Angular structure factor of the hexatic-B liquid crystals: bridging theory and experiment

TL;DR

This study combines X-ray scattering experiments with theoretical analysis to understand the angular structure factor of hexatic-B liquid crystals, revealing how the peak shapes relate to underlying physical contributions over a range of temperatures.

Contribution

It provides the first detailed experimental validation of the Voigt function shape of the hexatic structure factor and links it to theoretical models of phase transition behavior.

Findings

Angular profiles fit well with the Voigt function across temperatures.

The shape results from the interplay of density and coupling contributions.

Supports theoretical predictions of the hexatic structure near phase transitions.

Abstract

We report results from X-ray scattering studies of the angular structure factor of liquid crystal hexatic-B films. According to the sixfold rotational symmetry of the hexatic-B phase, its characteristic scattering splits into six reflections. The shape of the radial and angular cross-sections of these reflections and their temperature evolution are analyzed. We find that over a wide temperature range of the hexatic-B phase existence the angular profiles of the in-plane X-ray scattering are well fitted by the Voigt function, which is a convolution of the Gaussian and Lorentzian functions. This result is supported by the known theoretical considerations of the hexatic structure factor below the smectic-hexatic phase transition temperture. Similar predictions for the angular shape of the hexatic peak in the vicinity of the smectic-hexatic phase transition temperature follow from the multicritical scaling theory of the hexatic-B phase in three dimensions. We find that the specific shape of the hexatic structure factor can be explained by the interplay of two distinct contributions to the free energy of the system, a liquid-like density term and a coupling term between the bond-orientational order and short-range density fluctuations.