Experimental evidence of predicted dynamics-structure-thermodynamic correlation 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 alpha relaxation time of nonpolar molecular liquids over 14 decades. We have re-visited this theory for monodisperse hard sphere metastable fluids using the modified-Verlet closure integral equation theory as structural input. Simulation comparisons show the equation-of-state, correlation lengths, radial distribution function, and structure factor are remarkably well captured. Numerical ECNLE theory calculations then predict the logarithm of the alpha time scales as an inverse power law of the dimensionless compressibility, 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 via pair structure (J.Phys.Chem.B,124, 6121 (2020)). 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.