Phase-behaviour in polydisperse liquid mixtures

Research project P 14371 Phase-behaviour in polydisperse liquid mixtures Gerhard KAHL 08.05.2000 Colloidal systems are suspensions of mesoscopic particles (of typically 10-4 to 10-8 m in size) in a matrix of microscopic size and represent hence a very complex system; however, by averaging out the degrees of freedom of the suspending fluid colloids can be considered as an effective one-component system where the particles behave like large idealized atoms. The renewed interest in colloid physics during the past years has several reasons. One of them is certainly the attractive feature that the interactions between colloidal particles can be `tuned`: by modifying the properties of the solvent the, shape of the interaction can be modified, which leads to an incredibly rich variety of phase behaviour. Further, experiments that possibly axe difficult to be performed on a microscopic scale can now be done on a more favourable length scale and liquid state theoreticians are able to apply a large number of successful frameworks that have been developed during the past decades to study the properties of liquids. Colloids are, in addition, not only of purely academic interest, they are part of our daily life: glues, paints, lubricants, foods, or pharmaceutics are everyday examples for colloids; and finally, industry has realized that the fundamental understanding of model systems can contribute to a better understanding of complex, technologically relevant systems. Due to their production process colloidal particles are - in contrast to atomic liquids - polydisperse in size (and hence in their interactions). This certainly makes their phase behaviour even more rich and more interesting: for instance, theoreticians have predicted recently for a system of polydisperse hard spheres a reentrant melting beyond the liquid/solid transition. On the other side, polydispersity complicates a straightforward application of standard liquid state methods. With this project we would like to contribute (at least a small piece) to the development of liquid state methods that allow the calculation of structural and thermodynamic properties of polydisperse liquid mixtures; this knowledge should lead to a deeper understanding of the phase behaviour of these fascinating systems. During the past years successful frameworks have been developed which view polydisperse systems as mixtures with an infinite number of components. We plan to merge these concepts with standard liquid state theories that were developed during the past decades: these methods will lead to a reliable and accurate description of the structure and thermodynamic properties of polydisperse systems. The development of these tools is in particular important when we proceed to the next step, i.e., the study of their phase behaviour. At present it does not seem clear how many phases can coexist in polydisperse systems, and there is evidence from experiments that often only a small number of phases is involved, i.e., that many degrees of freedom that are available are not actually used. In a fir,5t step we will hence restrict ourselves to two- or three-phase equilibria; we also plan to include in our work modern concepts, such as the moment-method that was proposed recently. While liquid state theories provide us with information about the homogeneous gas and liquid phase, the solid state is commonly viewed as a highly inhomogeneous, highly ordered liquid: classical density functional theory (which has to be generalized to the case of the polydisperse mixture) has become an indispensable tool for this task and helps us to study liquid/solid or solid/solid transitions. Equipped with these methods we intend to investigate the rich phase behaviour of a polydisperse system: reentrant melting or fractionation effects are only two examples of interesting features encountered in their phase diagrams.

Particles of mesoscopic fluids are, in contrast to atomic systems, polydisperse in their properties; this means that their characteristic features vary within certain limits. This is, even though often undesired, a consequence of their production process, since the particles themselves are complex aggregates built up by several thousands of atoms or molecules. Since dispersions of mesoscopic particles are ubiquitous in our every day life and, above all, do play an important role in technological processes, theoretical and experimental investigations of their properties are certainly not only of purely academic interest. Soon it was realized that polydispersity does have a distinct influence on the properties (i.e. structure, thermodynamics, and - above all - phase behaviour) of such systems. In the present project we wanted to contribute by means of theoretical methods to a qualitative and - if possible - quantitative understanding of the influence of polydispersity on the properties of polydisperse fluid mixtures: we intended to perform both basic investigations of their phase behaviour and to study realistic systems, with the aim to compare theoretical and experimental data. Our investigations started from a microscopic picture of the fluid; statistical mechanics then forms the link to the macroscopic properties (structure and thermodynamics). Even though we had to discard our original concept, a thermodynamic perturbation theory, to solve the problem due to unsurmountable numerical difficulties, we were able to propose an alternative approach, which turned out to be very successful. Finally we were able to predict - within a reasonable amount of computational effort - the complete phase diagram for particular polydisperse mixtures in a quantitative way. We could also determine polydispersity of the coexisting daughter phases: this leads to predictions of fractionation effects, which, in turn, are relevant in technological processes. With this approach we are now able to perform systematic investigations of the phase behaviour of polydisperse mixtures: quantitative comparisons with results from computer simulations and with experimental data are planned for the near future. We have also studied the properties of two mesoscopic suspensions, of star polymers and of charged microgels. It turned out that such systems show - in contrast to atomic fluids - a very surprising phase behaviour: upon compression they can remelt and are, in addition, characterized by rather unusual crystal structures in the solid phase. We plan to pursue our investigations in this very promising field, where certainly further unexpected features are to be awaited; these investigations will be carried out in close cooperation with experimental groups.