Liquid-liquid phase transitions and water-like anomalies in liquids

In this thesis we employ computer simulations and statistical physics to understand the origin of liquid-liquid phase transitions and their relationship with anomalies typical of liquid water. Compared with other liquids, water has many anomalies. For example the density anomaly: when water is cooled below 4 C the density decreases rather than increases. This and other anomalies have also been found to occur in a few other one-component liquids, sometimes in conjunction with the existence of a liquid-liquid phase transition (LLPT) between a low-density liquid (LDL) and a high-density liquid (HDL). Using simple models we explain how these anomalies arise from the presence of two competing length scales. As a specific example we investigate the cut ramp potential, where we show the importance of "competition" in this context, and how one length scale can sometimes be zero. When there is a clear energetic preference for either LDL or HDL for all pressures and temperatures, then there is insufficient competition between the two liquid structures and no anomalies occur. From the simple models it also follows that anomalies can occur without the presence of a LLPT and vice versa. It remains therefore unclear if water has a LLPT that ends in a liquid-liquid critical point (LLCP), a hypothesis that was first proposed based on simulations of the ST2 water model. We confirm the existence of a LLCP in this model using finite size scaling and the Challa-Landau-Binder parameter, and show that the LLPT is not a liquid-crystal transition, as has recently been suggested. Previous research has indicated the possible existence of a LLCP in liquid silica. We perform a detailed analysis of two different silica models (WAC and BKS) at temperatures much lower than was previously simulated. Within the accessible temperature range we find no LLCP in either model, although in the case of WAC potential it is closely approached. We compare our results with those obtained for other tetrahedral liquids and conclude that insufficient "stiffness" in the Si-O-Si bond angle might be responsible for the absence of a LLCP