Thermochimica Acta, Vol.325, No.1, 43-46, 1999
A new method for analysing non-isothermal thermoanalytical data from solid-state reactions
The rate equation in non-isothermal kinetics of a heterogeneous reaction involving a solid is d alpha/dt = Af(alpha) exp (-E/RT) where alpha represents the fractional conversion in the solid reactant; A the Arrhenius pre-exponetial factor; T the reactant temperature; f(alpha) a so-called kinetic function that depends on the reaction mechanism; E the activation energy for the reaction, and R the gas constant. In pratice, most, if not all, non-isothermal experiments in thermal analysis are carried out at some constant heating rate beta = dT/dt. In principle, the reaction kinetics may be determined (i.e. its parameters E and A measured) from several heating curves recorded at various beta. Such data are often analyzed using isoconversion methods, which consider points of the same alpha on different curves, so that f(alpha) has identical (though unknown) magnitude and can, therefore, be 'cancelled out'. However, all existing methods rely on some approximation to the temperature integral, and are therefore subject to systematic errors. Here, we present a new approach that needs to make no assumption about the kinetic model, involves no approximation to the temperature integral, and is easy to implement on the computer. Taking logarithms of both sides of the rate equation and then integrating with respect to alpha, we get (alpha)integral(0) ln (d alpha/dt) d alpha = -E/R (alpha)integral(0) ln d alpha/T + G(alpha) where G(alpha) = alpha ln A + integral(0)(alpha) ln f(alpha)d alpha has the same value for isoconversion points, irrespective of beta. A plot of integral(0)(alpha) ln (d alpha/dt)d alpha against integral(0)(alpha)(1/T)d alpha at a given alpha for a set of beta's will therefore have the slope -E/R.
Keywords:KINETICS