| Many features of Ziegler-Natta polymerizations are well understood, such as the use of selective poisons to enhance stereoselectivity, while others are yet to find a unified explanation, in particular with regard to the existence of broad molecular weight distributions. Despite considerable evidence supporting the two theories dealing with this (Multiplicity of Sites and Diffusional Limitation), no publication has appeared presenting a model where all balance equations are rigorously developed, allowing for multiplicity of sites and avoiding an a priori statement of homogeneity in monomer concentration within a particle.;Using the One-Site model, results obtained for homopolymerization demonstrate that only in cases of extreme catalyst activity, diffusional limitations cause broadening of the MWD. This suggests that other factors such as deactivation and/or multiplicity of sites should be considered. In the case of copolymerization, however, diffusional limitations can also produce inhomogeneities in the quality of the polymer.;It is shown that intraparticle temperature gradients are non-existent. The maximum temperature reached by the particle, however, can increase drastically under conditions near adiabatic even for low-activity catalysts.;Using the Two-Site model, it is found that the relative activity between sites has to be large for broad MWD's to be predicted in the absence of diffusional limitations. The best qualitative agreement is reached when only one site deactivates. It is concluded that in any serious efforts toward modeling of heterogeneous Ziegler-Natta polymerizations, two or more kinds of sites should be considered.;In this work, such a mathematical treatment is developed, providing a better means for analysis. Based on experiments performed on a titanium-based catalyst, different reaction conditions are simulated, considering either only one type of site or two types of sites.;An empirical dependence of the concentration of active sites on comonomer concentration, motivated by experimental copolymerization results, is used satisfactorily for rate and polydispersity predictions.;Using simple empirical relations between local polymerization rate and effective diffusivity, it is demonstrated that minor changes in transport coefficients can substantially affect the predicted properties of the resulting polymer, regardless of the number of types of sites. |
