Understanding the Limitations of Organic-Electrolyte-Based Reference Electrodes: A Quasi-Steady-State Model Accounting for Organic Electrolyte Partitioning, Ion Exchange, and Diffusion

Ideally, the half-cell potential of an organic-electrolyte-based reference electrode is determined by the equilibrium distribution of the organic electrolyte across the interface between an organic-electrolyte-doped membrane and the aqueous sample. When sample ions transfer into the reference membrane at high concentrations, the limit of applicability (LOA) of the reference electrode is reached. Recent insights highlight the need to evaluate the lipophilicity of the organic electrolyte’s anion and cation separately, but accurate predictions of the LOAs of organic-electrolyte-based reference electrode also require consideration of ion fluxes into and out of the reference membrane. LOAs are influenced not only by the concentration of interfering sample ions but also by the mobilities of the organic electrolyte and interfering ions in both the sample and the reference membrane, as recently shown with numeric simulations. However, plain expressions describing LOAs that take diffusion into account and can be used to select an optimum organic electrolyte for specific types of samples have been missing. Here, a quasi-steady-state model is presented that describes the LOAs on the basis of organic electrolyte partitioning into the sample, ion exchange at the sample–membrane interface, and diffusive mass transfer limitations. Depending on whether the hydrophilicity of the organic electrolyte is high or relatively low and whether diffusion in the membrane is fast or slow, four limiting cases can be identified. Above the LOA, they exhibit characteristic Nernstian, half-Nernstian, or super-Nernstian responses to the sample ions. The respective LOAs can be quantitatively predicted as a function of the sample composition using a set of two straightforward equations.