Non-equilibrium potentiometry—the very essence

Abstract

In most interpretations of potentiometric ion sensor responses with glass, solid, or liquid/polymer membranes, a model assuming electrochemical equilibrium between the aqueous sample and the membrane is used. This model is often called a phase boundary model to emphasize the importance of ion-exchange processes at the interface. The essence of the phase boundary model is that it accepts electroneutrality and thermodynamic equilibrium, and thus ignores electrochemical migration and the time-dependent effects. For this reason, this model is in conflict with many 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 the detection limits are deliberately used. To respond to the experimental challenges in the author’s groups, we elevated the potentiometric modeling by using the Nernst–Planck–Poisson (NPP) equations system to model the non-equilibrium response. In the NPP model, electroneutrality and steady-state/equilibrium assumptions are abandoned, and thus we access the space and time domain. This approach describes the concentration changes of ions participating in the ion-exchange and transport processes, as well as the electrical potential evolution over space and time, and allows in particular, the inspection of the equilibrium set by the phase boundary models as a special “stationary” case after infinite time. Additionally, directly predicting the selectivity and the low detection limit variability over time and the influence of other parameters, e.g., ion diffusibility, is possible. As a coherent and non-arbitral model, the NPP system facilitates solving the inverse problem, i.e., to optimize the sensor properties and measurement conditions in a customized way via desired target functions and hierarchical genetical strategy modeling. In this way the NPP allows setting the conditions under which the experimentally measured selectivity coefficients are true (unbiased) and the detection limits are optimized.