Orthogonal collocation applied to analysis of heterogeneous Ziegler-Natta polymerization

Heterogeneous Ziegler-Natta polymerization of ethylene and α-olefins occurs in small particles that grow with time as polymer is produced. Work is progressing on models for predicting the molecular weight and sequence distributions of the polymer product produced under these conditions, where diffusional accessibility and activity of catalyst sites may vary with time and position in the growing particle. Any model for these phenomena must be solved numerically and it is therefore important to put some effort into determining what sort of numerical analysis works best for these stiff, moving boundary diffusion reaction problems. The present work demonstrates the use and simplicity of orthogonal collocation for this problem and permits us to draw some new conclusions about the origin of the broad molecular weight distributions in Zielger-Natta polymers.