Integration of the rate constant and linearization of the kinetic equations in non-isothermal reaction kinetics

The theory of reaction rates gives approximations of the type A T^b e^?E/RT for rate constants. In thermal analysis the case where b = 0 is used in kinetic calculations. However, if b is regarded as a variable, treatment of the non-isothermal kinetic equations is not more complicated than in the special case of b = 0. In this paper Padé approximations, described in the literature of the special functions, and Legendre's continued fractions are proposed for evaluation of the A∫T^b e^?E/RT dT integrals. The Coats—Redfern types methods for the determination of the kinetic parameters are discussed analysing the errors of approximation involved in their deduction. On this basis a modified parameter estimation scheme is proposed.