Kolloidale Dispersionen in nematischen Flüssigkristallen

Abstract

This thesis shows that the wetting of a colloidal surface by a nematic liquid crystal with planar surface-anchoring leads to a configuration of two or four topological defects which are, respectively, located on the opposite poles of the colloid or on the corners of a tetrahedron. The tetrahedral configuration opens the prospect of tetravalent colloidal bonds corresponding to the bonds of the sp3 hybridised carbon atom, which could be realised with linker-elements like DNA molecules. In order to determine the orientational order of the liquid crystal molecules represented by a three-dimensional order-parameter tensor field, Euler-Lagrange equations are derived by minimising the Landau-de Gennes free energy, which are then solved numerically by means of the Newton-Gauss-Seidel method combined with the method of adaptive grids. In order to create a preferred orientational axis and thus to allow for the existence of defects, a biaxial-oblate orientational order is necessary. Hence wetting transitions from the uniaxial to the biaxial phase are first studied on a plane surface for different surface potentials. The investigations are then expanded to the case of spherical surfaces. Finally the thermodynamic stability of the different defect configurations is analysed.