Microscopically Based Calculations of the Free Energy Barrier and Dynamic Length Scale in Supercooled Liquids: The Comparative Role of Configurational Entropy and Elasticity

We compute the temperature-dependent barrier for a-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition (RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes (Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 2990), which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko (J. Chem. Phys. 2013, 138, 12A534), which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance a kinetic quantity from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. (Science 2005, 310, 1797) procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.