Modeling the Glass Transition in Polymers using a Mean-Field “TS2” Model: Bulk and Thin Films

A phenomenological model is proposed to describe the equilibrium dynamic behavior of amorphous, glass-forming polymers. We postulate that a material can be represented by a lattice of cooperatively re-arranging regions (CRR), with each CRR having two states, the low-temperature “Solid” and the high-temperature “Liquid”. At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion involving multiple “solid” CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the “Coupling Model” framework. This approach is labeled “Two-state, two (time)scale model” or TS2. We show that the TS2 treatment can successfully describe the low-temperature Arrhenius a-relaxation time behavior described in several recent experiments. We also apply TS2 to describe the molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.