Unified Theory of Activated Relaxation in Liquids over 14 Decades in Time

We formulate a predictive theory at the level of forces of activated relaxation in hard-sphere fluids and thermal liquids that covers in a unified manner the apparent Arrhenius, crossover, and deeply supercooled regimes. The alpha relaxation event involves coupled cage-scale hopping and a long-range collective elastic distortion of the surrounding liquid, which results in two inter-related, but distinct, barriers. The strongly temperature and density dependent collective barrier is associated with a growing length scale, the shear modulus, and density fluctuations. Thermal liquids are mapped to an effective hard-sphere fluid based on matching long wavelength density fluctuation amplitudes, resulting in a zeroth-order quasi-universal description. The theory is devoid of fit parameters, has no divergences at finite temperature nor below jamming, and captures the key features of the alpha time of molecular liquids from picoseconds to hundreds of seconds.