Radiation-induced catalytic polymerization. I. Theory

The kinetics of radiation polymerization on a solid catalyst is discussed, under the condition that only linear termination of the chain takes place. All the kinetic equations are balance equations of particles of each type adsorbed by unit mass of the catalyst, and this makes it possible to account for the effect on the kinetics of the time dependence of the magnitude of the part of its surface on which the reactions we are considering may take place. Integro-differential equations are used for calculating the molecular weight distribution of the resulting polymer; this ensures higher accuracy of the formulas obtained than when differential equations are used and makes it possible to eliminate a number of limitations generally involved in the transition to differential equations. An expression has been found for the molecular weight distribution of the polymer product which allows for the possibility of radiation-induced catalytic polymerization on the resulting adsorbed polymer. Expressions have been derived for the average molecular weight and yield (weight and molecular) of the polymer formed. Asymptotic formulas have been obtained (for large irradiation times) for all the above values. The conclusions that can be drawn concerning the mechanism of the process based on a comparison of the formulas obtained with kinetic curves plotted from experimental data are given. It is shown how such a comparison can be utilized for calculating the rate constants for polymerization and chain termination reactions.