Inverse Problems in Mass and Charge Transport

Inverse Problems in Mass and Charge Transport

Krzysztof Szyszkiewicz Jerzy J. Jasielec Janusz Fausek Robert Filipek 

AGH University of Science and Technology, Faculty of Materials Science and Ceramics, al. Mickiewicza 30, Krakow, 30-059, Poland

1 October 2015
7 January 2016
11 May 2016
| Citation



Inverse problems have been becoming an important method for determination of materials properties, size and shape design, identification of the proper boundary and/or initial conditions. In this work we show the application of the inverse method to multi-component electrochemical systems. The basic process operating in these systems is electrodiffusion which can be described by the full form of the Nernst-Planck and Poisson equations for arbitrary initial conditions and Neumann-like boundary conditions. No simplifications like electroneutrality or constant electric field assumption are used. Results for several examples are demonstrated: determination of chloride diffusion coefficient in concrete, optimization of detection limit for ion selective electrodes and determination of EIS spectra using NPP model.

1. Introduction
2. Multilayer Nernst-Planck-Poisson Model
3. Determination of Chloride Diffusion Coefficientin Concrete - Two Compartments and Time Dependent Dirichlet Boundary Conditions
4. Detection Limit of Ion-Selective Electrodes
5. Electrochemical Impedance Spectroscopy
6. Conclusions

Financial support from INNOTECH project no. K1/IN1/25/153217/NCBR/12 and AGH grant no. 11.11 .160 .257 is acknowledged.


[1] A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Springer, 2007 .

[2] J.P. McKelvey, Solid State and Semiconductor Physics, Krieger: Malabar, FL, 1982.

[3] D.L. Scharfetter, D.L. Gummel, IEEE Trans. Elect. Dev. ED-16 1969, 64-77.

[4] J. Marchand, B. Gérard, A. Delagrave, Ion transport mechanism in cement-based materials. In: Materials Science of Concrete, vol.V, J.P. Skalny (Ed.), Am. Ceram. Soc., Ohio 1998, p. 307

[5] N. Lakshminarayanaiah, Equations of Membranc Biophysics; Academic: New York. 1984.

[6] R.F. Probstein, Physicochemical Hydrodynamics, Butterworth: Stoneham, NA, 1989.

[7] H. Cohen, J. Cooley, Biophys. J. $5(1965) 145-162 .$

[8] J.J. Jasielec, R.Filipek, K.Szyszkiewicz, J.Fausek, M.Danielewski, A.Lewenstam, Comp. Mat.

Sci. $63(2012) 75-90$

[9] E. Bakker, M.Telting-Diaz, Anal. Chem. 74 (2002) 2781-2800.

[10] E. Bakker, P. Bühlmann, E. Pretsch, Chem. Rev. 97 (1997) 3083-3132.

[11] P. Bühlmann, E. Pretsch, E. Bakker, Chem. Rev. 98 (1998) 1593-1688.

[12] T. Sokalski, A. Cereza, T. Zwickl, E. Pretsch, J. Am. Chem. Soc. 119 (1997) 11347-11348.

[13] W.E. Morf, G. Kahr, W. Simon, Anal. Chem. $46(1974) 1538-1543$.

[14] A. Hulanicki, A. Lewenstam, Talanta 23 (1976) 661-665.

[15] J.J. Jasielec, B. Wierzba, B. Grysakowski, T. Sokalski, M. Daniclewski, A. Lewenstam, ECS Trans. 33 (26), 19 (2011) 19-29.

[16] E. Barsukov, J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment and Applications, Wiley-Interscience, $2^{\text {nd }}$ ed., 2005 .

[17] Vadim F. Lvovich, Impedance Spectroscopy. Applications to Electrochemical and Dielectric Phenomena, Wiley, 2012.

[18] D.D. Macdonald, Electrochim. Acta, 51(2006) 1376-1388.

[19] T. Sokalski, P. Lingenfelter, A. Lewenstam. J. Phys. Chem. B. $107(2003), 2443-2452$.

[20] T.R. Brumleve, R.P. Buck, J. Electroanal. Chem. 90 (1978)1-31.