Phase behaviour and criticality in simple liquids

Phase transitions are practically ubiquitous in our everyday lives, ranging from simple, commonplace events to complicated production processes in industry where an accurate knowledge of the phase diagrams of the substances involved is required. Therefore investigations dedicated to a deeper understanding of these phenomena are motivated not only by purely academic reasons; also from the technological point of view there is considerable interest in this problem. However, the (microscopic) processes that are responsible for phase transitions and criticality are very complex so that a theoretical description of these phenomena represents one of the most challenging and most fascinating problems in physics. The development of concepts that are able to give quantitatively accurate results for phase transitions and critical phenomena in fluids (and their mixtures) has been representing a central objective of statistical mechanics over the last decades. Renormalization group is undoubtedly one of the most successful tools to study cooperative phenomena in statistical mechanics and has lead to a deeper understanding of phase transitions and critical phenomena; however, non-universal quantities (such as the critical temperature) cannot be determined. Computer simulations represent another access to the problem: here one is faced in particular in the critical region with the conflict between diverging (thermodynamic) quantities and the finite volume of the simulation cell; sophisticated techniques are meanwhile available to cope with this problem in a very satisfactory way. Finally, there is the group of microscopic liquid state theories: their aim is to describe the phase behaviour and criticality starting from the microscopic properties of the system. Although results for non-universal quantities axe now within reach, most of the (conventional) liquid state theories suffer, unfortunately, from the fact that they are not able to properly include those complex microscopic processes that are responsible for phase coexistence and critical phenomena. In an effort to overcome the drawbacks of these conventional concepts, particular effort has been dedicated during the past two decades to develop advanced liquid state theories that remain successful even in the critical region. In the present project we intend to contribute to the development of two of such microscopic approaches: the hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA). These two concepts cope with the problems encountered near criticality and near phase boundaries with different ideas: the HRT merges concepts of renormalization group theory with liquid state methods, while the success of the SCOZA can be traced back to its internal (thermodynamic) self-consistency. Both methods are indeed able to describe with high accuracy how non-universal quantities depend on the microscopic properties of the system which leads to a deeper insight into the complex mechanisms that govern phase behaviour and criticality. In this project we plan to contribute to extensions of the two liquid state methods, we propose some amendments of the respective concepts, and we test these modifications in realistic applications or in direct comparison with data obtained via other theoretical concepts.

Since phase transitions represent such a natural part of our daily life one hardly ever poses the question which processes are after all responsible for these fascinating phenomena. From the researcher`s point of view a quantitative description of phase transitions and criticality represents, however, a considerable challenge. It was the aim of the present project to contribute to the development of theoretical concepts that allow a quantitative prediction of the phase diagram of simple fluids. Our concepts are based on statistical mechanics, i.e., we consider the problem from a microscopic point of view. And indeed, we were able to propose and to develop methods that can contribute to a deeper understanding of these complex phenom-ena. With our concepts we can predict the phase diagram of a wide class of simple fluids very accurately. This refers not only to the localization of the stability regions of the phases but also to a reliable description of the critical behaviour. In particular for binary mixtures, which show - compared to one component fluids - a considerably richer and more complex phase behaviour we succeeded in describing critical phe-nomena that had not been investigated in literature up to date. New and surprising results that were obtained in the highly actual field of soft matter physics during the run of the project motivated us to extend our expertise also to these fascinating systems. Apart from atomic fluids we thus started to include also colloidal dispersions in our investigations. They are composed of mesoscopic parti-cles (such as dendrimers, polymers, or microgels) that are characterized by a rather complex but loose internal structure and that are suspended in a microscopic solvent. The interparticle potentials of soft matter systems show completely different proper-ties than those of atomic (`hard`) particles. In particular, their interactions are only very weakly repulsive at short distances, expressing thus the fact that they can over-lap or even intertwine. This characteristic difference is one important reason why many properties in soft matter are distinctively different from those of hard matter. In our studies we have focused on the phase behaviour of particular soft matter sys-tems. Using model systems we could show that they behave under pressure com-pletely different than one would expect from our experience with hard matter. For instance, we predict for microgels a re-entrant scenario: with increasing pressure the fluid becomes solid but remelts again at higher densities. Further, we dedicated activ-ties to study the clustering transition, a phenomenon, that has not been investigated in literature on a quantitative level: particular soft systems start to form clusters upon compression which arrange themselves with increasing pressure on regular lattices. The obviously unlimited possibilities to influence the properties of soft matter systems in a suitable synthesis process let us await many further surprising and unexpected phenomena. The expertise that we have acquired in this project provides a sound basis to contribute to this exciting field also in the future.