A numerically solvable engineering model has been proposed that predicts the sensitivity of metal oxide- (MO_X-) based potentiometric pH sensors. The proposed model takes into account the microstructure and crystalline structure of the MO_X material. The predicted pH sensitivities are consistent with experimental results with the difference below 6% across three MO_X (RuO₂, TiO₂, and Ta₂O₅) analysed. The model distinguishes the performance of different MO_X phases by the appropriate choice of surface hydroxyl site densities and dielectric constants, making it possible to estimate the performance of MO_X 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 MO_X. The model has been applied across different types of metal oxides, namely, expensive platinum group oxides (RuO₂) and cheaper nonplatinum group MO_X (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 MO_x as alternative sensor electrode materials. Separately, the usefulness of relatively less investigated, cheap, and readily available MO_X, 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.

中文翻译：

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使用不变性原理估算电位金属氧化物pH传感器的pH灵敏度

已经提出了一种数值可解的工程模型，该模型可预测基于金属氧化物（MO _X-）的电位pH传感器的灵敏度。提出的模型考虑了MO _X材料的微观结构和晶体结构。预测的pH敏感性与实验结果一致，对三种MO _X（RuO ₂，TiO ₂和Ta ₂ O ₅）的分析结果差异均低于6％。该模型区分不同MO的性能_X由表面羟基部位的密度和介电常数的合适的选择阶段，使得有可能估计MO的性能_X通过不同的高温和低温退火方法制造的电极。如理论家所言，它进一步解决了在将三层模型应用于pH传感器时独立确定C ₁内部亥姆霍兹电容参数的问题。这可以通过改变C ₁电容参数来完成，直到获得跨不同电解质离子强度的不变pH灵敏度为止。该不变点确定C ₁电容。相应的pH敏感性是MO _X的特征敏感性。该模型已应用于不同类型的金属氧化物，即昂贵的铂族氧化物（RuO ₂）和便宜的非铂族MO _X（TiO ₂和Ta ₂ O ₅）。高温退火后，RuO ₂产生59.1082 mV / pH的高pH敏感性，而TiO ₂和Ta ₂ O ₅产生的亚能斯特敏感性分别为30.0011和34.6144 mV / pH。低温退火后，TiO ₂和Ta ₂ O _5分别产生的Nernstian灵敏度分别为59.1050和59.1081 mV / pH，这说明了使用便宜的非铂族MO _x的潜力作为传感器电极的替代材料。分别地，相对较少研究，便宜且容易获得的MO _X的有用性，即。分析了作为电极材料的Al ₂ O ₃。Nernstian灵敏度为59.1050 mV / pH的低温退火Al ₂ O ₃可以被认为是一种潜在的电极材料。拟议的工程模型可以用作选择可能更便宜的替代传感器电极材料的初步预测机制。