Computation of molecular weight distributions by polynomial approximation with complete adaptation procedures

Abstract

The choice of appropriate reference functions is still the major drawback for collocation techniques to be used during the computation of molecular weight distributions (MWDs) in polymerization reactions and other problems constituted by systems of differential-difference equations. Complete adaptation procedures provide significant improvement of numerical approximations obtained, but convergence to the real solution is not assured and oscillatory numerical approximations may be obtained when the actual solution experiences large variations during time integration. An alternative method to compute the reference function in an adaptative manner, called here the integration of the reference function procedure, is presented. The technique is used to allow the computation of MWDs in two polymerization problems: the metallocene-based propene polymerization and the methyl methacrylate/butyl acrylate emulsion polymerization. The integration of the reference function procedure allowed the proper computation of broad, bimodal and fast changing distributions with polynomials of very low order (below 4), where other approximation techniques failed. The method may be easily implemented and does not require any pre-processing before implementation.