Generalized Entropy Theory of Glass Formation in Graft Polymer Melts Having Variable Grafting Density

Molecular branching, an important characteristic of both synthetic and natural polymers, plays a crucial role in determining the physical properties of polymeric materials. Nevertheless, the mechanisms of how branching affects polymer glass formation are not fully understood. Here, the generalized entropy theory (GET) is extended to study the glass formation of graft polymer melts having variable grafting density. Our theoretical calculations indicate that polymers with a flexible backbone and rigid side chains exhibit opposite trends in the characteristic properties of glass formation compared to other classes of polymers when grafting density is varied, supporting the previous finding that the relative rigidities of backbone and side chains serve as a key factor governing the glass formation of graft polymers. The predictions from the GET are shown to be consistent with molecular dynamics simulation results of a coarse-grained graft polymer melt. Moreover, the GET framework allows us to offer insights into the grafting density dependence of the glass transition temperature (Tg) and fragility (m) from a perspective of packing frustration. Remarkably, the GET predicts universal relations between the change in the extent of collective motion at Tg relative to the polymer fluid in the Arrhenius regime and both Tg and m.