Liquid Crystal Colloids

Colloids Shape Liquid crystals are known for their anisotropic mechanical and optical properties which originate from the long-range orientational molecular ordering. If a liquid crystal is used as a host liquid in a colloidal suspension, this ordering gives rise to long-range effective interactions between the colloidal particles. The type of the interaction is controlled by the presence and symmetry of topological defects in the alignment field of anisotropic liquid crystal molecules. Particles clustering, formation of superstructures, and even new phases are immediate consequences of these anisotropic interactions.

For these liquid crystalline systems molecular structure of the host liquid is usually not important, and often a continuum description of liquid crystals is used. Several continuum models, each characterized by its own order parameter, such as the director field, tensorial order parameter, or particle density exist and describe phenomena occurring on a particular length-scale. We base our study on the Landau-de Gennes model with tensorial order parameter. This formalism is applicable for intermediate distances between colloidal particles, where nonlinear effects become important. Liquid crystal colloids are characterized by widely separated length scales (the particle's size and the nematic correlation length). In order to resolve this problem we use adaptive finite elements methods in order to minimize the corresponding Landau-de Gennes free energy functional and obtain the equilibrium nematic configurations around particles.

With this technique at hand we analyze the structure of topological defects as a function of boundary conditions at particles surfaces, particles size, shape and topology, temperature or anisotropy of elastic constants. We are also studying nematic-mediated effective interaction between two colloidal particles and the role played by the topological defects at the intermediate particle-particle separations. In particular, topological defects which often accompany colloids bind colloidal particles into "colloidal molecules" via defects-sharing mechanism an analogue of a covalent bond in atomic systems.
 
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