The detection limit (DL) of an analytical method determines the range of its applicability. For ion selective electrodes (ISE) used in potentiometric measurements, this parameter can vary by several orders of magnitude depending on the inner solution concentrations or the time of measurement. The detection limit of ISE can be predicted using the Nernst-Planck-Poisson model (NPP), as a general approach to the description of the time-dependent electro-diffusion processes. To find the optimal parameters, we need to formulate the inverse electrodiffusion problem. In this work, we combine the Nernst-Planck-Poisson model with the Hierarchical Genetic Strategy with real number encoding (HGS-FP). We use the HGS-FP method to approximate inner solution concentrations as well as the measuring time that provide a linear dependence of the membrane potential over the widest concentration range. We show that the HGS-FP method allows us to find the solution of the inverse problem. The presented calculations show a great future potential of the NPP method combined with the HGS-FP strategy.
Numerical simulations of evolution of the potentials and impedance spectra of ionselective
membranes (ISEs) with ionic sites are presented. The Nernst–Planck–Poisson and
continuity equations (NPP) are solved numerically by means of the finite difference method, the
Rosenbrock solver and with the use of Matlab platform. Transient solutions for ion-selective
electrodes under open- and closed-circuit conditions are computed. The potential-time response to
small-current perturbation is used for determination of complex impedances. We present
simulations of ISEs as a function of varying diffusivities and ionic concentrations in the “bathing”
solutions at interfaces. It is shown that the non-Nernstian behavior of passive membrane electrodes
is a result of kinetic constraints at the interfaces, which is manifested in the appearance of an
additional arc between the high-frequency 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
features of impedance spectra (dimensions and characteristic radial frequencies). NPP problem
solved on the Matlab platform allows simulating of the non-linear effects in electro-diffusion.
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