Research objectives and content
The subject of the present project is the theoretical analysis and explanation of the structure of colloidal crystals. As a model system the hard sphere fluid will mainly be considered as it is the simplest model which exhibits a freezing transition. We will choose appropriate variants of density-functional theory and apply them to the bulk structure of the hard sphere solid as well as to a solid near a substrate. The stable solid has a close packed fcc or hcp structure. We will focus on the role of the metastable bcc phase, which, according to general symmetry arguments provided by the Landau theory of phase transitions, should be the first solid phase to bifurcate from the liquid. By using the symmetry based Landau theory and bifurcation analysis we will try to find a continuous path from the liquid to the stable solid phase, thereby predicting the equilibrium solid structure. For a colloidal crystal near a substrate sedimentation profiles and structural details in the presence of the wall will be determined from the density-functional theory. Particular attention will be paid to the case of a templated substrate with periodically arranged holes, because it has been shown recently at the host institution that in this way large single crystals can be grown. The repercussions of a lattice constant mismatch between the template and the bulk solid will also be explored. These demanding problems will require large scale numerical minimizations of the density functional. Training content (objective, benefit and expected impact)
During my work in Amsterdam I expect to broaden my expertise in density-functional theory by using new approximations and applying them to new physical problems. I also expect to gain experiences in Landau theory and bifurcation analysis and to obtain increased insight into the possibilities and limitations of computer simulations. This training will allow me to develop a number of skills that are essential in modern theoretical research on complex fluids.
Links with industrv / industrial relevance (22)
Although there is no direct link to the industry, colloids in general are important for a wide range of applications, e.g. in food, pharmaceutical, and detergent industries and in oil recovery. Moreover the colloidal crystals, which I will study from a theoretical point of view in this project, may find new applications in nonlinear optics in the future.