The Measurement of the Nematic Order Parameter by X-ray Scattering Reconsidered

P. Davidson; D. Petermann; A. M. Levelut

doi:doi:10.1051/jp2:1995117

Numéro		J. Phys. II France Volume 5, Numéro 1, January 1995


Page(s)		113 - 131
DOI		https://doi.org/10.1051/jp2:1995117

DOI: 10.1051/jp2:1995117
J. Phys. II France 5 (1995) 113-131

The Measurement of the Nematic Order Parameter by X-ray Scattering Reconsidered

P. Davidson, D. Petermann and A. M. Levelut

Laboratoire de Physique des Solides associé au CNRS, Bât. 510, Université Paris Sud, 91405 Orsay, Cedex, France

(Received 15 June 1994, received in final form 6 October 1994, accepted 12 October 1994)

Abstract
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.