Continuum lumping modelling for step growth polymerisation mechanism

Polymerisation occurs by chain addition or step-growth mechanisms. The yield and the concentration distribution of monomers, dimers, trimers and higher order polymers can depend on the molecular weight or some other variable which can be unequivocally linked to any given compound. Continuum lumping is a methodology widely used to describe the kinetic and thermodynamic behaviour of complex reactive mixtures of diverse components all undergoing similar types of reactions (e.g., cracking, pyrolysis, oligomerisation). The methodology is particularly convenient when the number of species involved is very large and the species can be characterised by properties which are measured in a continuous fashion, as for instance in a chromatogram. By applying the lumping methodology, a large reactive system can be reduced to a simpler and more tractable one. A model, based on the continuum lumping approach, is proposed to predict the molecular weight distribution of polymers during polymerisation. The main aim of this work is to assess the suitability of the application of the continuum lumping approach to polymerisation. The results obtained from a continuous model are assessed, at this stage, only qualitatively; nevertheless, by analysing the weight distribution and the average of such distribution, conclusions can be reached to assess the predictive capability of the lumping methodology. The model is tested for two selected case studies and the product distribution is obtained at various times.

► The continuum lumping methodology is applied to step-growth polymerisation.
► The role of the “type-distribution” function is investigated.
► The role of the yield function is investigated.