Communication: Molecular gears.

The (1)H nuclear magnetic resonance spectrum of hexamethylbenzene orientationally ordered in the nematic liquid crystal ZLI-1132 is analysed using covariance matrix adaptation evolution strategy. The spectrum contains over 350 000 lines with many overlapping transitions, from which four independent direct dipolar couplings are obtained. The rotations of the six methyl groups appear to be correlated due to mutual steric hindrance. Adjacent methyl groups show counter-rotating or geared motion. Hexamethylbenzene thus behaves as a molecular hexagonal gear.

Communication: molecular dynamics and (1)H NMR of n-hexane in liquid crystals.

The NMR spectrum of n-hexane orientationally ordered in the nematic liquid crystal ZLI-1132 is analysed using covariance matrix adaptation evolution strategy (CMA-ES). The spectrum contains over 150 000 transitions, with many sharp features appearing above a broad, underlying background signal that results from the plethora of overlapping transitions from the n-hexane as well as from the liquid crystal. The CMA-ES requires initial search ranges for NMR spectral parameters, notably the direct dipolar couplings. Several sets of such ranges were utilized, including three from MD simulations and others from the modified chord model that is specifically designed to predict hydrocarbon-chain dipolar couplings. In the end, only inaccurate dipolar couplings from an earlier study utilizing proton-proton double quantum 2D-NMR techniques on partially deuterated n-hexane provided the necessary estimates. The precise set of dipolar couplings obtained can now be used to investigate conformational averaging of n-hexane in a nematic environment.

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals.

The proton NMR spectra of n-pentane orientationally ordered in two nematic liquid-crystal solvents are studied over a wide temperature range and analysed using covariance matrix adaptation evolutionary strategy. Since alkanes possess small electrostatic moments, their anisotropic intermolecular interactions are dominated by short-range size-and-shape effects. As we assumed for n-butane, the anisotropic energy parameters of each n-pentane conformer are taken to be proportional to those of ethane and propane, independent of temperature. The observed temperature dependence of the n-pentane dipolar couplings allows a model-free separation between conformer degrees of order and conformer probabilities, which cannot be achieved at a single temperature. In this way for n-pentane 13 anisotropic energy parameters (two for trans trans, tt, five for trans gauche, tg, and three for each of gauche+ gauche+, pp, and gauche+ gauche-, pm), the isotropic trans-gauche energy difference Etg and its temperature coefficient Etg(') are obtained. The value obtained for the extra energy associated with the proximity of the two methyl groups in the gauche+ gauche- conformers (the pentane effect) is sensitive to minute details of other assumptions and is thus fixed in the calculations. Conformer populations are affected by the environment. In particular, anisotropic interactions increase the trans probability in the ordered phase.

NMR of solutes in nematic and smectic A liquid crystals: the anisotropic intermolecular potential.

Orientational order parameters determined from (1)H NMR spectroscopy of solutes in liquid crystals that form both nematic and smectic A phases are used to determine the solute smectic A order parameters and the smectic-nematic coupling term. For the analysis, it is necessary to know the nematic part of the potential in the smectic A phase: various ways of extrapolating parameters from the nematic phase to the smectic phase are explored.

NMR of short-chain hydrocarbons in nematic and smectic a liquid crystals.

The proton NMR spectra of ethane, propane, and n-butane codissolved and orientationally ordered in two liquid-crystal solvents that exhibit both nematic (N) and smectic A (SmA) phases (one of which also has a reentrant nematic (RN) phase) are analyzed using CMA-ES (covariance-matrix adaptation evolution strategy). To deal with problems arising from the broad liquid-crystal background signal, a smoothed experimental spectrum is fitted to a smoothed calculated spectrum. The ethane and propane dipolar couplings and anisotropic energy parameters scale with each other, and the n-butane couplings are assumed to behave likewise. This restriction on the relative values of the n-butane energy parameters facilitates a fit to the temperature dependence of the n-butane dipolar couplings, in which the six n-butane energy parameters (three for trans and three for gauche), the isotropic trans-gauche energy difference E(tg), and its temperature coefficient E(tg)', and the methyl CCH angle decrease are obtained. Unlike earlier studies, the fit does not employ a model for the anisotropic intermolecular potential. The nematic potential in the SmA phase of the liquid-crystal mixture 6OCB/8OCB is estimated by interpolated values obtained from the ethane spectra for the N and RN regions. Analysis of results for the SmA phase involves adding a nematic-smectic coupling prefactor and a smectic prefactor. Spectra obtained in the liquid-crystal 8OCB are calculated with no adjustable parameters, scaling the potentials using the ethane values, and the agreement between experiment and calculation is outstanding. Conformer populations are affected by the environment, and the isotropic solute-solvent interactions result in increased gauche populations, whereas anisotropic interactions increase the trans probability. The trans probability in the SmA phase is slightly lower than expected from the nematic results.

Efficient analysis of highly complex nuclear magnetic resonance spectra of flexible solutes in ordered liquids by using molecular dynamics.

The NMR spectra of n-pentane as solute in the liquid crystal 5CB are measured at several temperatures in the nematic phase. Atomistic molecular dynamics simulations of this system are carried out to predict the dipolar couplings of the orientationally ordered pentane, and the spectra predicted from these simulations are compared with the NMR experimental ones. The simulation predictions provide an excellent starting point for analysis of the experimental NMR spectra using the covariance matrix adaptation evolutionary strategy. This shows both the power of atomistic simulations for aiding spectral analysis and the success of atomistic molecular dynamics in modeling these anisotropic systems.

Nuclear magnetic resonance study of alkane conformational statistics.

NMR spectra of ethane, propane, and n-butane as solutes in the nematic liquid crystals 4-n-pentyl-4(')-cyanobiphenyl (5CB) and Merck ZLI 1132 (1132) are investigated over a wide temperature range. The ratios of dipolar couplings of ethane to propane are constant over the entire temperature range. Assuming that this constancy applies to the butane conformers facilitates the separation of probability from order parameter. This separation allows the investigation of conformational distribution without the need of invoking any model for the anisotropic intermolecular potential. The results give an order matrix that is consistent with that predicted from model potentials that describe the orientational potential in terms of short-range size and shape effects. The isotropic intermolecular potential contribution to the trans-gauche energy difference E(tg) is found to be temperature dependent with the values and variation in agreement with that found when the same results are analyzed using the chord model for anisotropic interactions [A. C. J. Weber and E. E. Burnell, Chem. Phys. Lett. 506, 196 (2011)]. The fit obtained for 9 spectra in 5CB (63 dipolar couplings) has an RMS difference between experimental and calculated dipolar couplings of 2.7 Hz, while that for the 16 spectra in 1132 (112 couplings) is 6.2 Hz; this excellent fit with nine adjustable parameters suggests that the assumption of equal temperature dependencies of the order parameters for ethane, propane, and each conformer of butane is correct. Also the fit parameters (E(tg) and the methyl angle increase) obtained for 1132 and 5CB agree. The results indicate that the chord model, which was designed to treat hydrocarbon chains, is indeed the model of choice for these chains. The temperature variation of E(tg) provides a challenge for theoreticians. Finally, even better fits to the experimental dipolar couplings are obtained when the energy in the Boltzmann factor is used for scaling ethane to butane results. However, in this case the values obtained for E(tg) differ between 1132 and 5CB.

Scope and limitations of accurate structure determination of solutes dissolved in liquid crystals.

The determination of accurate structures of relatively small molecules dissolved in liquid-crystal solvents is no trivial matter. Extensive vibrational corrections to the observed dipolar couplings are required. Vibrational force fields are often available, but the usual harmonic corrections are strictly limited to small-amplitude internal motions. Moreover, the need to also apply anharmonic corrections and to include the elusive vibration-reorientation interaction is problematic and can only be fulfilled for a very limited set of small molecules. In this paper we discuss the implications for the accuracy of the structure of larger molecules for which this information is not available. We discuss the examples of azulene and biphenylene, and set realistic limits on their proton structures, derived from (1)H dipolar couplings extracted from NMR spectra obtained in different liquid-crystal solvents and analyzed with sophisticated evolutionary algorithms.

The smectic effect on solute order parameters rationalized by double Maier-Saupe Kobayashi-McMillan theory.

From the dipolar couplings obtained by NMR spectroscopy we have calculated the order parameters of a wide variety of solutes in the nematic and smectic A phases of the liquid crystals 8CB and 8OCB. These measurements are then rationalized with the previously tested two Maier-Saupe Kobayashi-McMillan interaction potential from which smectic order parameters are calculated.

Orientational order of near D(3h) solutes in nematic liquid crystals. II. Description via Gay-Berne model with embedded quadrupoles.

We perform Monte Carlo simulations of a mixture of soft ellipsoids with embedded quadrupoles as a model of various chloro- and methyl-substituted benzenes dissolved in nematic liquid crystals. We find that oblate Gay-Berne ellipsoids with multiple embedded quadrupoles qualitatively reproduce the trend in the order parameter asymmetry experimentally observed in NMR spectra. The trend is opposite to what is expected on the basis of the interaction of the solute's quadrupole with the solvent's average electric field gradient "felt" by dissolved dihydrogen molecules. We identify the specific minimum of the solute-solvent interaction energy landscape that may produce the unexpected sign of the order parameter asymmetry that is seen in the experiment and the simulation.

Orientational order of near D(3h) solutes in nematic liquid crystals.

Solutes that are similar in size, have a shape that is close to D(3h) symmetry but contain dissimilar substituent groups (methyl versus chloro, contributing different electrostatic interactions to the anisotropic intermolecular potential), are used to delineate the short- and long-range anisotropic intermolecular interactions that lead to solute orientational order in nematic liquid crystals. The short-range interactions should be similar for all solutes and for D(3h) symmetry should yield a single independent order parameter, whereas the long-range interactions are expected to differ with solute. Short-range size and shape mechanisms account for solute orientational order measured in magic mixtures (e.g., 55 wt % ZLI-1132/N-p-ethoxybenzylidene-p(')-n-butylaniline), whereas additional mechanisms are required in other nematic liquid-crystal solvents. The results obtained for long-range interactions cannot be rationalized in detail using simple mean-field models that incorporate solute dipoles, quadrupoles, or polarizabilities. The results suggest that details of the solute electrostatics may need to be incorporated into the description of the anisotropic intermolecular potential.

Memory effects across surfactant mesophases.

We report a detailed analysis of deuteron NMR spectra of micellar, lamellar, cubic, and hexagonal mesophases in the aqueous non-ionic surfactant system C(12)E(6)/water. Samples are prepared with and without shear. Particular attention is paid to an interesting temperature-driven phase sequence that includes all of the above phases that are studied before and after shear parallel or perpendicular to the magnetic field direction. Surprising memory effects are found across mesophase transitions. These memory effects provide clues to the structure of the various phases.

NMR determination of smectic ordering of probe molecules.

The NMR spectra of the three solutes ortho-, meta-, and para-dichlorobenzene in the nematic and smectic A phases of the liquid crystals 8CB and 8OCB are analyzed to yield two orientational order parameters for each solute. Extrapolation of the asymmetry in the energy parameters that describe the orientational ordering in the nematic phase are used to provide estimates of the strength of the nematic potential in the smectic A phase. The experimentally determined asymmetry of the orientational order parameters in the smectic A phase is then used in conjunction with Kobayashi-McMillan theory applied to solutes to give information about the smectic A layering and the nematic/smectic A coupling. In both smectic A solvents, the solute smectic coupling constant, tau, is negative (with the origin fixed at the center of the smectic layer) for all solutes. The signs and relative values of tau indicate that the ortho and para solutes favor the interlayer region while the meta solute is more evenly distributed throughout the layers.

Testing assumptions about solute concentration dependence in liquid crystal NMR.

The NMR spectra of four solutes, used as probes of liquid crystal orientational order, were analyzed. For each solute, samples were prepared at different solute concentrations, and the concentration dependence was used to extrapolate zero-concentration properties. The mean-field (Maier-Saupe) model when applied to solutes neglects solute-solute interactions and assumes all solutes in a mixed-solute sample see the same average environment. The first assumption is only valid as one approaches zero concentration, while experiments are typically carried out at concentrations between 0 and 10 mol %. The solute concentration dependence has in the past been "scaled out" using an internal solute reference as an orientational standard. We measured the concentration dependence of the orientational order parameter and calculate the corresponding interaction energies based on a mean-field interaction potential for a solute. We find agreement at the 3% level between experiments for different solutes while using (i) the zero-concentration values as solute-dependent orientational references and (ii) scaling to either order parameters or interaction energies; these two scalings gave equivalent but not identical results. We find, too, that errors inherent in the experiment and the calculations will limit attempts to refine the theory to push the comparisons beyond the 2% level.

An NMR study of translational diffusion and structural anisotropy in magnetically alignable nonionic surfactant mesophases.

The diffusion of both water and surfactant components in aqueous solutions of the nonionic surfactant "C12E6"--which includes hexagonal, cubic, lamellar, and micellar mesophases--has been studied by pulsed-field-gradient NMR. Diffusion coefficients were measured in unaligned samples in all of these phases. They were also obtained in the hexagonal and lamellar phases in oriented monodomain samples that were aligned by slow cooling from the micellar phase in an 11.7 T magnet. Measured water and soap diffusion coefficients in the NMR-isotropic cubic and (high-water-content) micellar phases as well as diffusion anisotropy measurements in the magnetically aligned hexagonal phase were quantitatively consistent with the constituent structures of these phases being identical surfactant cylinders, with only the fraction of surface-associated water varying with the water-soap molar ratio. The values of the water and soap diffusion coefficients in the oriented lamellar phase suggest an increase in defects and obstructions to soap diffusion as a function of increasing water content, while those in the low-water-content micellar phase rule out the presence of inverse micelles.