Effect of pressure on the dynamics of water and other tetrahedral network forming liquids

On decreasing the temperature T , supercooled water and other tetrahedral network-forming liquids, such as BeF2 or SiO2, appear to display a dynamic crossover from non-Arrhenius dynamics (with T -dependent activation energy) to Arrhenius dynamics (with constant activation energy). Simulations for water models show that this crossover occurs on crossing the Widom line TW (P ), the locus of maximum correlation length in the pressure-temperature (P -T ) plane that emanates from a liquid-liquid critical point C ′. Using Monte Carlo simulations of a cell model, we show that the dynamic crossover at TW (P ) is a consequence of a local relaxation process. We calculate the relevant free energy barriers as a function of the probability pB of forming a bond (a hydrogen bond in the case of water) and we recover the relaxation time directly from the free energy associated with breaking a hydrogen bond an reorienting the molecule. We find that the non-Arrhenius to Arrhenius dynamic crossover becomes smoother by increasing P toward the critical pressure PC′ . Hence we conclude that for BeF2 and SiO2, where the crossover is smooth at ambient pressure, the critical pressure PC′ is closer to the atmospheric pressure than for water.