Kinetical analysis, nonisothermal

Mittemeijer E J, Gent A V and der Schaaf P J V 1986 Analysis of transformation kinetics by nonisothermal dilatometry Metall. Trans. A 17 1441... 

In the kinetic analysis of the experimental data with an autoclave, the non-linear least square method was used to estimate the rate constants under nonisothermal conditions. The simulation of liquefaction calculated by substituing the estimated values into the rate equations showed good agreement with experimental values. 

Nonisothermal reactions Numerous kinetic investigations of the thermal reactions of solids have used rising temperature techniques, often during a linear rate of reactant temperature increase. The kinetic analysis then requires the solution of three equations ... 

There has been a widespread belief in the literature that the kinetic triad [A, Ea, g(a) = kt] can be elucidated through kinetic analysis of data from a single nonisothermal experiment. This is an incorrect perception and conclusions calculated from any such restricted data sets must be regarded as unreliable. A useful discussion of the minimum number of experiments required to determine these kinetic parameters has been given by Gotor et al. (111). 

N. Okusa and K. Kinuno, Kinetic studies on prediction of stability of pharmaceuticals. 1. Kinetic analysis by a nonisothermal method [in Japanese], Yakuzaigaku 28, 17-20(1968). 

Rajeshwar I52) determined the kinetics of the thermal decomposition of Green River oil shale kerogen by using direct Arrhenius. Freeman and Carroll, and Coats and Redfern methods. The E, A, and values are given in Table 2.7. Rajeshwar concluded that the ability to resolve multiple processes hinges on the efficacy of the particular kinetic analysis employed and is not an inherent difficulty with nonisothermal TG techniques in general. The direct Arrhenius and Coats and Redfern methods clearly indicate the presence of two reactions with distinctly different kinetic parameters. On the olher hand, the Freeman and Carroll method is handicapped at low fractional... 

Another important practical objective of kinetic analysis is predictions. Their purpose is to evaluate the kinetic behavior of materials under temperature conditions that are different from those used in the actual experimental runs but important for practical applications. A typical example is the use of nonisothermal TGA runs for estimating thermal stability of a material at a certain temperature. Thermal stability can be evaluated as the time to reach a specific but low extent of conversion at a given temperature. Integration and rearrangement of Eq. (3.7) gives... 

It is clear from the preceding that the kinetic analysis of a process based upon nonisothermal data may be a demanding problem from the computational point of view. The reverse problem — designing or simulating a reactor when the... 

Knowing A and for a given reaction in the temperature interval of interest, one can calculate reaction kinetics in nonisothermal experiments. One can also, in reverse, derive values for the activation energy, the pre-exponential factor, and the order of the reaction fi-om nonisothermal experiments. For this purpose one inserts Eq. (7) into Eq. (3) of Fig. 2.8 and gets Eq. (8) as an expression for the nonisothermal reaction kinetics. For analysis, one may take the logarithm on both sides of the equation to make the exponential disappear. In addition, one may differentiate both sides with respect to ln[A], to get an explicit equation for the reaction order n. The result of this mathematical operation is shown in Eq. (9). This is a somewhat arduous equation, usually attributed to Freeman and Carroll. Note that experimentally one knows the parameters concentration, [A], rate, -d[A]/dt,... 

A kinetic analysis based on the Coats-Redfern method applied nonisothermal TGA data to evaluate the stability of the polymer during the degradation experiment. Of the different methods, the Coats-Redfern method has been shown to offer the most precise results because gives a linear fitting for the kinetic model function [97]. This method is the most frequent in the estimation of the kinetic function. It is based on assumptions that only one reaction mechanism operates at a time, that the calculated E value relates specifically to this mechanism and that the rate of degradation, can be expressed as the basic rate equation (Eq. 5.3). This method is an integral method that assumes various... 

Cai, J., Han, Y. Morphology, structure, and kinetic analysis of nonisothermal cold- and melt-crystallization of syndiotactic polystyrene. J. Appl. Polym. Sci, 103,1311-1324 (2007). 

Smith Kevin W, Cain Fred W, Talbot G. Kinetic analysis of nonisothermal differential scanning calorimetry of l,3-dipalmitoyl-2-oleoylglycerol. / Agric food Cftem2005 53(8) 3031-3040. 

Mittemeijer E J, Cheng L, der Schaaf P J V, Brakman C M and Korevaar B M 1988 Analysis of nonisothermal transformation kinetics tempering of iron-carbon and iron-nitrogen martensites Metall. Trans. A 19 925... 

The temperature of maximum transformation rate is easily determined using either of two similar techniques called differential scanning calorimetry (DSC) or differential thermal analysis (DTA). These techniques are extremely useful in the kinetic study of both isothermal and nonisothermal phase transformations. 

Ohva, A., Llabres, M., and Farina, B. (2006), Data analysis of kinetic modeling used in drug stabihty studies Isothermal versus nonisothermal assays, Pharm. Res., 23, 2595-2602. 

A more quantitative analysis of the batch reactor is obtained by means of mathematical modeling. The mathematical model of the ideal batch reactor consists of mass and energy balances, which provide a set of ordinary differential equations that, in most cases, have to be solved numerically. Analytical integration is, however, still possible in isothermal systems and with reference to simple reaction schemes and rate expressions, so that some general assessments of the reactor behavior can be formulated when basic kinetic schemes are considered. This is the case of the discussion in the coming Sect. 2.3.1, whereas nonisothermal operations and energy balances are addressed in Sect. 2.3.2. 

A detailed two-dimensional numerical analysis of nonisothermal spinning of viscoelastic liquid with phase transition was carried out recently by Joo et al. (15). They used a mixed FEM developed for viscoelastic flows (16) with a nonisothermal version of the Giesekus constitutive equation (17), the Nakamura et al. (18) crystallization kinetics... 

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. 

Several recently published reviews74-7sum up the results of investigations in this field, but the individual works differ in value. Three problem areas concerning modeling are examined below. These include methods for determining the kinetic constants, analysis of nonisothermal processes, and applied calculations. 

The analysis of steady-state multiplicity of a nonisothermal chemical reactor is complicated due to the number of parameters involved and the exponential nonlinearity in the temperature dependence of the kinetic function. In this and the next subsection, the results of the analysis of steady-state multiplicity are presented. The derivations of these results are detailed in a review chapter by Morbidelli et al. (1986). 

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