Applications of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liquids, part I: Theory

A critical review is presented of mathematical methods advanced over the last 20 years for the analysis of data obtained from non-isothermal thermoanalytical studies of crystallization of glass-forming liquids. Methods proposed by Ozawa, Piloyan and Borchardt, Coats, Redfern and Sestak, Ozawa and Chen, Takhor, Kissinger, and Augis and Bennett are examined in detail. All these methods are based on the Avrami treatment of transformation kinetics and define an effective crystallization rate coefficient having an Arrhenian temperature dependence. Several different ways of mathematically treating the data have been proposed. Most are shown to be based on an incorrect neglect of the temperature dependence of the rate coefficient. By taking proper account of the temperature dependence of the crystallization rate coefficient, all the methods are shown to lead to similar conclusions. In detail, it is shown that the effective activation energy of the overall crystallization process can be calculated from the slope of the line obtained by plotting 1n[Q/(T^P - T₀)] versus 1/T^P is the temperature of maximum crystallization rate, T_O is an initial temperature and Q is the heating rate employed in the experiment. It is further argued that in general the overall crystallization rate coefficient is not Arrhenian in character. Thus, in general, non-isothermal transformation cannot be treated analytically. A detailed description of nonisothermal transformation can, however, be obtained by numerical methods. Such a method is described and its uses in obtaining kinetic data from thermoanalytical studies are demonstrated.