Cooperative intramolecular dynamics control the chain-length-dependent glass transition in polymers

The glass transition is a long-standing unsolved problem in materials science. For polymers, our understanding of glass-formation is particularly poor due to the added complexity of chain connectivity and flexibility; structural relaxation of polymers thus involves a complex interplay between intra- and inter-molecular cooperativity. Here we study how the glass transition temperature Tg varies with molecular weight M for different polymer chemistries and chain flexibilities. We find that Tg(M) is controlled by the average mass (or volume) per conformational degree of freedom, and that a `local' molecular relaxation (involving a few conformers) controls the larger-scale cooperative alpha relaxation responsible for Tg. We propose that dynamic facilitation where a `local' relaxation facilitates adjacent relaxations, leading to hierarchical dynamics, can explain our observations including logarithmic Tg(M) dependences. Our study provides a new understanding of molecular relaxations and the glass transition in polymers, which paves the way for predictive design of polymers based on monomer-scale metrics.