The Freeman-Carroll Method Applied to DTA

At any time, a is the fraction decomposed while a is the fraction which has yet to react. We can set up equations as before  

The first part of the equation is the general kinetic equation, from which it is easy to obtain the last part (as we have shoAvn). If we perform the mathematical operations of 1) take the naperian log 2) differentiation, and then 3) integration, we obtain the following equation  

Thte allows us to plot A (In AT) / A (In a ) vs A (1 /T In a ) so as to obtain a straight line. The slope is E/R and the intercept is n, the order of reaction. Having thus obtained the activation energy and order directly, we can then calculate the reaction rate. 

As in the DTA method, we define weight reacted in time, t, as wt and final weight, wf. This allows us to define weight to be reacted as w = wt - Wf. Our weight function is then to be defined  

We now do the mathematical manipulations in the order given above to obtain  

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The following is a description of the Freeman-Carroll method applied to DTA data. Consider the following DTA peak in which AT is plotted vs time, t, a representation of which given as follows ... 

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