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

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 I(q) 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 1.2pi</q/D<2pi which agrees well with the assumption proposed by Leadbetter that I(q,psi) along the equatorial arc is independent of /q/. 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.