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 equilibrium distribution of the organic electrolyte across the interface between an organic-electrolyte-doped membrane and the aqueous sample. The limit of applicability (LOA) of these reference electrodes is reached when sample ions transfer into the reference membrane at high concentrations. Recent insights highlight the need to evaluate the lipophilicity of the organic electrolyte's anions and cations separately; however, accurate predictions of the LOAs also require consideration of ion fluxes. 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 the sample and membrane. This was recently shown with numerical simulations and described with expressions for limiting cases in which the interfering ion enters the membrane by either ion exchange with the organic electrolyte ion of the same charge sign or co-extraction with the organic electrolyte ion of opposite charge sign. More general expressions describing LOAs that take diffusion into account and apply when ion exchange and co-extraction occur simultaneously have been missing. Here, a quasi-steady-state model is presented that describes the LOAs based on organic electrolyte partitioning, ion exchange, and diffusive mass transfer limitations. Depending on the lipophilicity of the organic electrolyte and the rate of diffusion in the membrane, four limiting cases can be identified. Above the LOA, these reference electrodes exhibit characteristic sub-Nernstian, Nernstian, or super-Nernstian responses to the sample ions. The respective LOAs can be quantitatively predicted as a function of sample composition using two straightforward equations.