The primary bifurcation to electroconvection of the liquid crystal ${4-\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}-2-\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{o}\mathrm{r}\mathrm{o}-4}^{\prime }$[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 $V_c$ 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 $V_c.$ We found that worms appear already well below $V_c.$ Thus the bifurcation is subcritical. Measurements of the lifetime of the conduction state below $V_c$ gave information about the voltage $V_s$ corresponding to the saddle node below which no worms form. We measured $V_c$ and ${\epsilon }_s{=V}_s^2{/V}_c^2-1$ as a function of the conductance $\sigma$ for a cell of thickness 24 $\mu$m and found for our sample that ${\epsilon }_s$ approaches zero from negative values near $\sigma \simeq 1.2\times {10}^{-8}$ ${\Omega }^{-1}{\mathrm{m}}^{-1}$ as $\sigma$ increases. For larger $\sigma$ we found the bifurcation to be supercritical. We have been unable to determine so far whether the experimentally observed transition with decreasing $\sigma$ 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.

• Received 25 February 1999

DOI:https://doi.org/10.1103/PhysRevE.60.3910