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 wit h the conduction state. They have a unique small width in the direction per pendicular to the director and a varying, usually much greater, length para llel to the director. Previous experiments had not determined whether the b ifurcation to worms is supercritical or subcritical. We estimated the volta ge V-c corresponding to the stability limit of the conduction state by meas uring the mean-square amplitude of the thermally induced fluctuations below onset and extrapolating to V-c. We found that worms appear already well be low 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 co rresponding to the saddle node below which no worms form. We measured V-c a nd epsilon(s) = V-s(2)/V-c(2) - 1 as a function of the conductance sigma fo r a cell of thickness 24 mu m and found for our sample that epsilon(s) appr oaches zero from negative values near sigma similar or equal to 1.2 x 10(-8 ) Omega(-1) m(-1) as sigma increases. For larger sigma we found the bifurca tion to be supercritical. We have been unable to determine so far whether t he experimentally observed transition with decreasing a from a supercritica l to a subcritical bifurcation occurs via a tricritical bifurcation, or whe ther the worm saddle node is disconnected from the primary supercritical bi furcation line as suggested by theory. [S1063-651X(99)06010-9].