THE MEASUREMENT OF THE NEMATIC ORDER-PARAMETER BY X-RAY-SCATTERING RECONSIDERED

This paper reviews and extends the procedure used to measure the nematic order parameter by X-ray scattering. We show that the well-known integral equation derived by Leadbetter and coworkers, relating the scattered intensity I(theta) to the orientational distribution function f(beta), can be analytically simplified both in the general case and in the case of the Maier-Saupe distribution function. The Maier-Saupe distribution leads to a particularly simple analytical result previously obtained by Paranjpe and Kelkar. This result is extensively discussed here and tested on a large variety of thermotropic liquid crystals. In most cases, this very simple and practical approach provides a good description of the data. This supports at the same time the analysis of the scattering leading to Leadbetter's integral equation and the Maier-Saupe distribution. We also discuss the validity and accuracy of this simple method compared to other ones.