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Effect of the Geometry of Colloidal Particles on Nematic Liquid Crystals

Hashemi, Masoumeh | 2016

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 49134 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza; Mozaffari, Mohammad Reza
  7. Abstract:
  8. A liquid crystal is a state of matter composed of highly anisotropic building blocks. When liquid crystals are exposed to surfaces with given shapes and anchoring conditions, the orientation of their molecules gets spatially disordered and topological defects may form in the system. The interplay between liquid crystals and the geometry and topology of the colloidal particles has motivated extensive recent studies.In this thesis, we present the numerical modeling results for two faceted colloidal particles in a thermotropic nematic liquid crystal. To obtain the equilibrium nematic field with a finiteelement method, we numerically minimize the free energy of the system that based on the Landau-de Gennes model is a summation over a free energy for the isotropic-nematic phase transition, an elastic free energy, and an anchoring free energy.Firstly, we investigate the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. We show that the equilibrium state of this colloidal geometry is sensitive to two geometrical parameters: Aspect ratio and length scale of the particle. Particles with radiuses from 20 nm to 400 nm and aspect ratios ranging from 1/6 to 8/1 are investigated.We show that the equilibrium angle that is about 90 degrees for long rod-like colloidal particles, ultimately reaches about 0 degrees for thin discotic particles. Thus, when the equilibrium angle is about 0 degree for a thin discotic particle with aspect ratio 8/1 and 55 ± 5 degrees for a particle with aspect ratio 1/1, it increases to 85 ± 5 degrees for a long rod-like particle. cherefore, for a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. The equilibrium behavior of nanoparticle with the radius of about 20 nm differs remarkably from mesoparticle, in such a way that the equilibrium angle tends toward 0 degree for nanodiscs with aspect ratio larger than 1/1 but it goes to 90 degrees for nanorods with aspect ratio smaller than 1/1. A veriaty of defect shapes are also reported for different sizes of colloidal particles.We have also shown geometry-induced formation of fractal topological states in Koch fractal nematic colloids. THe Koch fractal confinement results in the formation of local compensating pairs of topological defects with winding numbers ±1/2 in such a way that a power-law relation between the number of the pair defects, that reaches to about a few 100 defects for Koch fractal iteration four, and the Koch iteration is found. Besides, self-similarity functions are introduced for the nematic director and the scalar order parameter to quantify the fractal self-similarity of the nematic order and show self-similarity better than 90%. between nematic orders of the structures
  9. Keywords:
  10. Liquid Crystal ; Nematic ; Colloid ; Topological Defect ; Landau De-Gennes Energy ; Non-Spherical Drops

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