Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T_g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T_g. Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.