Multiple steady states, viscosity, and high conversion in continuous free‐radical polymerization

Using existing literature data on the rate of a bulk polymerization of styrene in a batch reaction carried to high conversion, it is mathematically demonstrated that there is a clear possibility of the existence of multiple steady states induced by viscosity effects in isothermal continuous stirred tank reactors. In solutions of high viscosity, the rate of free‐radical polymerization increases with conversion, reaching a peak at very high viscosity, then falling off rapidly. Given this sort of behavior, it is demonstrated mathematically that steady‐state mass balance solutions are possible at three levels of conversion. The lower and higher steady states are stable while the middle steady‐state condition is shown to be necessarily unstable. This multiplicity of steady states with its particular problems of stability is analogous to the much studied phenomena of temperature stability. It is closely related to the problems of concentration stability characteristic of autocatalytic and heterogeneous catalytic reactions. This multiple steady‐state problem is qualitatively discussed in relation to reactor stability, control, and optimization.