Nj. Inkson et al., Predicting low density polyethylene melt rheology in elongational and shear flows with "pom-pom" constitutive equations, J RHEOL, 43(4), 1999, pp. 873-896
A recent constitutive equation derived from molecular considerations on a m
odel architecture containing two branch points a "pom-pom" captures the qua
litative rheological behavior of low density polyethylene (LDPE) in shear a
nd extension for the first time [T. C. B. McLeish and R. C. Larson, J. Rheo
l. 42, 82 (1998)]. We use a hypothetical melt of pom-poms with different nu
mbers 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 non
linear parameters of each mode giving predictions for shear and planar exte
nsion with no free parameters. This process was carried out for data in the
literature and for our own measurements. We find that multimode versions o
f the pom-pom equation, with physically reasonable distributions of branchi
ng, 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 branc
hing in polymer melts. (C) 1999 The Society of Rheology.