Finite element model of interdiffusion and reaction in polydisperse polymer blends

Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathe- matical formulation of such problems, where molecular weight distribution may range over several hundreds| which are very frequent in practice|leads to a huge set of coupled di erential equations. In this work a numerical technique is presented that reduces the problem to a manageable number of degrees of freedom while keeping the essential physics of the original statement. For this purpose the distributions of molecular degrees of polymerization are approximated by continuous variables, and the set of concentration pro les replaced by a continuous eld. The resulting equations are then reexpressed in weak form as a Galerkin integral identity and discretized using nite elements. Mass conservation and interchange chemical reactions as transesteri cation are treated using Lagrange multipliers. The accuracy of the technique|which can also be applied to the monodisperse case|is assessed through a number of simulations, and comparisons with experimental results published earlier.