a Study in Pattern Formation: Electroconvection in Nematic Liquid Crystals.
Abstract
I have studied fundamental issues in pattern formation using electroconvection in the nematic liquid crystal I52. An electroconvection cell consists of a nematic liquid crystal, which is doped with ionic impurities, confined between two glass plates which have transparent electrodes on their inner surfaces. The electrodes are used to apply an ac voltage perpendicular to the plates. By appropriate surface treatment of the glass plates, the average molecular alignment (the director) is made to be parallel to the plates. The nematic liquid crystals which are used for electroconvection typically have a negative dielectric anisotropy. As part of this thesis, I will provide a detailed prescription for the making of electroconvection cells. Above a critical applied voltage V_ {c} and below a critical applied frequency (the Lifshitz point), there is an instability to a spatially varying state with a wavevector at a nonzero angle Theta {rm or} pi -Theta to the director (oblique rolls, the two states are degenerate). The state can either be traveling (Hopf bifurcation) or stationary. The experimental results are divided into three sections. The first section presents experimental measurements of the critical voltage, the angle between the director and the wavevector of the pattern, and the traveling frequency of the pattern. Comparison of the experimental observations with a detailed linear stability analysis carried out by Martin Treiber and Lorenz Kramer is made, and the agreement between the theory and experiment is found to be good. The second section presents observations of states of spatio-temporal chaos which occur as the initial state above V_{c}. I observe both states which are extended in space and localized states. These states involve the interaction of four modes: right- and left-traveling oblique rolls. The third section summarizes the wide variety of patterns which are observed well above V_ {c}. I report on the existence of the observed patterns as a function of conductivity of the cell, applied voltage, and applied frequency. Also, I discuss the nature of the transitions between the different patterns.
- Publication:
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Ph.D. Thesis
- Pub Date:
- January 1995
- Bibcode:
- 1995PhDT.......110D
- Keywords:
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- Physics: Condensed Matter