(550d) Continuum Lumping Modelling for Polymerisation Kinetics
Polymerisation occurs when two “units”, called monomers, join by either chain addition or step-growth process leading to a product with a higher molecular weight characterised by repeating chemical units. A model based on the continuum lumping methodology is proposed and implemented to predict the molecular weight distribution during polymerisation. The work is aimed at assessing the benefit of the continuum lumping approach to obtain information about some specific features of the reaction. The model is tested for two selected case studies furnishing the product distribution at various times. Since many properties of a polymer depend on the molecular weight distribution (MWD) and on the average of such distribution, the results will pave the way for future work assessing the predictive capability of the lumping methodology as applied to polymerisation. The aim is twofold: to develop a model which could predict the polymer MWD at various times, and to assess the capability of the continuum lumping methodology as applied to polymerisation. The work focuses on step growth polymerisation only, since we think that the underlying kinetic mechanism is amenable to be described through a continuum lumping procedure. We show that the polymerisation yields distribution can be obtained through the methodology. The model is based on the assumption that the MWD evolves in time as described by an integro-differential equation. A Skewed Gaussian distribution function for determining product yield distribution of the polymerisation reaction is introduced. The model is based on the assumption that the kinetics is liner and first order, and the reaction is irreversible. The model captures successfully the effect of the reaction time and reaction rate constant on the MWD.