Coats-Redfern equation

Kinetic Expressions. In this study, we have analyzed nonisothermal TGA data using the Chen-Nuttall equation, the widely accepted Coats-Redfern equation, and the Anthony-Howard equation. These equations are derived from simple rate expressions. The basic single reaction kinetic equation for the decomposition of a solid has been presented by Blazek (24) as... 

CR-AH denotes the Anthony-Howard equation, (25), where the first integral is approximated using the Coats-Redfern equation. 

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... 

TABLE VI. Comparison of the Kinetic Parameters and AAD Values Determined from Chen-Nuttall and Coats-Redfern Equations ... 

The imphcation from the above work is that polymer present in the galleries of montmorillonite through intercalation and exfoliation has enhanced thermal stability provided by a different thermal degradation mechanism when compared to the pure polymer. Calculations of the activation energy of polyurethane-imide-clay nanocomposites [37] utilizing the Broido [38] and Coats-Redfern equations were consistent with a mechanism that increased the thermal stability of the polymer-clay nanocomposite in relation to the pure polymer. An optimization of melt-blending processing that improved the exfoliation efficiency of polymer-clay nanocomposites resulted in increased thermal stability by TGA when compared to polymer-clay nanocomposites with inferior exfoliation, and pure polymer [39]. 

Three kinetic models were tested the Chen-Nuttall model ( 5) and the Coats-Redfern model (6) both assume a single first order rate equation to describe the decomposition reaction and the Anthony-Howard model (7) (as developed for coal decomposition studies), which assumes multiple parallel first order reactions to describe the decomposition reaction. 

Comparison Between Coats-Redfern and Chen-Nuttall Equations. The single heating rate data for the temperature range of 300-500°C have been correlated to the CR equation, Eq. (14), and the CN equation, Eq. (8). Three techniques were used to find the optimum values for E and Z in each of these equations. These techniques include 1) iterative linear regression, 2) Levenberg-Marquardt... 

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 ... 

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

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) ... 

When it is used the Coats—Redfern calculation procedure, if a compensation effect between InA and E exists, then by plotting InA versus E straight lines should be obtained for each of the heating rate studied, according to the next equation ... 

For measuring kinetic parameters, we treated data following the procedure of Coats and Redfern ( and Mickelson and Einhorn ( by taking logarithms from Equation (T) at temperatures, T - and Tj ... 

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 ... 

With this equation, a plot of ln[- (ln(l - straight line of slope E/R. (The first term in the right side of Eq. (14) remains essentially constant for most values of E, Coats and Redfern (6>).) By extrapolating the curve, a value for Z can be obtained. 

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). 

Integrating equation (5.46X as described by Coats and Redfern (189), using as a lower integration limit of temperature, T0, previously calculated from equa-... 

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... 

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