Dynamic Diffusion Model for Tracing the Real-Time Potential Response of Polymeric Membrane Ion-Selective Electrodes

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A numerical solution for the prediction of the time-dependent potential response of a polymeric-based ion-selective electrode (ISE) is presented. The model addresses short- and middle-term potential drifts that are dependent on changes in concentration gradients in the aqueous sample and organic membrane phase. This work has important implications for the understanding of the real-time response behavior of potentiometric sensors with low detection limits and with nonclassical super-Nernstian response slopes. As a model system, the initial exposure of membranes containing the well-examined silver ionophore O,O' '-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene was monitored, and the large observed potential drifts were compared to theoretical predictions. The model is based on an approximate solution of the diffusion equation for both aqueous and organic diffusion layers using a numerical scheme (finite difference in time and finite elements in space). The model may be evaluated on the basis of experimentally available parameters and gives time-dependent information previously inaccessible with a simpler steady-state diffusion model. For the cases studied, the model gave a very good correlation with experimental data, albeit with lower than expected diffusion coefficients for the organic phase. This model may address numerous open questions regarding the response time and memory effects of low-detection-limit ion-selective electrodes and for other membrane electrodes where ion fluxes are relevant.