Classical DFT and liquid-liquid phase transitions

Abstract

This dissertation examines how classical density functional theory (DFT) can be applied to study liquid-liquid phase transitions in simple fluids under confinement. Here, two model system are investigated. The primary focus is on the construction of a DFT for the Jagla fluid which exhibits a liquid-liquid critical point in the bulk phase diagram as well as a density anomaly, and, thus, is a suitable simple model system for water. Furthermore, the effect of confinement by the infinite slit geometry on the liquid-liquid phase transition of colloids in a ternary colloid-polymer mixture is investigated. For this, the Asakura-Oosawa model is applied.

First, we determine the bulk phase diagram of the Jagla fluid by using perturbation theory. We find that the perturbation approaches of Barker and Henderson (BH) as well as of Week, Chandler, and Andersen (WCA) are not suited to obtain the liquid-liquid binodal of the Jagla fluid due the long range of the Jagla interaction potential. Instead, we succeed to compute the gas-liquid and the liquid-liquid binodal of the Jagla fluid using first-order perturbation theory by separating the Jagla potential twice into reference and perturbation part. Based on this, we continue to construct a perturbation DFT for the Jagla fluid, where we follow the route of Sokolowski and Fischer, to be able to describe the inhomogeneous fluid. While our perturbation DFT produces correct density profiles in the infinite slit geometry at high temperatures and not too close to the binodals, it fails at low temperatures where the bulk liquid-liquid critical point of the Jagla fluid is located. Nevertheless, our perturbation DFT performs significantly better than standard mean-field DFT. In a second approach to describe the inhomogeneous Jagla fluid, we try to use Monte Carlo (MC) simulation data of the Jagla bulk fluid to compute an optimized interaction potential which, if applied in standard mean-field DFT, recovers the quasi-exact MC results of the inhomogeneous fluid. We find the density profiles of the MC-optimized DFT in the infinite slit geometry to have improved compared to the results of the perturbation DFT. Especially at state points not too close to the bulk binodals, the agreement between MC and optimized DFT profiles is excellent, even at state points where perturbation DFT produces unphysical oscillations. In the low temperature region, where the bulk liquid-liquid critical point of the Jagla fluid is located, the optimized DFT profiles are at least in the same range as the MC data. It turns out, however, that our optimized DFT fails to predict phase transitions inside the slit caused by the reduction of the wall separation distance, and, thus, is not suited to compute the phase diagram of the inhomogeneous Jagla fluid.

Interestingly, it is also possible to encounter a liquid-liquid transition in a model for colloid-polymer mixtures within the so-called Asakura-Oosawa model, if the polymers are bi- or polydisperse and thus give rise to a second length scale in the effective colloid-colloid interaction. Here, we use the framework of fundamental measure theory (FMT) to describe the bulk mixture as well as the inhomogeneous mixture within DFT. We find that under the confinement of the infinite slit with hard walls, the binodals (gas-liquid and liquid-liquid) are shifted towards higher colloid packing fractions, where the density jump between coexisting phases decreases. The critical points are shifted to higher polymer reservoir packing fractions.