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.