Estimation of the Molecular Weight Distribution of Linear Homopolymer Blends from Linear Viscoelasticity for Bimodal and High Polydisperse Samples

This work is concerned with the approximate solution of the problem generated by the integral of first kind relating the shear relaxation modulus of entangled, linear and flexible homopolymer blends and the molecular weight distribution (MWD). Procedures are proposed to estimate the density distribution function (DDF) of the MWD from numerical solutions of the theoretical model composed by the double reptation mixing rule and a law for the relaxation time of chains in polydisperse matrixes. One procedure uses the expansion of the DDF through orthogonal polynomial functions. This expansion is formulated for two cases: a) Hermite polynomials associated with the normal-DDF and b) Laguerre polynomials associated with the gamma-DDF. The other procedure uses the mean value theorem of continuum functions, which turns out the integral problem into a differential form. Calculations are carried out with dynamic rheometric data of linear viscoelasticity for samples of polydimethylsiloxane, polypropylene and polybutadiene. High values of polydispersity are considered. The predictions of the DDF through these procedures compare well with experimental data of size exclusion chromatography (SEC). Keywords-Bimodal Molecular Weight Distribution, High Polydipersity, Hermite and Laguerre Series, Double Reptation Model, Linear Flexible Homopolymer Blends.