Coats-Redfern method

Fig. 19. First order kinetic plot by Coats-Redfern method. poly (BMIP) poly(BACY)...

The parameters E and A of the coal samples were obtained from the kinetic analysis of TG data. The Coats-Redfern method has a great advantage of simplicity among the kinetic approaches and is extensively acknowledged. The reaction kinetic equation can be deduced as ... 

Based on the TG/DTG profiles, the kinetics parameters such as activation energy (E) and frequency factor (A) were obtained by Coats-Redfern method. The following conclusions can be drawn ... 

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 ... 

According to the Coats-Redfern method, the right side of Eq. (5.8) can be written as ... 

The loss of the guest molecules corresponds to endothermic processes with low enthalpic values ( AH(jec l3-30 KJ rool l). The rate constants for such processes were evaluated for each compound at several temperatures, by fitting isothermal TG curves to different kinetic physical mechanisms of solid state reactions (diffusion, nucle-ation, growth, nucleation-growth and homogeneous)The kinetic parameters (Ko, Ea) were calculated from an Arrenhius plot of the rate constants. The declathration physical mechanisms were assigned on the basis of agreement between these calculated kinetic parameter and those determined from non-isothermal TG curves by mean of Coats--Redfern method. 

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... 

In this method, the different reaction orders are taken into account and compare the linearity of each to select the correct order. Principle of the Coats-Redfern method describes Eq. (5.4). The derivation for this method has been described previously [114]. The final operative equations are given in Eq. (5.4) ... 

The kinetics of dehydration and decomposition have been studied for the Pr sulfate. Bukovec et al. (1980a) found that the decomposition of anhydrous Pr2(SO )3 follows a linear law up to a = 0.5. Niinisto et al. (1982) used the Coats-Redfern method for determining the apparent reaction order for the dehydration of Pr2(S04)3 5H2O. The dehydration steps are difficult to resolve owing to the limited stability of the intermediate hydrates, but the use of kinetic calculations or a quasi-isothermal heating mode (Paulik and Paulik, 1981) shows the existence of the dihydrate and monohydrate. The relation between the dehydration mechanism of Pt2(S04)3 SHjO and its structure has been discussed (Niinisto et al., 1982) and comparisons have been made with CsPr(S04)3 4H2O, which likewise has differently bound water (Bukovec et al., 1979b). Recently,... 

Comparison of Anthony-Howard and Coats-Redfern Equations. Because the CR equation and the CN equation yielded similar results, the CR equation was chosen as a basis for comparison with the AH equation. The correlated results based on the AH multiple reaction model and the CR model are presented in Table VIII. The kinetic parameters were determined using an equally weighted regression method. From Table VIII, it can be seen that the AH model yields... 

I. The weight loss data were first treated using the two parameter models (Coats-Redfern and Chen-Nuttall). The calculated activation energies were generally very low in comparison to the energies of the bonds that are considered to be breaking in the reaction, thus leading to the evaluation of more sophisticated treatment methods and kinetic models. 

From the viewpoint of ease of computation, Doyle s method seems to be very simple because the kinetic data are obtained from a single point on the curve. The necessity of knowing the reaction order ahead of time appears to be a disadvantage which finds a partial remedy in the Coats and Redfern method. 

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... 

Many other mathematical methods have been proposed to analyze non-isothermal kinetic data to determine unequivocally the exact kinetic model using functional forms of < (a) or /(a) of the rate-controlling step (154). Criado (155) found that it was impossible in the Coats and Redfern method to distinguish between an interface chemical reaction-controlled mechanism (R3) and the Jander diffusion mechanism (D3). Bagchi and Sen (156) also demonstrated the inadequacy of the Coats and Redfern method in identifying unambiguously the rate-controlling mechanism of the dehydroxylation of Mg(OH)2. 

An interesting variation on the Coats and Redfern method has been developed by Reich and Stivala (1980). The method makes use of an iterative technique to arrive at the best value of n to fit the a,T data to a rate law. It is best employed using a computer to perform aU of the computations. The integrated rate equation is written in the form... 

Kissinger, Akahira and Sunose (Kissinger, 1957 Ozawa, 1%5 Augis Bennett, 1978 Boswell, 1980 Flynn Wall, 1966 Akahira Sunose, 1971) used the approximation given by Coats Redfern (Coats Redfern, 1964) to evaluate the integral in the rate Eq. (4). KAS method is based on the expression... 

One of the most popular model-fitting methods is the Coats and Redfern method (Coats Redfern, 1964). This method is based on the equation... 

Many methods have been devised for the application of Eqs. (2-16) to (2-20) to thermo-analytical data which involve various approximations of the exponential integral, p(y). Notable examples are the methods of Doyle 24,25), Horowitz and Metzger i6), Coats and Redfern 27), and Ozawa 28-30>. The method of Ozawa is frequently used. By taking Doyle s approximation for p(y) in Eqs. (2-20) and (2-21) Ozawa obtained the approximate relationship... 

Coats and RedfernTs Equation. A method developed by Coats and Redfern (6) utilizes the following expression as an approximation of the integral in Eq. (6) to determine the energy of activation, E, and the frequency factor, Z, for the thermal decomposition reaction ... 

The right-hand side of this equation can be solved by various methods, and the final solution to the equation is an infinite series of which the first two terms are of interest generally. These methods are used by Doyle (84) and coats and Redfern (85) as well as by others (86,87). 

Sestak (43) compared the kinetic results calculated by five different methods for a system corresponding to the dehydration of -CaS04 0.5H2O. The five methods evaluated mathematically were (1) Freeman and Carroll (83) (2) Doyle (84) (3) Coats and Redfern (85) (4) Horowitz and Metzger (88) and (5) Van Krevelen et al. (87). From these calculations it was found that the deviations of computed values oF E did not differ by more than 10%. Thus, all the methods appear to be satisfactory for the calculation of E within the limits of accuracy required. The errors of each method due to the inaccuracy of visual deduction of values from the TG curves were also calculated. These errors, % and e (errors in calculation of E or n, respectively), were as follows (1) Freeman and Carroll method, eE = 4% and e = 12% (2) Horowitz and Metzger method, ee = 2% (when the correct value of n is assumed) (3) Doyle method. eE = 4%. However, the magnitude of this error depends primarily on the position of the point on the TG curve on which the calculations are being performed. In the case of differential methods, me most accurate data are calculated from the medium-steep parts of the curve. For the approximation method, the accuracy depends on the determination of the curve inflection point temperature. 

Three kinetic methods were evaluated by Sharp and Wentworth (76) using the thermal decomposition of calcium carbonate under various conditions. The physical state of the sample was as a pellet, a powder, or as 1 1 molar ratios with a-aluminum oxide or a-iron(III) oxide. The three methods used were Method 1, Freeman and Carroll Method II, Coats and Redfern and Method HI, Achar et al. (102). The kinetic data calculated by Methods II and III are presented graphically in Figure 2.41 and in Table 2.3. In every case a linear plot was obtained over a wide range of a with n = When these methods were applied with n — j, the range of x was less, especially in the case of Method III, which led to noticeable curvature at... 

Barbooti (151) compared the Coats and Redfern (85) and Horowitz and Metzger (88) methods for the kinetics of the decomposition of M MaI 3H20 complexes (M = Mn, Co, Ni, and Cu and Mai = malonate). It was concluded that multistep reactions may be investigated employing these methods and accurate isolation of the overlapping reactions can be obtained. 

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