On the relationship between the order parameter and the shape of orientation distributions

Abstract

The molecular orientation is generally expressed by an "order parameter," [Formula: see text] which depends on both the angular position and the shape of the orientation distribution. This parameter is an average made over all orientations of the structural units studied in a sample and, consequently, a given [Formula: see text] value can correspond to different orientation distributions. In this article, model distributions are used to show the relationship between the shape, width, and angular position of the center of the orientation distribution on the [Formula: see text] coefficient, for the case where the distribution of the molecular chains exhibits cylindrical symmetry with respect to the reference direction. A significant difference is observed between the order parameters calculated for distributions of Gaussian and Lorentzian shapes with similar width at half-height. The variation of the [Formula: see text] coefficient as a function of the width at half-height, W_1/2, and of the position of the center of the distribution, θ_C, is analyzed. Figures showing the range of W_1/2–θ_C coordinates that can correspond to a given [Formula: see text] value are presented. As an example, the influence on the order parameter of the disorder between the different domains of phospholipid samples (mosaic spread) and of the conformational disorder in the acyl chains of these molecules is also studied. This example permits the evaluation of the magnitude of the errors that can be introduced in calculations of the tilt angle of the molecular chains in the case of distributions of finite widths or of bimodal character. Keywords: orientation, orientation function, phospholipid bilayers, conformational disorder, mosaic spread.