Physical Principles Underlying the Experimental Methods for Studying the Orientational Order of Liquid Crystals

Abstract

The basic physical principles underlying different experimental methods frequently used for the determination of orientational order parameters of liquid crystals are reviewed. The methods that are dealt with here include the anisotropy of the diamagnetic susceptibility, birefringence, linear dichroism, Raman scattering, fluorescence depolarization, electron paramagnetic resonance (EPR), and nuclear magnetic resonance (NMR). The fundamental assertions that can be obtained by the different methods as well as their advantages, drawbacks and limitations are inspected. Typical sources of uncertainties and inaccuracies are discussed. To quantitatively evaluate the experimental data with reference to the orientational order the general tensor formalism developed by Schmiedel (Wiss. Z. KMU Leipzig, Math.‐Naturwiss. R. 33 (1984) 441) was employed throughout according to which the order matrix comprises 25 real elements yet. Within this context the interplay of orientational ordering and molecular conformation is scrutinized.

NMR order parameter analysis of a peptide plane aligned in a lyotropic liquid crystal

“…0"iso = 0; and 0" is in the traceless representation [36]). The above result is equivalent to that obtained recently by Limmer [5]. Thus by measuring Av for five interactions and substituting the orientation (a, 3, 7) and magnitude of T, the elements Sij of the order matrix S can be determined using equation (2).…”

“…77 = (Tll -T22)/T33 where Tii are the principal values of the sencond rank interaction tensor T being considered. For methyl and methylene groups, there is general agreement that r/= 0 [5,6]. Most studies of order within lipid bilayers have involved -CD2-groups, which has simplified the analysis [7][8][9][10][11][12][13].…”

“…Kumar et al [32], used the 13C shielding anisotropy to determine the sign of the order parameter Szz for benzene and chloroform oriented in a liquid crystal and recently, Guo and Fung [33] determined the order of liquid crystals from 13C chemical shifts. Due to the lack of available tensor data the reverse path often has been taken: the Sij obtained by proton NMR has been used to obtain an estimate of the chemical shift anisotropy [5]. In the present study, 13C and 15N chemical shift anisotropies together with dipolar and quadrupolar couplings have been used to Downloaded by [University of California, San Diego] at 12:51 29 June 2016 determine the full five-order parameter matrix for the Gly2-Ala3 peptide plane of gramicidin A, a 15 amino acid ion channel, oriented in aligned phospholipid bilayers.…”

“…Most studies of order within lipid bilayers have involved -CD2-groups, which has simplified the analysis [7][8][9][10][11][12][13]. For molecules with a high degree of symmetry, the molecular axes can be chosen so that only one or two independent Sij are required [4][5][6][7][8][9][10][11][12][13][14][15][16]. An extensive literature exists on the use of liquid crystals to determine the geometry of aligned solute molecules [17,18].…”

All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples

“…To describe the dynamic properties of flexible molecules, however, the Saupe approach is not sufficient, since molecular groups like peptide side chains may exhibit a larger mobility than the rest of the molecule. For this purpose Limmer (1989) introduced a segmental or site-specific order tensor W , which is the tensorial product of the Saupe order tensor and a conformational order tensor.…”