Distribution Kinetics of Polymer Thermogravimetric Analysis:  A Model for Chain-End and Random Scission

Abstract

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.

Structural and thermal behavior of comb‐like polymer having n‐octadecyl side chains

“…Although the chemical reactions underlying the pyrolysis are known, the usual methods for interpreting TGA data are based on distribution kinetics, a comprehensive approach for dynamics of systems having a distributed property. 20 The model describes the isothermal and constant heating rate TGA as a function of time and temperature. Thermal degradation of POMA and its blended samples with C 18 proceeded via a one-step reaction, i.e., T ini ¼ 150-2008C and T max ¼ 325-4008C.…”

Distribution Kinetics of Plastics Decomposition

“…We have negligible difference of the slopes in nonisothermal TGA of poly(ether-ether-ketone) 51) . Then, the similar slope is supported by Eq.…”

“…A thermobalance is designed to perform pyrolysis with minimum mass transfer resistance and sufficient heat transfer so that the reactions of chain scission and recombination mainly control the TG data. A kinetic model describing formation of volatile products in TG pyrolysis with negligible mass transfer resistance was derived from the distribution kinetics, and the kinetic parameters of chain-end degradation were determined 51) . In this section, distribution kinetics is developed to interpret TG data in terms of random/specific degradation and recombination.…”

“…The pre-exponentials, Ad, Aa, and As were set to estimated values, 6 × 10 12 , 6 × 10 9 , and 6 × 10 12 min −1 , respectively, and the three unknown activation energies, Ed, Ea, and Es, were obtained by the non-linear fitting procedure. We reported the results of the activation energies for PS pyrolysis by isothermal TGA at 335-355°C, and Ed, Ea, and Es were given at 170.1-176.0, 77.3-86.9, and 142.1-151.7 kJ/mol, respectively 51) . Nonisothermal TGA gives results over wider ranges possibly due to various underlying reactions during the pyrolysis at wide-ranging temperatures 53) .…”

Oxidative thermal degradation of LDPE and the determination of some thermodynamic quantities

“…While the random breakage mechanism described the nonisothermal data well, the results suggest significance of an additional mechanism at temperatures below 400 8C [7]. The second kinetic approach described the breakage of polymer bonds by using of population balance equations, which track the number of molecules of each size in the reaction mixture [8][9][10][11]. In general polymers are bioinert; so they have been high resistant to assimilation by microorganisms such as fungi, bacteria and like.…”