Electrohydrodynamic convection (EHC) in nematic liquid crystals is a crucial model system for the study of spontaneous, non-equilibrium pattern formation in anisotropic systems. To characterize the EHC patterns, I have utilized two nematic samples: 4-ethyl-2-fluoro-4'-[2-(trans-4-n-pentylcyclohexyl)-ethyl]-biphenyl (I52) and a mixture of 65 wt.-% p-butyl-p'-methoxy-azoxybenzene and 35 wt.-% p-ethyl-p'-methoxy-azoxybenzene (Phase 5), filled in standard planar cell. In I52, over certain range of the conductivity, the initial transition leads to two families of counter-propagating oblique modes that loose stability at onset. This is consistent with a stability analysis of the EHC equations, which predict a Hopf bifurcation with four oblique critical wave numbers. The critical voltage, the wave vectors and the Hopf frequencies are measured at different controlled parameters. These experimental observations are in agreement with the standard model and weak electrolyte model of electroconvection. Time evolution of spatial Fourier transform (FT) of a series of these images taken under same controlled parameters are studied using two-wave demodulation technique to extract envelopes. The temporal variation of the amplitudes of these envelopes is periodic between zig and zag modes which is consistent with the theoretical predictions. To study spatiotemporal chaos (STC), four-envelopes of the pattern are extracted by applying 2D spatial Fourier transform and 1D temporal Fourier transform. The temporal variation of the amplitudes of these envelopes is chaotic in space and time. Localized states called `worms' are in existence for another set of parameters at higher frequencies in the conduction regime. In Phase 5, I observed oblique stationary (OS) modes at lower frequencies and normal traveling (NT) modes at higher frequencies during electroconvection. Discontinuous jump in the Hopf frequency is observed from zero to over 20 rad/s as the driving frequency is increased along the threshold curve in the conduction regime. Measurements of the wave vector components also exhibit an abrupt jump in their values at the OS to NT transition regime.

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