Comments on the analysis of experimental data in nonisothermal kinetics
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10/8/03
2:51 PM
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The derivative with respect to the temperature of g() generates
Communications Comments on the Analysis of Experimental Data in Nonisothermal Kinetics
1 da dI G(a) dT dT
N.J. LUIGGI The study of the reaction mechanisms occurring during a chemical or physical process is a subject of interest for chemists, physicists, and metallurgists. In this article, I comment on two situaions of interest for the researchers who usually resort to the reaction theory[1–5] to analyze nonisothermal data.[6–10] The first refers to the error introduced when the meaning of isothermal and nonisothermal times are mixed, and in the second, I propose a generic way to analyze nonisothermal data, obviating the considerations regarding specific reaction models and the initial temperature of reactin, T0. My first observation concerns the ambiguous mixture of mathematical equations deduced from isothermal and nonisothermal processes in some references.[11] Although the basic equation for the kinetic of transformation from reaction rate models is presented as a derivative with respect to time t of the fractional extent of the reaction or transformed fraction , it is obvious that is a function (T,t), T being the temperature. da (a,T,t) K(T(t)) G(a) dt
a a(T,t) and
T T(t)
The solution to Eq. [4], g() Kt, is valid only for an isothermal process. In that case, b dT/dt is zero, and no term of any equation containing b can participate in the kinetic equation. The time t of isothermal processes is the time elapsed during transformation at a fixed T, while the time t of nonisothermal process is the time necessary to attain temperature T. It is evident that under certain conditions, a similar product of the reaction can be obtained by either isothermal or nonisothermal treatment. In the case of metallic alloys that signifies that the state of transformation of the microstructure obtained by nonisothermal means can coincide with a microstructural state obtained by isothermal methods, time t of the equations referenced in Reference 11 is not the adequate parameter of correlation. For that reason, the results presented in Reference 11 must be considered with caution. My second observation is more general and I propose a simple method to eliminate the consideration T0 0 in the lower limit of the thermal or exponential integral signaled[11] as the cause of erroneous results in some theoretical methods of analyses regarding kinetic studies.[11] Accepting that the reaction constant K for an activation energy Q follows an Arrhenius relation, K(T ) K0 exp a
[1]
where is a generic funtion dependent on the integral form of the fractional extent, the temperature, and the time of the reaction. Starting from it, we can include all physically supported hypotheses. The supposition most used separates the reaction constant K from the impingement function, or kinetic function, G, as in the second term of Eq. [1]. As varies with time and temperature, Eq. [1] can be used alternatively for isothermal or noniso
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