Diffusion model of the phase-boundary potential of ion-selective electrodes

A model of the phase-boundary potential of ion-selective electrodes is presented, combining the simplicity of steady-state approaches with the ability to describe the dynamic response characteristic of dynamic diffusion models. Within the framework of the proposed model, equations were obtained that explicitly describe the dependence of the phase-boundary potential of potentiometric sensors on time, observed when working with highly selective electrodes in solutions of foreign ions, as well as in mixed solutions containing foreign and primary ions, in particular, when determining the selectivity coefficients using the methods recommended by IUPAC. An advantage of the proposed model is the minimization of computational time to fractions of a second (in contrast to the numerical solution of systems of differential equations within known analogs, which requires tens of minutes). By obtaining equations in analytical form, the proposed approach eliminates the need for resource-intensive computer algebra systems (such as Wolfram Mathematica) and enables the rapid calculation of the response of ion-selective electrodes. The high predictive ability of the developed model is confirmed by comparing the calculation results with experimental data on the dynamics of changes in the response of tetrabutylammonium- and picrateselective electrodes in solutions containing foreign ions, and with the results obtained within the framework of the interface-equilibria-triggered dynamic diffusion model.

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