Density anomaly and liquid-liquid transition from perturbation theories

Abstract

We report on theoretical results concerning the relation between the liquid-liquid transition and the density anomaly for a family of ramp potentials (hard-core plus linear short range repulsion and linear long range attraction). Using first order perturbation, we have studied the influence of the range of the attractive interactions, taking the repulsive part of the interaction as the reference system. Two different mechanisms of liquid-liquid coexistence have been predicted: attraction and compression. The attractive case is attributed to long ranged potentials, while the second one is obtained when the interaction is shortened. The density anomaly appears linked to regions where the temperature derivative of the density derivative of the energy is bigger (in absolute value) than a limit. This condition is fulfilled when the range of the attractive part of the potential is short enough.

Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly

“…The main qualitative difference with the case of squared potentials is that the continuous potential shows the density anomaly, typical of network-forming liquids such as water, and observed in other soft-core potentials [39,40,41,43,44,45,46,47,48]. Further investigation is necessary to understand how the appearance of this anomaly is related to the parameters of the potential.…”

“…The reason is twofold. On the one hand, within acceptable limitations, they are models for a variety of systems including liquid metals, metallic mixtures, electrolytes, colloids and protein solution, as well as anomalous liquids, like water and silica [30,31,32,33,34,35,36,37,38,39,40,41]. On the other hand, their simple definition encourages to investigate the possibility of an intriguing relation between the liquid-liquid phase transition and the anomalies in specific observables, such as the density or the diffusivity, in network-forming liquids, like water and silica.…”

Phase diagram of a two-dimensional lattice gas model of a ramp system

“…Since then, a good number of works have been devoted to the continuous ramp potential. 19,20,21,22,23,24 Other simple models with competing ranges of interaction, such as the hard-sphere square shoulder-square well potential have also been shown to exhibit LL equilibria. 25 But not only continuous models can furnish an illustrative qualitative picture of the phase behavior and various anomalies found in water and related systems.…”

Which Shape Characteristics of the Intermolecular Interaction of Liquid Water Determine Its Compressibility?

“…Toward this aim, a number of core-softened and simplified models have been put forward and used to perform numerical simulations. None of them [20][21][22][23][24][25][26][27][28][29][30][31][32]., however, has quantitatively reproduced any anomaly of liquid water or elucidated the thermodynamic mechanisms that cause the anomaly. The author believes that the self-consistent Ornstein-Zernike approximation (SCOZA) with hardcore repulsion plus Yukawa tails is presently the most useful.…”