Chaos near the onset of electroconvection of a homeotropic nematic liquid crystal

We report on shadowgraph measurements of spatio-temporal chaos patterns of electro-convection in the homeotropically aligned nematic liquid crystal MBBA. The cell had a thickness of $27$ $\mu\rm m $ and a conductivity of $7.3\times10^{-8}\, (\Omega\,{\rm m})^{- 1}$. An AC voltage of amplitude $V$ and frequency $f$ with $20 \leq f \leq 200$ Hz was applied orthogonal to the cell plane. We found oblique (normal) rolls for $f < f_L$ ($f > f_L$) with $f_L \simeq 75$ Hz. From the structure factor (square of the modulus of the Fourier transform) of the images we determined a correlation length $\xi$ (inverse half-width) and maximum $S_0$. For small $\epsilon \equiv V^2/ V_c^2 -1 > 0$ fits of power laws to the results for $\xi$ ($S_0$) yielded an exponent smaller (larger) than that predicted from Ginzburg-Landau equations. The departure from theory is similar to that found previously for domain chaos in rotating Rayleigh-Benard convection\footnote{Y. Hu, R. E. Ecke and G. Ahlers, Phys. Rev. Lett. {\bf 74}, 5040 (1995).} and recent electro-convection measurements in a planar nematic liquid crystal.\footnote{X.-C. Xu and G. Ahlers, unpublished.}