Information on Bond Orientation Distributions in Lipids and Liquid Crystals from Segmental Order Parameters

Abstract

The information content of segmental order parameters in liquid-crystalline lipids is analyzed in terms of orientation distributions. First, we discuss the use of segmental order tensors, determined from motionally averaged NMR anisotropies, for obtaining approximations to the orientation distribution of the director in the molecular segment. In addition to the distribution consisting of second-order spherical harmonics, two physically reasonable five-parameter distributions are examined, and the relation of the two shape parameters of these distributions to the principal order parameters is presented. The usefulness of these distributions for the determination of torsional angles is also discussed. Furthermore, we introduce a novel approach for obtaining model-independent limits to bond orientation probabilities from bond order parameters. The analysis shows, for instance, that the C−H bonds of the glycerol sn-3 CH2 group in phosphatidylcholine, with bond order parameters of −0.22, are oriented preferentially at angles between 52° and 128° from the director. The probability that these bonds are oriented at angles smaller than 30° or larger than 150° is less than 25%. Assuming an upper limit to the ruggedness of the distribution, even more stringent probability limits can be given. For instance, using a minimum standard deviation of 10° for any conformation, a C−H order parameter of −0.22 corresponds to a probability of less than 25% for C−H orientations below 51° and above 129°. The approaches described here are generally applicable to uniaxial liquid-crystalline systems.