Scaling of Bond-Orientational Order Parameters in Thin Hexatic Liquid-Crystal Films

Quantitative measurement of the higher-order bond-orientational order parameters in free-standing liquid-crystal films exhibiting hexatic phases has been demonstrated in x-ray and electron-diffraction experiments. These order parameters are related by scaling relations which depend sensitively on the effective spatial dimension. We present additional electron-diffraction data on hexatic liquid- crystal films of different thicknesses down to two molecular layers to examine the effect of dimension on the scaling behavior among the bond-orientational order parameters.