pH Sensitivity Estimation in Potentiometric Metal Oxide pH Sensors Using the Principle of Invariance

A numerically solvable engineering model has been proposed that predicts the sensitivity of metal oxide- (MOX-) based potentiometric pH sensors. The proposed model takes into account the microstructure and crystalline structure of the MOX material. The predicted pH sensitivities are consistent with experimental results with the difference below 6% across three MOX (RuO2, TiO2, and Ta2O5) analysed. The model distinguishes the performance of different MOX phases by the appropriate choice of surface hydroxyl site densities and dielectric constants, making it possible to estimate the performance of MOX electrodes fabricated through different high-temperature and low-temperature annealing methods. It further addresses the problem, cited by theoreticians, of independently determining the C1 inner Helmholtz capacitance parameter while applying the triple-layer model to pH sensors. This is done by varying the C1 capacitance parameter until an invariant pH sensitivity across different electrolyte ionic strengths is obtained. This invariance point identifies the C1 capacitance. The corresponding pH sensitivity is the characteristic sensitivity of MOX. The model has been applied across different types of metal oxides, namely, expensive platinum group oxides (RuO2) and cheaper nonplatinum group MOX (TiO2 and Ta2O5). High temperature annealed, RuO2 produced a high pH sensitivity of 59.1082 mV/pH, while TiO2 and Ta2O5 produced sub-Nernstian sensitivities of 30.0011 and 34.6144 mV/pH, respectively. Low temperature annealed, TiO2 and Ta2O5 produced Nernstian sensitivities of 59.1050 and 59.1081 mV/pH, respectively, illustrating the potential of using cheaper nonplatinum group MOx as alternative sensor electrode materials. Separately, the usefulness of relatively less investigated, cheap, and readily available MOX, viz. Al2O3, as the electrode material was analysed. Low-temperature-annealed Al2O3 with a Nernstian sensitivity of 59.1050 mV/pH can be considered as a potential electrode material. The proposed engineering model can be used as a preliminary prediction mechanism for choosing potentially cheaper alternative sensor electrode materials.