MATHEMATICAL-MODELING OF SINGLE-LINE FLOW-INJECTION ANALYSIS SYSTEMS WITH SINGLE-LAYER ENZYME ELECTRODE DETECTION .1. DEVELOPMENT OF THE MATHEMATICAL-MODEL

A mathematical model for the description of the analytical signal in single-line flow-injection systems with enzyme electrode detection is reported. A flow system composed of tubular sections with equal Peclet numbers, which can be calculated according to Taylor's theory, is considered. The detector is a single-layer membrane containing the necessary enzyme and an appropriately chosen pH buffer. The biocatalytic process obeys Michaelis-Menten kinetics. It is accompanied by consumption of protons. For that reason, during the course of the reaction the pH of the reaction medium changes. These changes can also be used for evaluating the analyte (substrate) concentration in the sample. The mass transport within the membrane is described on the basis of Fick's second law. The solution of the mathematical model, developed on the basis of the assumptions mentioned above, was obtained in both the Laplace and the time domains in the special case of pseudo-first-order kinetics )i.e., when the Michaelis constant considerably exceeds the substrate concentration). The region of model parameter values in which the simplification mentioned above holds was determined. It was found that in many practical cases the simplified model could be used fairly successfully. By model simulation the influence of the main system parameters on the formation of the analytical signal can be investigated in order to find their optimum values.