High-Speed Computations in the Kinetics of Free-Radical Degradation. I. Random Initiation

Abstract

The theory of free-radical degradation leads to large sets of difference-differential equations for the reacting species, which can be solved analytically for practical purposes only in the extremes of preponderant chain depropagation and random or terminal scission, respectively. Moreover, the equations are linearized by neglecting the variation of the steady-state radical concentration with degree of volatilization. Numerical solutions of the linearized set were obtained on the SEAC and the resulting zeroth and first moments of the distribution tabulated for the case of random initiation. Thus the rate of volatilization and the number-average degree of polymerization can be computed as functions of conversion. Initially monodisperse systems and a maximum chain length of 400 C atoms, which determines the size of the set, were assumed. In addition to the latter there are three parameters, viz., the average ``zip'' length, (1/ε—1), a transfer constant, σ, and the maximum size of vaporizing chain fragments. All of these were varied over a wide range so as to reproduce the wide spectrum of behavior found experimentally. Where applicable, earlier analytical results were confirmed. The errors inherent in the linear approximation can be estimated and are found not to affect the results significantly over a useful extent of reaction. For a certain range of parameters, ``corresponding states'' rules can be established and the results applied regardless of the absolute magnitude of the initial chain length. Depending on the parameter values, and hence on the molecular structure, the initial rates also exhibit wide variations in absolute magnitude and sensitivity to initial molecular weight. The kinetics in polystyrene and particularly poly-α-methyl styrene are discussed in the light of the theory. For the latter polymer, both the decrease in molecular weight, and the dependence of initial rates on the initial chain length lead to a consistent picture of a long average zip length, approximately 1.3×103 monomer units, combined with a random initiation. The upper limit for the initiation constant is 3.42×10—6 sec—1 at 272°C.