Regression rates and the kinetics of polymer degradation

Abstract

A method of calculating regression rates r˙ of simple polymer fuels has been worked out and applied to poly(methyl methacrylate), polystyrene, and polyethylene. The method depends upon (a) invoking the concept of a critical fragment size (c.f.s.) and (b) the use of a first-order rate equation −dn/dt=kn, for describing the scission of backbone bonds in the polymer. The c.f.s. is the chain length of the volatile product of chain degradation, above which size it is energetically more economical to continue breaking backbone C-C bonds than to remove the fragment from its environment. From random scission of these bounds, we have derived a rate of loss-in-weight law m1/m0=1−exp (−ikt)[i+1−exp (−kt)], in which i is the maximum chain-length of the c.f.s. For other mechanisms of chain degradation, the average chain-length of the c.f.s. was used and a rate of loss-in-weight law m1/m0=1−exp (−kt) was involved. The first-order rate equation, above, was shown to be consistent with these laws. Agreement with measured r˙ values is very good, being off by not more than a factor of 2, but depends upon the application of the appropriate surface temperature Ts. Extension of this method to composite fuels does not give results in agreement with experiment, even when limiting values of Ts are used, and KClO4 or NH4ClO4 is the oxidizing filler. The conclusion was drawn that the two-temperature model of a burning composite fuel was more likely to succeed. It was shown that a crystallite surface temperature for NH4ClO4 of 1010°K could be calculated without invoking a solid-phase reaction.