Determination of the order parameter and its critical exponent for nCB (n=5–8) liquid crystals from refractive index data

Abstract

We describe the order parameter S(T) of liquid crystals in the nematic state by a four-parameter expression which is consistent with mean-field theory. A two-step fitting method is applied to high resolution refractive index data for the nCB (n=5–8) liquid crystals, processed according to Vuks and Neugebauer models. We find quasi-universal parameter values. The average critical exponent is β=0.241±0.012, in agreement with the mean-field prediction for a tricritical point. Thus the temperature dependence of the nematic order parameter is quasi-tricritical in all cases. The order parameter at the effective transition point T** is S**=0.143±0.05 and the relative polarizability anisotropy Δα/⟨α⟩=0.69±0.03. We show that earlier results using the Haller approximation were too low (β=0.16–0.19) because of the assumption S**=0 and T**=T _NI. The chosen fitting function provides the best description of S(T) both close and far from T**. For all parameters, the alternating odd–even effect with the number of C atoms in the alkyl chain is about ±5% except for S** for which it is ±30%. 6CB is singled out by a somewhat different set of fitting parameters. 8CB shows a pretransitional smectic behaviour starting from 4 K above the smectic–nematic transition point.