Model-free method for evaluation of activation energies in modulated thermogravimetry and analysis of cellulose decomposition

In modulated thermogravimetry the classical linear temperature–time relationship is perturbed by sinusoidal temperature oscillations of small amplitude. Mass loss and its hypothetical unperturbed derivative are connected by an integral equation with the kernel expressed as the ratio of Arrhenius exponentials with the perturbed and unperturbed temperature in the numerator and denominator, respectively. The solution of this equation by the least-squares method gives activation energy, E. The method is model-free, since E   is determined on the basis of the experiment without any theoretical functions. Such a method has been applied to study the decomposition of cotton in air. The plot of activation energy versus the degree of conversion, αα, shows that the decomposition is characterized at least by three successive processes. The first one (≅5%≅5% of mass loss) with E≅90E≅90–167kJmol-1 can be attributed to the formation of the ether bond between hydroxymethyl groups and hydroxyls in adjacent chains of cellulose an/or to oxidation of chain ends and products of cellulose decomposition. The second process with E≅195.9kJmol-1 over the range 0.2<α<0.620.2<α<0.62 is the first rate-limiting step attributed to depolymerization of cellulose by transglycosylation. The third process with E=153.1kJmol-1 over the range 0.7<α<10.7<α<1 is again the rate-limiting step. It corresponds to the oxidation of the carbon matrix of partly (or completely) carbonized cellulose. Plateaus in E(α)E(α) can be used to predict the mass loss and provide valuable information about chemistry of decomposition.