Structural studies of the bond-orientational order and hexatic–smectic transition in liquid crystals of various compositions

Abstract

We report on the X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of the existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent β ≈ 0.1 of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with an exponent equal to the harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. We demonstrate that compounds of various compositions, possessing different phase sequences at low temperatures, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.

Angular X-ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

“…Since scattering at q0~2π/a corresponds to the average interparticle distance a in real space, the coefficients 0≤Cn≤1 are sensitive to the orientation of bonds between neighboring particles separated by a. Thus, the set of coefficients Cn can be considered as the BO order parameters determined in reciprocal space [17,39,40,41,42], in contrast to the complex-valued orientational field Ψn(r) determined in real space.…”

“…In parallel, the first measurements of angular correlations in structural studies of colloidal systems were reported using light scattering in optical range [10,11]. In the last decade, it was realized that the analysis of X-ray angular correlations can provide otherwise hidden information on the structure of a dense systems, such as colloids [12,13], organic films [14,15], LCs [16,17], and mesocrystals [18,19].…”

Heterogeneous local order in self-assembled nanoparticle films revealed by X-ray cross-correlations

“…The possibility of gaining structural information in dense systems such as liquids or glasses was demonstrated in laser scattering experiments in the 1980s (Clark et al, 1983;Ackerson et al, 1985) and revived by X-ray studies of colloidal glasses (Wochner et al, 2009). In recent years, the potential of XCCA to study structures beyond gðrÞ has been investigated by various theories and simulation studies of two-dimensional systems (Altarelli et al, 2010;Kurta et al, 2012;Lehmkü hler et al, 2014;Malmerberg et al, 2015;Latychevskaia et al, 2015;Martin, 2017;, and shown experimentally for thin colloidal and polymer systems (Schroer et al, 2014(Schroer et al, , 2015Gutt et al, 2014;Liu et al, 2017), liquid crystals (Zaluzhnyy et al, 2016(Zaluzhnyy et al, , 2017 and colloids and nanocrystals (Mendez et al, 2014;Mancini et al, 2016;Schroer, Westermeier et al, 2016;Zaluzhnyy et al, 2017). In addition, cross-correlation has recently been demonstrated as a valuable tool for optimizing scattering signals of noisy data .…”

Local orientational order in self-assembled nanoparticle films: the role of ligand composition and salt

“…X-ray cross-correlation analysis (XCCA), also known as fluctuation X-ray scattering, has been shown to overcome this limitation. Recently, the potential of XCCA has been demonstrated by various theoretical and simulation studies on 2D systems (Altarelli et al, 2010;Kurta et al, 2012;Lehmkü hler et al, 2014;Malmerberg et al, 2015;Latychevskaia et al, 2015;Martin, 2017;Lhermitte et al, 2017) and shown experimentally for thin polymer systems and NPs (Gutt et al, 2014;Schroer et al, 2015;Liu et al, 2017;, liquid crystals (Zaluzhnyy, Kurta, Sulyanova et al, 2017), and colloids and nanocrystals (Mendez et al, 2014;Mancini et al, 2016;Schroer, Westermeier et al, 2016;Mendez et al, 2016;Zaluzhnyy, Kurta, André et al, 2017;Mancini et al, 2018). We previously measured the local orientational order of self-assembled NP films of thicknesses of up to a few micrometres by means of XCCA (Schroer et al, 2015;Lehmkü hler et al, 2018).…”