Internal and external colloidal anisotropy : pair interactions, sedimentation, and non-equilibrium lane formation

Abstract

This Thesis is devoted to the theoretical description of anisotropic effects in colloidal systems. We consider both internal anisotropy of the microscopic interactions between colloidal particles and external anisotropy originated from external fields [1–4]. First, we focus on internal anisotropy in hard body models in which the particles are not allowed to overlap. We investigate two-dimensional hard core systems with particles of arbitrary shape. The interaction between two hard particles is characterized by the excluded area, i.e. the area inaccessible to one particle due to the presence of another particle. The magnitude of the excluded area depends on the relative orientation between the two particles and it has a major impact on the bulk phase behaviour of a macroscopic system of hard particles. Using Principal Component Analysis we perform a statistical study of a large collection of excluded areas corresponding to randomly generated particle shapes. The study shows that the magnitude of the excluded area as a function of the relative particle orientation is dominated by global features of the particle shape such as the elongation of the particle. Hence, despite the vast diversity of particle shapes, the variety of possible excluded areas is more restricted. We identify limiting cases of particle shapes that form mesophases with different orientational symmetries. We complement the analysis with Monte Carlo simulations for selected particle shapes showing examples of the validity and the limitations of two-body Onsager-like theoretical approaches to describe hard core systems. Anisotropy can also arise from external fields even if the interparticle interactions are isotropic. A prominent example is colloidal sedimentation, i.e. the equilibrium and migration of colloidal particles in a gravitational field. We develop a theory to study the effect of the height of the sedimentation test tube on the stacking sequence of binary colloidal mixtures. The stacking sequence is the sequence of macroscopic layers that appear under gravity in sedimentation-diffusion-equilibrium. We apply the theory to model binary mixtures and to mixtures of patchy colloids that differ either in the number or the types of patches. Patchy colloids are colloidal particles with anisotropic valence-based bonding interactions. We show that the height of the sample can change the stacking sequence of a colloidal mixture even if all other parameters such as the relative concentrations are fixed. For example, there can be stacking sequences that only appear for certain sample heights. We demonstrate that the sample height, which is often not systematically varied in experimental work, is an important parameter in sedimentation. Besides the sedimentation-diffusion-equilibrium of colloidal mixtures we also consider the dynamics of sedimentation. We investigate an oppositely driven binary colloidal mixture in which two species migrate through each other. We identify three states depending on the driving strength. If the driving strength is low, then the two…