NMR polarization echoes in a nematic liquid crystal

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.     

Measurement of carbon-proton dipolar couplings in liquid crystals using DAPT

Dipolar couplings provide valuable information on order and dynamics in liquid crystals. For measuring heteronuclear dipolar couplings in oriented systems, a new separated local field experiment is presented here. The method is based on the dipolar assisted polarization transfer (DAPT) pulse sequence proposed recently (Chem. Phys. Lett. 2007, 439, 407) for transfer of polarization between two spins I and S. DAPT utilizes the evolution of magnetization of the I and S spins under two blocks of phase shifted BLEW-12 pulses on the I spin separated by a 90 degree pulse on the S spin. Compared to the rotating frame techniques based on Hartmann-Hahn match, this approach is easy to implement and is independent of any matching conditions. DAPT can be utilized either as a proton encoded local field (PELF) technique or as a separated local field (SLF) technique, which means that the heteronuclear dipolar coupling can be obtained by following either the evolution of the abundant spin like proton (PELF) or that of the rare spin such as carbon (SLF). We have demonstrated the use of DAPT both as a PELF and as a SLF technique on an oriented liquid crystalline sample at room temperature and also have compared its performance with PISEMA. We have also incorporated modifications to the original DAPT pulse sequence for (i) improving its sensitivity and (ii) removing carrier offset dependence.     

Determination of long range dipolar couplings in ferroelectric liquid crystals

Long range dipolar coupling constants have been determined in three ferroelectric liquid crystals in their racemic forms using ¹³C NMR. Two of these liquid crystals are esters of α-chloroacids and 4-octyloxy-4'-hydroxybiphenyl, and have a very large spontaneous polarization in the smectic C* phase. The strategy used in the present study is the observation and measurement of ²H-¹³C splittings in the ¹³C spectra of monodeuterated compounds. The order parameters were calculated from the 1D spectra, and some of the coupling constants are compared with the ¹H-¹³C coupling constants previously obtained from 2D experiments. In addition, the deuterium quadrupole splitting of these compounds was determined from their ²H NMR spectra. The experiments were carried out over the whole mesomorphic ranges of the liquid crystals, covering the smectic A and smectic C phases.     

Addressing non-idealities in NMR experiments on rotating liquid crystals

Unequivocal evidence for a biaxial nematic phase in low-molar-mass calamitic thermotropic liquid crystals has been challenging to generate. Recently we provided NMR evidence that nonlinear calamitic mesogens based on the oxadiazole heterocycle exhibit a biaxial nematic phase (Phys. Rev. Lett., 2004, 92, 145505). Herein we probe the robustness of that claim by exploring potential variations of the director distribution from the ideal one that would apply to nematics rotated about an axis perpendicular to the spectrometer magnetic field. Moreover, we demonstrate that our methodology, when applied to the high temperature uniaxial nematic TBBA, yields a biaxial order parameter η = 0.0, thereby confirming the validity of our procedures. Our findings suggest that the original claim of biaxial order (η∼0.1) as reflected by probe molecule studies of oxadiazole mesogens is still valid.     

Suppression of undesired peaks due to residual intermolecular dipolar interactions in liquid NMR

Residual intermolecular dipolar interactions may result in undesired spectral features on highly concentrated samples in liquid NMR. Although homonuclear decoupling can be employed to suppress the interactions, it may cause a strong irradiation peak, which obscures the nearby peaks. In order to overcome this shortcoming, a modified CRAZED sequence with three radio-frequency pulses was proposed. The analytical expression derived from the dipolar field treatment was employed to select proper flip angles and phase cycling. Theoretical predictions, experimental observations, and computer simulations demonstrated that the new method effectively suppresses the undesired peaks due to residual dipolar effects.     

NMR in chiral polypeptide liquid crystals: the problem of amines

It is shown that lyotropic liquid crystal mixtures made of poly-γ-benzyl-l-glutamate (PBLG) dissolved in N,N-dimethylformamide (DMF) are efficient anisotropic NMR solvents to distinguish the enantiomers of chiral amines through the effects of the differential ordering of enantiomers. This type of solvent overcomes problems often encountered when dissolving amines into the more conventional PBLG/CHCl₃ or PBLG/CH₂Cl₂ liquid crystals. Furthermore, it is shown that perdeuterobenzyl chloride is an excellent achiral deuterated derivatizing agent for enantiomeric excess measurements of chiral amines in conjunction with the PBLG/DMF solvent.     

NMR spectra of chiral smectic liquid crystals differing in helical parameters

Chiral liquid crystals with three-ring rigid core were examined. The method based on the selectively reflected light was used to determine the helical pitch. The helical twist sense was worked out using the polarimetry method. ¹H and ¹³C NMR measurements were performed. The influence of three molecular structure parameters: the type of chiral centre, the length of non-chiral chain and substitution of benzene ring by fluorine atoms, on helical pitch, handedness of helical structure and values of chemical shift in proton and carbon spectra was determined. The change of the length of non-chiral terminal chain has the most significant influence on the temperature dependence of helical pitch. All tested parameters have the biggest influence on the values of chemical shift of atoms in the chiral centre.     

Deuterium NMR of the TGBA* phase in chiral liquid crystals

A deuterium NMR (DNMR) study of the TGBA* (twist grain boundary smectic A*) phase in an NMR magnetic field of 9.4 T for the chiral compound 4-[4'-(1-methyl heptyloxy)] biphenyl 4-(10-undecenyloxy) benzoate (11EB1M7) is reported. The deuterium two-dimensional (2D) exchange spectra were observed for the first time in this phase. The present study allows us to learn how the helicoidal structures arrange in an external magnetic field. To derive quantitative kinetic parameters of this novel phase, both 1D and 2D experimental spectra were simulated by means of a jump diffusion model. By comparing the experimental and simulated spectra, an accurate determination of the dynamic parameters in the TGBA* phase was obtained. Furthermore, the twist angle between two neighboring smectic A blocks is found as 26 +/- 10 degrees, which is consistent with the X-ray results for similar chiral liquid crystals. The diffusion constant (D(parallel)) is estimated to be 3.2 x 10(-12) m(2)/s at 379.5 K.     

Modulation of NMR spin echoes in coupled systems

A new theoretical approach to NMR spin echoes is described. The xy magnetizations which correspond to the lines in the spectrum are dealt with directly, by the use of the angular momentum properties of Liouville space. This simplifies the calculations for the AB spin systems and opens the way to larger systems.     

The impact of NMR on the field of liquid crystals

In the fifty years that it has been available as an investigative technique, NMR has strongly promoted the advancement of knowledge in the field of liquid crystals. This article provides a brief overview of its contributions to the subject.     

Deuterium NMR studies of inositol liquid crystals [1]

Deuterium NMR investigations are presented on members of two new mesogenic series derived from the naturally occurring stereoisomers myo- and scW/o-inositol. Tetraethers of these two series exhibit thermotropic columnar phases in which the columns are apparently formed by stacked hydrogen bonded dimers of these molecules which chemically are vicinal diols. Deuterium NMR measurements were performed on the tetraoctyl homologues 2e (a cis diol) and 3e (a trans diol) of these series. We have investigated mixtures of these diols with small amounts of benzene-d₆ as probe molecules as well as samples of the neat diol compounds deuteriated at their hydroxyl groups. The results obtained show that the mesophases of both compounds are uniaxial and align partially in a magnetic field upon slow cooling from their isotropic liquids. The alignment is with the director parallel to the field direction indicating that the anisotropic magnetic susceptibility of this mesophase is positive. The deuterium quadrupole splitting of the benzene-d₆ probe in both systems is temperature dependent and in the trans diol 3e it even changes sign. This is interpreted in terms of a model in which the benzene-d₆ probe equilibrates rapidly between two (or more) solvation sites with quadrupole splittings of opposite signs The deuterium spectra of the neat deuterium labelled cis diol 2e exhibit two different signals due to the two deuterons which are located at the axial and equatorial hydroxyl groups. This indicates that there is no fast intra- or intermolecular exchange of the hydroxyl hydrogens. The overall quadrupole splittings of the hydroxyl deuterons in this compound are highly reduced compared to their static values and this is interpreted in terms of motional modes involving both reorientation of the hydroxyl deuterons about their C-O axis and overall reorientation of the molecules (or pairs of molecules) around the columnar axes. The corresponding spectra of the neat deuteriated trans diol 3e exhibit a single spectrum indicating that both hydroxyl deuterons in this compound are equivalent, or very nearly so. Within the mesophase region the spectrum undergoes gradual changes due to the increase in the molecular mobility, but the overall motional narrowing is less than in the cis isomer 2e. Apparently due to stronger hydrogen bonding in the trans isomer 3e the precession of the hydroxyl groups is hindered and a fast molecular reorientation is only possible at high temperatures.     

The impact of NMR on the field of liquid crystals

In the fifty years that it has been available as an investigative technique, NMR has strongly promoted the advancement of knowledge in the field of liquid crystals. This article provides a brief overview of its contributions to the subject.     

Nuclear magnetic resonance proton dipolar order relaxation in thermotropic liquid crystals: a quantum theoretical approach

By means of the Jeener-Broekaert nuclear magnetic resonance pulse sequence, the proton spin system of a liquid crystal can be prepared in quasiequilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a characteristic time (T1D). Previous studies of the Larmor frequency and temperature dependence of T1D in thermotropic liquid crystals, that included field cycling and conventional high-field experiments, showed that the slow hydrodynamic modes dominate the behavior of T1D, even at high Larmor frequencies. This noticeable predominance of the cooperative fluctuations (known as order fluctuations of the director, OFD) could not be explained by standard models based on the spin-lattice relaxation theory in the limit of high temperature (weak order). This fact points out the necessity of investigating the role of the quantum terms neglected in the usual high temperature theory of dipolar order relaxation. In this work, we present a generalization of the proton dipolar order relaxation theory for highly correlated systems, which considers all the spins belonging to correlated domains as an open quantum system interacting with quantum bath. As starting point, we deduce a formulation of the Markovian master equation of relaxation for the statistical spin operator, valid for all temperatures, which is suitable for introducing a dipolar spin temperature in the quantum regime, without further assumptions about the form of the spin-lattice Hamiltonian. In order to reflect the slow dynamics occurring in correlated systems, we lift the usual short-correlation-time assumption by including the average over the motion of the dipolar Hamiltonian together with the Zeeman Hamiltonian into the time evolution operator. In this way, we calculate the time dependence of the spin operators in the interaction picture in a closed form, valid for high magnetic fields, bringing into play the spin-spin interactions within the microscopic time scale. Then, by adopting the spin-temperature density operator to represent the collective state of the spin system, and removing the traditional hypothesis of high temperature, we deduce an expression for the first order quantum contribution to T1D (-1), in terms of spectral densities, with coefficients in form of spin traces. The properties that distinguish our result from the high-temperature T1D (-1) are as follows. (a) It is exclusively associated to cooperative fluctuations. (b) Because of its quantum character, it relies on both considering the lattice degrees of freedom quantum mechanically and including the spin-spin interactions in the microscopic time scale. With regard to the average dipolar Hamiltonian, only the nonsecular part plays a relevant role. (c) Associated with the structure of the spin operator involved in the quantum contribution, a term arises which is proportional to the number of spins in the correlated molecular domains, showing that the quantum contribution may be of macroscopic size in highly correlated systems. When applied to nematic liquid crystals, the new term exhibits the typical nu(-1/2) Larmor frequency dependence through the spectral density of the OFD, in consistence with the experimental results.     

Structure of polymer networks in liquid crystals studied by 13C NMR

We report on 13C NMR measurements above and below the clearing temperature of the liquid crystal 4-n-hexyloxyphenyl 4-methoxybenzoate constrained to an oriented, low concentration polymer network. The network is obtained by UV-irradiation of the reactive monomer 1,4-di-[4-(6-acryloyloxyhexyloxy)benzoyloxy]-2-methylbenzene which is in admixture with the liquid crystal. The characterization of orientational order of the mixtures before UV-radiation, and hence before polymerization, reveals the high order of the components at the polymerization temperature. The chosen geometry explains the LC director orientation only by the aligned network. Above the nematic-isotropic transition a strong pretransitional order is detected. Fast molecular translational diffusion averages the order over dimensions smaller than 1 mum. The Landau-de Gennes theory predicts a relation between pretransitional order and the lateral dimension of the LC regions. The experimental data are successfully explained by pore diameters of 35 and 98 nm for concentrations of 20 and 8 mol% of monomer, respectively. The results support the model of nearly cylindrical shaped liquid crystal domains surrounded by thin walls of crosslinked network.     

Rotational spin echoes and high resolution NMR in powders

When a powder having linewidth Δ arising from inhomogeneous second-rank tensor in interactions is rotated about the magic axis at ν_rot < Δ, the free induction decay is a spin echo train, the Fourier transform of whose envelope is the isotropic spectrum.     

Conformational constraint in ferroelectric liquid crystals incorporating a pyrrolidine-type ring: FLC materials comprising parallel dipolar moments

Ferroelectric liquid crystals bearing a chiral pyrrolidine-type ring were prepared using (-)-(S)-malic acid as a building block. The compounds were characterized using the thermal analysis techniques of DSC and POM, electrical measurements and temperature-dependent XRD. Samples showed moderate spontaneous polarization values (P _S) with helical pitches of about 2.997 µm and an average tilt angle of 16.2° for the SmC* planes. Conformational analysis of the chiral pyrrolidinol subunit and of all of the mesogenic targets was performed using several quantum methods including large basis sets and different treatments of electron correlation in order to correlate experimental results and theoretical predictions. For the most stable conformations, a very small dipole moment component perpendicular to the tilt plane was found which, according to the Boulder model, may be responsible for the moderate P_S values obtained.     

Frequency-selective homonuclear dipolar recoupling in solid state NMR

We introduce a new approach to frequency-selective homonuclear dipolar recoupling in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS). This approach, to which we give the acronym SEASHORE, employs alternating periods of double-quantum recoupling and chemical shift evolution to produce phase modulations of the recoupled dipole-dipole interactions that average out undesired couplings, leaving only dipole-dipole couplings between nuclear spins with a selected pair of NMR frequencies. In principle, SEASHORE is applicable to systems with arbitrary coupling strengths and arbitrary sets of NMR frequencies. Arbitrary MAS frequencies are also possible, subject only to restrictions imposed by the pulse sequence chosen for double-quantum recoupling. We demonstrate the efficacy of SEASHORE in experimental (13)C NMR measurements of frequency-selective polarization transfer in uniformly (15)N, (13)C-labeled L-valine powder and frequency-selective intermolecular polarization transfer in amyloid fibrils formed by a synthetic decapeptide containing uniformly (15)N, (13)C-labeled residues.     

Determination of order parameters of liquid crystals: use of dipolar oscillations enhanced by Lee-Goldburg decoupling

Lee-Goldburg decoupling has been applied to enhance dipolar oscillations during the t1 period of the two-dimensional experiment used for obtaining order parameters of the liquid crystal N-(4-ethoxybenzylidene)-4-n-butylaniline (EBBA) at different temperatures. The order parameters of the aromatic core obtained by this method are in agreement with values obtained from the 2H NMR spectra of a selectively labelled compound and are observed to follow the empirical Haller equation.     

From colloids in liquid crystals to colloidal liquid crystals

ABSTRACT

Liquid crystals in combination with nanoparticles are a fascinating topic of research, because of the wealth of aspects and questions to study. These range from simple effects of nanoparticles on phase transitions and phase diagrams, to the tuning of physical properties, adding of novel functionalities, all the way to the formation of spontaneous order by nanoparticles themselves and the possibilities that templating has for future materials design and applications. This article intends to provide a flavour of the multiplicity, variety and diversity that these thermotropic and lyotropic systems have to offer in the area of materials development, which we believe will become increasingly important, especially for switchable non-display applications and nanotechnology. It is not intended to provide a conclusive overview, which would be a presumptuous attempt considering the limited space available, but rather to place our own work into a wider context and to point out some more recent developments and trends in liquid crystal – nanoparticle dispersions.