Anharmonic dynamics: melting and mass transfer in liquid

In view of the anharmonic model of the lattice vibrations, the origin and development of the chaotic motion in the condensed state are analyzed. The distribution function for the instantaneous local mode is obtained which is used then to calculate the unstable mode fraction and mean-square translational velocity. The transition to the liquid dynamics is discussed and the expression for the temperature of melting is derived. The analytical expressions for both self-diffusion coefficient and viscosity connecting these quantities with the unstable mode fraction and mean-square translational velocity (for the diffusion) are obtained. The temperature dependencies of both the self-diffusion and viscosity coefficients of water and corresponding isotope effects are described in excellent agreement with the experiment over the wide temperature interval including both the supercooled and overheated states. It is shown the isotope effects on both properties are defined by the mass ratio. The pressure dependencies of the viscosity calculated at various temperatures reproduce the actual dependencies rather well.