Modeling Non Equilibrium Potentiometry to Understand and Control Selectivity and Detection Limit

Abstract

The majority of present theoretical interpretations of ion-sensor response focus on phase boundary potentials. They assume electroneutrality and equilibrium or steady-state, thus ignoring electrochemical migration and time-dependent effects, respectively. These theoretical approaches, owing to their idealizations, make theorizing on ion distributions and electrical potentials in space and time domains impossible. Moreover, they are in conflict with recent experimental reports on ion-sensors, in which both kinetic (time-dependent) discrimination of ions to improve selectivity, and non-equilibrium transmembrane ion-transport for lowering detection limits, are deliberately used.For the above reasons, the Nernst-Planck-Poisson (NPP) equations are employed here to model the non-equilibrium response in a mathematically congruent manner. In the NPP model, electroneutrality and steady-state/equilibrium assumptions are abandoned. Consequently, directly predicting and visualizing the selectivity and the low detection limit variability over time, as well as the influence of other parameters, i.e. ion diffusibility, membrane thickness and permittivity, and primary to interfering ion concentration ratios on ion-sensor responses, are possible. Additionally, the NPP allows for solving the inverse problem i.e. searching for optimal sensor properties and measurement conditions via target functions and hierarchical modeling. The conditions under which experimentally measured selectivity coefficients are true (unbiased) and detection limits are optimized are demonstrated, and practical conclusions relevant to clinical measurements and bioassays are derived.