A numerical study of various rheological polydispersity measures

Abstract

Model calculations were performed in order to investigate the sensitivity of various rheological polydispersity parameters for variations in the moments of the molar mass distribution (MMD) of linear polymers. Molar mass distributions were generated with the Gaussian and the Generalised exponential distribution functions, using a fixed weight average molar mass Mw and variable Mw/Mn and Mz/Mn. Assuming linear entangled polymeric chains, the linear viscoelastic properties were predicted by calculating the stress relaxation modulus of the consecutive monodisperse fractions with the BSW relaxation time spectrum and blending these curves with the double reptation blending rule. BSW relaxation parameters appropriate for polypropylene were used. It was found that both the zero-shear viscosity and the so-called cross-over frequency, at which \(\) and \(\) are equal, depend mostly on Mw but also significantly on both Mw/Mn and Mz/Mw. By contrast, the steady-state compliance depends mainly on Mz/Mw, its functional dependence on moments of the MMD being best described by the Ferry equation. None of the polydispersity parameters PI (from the \(\) modulus cross-over), MODSEP (the \(\) modulus separation) or PDR (from the shape of the flow curve), as introduced in literature depends solely on the polydispersity Mw/Mn. PI is the most sensitive indicator for this purpose. Finally, the parameters ER (\(\) at a fixed low value of \(\), MODSEP en DRI (from the shape of the flow curve) are shown to be good indicators for the weight (Mz/Mw) of the high molar mass tail of the molar mass distribution.