Bifurcation to worms in electroconvection

The primary bifurcation to electroconvection of the liquid crystal 4-ethyl-2-fluoro-4^'[2-(trans-4-pentylcyclohexyl)ethyl]-biphenyl (I52) with planar alignment leads to localized structures of convection rolls known as ``worms'' when the conductivity of the fluid is relatively small. Worms coexist with the conduction state. They have a unique small width in the direction perpendicular to the director and a varying, usually much greater, length parallel to the director. Previous experiments had not determined whether the bifurcation to worms is supercritical or subcritical. We estimated the voltage Vc corresponding to the stability limit of the conduction state by measuring the mean-square amplitude of the thermally induced fluctuations below onset and extrapolating to Vc. We found that worms appear already well below Vc. Thus the bifurcation is subcritical. Measurements of the lifetime of the conduction state below Vc gave information about the voltage Vₛ corresponding to the saddle node below which no worms form. We measured Vc and εₛ=Vₛ²/Vc²-1 as a function of the conductance σ for a cell of thickness 24 μm and found for our sample that εₛ approaches zero from negative values near σ1.2×10^-8 Ω^-1m^-1 as σ increases. For larger σ we found the bifurcation to be supercritical. We have been unable to determine so far whether the experimentally observed transition with decreasing σ from a supercritical to a subcritical bifurcation occurs via a tricritical bifurcation, or whether the worm saddle node is disconnected from the primary supercritical bifurcation line as suggested by theory.