Phase transitions and correlations in complex fluids

The description of physical systems as liquids or magnets starts from simple models like a system of movable spheres interacting with a distance dependent potential or elementary magnets (spins) sitting on a lattice with an interaction only dependent on the direction of these spins. Even in such simple models a rich phase behavior can be observed and the description of this is difficult. Before one applies such models to real systems one has to clarify what the model itself can accomplish and which properties can be analytically described. The first point can be checked by simulations (Mont Carlo simulations or molecular dynamic simulations), the last point is studied by using analytic approximation methods like integral equation methods for liquid systems. But even then one gets a system of equations which can be solved only numerically but from the results one can get ideas what is important for a certain phase or at a certain phase transition. At special points, lines or surfaces in the thermodynamic phase space, depending on the topology of the phase diagram, one finds special phase transitions where physical quantities behave singular. For example the thermal conductivity of a liquid diverges at the critical point. The description of such a behavior needs special renormalization group theoretical methods, since the system loses its typical length- and time scales at this special point. In this project starting from earlier development made by the project group and results of others complex systems like magnetic liquids and mixtures, ionic solutions (charged liquid particles), mixtures of He3 and He4 , which show a superfluid phase and a tricritical line, but also solid state systems like ferro- and antiferromagnets will be studied. We consider static and dynamical properties of these systems. The goal of the project is on the one hand to explain quantitative experimental results (e.g. the temperature and concentration dependence of transport coefficients in He3 -He4 mixtures near the tricritical point, or the dynamical structure function in ferro- and antiferromagnets near the Curie and Neel point, respectively, or the excitations in magnetic ionic or dielectric liquids) on the other hand the methods used should be developed (e.g. the method of integral equations in order to achieve better thermodynamic consistency).

The project `Phase transitions and correlations in complex fluids` studies static and dynamical properties of fluids, whose constituting molecules have not only translational degrees of freedom but also additional internal degrees of freedom. Already pure systems show several phases and one of the interesting problems is the formation and behavior of the surfaces separating two such phases. Such interfaces constitute an inhomogeneity and require the extension and development of new analytic and computational methods for their analysis. Moreover when the internal degrees of freedom can be controlled by an external field their influence on the fluid properties is of great importance. `Complex` situations also arise when mixtures of liquids are considered. The dynamics of such systems has been studied over a wide range of length and time scales. In the hydrodynamic region the transport coefficients like diffusion or viscosity are of interest. In a wider range the excitations and their energy have been calculated besides thermodynamic quantities like compressibility or specific heat. Thus analytical methods developed for pure systems have been extended to describe ternary mixtures representing a complicated system of interacting modes. An interesting fundamental system is represented by a two component mixture of fluids differing only in their mass but interacting with the same potential. By choosing the value of the mass ratio and the concentration one can cross over from a pure liquid to a liquid in a random matrix of fixed particles. The dependence of the mixture properties on the mass ratio and the concentration has been studied and Stokes` law was found for the relation between the mass diffusion and the viscosity. `Complex` behavior is found when more than two phases meet at a so called multi-critical point. Then one has to treat more than one fluctuating quantity in order to find out the correct singular behavior of the properties of a system when one approaches this multicritical transition point. A longstanding problem of such kind is the temperature dependence of the mass diffusion in He3- He4 mixtures near the superfluid transition. We have contributed to this problem by extending the theoretical approach used so far but no final solution could be found. Several different theoretical approaches had to be used in this research. In order to test analytical results obtained by solving integro-differential equations of many body theory computer simulations have been performed. These covered Monte Carlo simulations as well as molecular dynamic simulations. For the study of critical phenomena field theoretic renormalization group methods had to be used.