A Quantitative Model of Super-Arrhenian Behavior in Glass-Forming Polymers

The super-Arrhenian temperature dependence of the mobility is a key signature of glass-forming polymers, where the mobility can decrease by 10 orders of magnitude or more as the temperature is decreased toward T-g. A fundamental description of the super-Arrhenian behavior has been developed, including the pressure dependence of the mobility. Specifically, the log a mobility is proportional to B/(H) over bar (c), where B is a material-dependent constant and (H) over bar (c) is the difference between the liquid and glassy enthalpies which are determined from experimentally measured heat capacity data. The 1/(H) over bar (c) mobility model has two material parameters and quantitatively describes the temperature and pressure dependence of the mobility for 12 glass-forming polymers, which are the only polymers where there is sufficient experimental data for analysis. Similar configurational-based B/(U) over bar (c) (internal energy) and 1/T (S) over bar (c) (entropy) models were examined. The 1/T (S) over bar (c) model, which is the traditional Adam-Gibbs model, can describe the 1 atm data but cannot describe the elevated pressure mobility data, and the 1/(U) over bar (c) model has slightly worse predictions at elevated pressures than the 1/(H) over bar (c) model, where better high-pressure data are needed to clearly discriminate between the 1/(H) over bar (c) and 1/(U) over bar (c) models. The implications of the 1/(H) over bar (c) model describing the super-Arrhenian mobility in glass-forming polymers are discussed.