A multi-ion interference decoupling model based on ion-selective electrode arrays

Compared to traditional liquid-junction ion-selective electrodes, solid-contact ion-selective electrodes (SC-ISEs) have attracted much attention and undergone rapid development due to their compactness and ease of integration. However, the application and widespread use of SC-ISEs are limited by their non-ideal selectivity and susceptibility to signal drift. Although the principles of artificial neural network (ANN) methods have shown significant progress in partially resolving the selectivity issue, they generally require extensive calibration steps and computational resources to implement. As a result, numerical computation models are more practical and economical, but existing approaches often overlook experimental phenomena and have relatively complex modeling principles. In this study, we propose a proportional factor model based on the trend of SC-ISEs affected by the multiple ions, along with a scalable dynamic correction procedure to improve its robustness. This model utilizes an estimated response surface method to solve nonlinear equations, requiring fewer calibration experiments. It accurately extracts the concentrations of multiple target ions in the presence of multi-ion interference and dynamically adjusts the model parameters for different types of ISEs. Additionally, we design a multi-channel SC-ISE array as a carrier for theoretical validation. In a case study, we demonstrate the feasibility of decoupling multiple ions using the SC-ISE array, obtaining concentrations of calcium, magnesium, sodium, and potassium ions, and verify the accuracy of the multi-ion detection system for real-world water samples.