| Abstract: | The recently developed mathematical technique for studying the parametric sensitivity of reactors is extended to include chain polymerization systems exhibiting the gel and glass effects, as well as physical property variations. The sensitivities of the two temperature maxima with respect to various parameters are computed. It is found that, for a sample system, poly(methyl methacrylate), all the sensitivities of the gel effect induced temperature peak attain their maxima at the same conditions—this leads to a generalized temperature sensitivity constraint applicable to reactor design or operation. This sensitivity boundary is associated with high conversions and high molecular weights. The analysis shows that the dimensionless propagation activation energy, ?p, and the dimensionless initiation activation energy, ?d, are the two most important parameters governing the system performance. Sensitivities of the gel effect-induced number average chain length peak with respect to various parameters are also obtained. Again, all of these chain length sensitivities show maxima at the same condition, leading to the concept of a generalized chain length sensitivity criterion of constraint. Most importantly, the temperature and chain length sensitivity boundaries are virtually identical. |
