Pulsed titration sensors: Part 2. A general theoretical model for the breath-by-breath CO 2 sensor

Abstract

A general theoretical model is presented which describes the transport and kinetics of a pulsed titration sequence used for the determination of end-expired CO 2 at a Clark-type sensor. The sensor works by generating ▪ from the reduction of the O 2 component of the expired breath in dimethyl sulphoxide (DMSO) in a generating pulse. There is a rapid titration reaction between the ▪ and any CO 2 present. In the recovery pulse the amount of unreacted ▪ is determined. The larger the concentration of CO 2, the less ▪ is found in the recovery pulse. The model is derived from the fundamental differential equations describing the concentration profiles of O 2, ▪ and CO 2 in the thin layer of DMSO trapped behind the membrane of the sensor. Normalization of the equations shows that the observed behaviour will depend on two parameters: k, which describes the kinetics of the titration reaction, and γ, which describes the ratio of the concentration of carbon dioxide to that of oxygen. A number of different cases arise depending on the values of k and γ. Expressions are derived for the ▪ generation transient in all cases, and for the ▪ recovery transient in those cases in which there is a response to CO 2.