Free-radical polymerization engineering—III. Modelling homogeneous polymerization of ethylene: mathematical model and new method for obtaining molecular-weight distribution

Abstract A specific approach based on a “tendecy model”, intermediate between the “black-box” and the “detailed analytical” models, has been developed. It makes it possible to predict both the amount of polymer produced in the autoclave process, and the quality of the polymer, expressed in terms of molecular structure: molecular-weight distribution (MWD), average molecular weights, long- and short-branching indices, double-bond indices. The prediction of conversion requires an appropriate representation of partial segregation of the initiator feedstream. The prediction of quality is based on a kinetic model taking into account the most important mechanism recognized for this reaction. Several kinds of free radicals are involved to which the quasi-steady-state assumption is applied. Processes giving rise to new chains are identified and the statistical moments for the corresponding distributions are derived. The moments of the overall dead polymer population are finally derived,thanks to a mixing theorem. In spite of the difficulties caused by transfer to polymer and scission of free radicals, equations for the moments are obtained in a closed form and this constituents a remarkable property of the present model. An expression for the MWD can then be obtained from its statistical moments by an original method based on the deformation of a known distribution.