title: Internal and external colloidal anisotropy : pair interactions, sedimentation, and non-equilibrium lane formation
Creators: name: Geigenfeind, Thomas
Publisher: name: University of Bayreuth
Year: 2019
Subjects: subject: Statistische Physik
subject: Kolloide
subject: Nichtgleichgewicht
subject: Sedimentation
subject: Laning
subject: Paarwechselwirkungen
subject: Anisotropie
subject: 530

description: 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 species diﬀuse through each other without any ordering eﬀects. At suﬃciently high driving strength, however, the two species demix and form dynamic lanes along the direction of the driving. For intermediate driving strengths the two species can block each other and form a quasi-static jammed state. Using Brownian dynamics simulations, we sample all the contributions to the one-body force ﬁeld due to the internal interactions, the external ﬁelds, and the thermal diﬀusion. Of particular interest is the internal force ﬁeld, which we split into adiabatic and superadiabatic contributions. The adiabatic contribution is obtained by sampling a reference equilibrium system with the same one-body density as the non-equlibrium system. We demonstrate that laning is a purely superadiabatic eﬀect and identify a speciesdependent structural superadiabatic force that counteracts the entropy of mixing of both species. In addition, we develop a Power Functional Theory based on a velocity gradient approximation that reproduces the observed phenomenology. As a practical example of self-assembly in a non-equilibrium colloidal system with both internal and external anisotropy we consider a system of patchy colloids with three patches adsorbed on a surface patterned with a square lattice of external potential wells. We investigate the eﬀect of the width of the potential wells on the relaxation of a homogeneous state of patchy colloids. A competition between the potential energy of the cores, which is minimized if the particles aggregate in close packing near the centers of the potential wells, and the bonding energy of the patches, which is minimized if open networks with low packing fraction are formed, determines the dynamics of the system. For very narrow potential wells a close packed structure with six-fold symmetry is formed, whereas for wide potential wells the three-fold symmetry of the bonding sites of the patchy colloids leads to the formation of an open network. For intermediate widths a core-shell structure with a six-fold core and a three-fold shell appears. The relaxation times associated with the formation of both structures are signiﬁcantly diﬀerent, which can be used to dynamically control the self-assembly.