Accuracy of measuring the nematic order from intensity scatter: A simulation study

Abstract

The determination of the nematic order parameter S and the orientational distribution function (ODF) from scattering data involve severe approximations. The validity of these are studied here using Monte-Carlo simulations of hard spherocylinders with an aspect ratio of 15 for varying densities in the isotropic and nematic phase. The "exact" ODF of the rods, the "exact" value of S, and the intensity scatter I͑q ជ͒ are determined directly in simulation. In addition, we determine the ODF and S from the simulated intensity scatter which includes spatial and orientational correlations of the particles. We investigate whether correlations present in the interparticle scatter influences the determination of the single particle orientational distribution function by comparing the results obtained from scattering with the "exact" results measured directly in our simulations. We find that the nematic order parameter determined from the intensity scatter underestimates the actual value by 2 -9%. We also find that the values of S and the ODF are insensitive to the absolute value of the scattering vector for 1.2 Ͻ ͉q ជ͉D Ͻ 2 which agrees well with the assumption proposed by Leadbetter that I͑q , ͒ along the equatorial arc is independent of ͉q ជ͉. We also observe that the best fit of the "exact" ODF is given by the Maier-Saupe distribution when nematic director fluctuations are ignored, while the Gaussian distributions provides the best fit when these fluctuations are included.

Small Angle Neutron Scattering Study of Polyelectrolyte Conformation Incorporated into Hybrid Threadlike Micelles under Strong Shear Flows

“…Although we do not have quantitative information on the orientation of the rod particle including the distribution function of θ and φ as a function of shear rate, γ̇, the fact that hybrid threadlike micelles significantly aligned toward the flow axis providing q * as observed in Figure significantly suggests that the maximum probability of orientation should be located at θ = 0 rad at γ̇ = 10 s -1 . In other words, the director of the rod is parallel to the flow axis . Next, we suppose two kinds of conventional and simple distribution functions, p (θ), of the orientation angle θ to the shear axis with only one dispersion parameter, α, simply assuming isotropic orientation around the axis in the angle of φ as where N (α) in the Maier-Saupe (M−S) distribution function is a normalizing front factor satisfying the relationship 2π p (θ) sinθ dθ = 1 taking account of integration from φ = 0 to 2π, while the Onsager distribution function is normalized.…”

Order Parameters and Areas in Fluid-Phase Oriented Lipid Membranes Using Wide Angle X-Ray Scattering

“…0 is a parameter related to the width of the distribution, and Z is a normalization factor. This distribution function has been used to fit scattering data for a number of liquid-crystalline systems (13,14,(41)(42)(43). Insertion of f(b) in Eq.…”

Liquid-Liquid Domains in Bilayers Detected by Wide Angle X-Ray Scattering

“…We note that criterion 3 depends upon the choice of the f(b) orientational distribution. Although the Maier-Saupe distribution works well to describe the scattering from many liquid crystalline systems, other distributions could sometimes be more appropriate (34), and so it is important to establish that a single Maier-Saupe distribution fits the data when the sample is known to have a single phase. Our interpretation that a poor single-order parameter fit is evidence of phase coexistence is therefore supported by the observation that these ternary mixtures for T $ 35°C and the singlephase DOPC/Chol and DPPC/Chol mixtures (31) are all well fitted by a single Maier-Saupe distribution.…”