Optimization of diffusion‐controlled free radical polymerizations in lumped‐parameter systems

Open‐loop optimal temperature control strategies for the batch free radical polymerizations of styrene are investigated using the minimum principle. Two kinetic models, one considering the gel effect and the other incorporating both the gel effect and the glass effect, are employed. By using the Min‐H strategy, a control variable program that minimizes one objective function and yields values of other terminal quantities can be obtained. It is found that the optimal temperature programs are highly dependent upon the kinetic characteristics of reactions. The gel and glass effects, which control ultimate molecular weights, play important roles in affecting the temperature programs. Numerical examples using two objective functions, one in which reaction time is minimized, and the other in which molecular weight distribution is minimized, are presented. The theoretical predictions using kinetic model with the gel and glass effects are also compared with experimental measurements of conversion, molecular weight, and molecular weight distribution. Although the agreement between the experimental work and the theory is less than satisfactory, the trends of policy improvements are consistent.