Phase transitions in soft condensed matter physic

Soft matter physics is a rather new and rapidly developing branch in physics; this is certainly due to the fact that soft systems do play an important role in a vast variety of applications that include biological, technological, as well as everyday life aspects: from milk to mayonnaise, from ink to smoke, from paints to lubricants, and from proteins to DNA - soft matter is what we are made of and what we encounter in countless occasions every day. Despite the fundamental role that soft matter plays in our lives, systematic investigations of its properties have been out of reach over many decades which is due to the intrinsic complexity of these systems. Only in recent years special experimental techniques in combination with new theoretical concepts have brought along - in a fruitful cooperation among soft condensed matter scientists - a deeper insight into the intriguing phenomena of these systems. In this project we want to contribute to the development of theoretical concepts to describe a particular class of soft systems, i.e. colloidal dispersions: here complex, mesoscopic particles -- such as polymers, dendrimers, or colloidal particles -- are dissolved in a microscopic solvent. Although statistical mechan-ics offers conceptually an ideal access to describe the properties of such systems, its direct application is prevented by the large number of degrees of freedom and the intricacy of the mesoscopic aggregates. This problem could be solved by introducing coarse graining methods which lead - by aver-aging over a large number of degrees of freedom of these complex particles - to so-called effective inter-actions between `effective` particles, which then depend only on a few degrees of freedom, such as the centers of mass of the complex aggregates. Now, microscopic theories for the solid and the fluid phases can be applied for the systems characterized by these effective potentials. However, this averaging procedure leads to interactions with new and particular features which have far-reaching con-sequences: while potentials in atomic systems are characterized by a strong repulsion at short distances, the interactions of soft systems show only a weak divergence or even remain finite close to the origin which means that the `effective` particles are now allowed to overlap. This leads to many new, intriguing and - above all - unexpected properties and phenomena; their investigation represents a par-ticular challenge both to experimentalists as well as to theoreticians. In our work we plan to proceed in two directions: first, we want to contribute to the development of sta-tistical mechanics based concepts that are able to describe in a quantitative way the structural properties and the phase behaviour of soft systems; this will provide a deeper insight into these new phenomena. From the methodological point of view we shall focus on advanced integral-equation theo-ries and computer simulation techniques for the fluid phase and on classical density functional theory for the solid phase. The concepts we propose take on the one side advantage of expertise of methods developed originally for systems with unbounded potentials, but will require, on the other hand, new methodological developments that take into account particular features of soft systems. In these investi-gations we shall restrict ourselves to model interactions: they are characterized by simple functional forms and a small number of system-parameters but capture, nevertheless the characteristic features of soft systems. Second, we want to develop effective interactions for realistic soft systems - dendrimers and temperature-sensitive core-shell microgels - and to study their properties, in particular their phase behaviour. This part of the project will be carried out in close cooperation with experimental-ists. We hope that our work will contribute to a deeper understanding of the complex and fascinating proper-ties of soft matter and that we will be able to establish a highly actual and rapidly developing scientific field in Austria that offers manifold interdisciplinary contacts.

Soft matter physics is a rather new and rapidly developing branch in physics; this is certainly due to the fact that soft systems do play an important role in a vast variety of applications that include biological, technological, as well as everyday life aspects: from milk to mayonnaise, from ink to smoke, from paints to lubricants, and from proteins to DNA - soft matter is what we are made of and what we encounter in countless occasions every day. Despite the fundamental role that soft matter plays in our lives, systematic investigations of its properties have been out of reach over many decades which is due to the intrinsic complexity of these systems. Only in recent years special experimental techniques in combination with new theoretical concepts have brought along - in a fruitful cooperation among soft condensed matter scientists - a deeper insight into the intriguing phenomena of these systems. In this project we want to contribute to the development of theoretical concepts to describe a particular class of soft systems, i.e. colloidal dispersions: here complex, mesoscopic particles - such as polymers, dendrimers, or colloidal particles - are dissolved in a microscopic solvent. Although statistical mechanics offers conceptually an ideal access to describe the properties of such systems, its direct application is prevented by the large number of degrees of freedom and the intricacy of the mesoscopic aggregates. This problem could be solved by introducing coarse graining methods which lead - by aver-aging over a large number of degrees of freedom of these complex particles - to so-called effective interactions between `effective` particles, which then depend only on a few degrees of freedom, such as the centers of mass of the complex aggregates. Now, microscopic theories for the solid and the fluid phases can be applied for the systems characterized by these effective potentials. However, this averaging procedure leads to interactions with new and particular features which have farreaching consequences: while potentials in atomic systems are characterized by a strong repulsion at short distances, the interactions of soft systems show only a weak divergence or even remain finite close to the origin which means that the `effective` particles are now allowed to overlap. This leads to many new, intriguing and - above all - unexpected properties and phenomena; their investigation represents a particular challenge both to experimentalists as well as to theoreticians. In our work we plan to proceed in two directions: first, we want to contribute to the development of statistical mechanics based concepts that are able to describe in a quantitative way the structural properties and the phase behaviour of soft systems; this will provide a deeper insight into these new phenomena. From the methodological point of view we shall focus on advanced integral-equation theories and computer simulation techniques for the fluid phase and on classical density functional theory for the solid phase. The concepts we propose take on the one side advantage of expertise of methods developed originally for systems with unbounded potentials, but will require, on the other hand, new methodological developments that take into account particular features of soft systems. In these investigations we shall restrict ourselves to model interactions: they are characterized by simple functional forms and a small number of system-parameters but capture, nevertheless the characteristic features of soft systems. Second, we want to develop effective interactions for realistic soft systems - dendrimers and temperature-sensitive core-shell microgels - and to study their properties, in particular their phase behaviour. This part of the project will be carried out in close cooperation with experimentalists. We hope that our work will contribute to a deeper understanding of the complex and fascinating properties of soft matter and that we will be able to establish a highly actual and rapidly developing scientific field in Austria that offers manifold interdisciplinary contacts.