Fluctuations and spatio-temporal chaos in electroconvection of nematic liquid crystals.

摘要

We have studied two fundamental issues in driven nonequilibrium systems using electroconvection in nematic liquid crystal I52 and N4.; We first report experimental results for electroconvection of the nematic Liquid Crystal I52 with planar alignment and a conductivity of 1.0 x 10-8 (Om)-1. The cell spacing was 19.4 mum and the driving frequency was 25.0 Hz. Spatio-temporal chaos consisting of a superposition of zig and zag oblique rolls evolved by means of a supercritical Hopf bifurcation from the uniform conduction state[14]. For small &egr; ≡ V2/V2cFsF - 1 (V is the applied voltage amplitude and Vc the value of V at the onset of convection), we measured the correlation lengths of the envelopes of both zig and zag patterns. These lengths could be fit to a power law in &egr; with an exponent smaller than that predicted from amplitude equations. The disagreement with theory is similar to that found previously for domain chaos in rotating Rayleigh-Benard convection [82].; In the following part, we developed a way to measure local current fluctuations in electroconvection. Several special cells were made and each cell had a small local detecting electrode. The detecting electrodes were squares of width 8. 16. 32, 48 and 128 mum at the center of one of the two large electrodes. The spacing of these cells was close to 20 mum. We used the NLC Merck phase IV (N4) with planar alignment. When the driving &egr; was from 0.8 to 6, we found that the distribution of the current fluctuations was strongly skewed towards larger values for detecting electrodes smaller than the cell spacing and slightly skewed towards smaller values for the rest of the cells. This is compared with global current-fluctuation measurements in similar cells which showed a Gaussian distribution. For the small electrodes, large fluctuations that extended below the current expected for the conduction state were found and a possible connection with the Gallavotti-Cohen Fluctuation Theorem is discussed.; This dissertation and all the supporting materials are also available on my dissertation webpage [151]. For some large files which are not printed in this dissertation, the reader should refer to this webpage.