Modeling the principal amorphous halo in quiescent melts of polyethylene and ethylene copolymers using wide-angle X-ray scattering and its implications

Wide-angle X-ray scattering (WAXS) studies of the melts of polyethylenes indicate that the low-angle amorphous halo (LAH) retains “sensible” information regarding the liquid state, which can be used to model the amorphous fraction in the semicrystalline state. The LAH was found to consist of a temperature-independent and a temperature-dependent region. A linear relationship was observed for the temperature dependence of the LAH peak value below 135 °C in branched ethylene copolymers, and was found dependent on comonomer concentration. When combined with group contribution theory, a simple model of average intermolecular separation determined from the WAXS–LAH peak value is consistent with free volume considerations, both with respect to predicting Tg(∞) and the free volume expansion coefficient. The polyethylene, without branches, shows a different behavior in the region 131–160 °C. A semiquantitative method is proposed to model the scattering from the LAH for use in the phase analysis of the copolymers through the separation of the temperature-dependent (intermolecular) and temperature-independent (intramolecular) fractions.