A simple dynamic model of the phase boundary potential of ion-selective electrodes is presented. The model is based on the calculations of the concentration profiles of the components in membrane and sample solution phases by means of the finite difference method. The fundamental idea behind the discussed model is that the concentration gradients in both membrane and sample solution phases determine only the diffusion of the components inside the corresponding phases but not the transfer across the interface. The transfer of the components across the interface at any time is determined by the corresponding local interphase equilibria. According to the presented model, each new calculation cycle begins with the correction of the components' concentrations in the near-boundary (first) layers of the membrane and solution, based on the constants of the interphase equilibria and the concentrations established at a given time as a result of diffusion. The corrected concentrations of the components in the boundary layers indicate the start of a new cycle every time with respect to the calculations of diffusion processes inside each phase from the first layer to the second one, and so on. In contrast to the well-known Morf's model, the above-mentioned layers do not comprise an imaginary part and are entirely localized in the corresponding phases, and this allows performing the calculations of the equilibrium concentrations by taking into account material balance for each component. The model remains operational for any realistic scenarios of the electrode functioning. The efficiency and predictive ability of the proposed model are confirmed by comparing the results of calculations with the experimental data on the dynamics of the potential change of a picrate-selective electrode in nitrate solutions when determining the selectivity coefficients using the methods recommended by IUPAC.

Computer simulations of ion-selective membrane electrodes using diffusion layer models based on finite-differences principle for calculating diffusion processes in both phases and taking into account the local ion exchange equilibrium at the interface are successfully used for clarifying and even predicting the influence of different diffusion factors on several time-dependent characteristics of electrodes. It is shown here that a well-established approach based on the assumption of the constant concentration of the interfering ion in the sample solution fails for solutions containing strongly interfering ions where the concentration of the interfering ion in the boundary layer of the solution can be far lower in comparison with its concentration in the bulk. The limitation is demonstrated by a drastic discrepancy between experimental and calculated curves for the dependence of potential on time. This limitation can be overcome by taking into account the change of the interfering ion concentration in the boundary layer in accordance with the electroneutrality condition. A good agreement between simulation results and experimental data is demonstrated.

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