A new numerical model is presented for analyzing the propagation of ionic concentrations and electrical potential in space and time in the liquid junction and in the solution/ion-exchanging membrane system. In this model, diffusion and migration according to the Nernst-Planck (NP) flux equation govern the transport of ions, and the electrical interaction of the species is described by the Poisson (P) equation. These two equations and the continuity equation form a system of partial nonlinear differential equations that is solved numerically. This yields the Nernst-Planck-Poisson (NPP) model that we exploit in this paper. Notably, as a result of the physicochemical properties of the system, which are clearly defined in this paper, both the contact/boundary potential and the diffusion potential contribute to the overall membrane potential. Previously, only the boundary potential at steady state was considered due to some arbitrary and clearly untested assumptions. By accessing space and time domains, it is shown that interpreting the electrical potential of ion-exchanging membranes exclusively in terms of boundary potential at steady state is incorrect. The NPP model is general and applies to ions of any charge in space and time domains. It is shown for the first time that the paradigmatic equations for every open circuit measurement, such as the Henderson liquid junction equation or the Nikolskii-Eisenman equation, are special cases of the NPP model. The NPP model is not only more rigorous but also more complete than previous models, and it is proposed to be a more appropriate and updated platform for dealing with the theory of ion selective membrane electrodes for analytical applications.

The variability of selectivity coefficients, resulting from potential changes over time and the concentration ratio of primary to interfering ions, impedes many practical applications of ion-selective electrodes (ISEs). Existing theoretical interpretations of ISE selectivity are restricted by severe assumptions, such as steady state and electroneutrality, which hinder theorizing on this problem. For this reason, for the first time, the Nernst-Planck-Poisson equations are used to predict and visualize the selectivity variability over time and the concentration ratio. Special emphasis is placed on the non-Nernstian response in the measurements with liquid-ion-exchanger- and neutral-carrier-based ISEs. The conditions under which measured selectivity coefficients are true (unbiased) are demonstrated.

Several types of liquid membrane and solid-state reference electrodes based on different plastics were fabricated. In the membranes studied, equitransferent organic (QB) and inorganic salts (KCl) are dispersed in polyvinyl chloride (PVC), polyurethane (PU), urea-formaldehyde resin (UF), polyvinyl acetate (PVA), as well as remelted KCl in order to show the matrix impact on the reference membranes’ behavior. The comparison of potentiometic performance was made using specially designed standardized testing protocols. A problem in the reference electrode research and literature has been a lack of standardized testing, which leads to difficulties in comparing different types, qualities, and properties of reference electrodes. Herein, several protocols were developed to test the electrodes’ performance with respect to stability over time, pH sensitivity, ionic strength, and various ionic species. All of the prepared reference electrodes performed well in at least some respect and would be suitable for certain applications as described in the text. Most of the reference types, however, demonstrated some weakness that had not been previously highlighted in the literature, due in large part to the lack of exhaustive and/or consistent testing protocols.