Two types of dynamic crossovers in a network-forming liquid with tetrahedral symmetry

Liquids with tetrahedral symmetry of the first coordination shell often display anomalous thermodynamic and dynamic behaviors. The main reason for these anomalies is that pressurizing such liquids leads to the disordering of this local symmetry by the particles migrating from the second to the first coordination shell. This in some cases may lead to the increase of entropy upon pressurizing and consequently to the volume increase upon cooling, as well as increase of diffusivity upon pressurizing. Under certain circumstances, pressurizing or cooling these substances may lead to a first-order phase transition between two liquids with different local structures, entropies, energies and densities. The liquid-liquid first-order phase transition can end in a liquid-liquid critical point (LLCP). The Widom line, defined as the line of zero ordering field, emanates from the LLCP into the supercritical region. In the vicinity of the LLCP thermodynamic response functions have extrema along different loci that converge to the LLCP and can approximate the Widom line. In particular, the maxima of the specific heat are associated to continuous structural changes in the liquid and, in general, to dynamic crossovers. Here we present a model of a network-forming liquid with tetrahedral symmetry in which each response function has two loci of maxima as function of temperature at constant pressure. One locus has positive slope in the pressure-temperature (P-T) thermodynamic plane, and the other has negative slope. We show that for each locus there is a dynamic crossover in the diffusivity and that the two crossovers are qualitatively different. For the positively sloped locus, occurring at P above the pressure PC of the LLCP, the crossover is from low activation energy at high T to high activation energy at low T. For the negatively sloped locus with P < PC, the crossover is characterized by an increase of activation energy in a certain temperature interval but with similar activation energies at low and high T. Such a behavior has been proposed for water where an apparent glass transition, associated with the increase of the activation energy at high T, could be avoided if the activation energy would decrease in the region where experiments are difficult, the so called “no-man's-land”.