Phase Transitions in Simple Liquids and their Mixtures

Phase transitions in condensed matter physics belong to the most challenging and most fascinating problems in physics. They are practically ubiquitous in our everday lives, ranging from simple, commonplace events to complicated production processes in industry where special knowledge of phase diagrams of the substances involved are required. Therefore a deeper understanding of these phenomena is of a more widespread interest and not only a pure academic problem. In particular, during the past years significant contributions to describe phase transitions in condensed matter physics have been proposed in theoretical or computational physics; meanwhile theoretical concepts in combination with computational tools can be considered as complements to experimental techniques: on the one side they are able to reproduce experimental results with high accuracy and contribute in this way to a deeper insight into these plienomena; on the other side they can sometimes even predict (at least in a qualitative way) results which - due to extreme experimental conditions - are barely accessible in experiment. With this project we would like to contribute (at least a tiny piece) to a deeper understanding of phase transitions. Among the various methods which were proposed to describe these phenomena from a theoretical point of view we have chosen an access, which focuses on the molecular aspect by trying to understand phase transitions from the microscopic point of view. The method we have chosen is based on statistical mechanics, it approaches the problem from the liquid state and can be separated into two clearly distinguishable ingredients, i. e., classical density- functional theory and classical liquid state theory. Classical density-functional theory is based on the reformulation of statistical mechanics in the language of functionals and correlation functions; its essence is that the grand potential of a given system is a unique functional of the (inhomogeneous) one-particle density and that this functional is minimized by the equilibrium one-particle density. Liquid state theories, on the other hand, provide us with information about the structure and the thermodynamics of the homogeneous liquid: these data are required for the liquid phase itself and for the solid phase when the ordered phase is viewed as a spatially modulated liquid. In this project we intend to contribute to both of these two ingredients. We plan to implement two recently developed unified liquid state theories, which - in contrast to "standard" liquid state theories - are able to give reliable results even in the vicinity of the phase boundary and of the liquid-vapour critical point: the "Hierarchical Reference Theory" achieves this goal by integrating concepts of the renormalization-group approach, while the "Self-Consistent Ornstein-Zernike Approximation" requires self-consistency between two thermodynamic routes. Most of the present-day density-functional models are closely related to the Weighted-Density Approximation, where the inhomogeneous density of the ordered phase is mapped onto the homogeneous density of a liquid. We plan to include three-particle correlation functions of the homogeneous liquid and to consider most recent developments in the field of density-functional theory. Applications will primarily be realized for square-well (square-shoulder) systems, i.e., at first sight, for a very simple, but very flexible interaction. However, since such interactions were found to be very useful to describe colloidal suspensions (which - as paints, glues, lubricants, or food - are part of our everyday life), investigations of the phase behaviour of such systems might also be of significant industrial relevance. We plan to consider one- and two-component systems and investigate - among others - also solid-solid, liquid-liquid transitions, or transitions into quasicrystalline structures. We hope to contribute with our work- to a deeper understanding under which conditions specific transitions are possible and to predict with the help of more refined and more sophisticated tools phase transitions more accurately.

Phase transitions in condensed matter physics belong undoubtedly to the most challenging and most fascinating problems in physics. They are practically ubiquitous in our everyday lives, ranging from simple commonplace events to complicated production processes in industry where special knowledge of phase diagrams of the substances involved are required. Therefore a deeper understanding of these phenomena is of a more widespread interest and not only a pure academic problem. In this project we have developed methods based on statistical mechanics that allow a quantitative description of phase transitions: classical liquid state methods (to describe the fluid and the gas phase) and classical density functional theory (to describe the ordered solid phase). The methods developed in our group have been implemented in program packages and allow a very accurate determination of phase coexistence curves and of critical points. In our description of phase transitions we have started at a microscopic level where the system is characterized by the interatomic forces acting between the particles. Using the framework of statistical mechanics we can develop under simplifying assumptions numerical methods that allow the determination of the structural and thermodynamic properties of the homogeneous fluid phase. Classical density functional theory, on the other hand, offers -- in combination with liquid state methods -- an access to describe the properties of inhomogeneous fluids; in this context, the solid is considered as a particular, strongly inhomogeneous fluid. The methods developed in our group and in cooperation with international partners were applied in a first step to test systems, where data from computer simulations were available as reference data. It turned out that the methods are indeed able to predict the coexistence curves and the location of critical points with high accuracy. In particular by enforcing thermodynamic self-consistency, which is realized in the rather involved concepts of advanced liquid state methods, a high accuracy of the data is guaranteed. Finally, these numerical methods were applied to realistic systems, such as colloid-polymer mixtures or fluids that are in contact with a porous matrix; in particular the latter ones are of technological relevance, since adsorption of fluids and gases in disordered solid structures represents an important part of several industrial processes.