A general differential method is developed and described which determines the Arrhenius parameters, energy of activation and the preexponential factor, as functions of degree of conversion from sets of two or more experiments with differing thermal programs. (These experiments may be performed at any combination of isothermal, constant heating rate or other temperature programs.) The method tests to see whether or not the kinetics follow the equation,f(α)=(1−α)n, and calculates the correct reaction order, n, when such an equation is applicable. The correct energy of activation,E, is determined as a function of both temperature and conversion. The correct preexponential term,A, is calculated for all cases described by equation, d(α)/dt=f (α) A exp(−E/RT), except for the ‘autocatalytic’ case in whichf(α)=0)=0. Calculation of parameters for equations involving other functions forf(α) will be described in a subsequent paper.
The kinetics of the heterogeneous, condensed-phase systems studied in thermal analytical techniques are often complex and usually affected by many experimental factors such as specimen geometry, thermal history, gaseous environment, etc. These complications impose many problems in experimental design, data analysis, and especially in interpretation of results. This paper concerns itself with practical applications of thermal analysis kinetics. Ways of overcoming, or at least ameliorating, some of the above problems are suggested, and caveats concerning overly simple and “canned” techniques of analysis of kinetics data are given. The limitations of one's reasonable expectations for the theoretical significance and empirical application of derived kinetics parameters are discussed.
Special problems are encountered in modeling the temperature dependence of the kinetics of heterogeneous, condensed phase systems. In the division of the model for the reaction rate into two parts, a)f(α) which is physical (translational) and b)k(T) which is chemical (vibrational), complications arise in defining the temperature dependence of part a) which may take various mathematical forms and then in coupling it with the Arrhenius temperature dependence of part b). The role off(α) in thermal analysis systems is discussed. The concept of rate-controlling step is applied to the simplification of the temperature dependent term. The significance of the compensation effect in these systems is described and an heuristic rationalization for it is suggested. Maximum practical temperature ranges for thermal analysis experiments and the effect of temperature measurement imprecision on obtaining meaningful Arrhenius parameters are discussed. The WLF and other equations used to describe the temperature dependence off(α) are not found to couple compatibly with the Arrhenius equation.