378, 111.Google Scholar
(24) Kontturi, K.; Manzanares, J.; Murtomaki, L.; Schiffrin, D. Journal of Physical Chemistry B 1997, 101, 10801.Google Scholar
(25) Mafe, S.; Pellicer, J.; Aguilella, V. M. J. Phys. Chem. 1986, 90, 6045.Google Scholar
(26) Mafe, S.; Pellicer, J.; Aguilella, V. M. An. Fis., Ser. B 1987, 83, 96.Google Scholar
(27) Manzanares, J. A.; Mafe, S.; Pellicer, J. Journal of Physical Chemistry 1991, 95, 5620.Google Scholar
(28) Manzanares, J. A.; Murphy, W. D.; Mafe, S.; Reiss, H. Journal of Physical Chemistry 1993, 97, 8524.Google Scholar
(29) Langtangen, H. P. Computational Partial Differential Equations. Numerical Methods and Diffpack Programming, Springer Verlag, Berlin: 1999.Google Scholar
(30) Nernst, W. Z. Phys. Chem. 1888, 2, 613.Google Scholar
(31) Nernst, W. Z. Phys. Chem. 1889, 4, 129.Google Scholar
(32) Planck, M. Ann. Phys. Chem. 1890, 39, 161.Google Scholar
(33) Planck, M. Ann. Phys. Chem. 1890, 40, 561.Google Scholar