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).}