Dynamical theory predicted correlation between activated relaxation and thermodynamics in glass-forming liquids

The microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of glassy dynamics, in conjunction with an a priori mapping of thermal liquids to an effective hard sphere fluid, captures the structural relaxation time of nonpolar molecular liquids over 14 decades. We re-visit this theory for monodisperse hard spheres using the modified-Verlet integral equation theory closure as equilibrium input. Comparison with simulation shows the equation-of-state, static correlation lengths, radial distribution function, and structure factor are remarkably well captured up to very high volume fractions. Numerical ECNLE theory calculations then reveal that the logarithm of the alpha time scales behaves as an inverse power law of the dimensionless compressibility which is a thermodynamic property that quantifies the amplitude of long wavelength density fluctuations. The scaling is linear (cubic) in the low (high) barrier regime, establishing an operational link between glassy relaxation and thermodynamics. The predicted connection is directly tested using solely experimental data, and is well verified for molecular liquids. By introducing one adjustable parameter to capture the low to high barrier crossover, experimental data over 14 decades can be linearized.