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/H̅_c, where B is a material-dependent constant and H̅_c is the difference between the liquid and glassy enthalpies which are determined from experimentally measured heat capacity data. The 1/H̅_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/U̅_c (internal energy) and 1/TS̅_c (entropy) models were examined. The 1/TS̅_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/U̅_c model has slightly worse predictions at elevated pressures than the 1/H̅_c model, where better high-pressure data are needed to clearly discriminate between the 1/H̅_c and 1/U̅_c models. The implications of the 1/H̅_c model describing the super-Arrhenian mobility in glass-forming polymers are discussed.