Application of Logistic Function and Evaluation of Hysteresis during Toluene Combustion over γ-Alumina-supported Platinum Catalyst

The temperature dependence of the reaction rate in a catalytic reaction is well known to follow an S-shaped curve. In the field of mathematics, several function systems that form an S-shaped curve are known, and the simplest of these is the logistic function. The present study proposes a method of using the parameters of the logistic function as an objective approach to determine the temperature at which the reaction rate becomes 50 % (T50), which is an index of catalytic combustion reactions. The combustion of toluene using a γ-alumina-supported platinum catalyst was examined as a model reaction. The temperature dependence of the reaction rate was highly correlated with the logistic function using a linear function is used as a function of temperature, and T50 could be objectively obtained from the parameters. Furthermore, the presence or absence of hysteresis, which is often observed in catalytic combustion reactions, could be determined by comparing the parameter values corresponding to the intercept of the temperature function. Furthermore, the magnitude of the hysteresis can be evaluated using statistical methods such as t-tests using the logit function, which is the inverse function of the logistic function.