Reliability of Orientational Order Parameters Determined from Two‐dimensional X‐ray Diffraction Patterns: A Simulation Study

Abstract

The orientational order parameter S2 is one of the most important quantities to describe the degree of long-range orientational ordering of liquid crystals. There are several approaches to experimentally measure this order parameter of liquid crystalline phases but every method includes substantial simplifications and assumptions. We present a simulation-based approach to elucidate the reliability of the method of Davidson, Petermann and Levelut to measure S2 via 2D X-ray experiments. We have found that this method slightly underestimates S2 by an absolute value of only 0.05 and thus provides reliable measures of S2 by X-ray diffraction.

Considerations in the determination of orientational order parameters from X-ray scattering experiments

“…It is interesting to note that a study of the reliability of order parameters determined from X-ray scattering patterns, carried out using the LN model, concluded that the approach underestimates the true values of hP 2 i by ca. 0.03-0.06 [38,39]; the results shown in Figure 7 suggest that this underestimation may at least partially be attributed to the error in Equation (4) in the LN approach. An equivalent comparison of hP 4 i values determined from the same scattering patterns of 5CB, 6CB, 7CB and 8CB was also carried out, as shown in Figure 8.…”

“…This expression readily enables the order parameters, hP L i, to be determined from the integrated intensity of the wide-angle X-ray peaks, the method for which is described fully in the literature [23]. As a result of the increasing ease of carrying out X-ray scattering studies of liquid crystal samples, this method has been used widely in the field of liquid crystal studies to interpret experimental data [ 14,15,17,[24][25][26][27][28][29][30][31][32][33][34][35], as well as forming the basis for a number of computational and theoretical studies [36][37][38][39]. Outside the field of liquid crystals, it was noted over a decade ago by Burger and Ruland that there had been an error in the derivation of Equation (4) [40], and that the correct formula had in fact been derived much earlier by Kratky [41].…”

Molecular Electron Density Distribution and X‐Ray Diffraction Patterns of Smectic A Liquid Crystals – A Simulation Study

“…[2][3][4] One of the most important methods to investigate the order of a liquid crystalline phase is X-ray diffraction. [4][5][6][7][8][9][10][11][12][13][14][15] The diffraction pattern of an aligned SmA phase exhibits two sets of intensity maxima. The diffuse and broad wide angle maxima correspond to the mean short distance of molecular centers.…”

“…While the validity of methods to extract information about the orientational order of a liquid crystal has been discussed the validity of methods that extract information about the translational order is still an open question. In general, the X‐ray intensity is proportional to the structure factor and the form factor in the sample volume ( ).…”

“…One of the most important methods to investigate the order of a liquid crystalline phase is X‐ray diffraction [4–15] . The diffraction pattern of an aligned SmA phase exhibits two sets of intensity maxima.…”