Electro-diffusion at different length scales - Grysakowski, Bartosz; Lewenstam, Andrzej; Danielewski, Marek (Diffusion Fundamentals, 2008)
The modelling of electro-diffusion in the multicomponent system in open space and time domains has been only recently addressed and made numerous applications in biology, fuel cells, electrochemical sensors and reference electrodes possible. In this work we show the numerical simulations of electrical potential over time and resulting electrochemical impedance spectra of ion-selective membrane electrodes (ISE’s). The numerical results are obtained by use of the coupled Nernst-Planck, Poisson and continuity equations (forming the NPP model). The equations are solved by means of the finite difference method, the Rosenbrock solver with the use of Matlab (by MathWorks) platform. The potential-time response of the ISEs in open- and closed-circuit conditions as a function of varying heterogeneous rate constants, ionic concentrations and membrane thickness are computed. The potential-time response to small-current perturbation is applied for simulations of the impedance spectra. The results obtained show that the membrane with Nernstian response presents only one capacitive arc in the impedance spectra, related to conductivity and dielectric properties of the membrane material. Non-Nernstian behaviour is related to slow ionic transport through the membrane|solution interfaces and is manifested by the appearance of an additional (capacitive) arc between the highfrequency bulk and the low-frequency (Warburg) arcs. The presented approach directly relates the diffusivities in the membrane and the interface properties (heterogeneous rate constants determining the transport across interfaces) to the characteristic properties of the impedance spectra (characteristic radial frequencies). It is concluded that the Matlab platform allows solving the NPP problem and simulating the non-linear effects in electrodiffusion in a convenient way.