Length Scales of Chaotic patterns near the onset of of Electroconvection in the Nematic Liquid Crystal I52*

We report experimental results for Electroconvection of the nematic Liquid Crystal I52 with planar alignment and a conductivity of $1.0\times10^{-8}\, (\Omega\,{\rm m})^{-1}$. The cell spacing was $19.4\, \mu {\rm m}$ and the driving frequency was 25.0 Hz. Spatio-temporal chaos consisting of a superposition of zig and zag oblique rolls evolved by means of a supercritical Hopf bifurcation from the uniform conduction state.\footnote{M. Dennin, G. Ahlers and D. S. Cannell, Science, {\bf 272}, 388 (1996).} For small $\epsilon \equiv V^2/ V_c^2 -1$, we measured the correlation lengths of the envelopes of both zig and zag patterns. These lengths could be fit to a power law in $\epsilon$ with an exponent smaller than that predicted from amplitude equations. The disagreement with 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).}