Distribution kinetics of polymer thermogravimetric analysis: A model for chain-end and random scission

Thermogravimetric analysis (TGA), through measurements of mass volatilized as a function of time, is an essential method for understanding pyrolysis of macromolecular materials. In this paper, we show that two differential equations for mass and moles of test sample allow interpretation of isothermal and nonisothermal TGA data for polymers. The equations, related to radical mechanisms and derived by means of distribution kinetics, are based on the actual fundamental chemical reactions that occur in the pyrolyzing sample: random-chain scission, recombination, and chain-end scission. The model describes the isothermal and constant heating rate TGA curves for polymer mass as a function of time or temperature. For isothermal TGA, the equations have an analytical solution identical to an empirical kinetics model that successfully correlates TGA data. Nonisothermal TGA requires a numerical integration of the two differential equations. Procedures for determining activation energies from TGA data are suggested by the new theory. Low-molecular-weight (MW) products of chain-end scission are assumed to volatilize instantaneously. TGA data for polyethylene, polystyrene, and polyether-ether-ketone are examined by nonlinear fitting precedures that yield activation energies for the three chemical reactions.