Patterns of electroconvection in a nematic liquid crystal

We present a survey of pattern formation in electroconvection of the nematic liquid crystal 4-ethyl-2-fluoro-4'-[2-(trans-4-pentylcyclohexyl)-ethyl] biphenyl (I52) as a function of three control parameters: the applied voltage, applied frequency, and electrical conductivity of the sample. The patterns are dominated by oblique-roll states. Over the lower range of conductivity, the initial transition is a supercritical Hopf bifurcation which leads to four degenerate modes: right-and left-traveling zig and zag rolls. For higher values of the conductivity, the primary instability is a subcritical bifurcation to a single set of stationary oblique rolls. The convecting states exhibit a rich variety of patterns as a result of the interactions between the four modes, including states of spatiotemporal chaos and localized states.