Kinetic method. Ozawa

To evaluate the apparent activation energy, the isoconversional methods are use as suitable analysis procedures. These methods are based on the assumption that at a constant extent of conversion degree (a), the decomposition rate da/dt is a function only of the temperature. In methods developed by Friedman and Flynn-Wall-Ozawa, linear functions are obtained from which slopes the apparent activation energy at constant conversion a is achieved. In the free kinetic method set by Kissinger is calculated from the slope of the linear function takes into consideration the relationship between the heating rate and peak temperature of the first-derivative thermogravimetric curve [97]. 

Reaction kinetics from DSC, DTA or TGA, have been used to examine the stability of a limited number of pharmaceutical materials. Various models have been used including the Power Law, Avarami-Erofeev and Prout-Tomkins models [72]. These methods are also based on the Kissinger [73], ASTME 698 [74] or Ozawa [75] methods [8]. Most frequently, they have been applied to the dehydration of various materials such as theophylline monohydrate [76], phenobarbitone monohydrate or hemihydrate [77], phenylbutazone [78], oxazepam [23] and trazodone tetrahydrate [79]. The uses are limited for pharmaceutical systems, not least because dehydration is particle size dependent. Thermal analysis, especially DSC, DTA and TG, has been used outside the pharmaceutical area in the prediction of reaction kinetics as described elsewhere in this handbook. Methods used include those by Borchart and Daniels [80], Kissinger [73], Freeman and Carroll [81] and Flynn and Wall [82]. Although these techniques are well established and, if used properly, can give pertinent information, their use in pharmaceutical arenas is restricted to dehydration and decomposition. 

For single reactions with uncomplicated kinetics and with availability of a truly representative sample, the DSC can be used with different scan speeds (temperature/time) to determine kinetic constants in the Arrhenius equation. This method, proposed by Ozawa [83] has been accepted by the ASTM Method E698. After determining kinetic constants by this method, it is desirable to check the constants by running an isothermal DSC aging test for a period of time followed by a DSC scan to see if the predicted fraction decomposition... 

Similar to studies reported by Litwinienko and co-workers discussed above, a recent report (Dunn, 2006b) demonstrated that non-isothermal (conventional) DSC, static mode P-DSC and dynamic mode P-DSC may be employed to study kinetics of the oxidation of SME. OT results obtained at ambient pressure for DSC and P = 2000kPa for P-DSC and with varying p = 1-20 °C/ min were analyzed by the Ozawa-Flynn-Wall method to calculate activation energies and rate constants. This work concluded that rates of the oxidation reaction could be calculated at any temperature based on accurate measurement of kinetic parameters from analysis of non-isothermal dynamic mode P-DSC scans. 

The random degradation and reaction kinetics of high-molecular weight polymers can be determined by an approximate integral method (Ozawa 1965, Hirose and Hatakeyama 1986). Generally, the fractional weight, W, of a reacting material can be expressed as a function of the fraction of a structural quantity which is represented by x, i.e.,... 

Ozawa, T. Kinetic analysis by repeated temperature scanning. Part 1. Theory and methods. Thermocim. Acta 2000, 356, 173-180. 

A comparison of the kinetic parameters for the thermal decomposition of 2, 2 -azobis(isobutyronitrile) (AIBN) obtained by different DSC methods is given in Table 5.14 (184). The ASTM E-698 method is a modification of the Ozawa method (181), whereas the single scan DSC method is that described by Prime (182, 183). 

DSC ts widely used to predict the potential explosive hazard of materials in an ASTM method. The basis of the method, developed by Committee E 27, is the determination of the reaction kinetics using Ozawa s procedure (206). Ozawa employs a ploi of the logarithm of the DSC heating rate versus the peak maxima temperatures E. Z, k. and t can be calculated from this plot. The ASTM method has been used to evaluate the thermal stability of irinitrotoluene (207). nitrocellulose (208). and many other substances. 

The experimental study of kinetics, as mentioned earlier, has as its basis the identification of the rate of reaction with instrument signal and the extent of reaction with fractional area of the peak. Analysis of experimental data often makes use of named approaches which exploit the advantages of dynamic experiments to achieve results without recourse to protracted experimental effort. Two popular but very different methods are those of Borchardt and Daniels and Ozawa and both appear in ASTM methods. Both are supported by commercial software. The concern here is with the Borchardt and Daniels method [ASTM E 2041 (1999)] which had a considerable impact on kinetic evaluation both by DTA and subsequently DSC. The analysis was devised originally for DTA experiments in which the thermocouples were in large volumes of stirred liquids. This is in direct contrast to the current application of the method to DSC studies of solids. A number of assumptions were made which were met more readily in stirred liquid systems than with solids. As a result there are a number of caveats associated with its application to solids. In particular the analysis assumed the absence of temperature... 

C. Popescu (1996). Integral method to analyze the kinetics of heterogeneous reactions under non-isothermal conditions A variant on the Ozawa-Flynn-Wall method. Thermochimica Acta 285 (2) 309-323. 

Transformation kinetics according to Ozawa Ozawa (2) proposed a method to predict crystallization of polymers under constant cooling or heating rate by modifying the Avrami equation ... 

Table 4.2 Kinetic parameters obtained from Friedman, Kissinger, and Ozawa methods [12].

DMA, the kinetic parameters of the glass transition can be determined by multicurves methods such as the Ozawa method (see Chapter 4). While only one heating rate is available here, the modified Coats-Redfern method is used [13, 14] as demonstrated in the following. Integration of Eq. (2.12) leads to ... 

The kinetics of thermal degradation have generally been studied using isothermal and nonisothermal methods. In earlier literature, isothermal methods were mostly employed for the study of the kinetics of solid-state reactions. During the past three decades, however, nonisothermal methods, for example, the Doyle method [17, 18], Freeman and Carroll method [19], Coats and Redfem method [24], Ozawa method [20], Flynn and Wall method [21, 22], Friedman method [25], and Kissinger method [26], have received more attention. 

---