Kinetics nonisothermal

Insertion of the Arrhenius equation into the rate expression leads to the an expression for the decrease in concentration -d[A]/dt. Taking the logarithm of both sides of the equation removes the exponential, and additional differentiation leads to the second equation with the activation energy, pre-exponential factor, and order of the reaction expressed in terms of measurable quantities. This analysis is known under the name Freeman-CarroU method [33]. 

In this section experimental results are discussed, concerned with analyses of melting and crystallization kinetics, as well as reversibility of the phase transition. The frame of the discussion is set by Fig. 3.76, which will be supported by experimental data on poly(oxyethylene). The thermal analysis tools involved are TMDSC, optical and atomic-force microscopy, DSC, adiabatic calorimetry, and dilatometry. Most of these techniques are described in more detail in Chap. 4. Results from isothermal crystallization, and reorganization are attempted to be fitted to the Avrami equation. This is followed by a short remark on crystallization regimes and finally some data are presented on the polymerization and crystallization of trioxane crystals. 

O first heating A cooiing 2 heating melting for crystals with 2 1 0 Folds 

Quashlsothermal TMDSC Proves Irreversibility of Polymer Melting 

Data on the supercooling of aliphatic polyoxides in Fig. 3.91 can be compared to the paraffin and polyethylene data used for the illusdation of the limits of molecular nucleation in Fig. 3.75. In the same range of chain length all three polymers, polyethylene, PE, poly(oxyethylene), POE, and POTM, decrease in amount of supercooling due to molecular nucleation. The polyoxides, however, show a second 

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The thermal decomposition of some 3,5-disubstituted-l,2,4-thiadiazoles has been studied and some nonisothermal kinetic parameters have been reported <1986MI239>. Polarographic measurements of a series of methylated 5-amino-l,2,4-thiadiazoles show that thiadiazoles are not reducible in methanolic lithium chloride solution, while thiadiazolines are uniformily reduced at 0.5 = — 1.6 0.02 V. This technique has been used to assign structures to compounds which may exist theoretically as either thiadiazoles or thiadiazolines <1984CHEC(6)463>. The photoelectron spectrum for 1,2,4-thiadiazole has been published <1996CHEC-II(4)307>. 

Edel, ., and Baltzer, M. O. (1980), Nonisothermal kinetics with programmed temperature steps, I. Pharm. Sci., 69,287-290. 

Gemperline, P. Puxty, G. Maeder, M. etal., Calibration-free estimates of batch process yields and detection of process upsets using in situ spectroscopic measurements and nonisothermal kinetic models 4-(dimethylamino)pyridine-catalyzed esterification of butanol Anal. Chem. 2004, 76, 2575-2582. 

Besides the isothermal kinetic methods mentioned above, by which activation parameters are determined by measuring the rate of dioxetane disappearance at several constant temperatures, a number of nonisothermal techniques have been developed. These include the temperature jump method, in which the kinetic run is initiated at a particular constant initial temperature (r,-), the temperature is suddenly raised or dropped by about 15°C, and is then held constant at the final temperature (7y), under conditions at which dioxetane consumption is negligible. Of course, for such nonisothermal kinetics only the chemiluminescence techniques are sufficiently sensitive to determine the rates. Since the intensities /, at 7 ,- and If at Tf correspond to the instantaneous rates at constant dioxetane concentration, the rate constants A ,- and kf are known directly. From the temperature dependence (Eq. 32), the activation energies are readily calculated. This convenient method has been modified to allow a step-function analysis at various temperatures and a continuous temperature variation.Finally, differential thermal analysis has been employed to assess the activation parameters in contrast to the above nonisothermal kinetic methods, in the latter the dioxetane is completely consumed and, thus, instead of initial rates, one measures total rates. 

In Table 3 the activation energies of tetramethyl-1,2-dioxetane by a variety of isothermal and nonisothermal kinetic methods are compared. The values range... 

M. A. Zoglio, H. V. Maudling, W. H. Streng and W. C. Vincek. Nonisothermal kinetic studies III rapid nonisothermal-isothermal method for stability prediction. /. Pharm. Sci., 64, 1381 (1975)... 

The kinetics of a drug are generally studied in solution under isothermal conditions. On the other hand, a nonisothermal kinetics study may be carried out in less time at the expense of accuracy. The isothermal solution kinetics include... 

Rate equations based on concentration dependence (reaction order) Under some conditions, the rate characteristics of solid-state processes can be expressed through a concentration-type dependence. For example, if the decomposition of a large number of small crystallites is controlled by an equally probable nucleation step at each particle, then this is a first-order process (Al, FI). These rate equations are also used in nonisothermal kinetic analyses of rate data in the form g(a) = kt and are therefore included in Table 5.1. 

In139) the researchers studied the nonisothermal kinetics of polyaddition reactions of oxiranes to aromatic amines up to high conversion levels, as well as the kinetic laws governing the curing of epoxide oligomers by diamines under the conditions of a propagating reaction front. 

J. Waltersson and P. Lundgren, Nonisothermal kinetics applied to drugs in pharmaceutical suspensions, Acta Pharm. Suec. 20, 145-154(1983). 

Deduction of the mechanism of the reaction by use of nonisothermal kinetic methods has been discussed by Sestak and Berggren (73) and Satava (105). The procedure used by Satava is based on the assumption that the noniso-thermal reaction proceeds in an infinitesimal time interval isothermaliy, where the rate may be expressed as... 

G. B. Manelis, L. P. Smirnov, and N. I. Peregudov, Nonisothermal kinetics of polymerization processes, finite cylindrical reactor. Combustion Explosion Shock Wave, 13 (1977), pp. 389-393. 

In DSC, the extent of reaction is obtained by first determining the total area of the peak that corresponds to the complete reaction. The required information from the experiment is the fraction of the complete reaction at a series of temperatures so that nonisothermal kinetics procedures can be applied. At a specific temperature, the partial peak area is determined, and the fraction of the complete reaction at that temperature is determined by dividing the area of the peak up to that temperature by the total peak area. A typical endothermic peak in a DSC trace is shown in Figure 8.2. In this case, the temperatures at which a is to be determined are indicated as... 

A very large number of methods have been developed for treating (a,T) data from nonisothermal kinetic studies to yield kinetic information. 

Brown, M. E. (1988). Introduction to Thermal Analysis, Chapman and Hall, London. A text describing the several types of thermal analysis and their areas of apphcation. Chapter 13 is devoted to nonisothermal kinetics. 

Coats, A. W., Redfem, J. P. (1964). Nature (London), 201, 68. The original description of one of the most widely used methods for analysis of nonisothermal kinetics. 

Reich, L., Stivala, S. S. (1983). Thermochim. Acta, 62, 129. The description of a versatile nonisothermal kinetic method complete with a program listing in BASIC. 

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