Predicting low density polyethylene melt rheology in elongational and shear flows with "pom-pom" constitutive equations

A recent constitutive equation derived from molecular considerations on a model architecture containing two branch points a "pom-pom" captures the qualitative rheological behavior of low density polyethylene (LDPE) in shear and extension for the first time [T. C. B. McLeish and R. C. Larson, J. Rheol. 42, 82 (1998)]. We use a hypothetical melt of pom-poms with different numbers of arms to model the behavior of LDPE. The linear relaxation spectra for various LDPE samples are mapped to the backbone relaxation times of the pom-pom modes. Data from start-up flow in uniaxial extension fixes the nonlinear parameters of each mode giving predictions for shear and planar extension with no free parameters. This process was carried out for data in the literature and for our own measurements. We find that multimode versions of the pom-pom equation, with physically reasonable distributions of branching, are able to account quantitatively for LDPE rheology over four decades in the deformation rate in three different geometries of flows. The method suggests a concise and functional method of characterizing long chain branching in polymer melts. (C) 1999 The Society of Rheology.