Kinetics of the multi-step catalytic degradation of a polymer to its constituent subunits

The stepwise catalytic degradation of a polymer to its constituent subunits results in many molecules of polymers of shorter chain length. Using the Law of Mass Action, ordinary differential equations for each species can be obtained from the set of elementary reactions and these can be integrated to obtain species concentrations as a function of time. A special case of catalytic degradation of polymers, in which one subunit is released at each step, is examined. A mathematical dissertation on the kinetics of the series of reactions involved is presented. The solution of the set of differential equations involve tedious computations and cannot be easily adapted to the analysis of experimental data. Two additional methods of analysis are described. The first one makes use of the property that for any intermediary polymer whose initial and final concentrations are zero, the integral of its concentration with respect to time is inversely proportional to the degradation rate constant. Stepwise calculation of the rate constants can thus be obtained by determining the area under the concentration-time trajectories while the degradation rate constant of the first polymer is known. The second method makes use of the property that the maximum concentration attained by any individual intermediary polymer is inversely proportional to its degradation constant. These methods have the advantage of being simple since the degradation constants can be obtained stepwise from experimental data.