Theory of thermodynamics of freezing and melting

Freezing of liquids are well known by laymen and are fundamental for many areas of the sciences. We present a theoretical framework for the thermodynamics of freezing [Nature Comm. 7, 12386 (2016)]. Properties of the crystal... [ view full abstract ]

Freezing of liquids are well known by laymen and are fundamental for many areas of the sciences. We present a theoretical framework for the thermodynamics of freezing [Nature Comm. 7, 12386 (2016)]. Properties of the crystal and liquid at a single state-point allow one to predict the coexistence pressure as a function of melting temperature, as well as the variation along the melting/freezing lines of quantities such as the entropy of fusion, the reduced crystalline vibrational mean-square displacement (the Lindemann ratio), the liquid diffusion constant or the viscosity. The fundamental assumption is hidden scale-invariance of liquid and crystalline states. An analytical expression is available for systems of particles interacting via pair potentials that are differences of two inverse power laws. The theory is validated by computer simulations of the freezing and melting properties of the 6-12 Lennard-Jones (LJ) system. The analytical theoretical predictions shown on the figures (red full lines) uses information at a single coexistence state point (T = 2), but does not involve any curve fitting.