Kinetic Equations for Ultrasonic Scission of Polymers

When a long chain of polymer is sonicated it is known that it preferentially breaks at the middle and long chain radicals result. The termination step is especially important to control the degree of polymerisation P_n. In this paper, in the absence of the radical traps the nature of the phenomenological kinetic equations derived in [4] are studied. It has been found that for all possible values of the parameters, the only equilibrium point is linearly stable. But because of the nonlinear effects, stability of the equilibrium point depends on the parameter space. For some set of parameters and initial conditions, it has been observed that the solutions are asymptotically periodic. But large time behaviour of all these solutions are not realistic in the sense that functions representing nonnegative physical quantities assume negative values. A modified version of the kinetic equations whose solutions remain nonnegative in the time course is also proposed.