An Interface Equilibria-Triggered Time-Dependent Diffusion Model of the Boundary Potential and Its Application for the Numerical Simulation of the Ion-Selective Electrode Response in Real Systems

Modern Potentiometric Biosensing Based on Non-Equilibrium Measurement Techniques

Modern potentiometric sensors based on polymeric membrane ion-selective electrodes (ISEs) have achieved new breakthroughs in sensitivity, selectivity, and stability and have extended applications in environmental surveillance, medical diagnostics, and industrial analysis. Moreover, nonclassical potentiometry shows promise for many applications and opens up new opportunities for potentiometric biosensing. Here, we aim to provide a concept to summarize advances over the past decade in the development of potentiometric biosensors with polymeric membrane ISEs. This Concept article articulates sensing mechanisms based on non-equilibrium measurement techniques. In particular, we emphasize new trends in potentiometric biosensing based on attractive dynamic approaches. Representative examples are selected to illustrate key applications under zero-current conditions and stimulus-controlled modes. More importantly, fruitful information obtained from non-equilibrium measurements with dynamic responses can be useful for artificial intelligence (AI). The combination of ISEs with advanced AI techniques for effective data processing is also discussed. We hope that this Concept will illustrate the great possibilities offered by non-equilibrium measurement techniques and AI in potentiometric biosensing and encourage further innovations in this exciting field.

Dynamic Potentiometry with an Ion-Selective Electrode: A Tool for Qualitative and Quantitative Analysis of Inorganic and Organic Cations

A study of the transient potential signals obtained with a cation-selective electrode based on an ion-exchanger was carried out for solutions of the following individual cations at different concentrations: H+, Li+, Na+, K+, Rb+, Mg2+, Ca2+, choline (Ch+), acetylcholine (AcCh+), and procaine (Pr+). Three different general types of transient signals were distinguished depending on the value of the selectivity coefficient of the corresponding ion. A principal component analysis (PCA) was performed on the signals, finding that the qualitative identification of the corresponding ion from the scores of two principal components is possible. The study was extended to the transient signals of solutions containing an analyte in the presence of an interfering ion. The PCA of the corresponding signal allows for the detection of the presence of interfering ions, thus avoiding biased results in the determination of the analyte. Moreover, the two principal components of the transient signals obtained for each of the ions at different concentrations allow for the construction of calibration graphs for the quantitative determination of the corresponding ion. All the transient signals obtained experimentally in this work can be reconstructed accurately from principal components and their corresponding scores.

Kinetic Description of the Membrane-Solution Interface for Ion-Selective Electrodes

The theoretical models for ISEs almost exclusively assume thermodynamic equilibrium at the membrane/solution-phase boundary. In this report, we present a new, congruent model which combines first-order reaction kinetics of ion-exchange at the phase boundary and diffusional mass transport in the adjoining phases in the continuity equation. The influence of the rate constant in the new kinetic model has significant impact on the predicted transients corresponding to instantaneous change in the sample solution composition. The simulated transients generated with the new model coincide with the transients recorded in common potentiometric experiments, e.g., with transients recorded upon step change in the primary or interfering ion concentrations. The simulated transients also align well with previously published transients representing special cases of potentiometry (e.g., super-Nernstian response, non-Nernstian responses in the presence of highly interfering ions). The implementation of the kinetic model for simulating the transients in the water layer test also resulted in a better agreement with the experiments compared to the previous models.

Overcoming of One More Pitfall in Boundary Element Calculations with Computer Simulations of Ion-Selective Electrode Response

Computer simulations of ion-selective membrane electrodes using diffusion layer models based on finite-differences principle for calculating diffusion processes in both phases and taking into account the local ion exchange equilibrium at the interface are successfully used for clarifying and even predicting the influence of different diffusion factors on several time-dependent characteristics of electrodes. It is shown here that a well-established approach based on the assumption of the constant concentration of the interfering ion in the sample solution fails for solutions containing strongly interfering ions where the concentration of the interfering ion in the boundary layer of the solution can be far lower in comparison with its concentration in the bulk. The limitation is demonstrated by a drastic discrepancy between experimental and calculated curves for the dependence of potential on time. This limitation can be overcome by taking into account the change of the interfering ion concentration in the boundary layer in accordance with the electroneutrality condition. A good agreement between simulation results and experimental data is demonstrated.

Application of the interface equilibria-triggered dynamic diffusion model of the boundary potential for the numerical simulation of neutral carrier-based ion-selective electrodes response

It is shown that a simple dynamic diffusion model of the boundary potential based on a separate, step-by-step, account of ion transfer across the membrane/aqueous solution interface and the diffusion processes within both phases which was proposed earlier for describing the response of ionophore-free membranes, can be successfully used for ionophore-based membranes as well. The model makes it possible to carry out both separate and joint account of the effects of co-extraction, transmembrane transport and ion exchange on the boundary potential and retains robustness in all the variants studied. The model adequately describes the ionophore-based electrode response over the entire range of concentrations and allows one to clearly demonstrate the dependence of lower detection limit on such parameters as the diffusion coefficients and the concentration of electroactive substances in the membrane phase, the thickness of the diffusion layer in the sample solution, the duration of the measurement, and the composition of the internal reference solution. The results of numerical simulation are in good agreement with the experimental data presented in the literature. As all the factors of influence considered above can easily be regulated in more or less wide limits, but at the same time, an estimation of their cumulative effect is not always possible on an intuitive level, the present model can be of practical interest for justifying the ways of optimizing the design of the ISE and the algorithm for performing measurements in solving specific analytical problems.