Thermal Jamming in Supercooled Liquids

We propose that supercooled liquids can quantitatively be described in terms of thermally jammed states. Our proposition rests on the well-known approach of partitioning a liquid state into a superposition of harmonic oscillators and hard spheres (HS). The fraction f_HS of atoms that comprise the HS partition governs the equivalent packing fraction φ of the hard sphere partition. We postulate that f_HS is inversely proportional to the radial distribution function’s value at the closest contact point for hard spheres, which can be connected to HS diffusion through Enskog’s theory. Using atomistic simulations of three model supercooled liquids, and using an appropriate equation of state for the metastable fluid branch of HS, we show that φ approaches the random-close-packed limit of ~0.64 (φ_c) for all three systems when the temperature is sufficiently lowered. Interestingly, we observe a power-law variation of the diffusion coefficients and f_HS with φ_c - φ that is universal for the three model systems. This universality compels us to view the dynamic slowing down as a property of the system. The vanishingly small f_HS in the limit φ → φ_c suggests an intriguing possibility of describing the glass transition as a consequence of thermal jamming.