A diffusion-kinetic model for optical sensors to predict heterogeneous rate constants, diffusion coefficients and Stokes radii of ions with the aid of chemometric methods

A new diffusion-kinetic model for optical sensors was proposed to predict the heterogeneous rate constants of the reaction of ions at the surface of the optical sensors and also to predict Stokes radii of ions in solution based on their reactions at the optical sensors with the aid of chemometric methods. According to the Fick diffusion law and surface kinetic equations, a mathematical model was obtained for an optical sensor. The concentration changes of the coated indicator at the sensor surface during the reaction with ions were obtained using multivariate curve resolution alternating least squares method (MCR-ALS). The experimental results were fitted to the proposed model through Newton–Gauss algorithm to calculate the model parameters such as diffusion coefficients and heterogeneous rate constants of reaction of ions. The model was applied to the estimation of heterogeneous rate constants of the reaction of Al3+, Be2+, F− and CN− at the optical sensor and their radii in aqueous solution. Stokes radii for Al3+, Be2+, F− and CN− was estimated as 4.19 Å, 3.81 Å, 1.52 Å and 1.73 Å, respectively and heterogeneous rate constants were obtained as 300, 165, 386 and 60 L mol−1 s−1 for Al3+, Be2+, F− and CN−, respectively. Also the effect of cetyltrimethyl ammonium bromide (CTAB) on the heterogeneous rate constant of the reaction of Al3+ at the sensor surface was investigated.