13C N.M.R. and 14N N.Q.R. in ferroelectric liquid crystals Polar versus quadrupolar ordering

Abstract

¹³C nuclear magnetic resonance and ¹⁴N nuclear quadrupole resonance spectra of ferroelectric smectic C?liquid crystals and their non-chiral analogues allow for a microscopic determination of the polar and quadrupolar (or bipolar) biasing of rotation around the long molecular axis as well as for a determination of the anisotropy in the fluctuations of this axis. The results show that the microscopic origin of the biquadratic coupling between the polarization and the tilt, which has been recently introduced into the extended Landau model of the S_A–S?_C transition, is the quadrupolar (or bipolar) rotational bias induced by the anisotropy in the fluctuations of the long molecular axis. The tilt induced anisotropy in the fluctuations is practically identical in chiral and non-chiral smectic C phases.     

Microscopic origin of spontaneous polarization in ferroelectric SC* liquid crystals

The origin of spontaneous polarization in the ferroelectric smectic C* phase is investigated within a mean-field microscopic model which describes the coupling between the tilt of molecules from the normal to the smectic layers and the rotation of a molecule around its long axis. The mean-field potential is studied which takes into account a chiral polar and a non-chiral quadrupolar biasing of the rotation of molecules around the molecular long axes. Each molecule is characterized by three transverse molecular axes: the chiral axis which turns parallel to the macroscopic C₂ axis at small tilts, the polar axis in the direction of the transverse dipole moment and the quadrupolar axis which tends to be parallel to the C₂ axis at very large tilts. A numerical analysis of the model shows that there are four different types of spontaneous polarization dependent on the temperature, including the sign-reversal type. The influence of three microscopic parameters, i.e. two angles between the three characteristic axes and the relative strength of the chiral versus the non-chiral biasing, on the type of spontaneous polarization is investigated. The relationship between the microscopic and the equivalent Landau model is established and discussed.     

De Vries smectic A phase formed by a liquid crystal side chain copolymer? A 13C NMR study

We study the orientation and order parameter of a liquid crystalline random side chain copolymer by ¹³C NMR. Evidence has previously been presented that this material forms a de Vries smectic A phase. The NMR data show that the molecular tilt angle in the smectic A phase is very small or zero and the smectic A-smectic C* transition is attributed predominantly to a change of the molecular tilt rather than azimuthal ordering. We discuss the NMR results in the context of earlier X-ray and elastic characterizations of structurally similar materials.     

Macroscopic properties of mixed chiral smectic liquid crystals

Binary mixtures of chiral and non-chiral smectogens, DOBAMBC and DBHP respectively, exhibit a chiral smectic C phase in two separated concentration regions (about 0-20 and 60-100 mol per cent of DOBAMBC) and a chiral smectic I phase in the region of 60-100 mol per cent of DOBAMBC. For the S*_cphase, the temperature and the concentration dependences of the spontaneous polarization, the tilt angle and the helical pitch were determined. The electric field switching properties of the S*_iphase have been studied. For higher concentrations, the switching is similar to that of the S*_iphase of pure DOBAMBC. When the concentration of DOBAMBC is lowered, bistable switching is observed.     

On the origin of high optical director tilt in a partially fluorinated orthoconic antiferroelectric liquid crystal mixture

We have investigated the orthoconic antiferroelectric liquid crystal mixture W107 by means of optical, X-ray and calorimetry measurements in order to assess the origin of the unusally high tilt angle between the optic axis and the smectic layer normal in this material. The optical birefringence increases strongly below the transition to the tilted phases, showing that the onset of tilt is coupled with a considerable increase in orientational order. The layer spacing in the smectic A* (SmA*) phase is notably smaller than the extended length of the molecules constituting the mixture, and the shrinkage in smectic C* (SmC*) and smectic C_a* (SmC_a*) is much less than the optical tilt angle would predict. These observations indicate that the tilting transition in W107 to a large extent follows the asymmetric de Vries diffuse cone model. The molecules are on average considerably tilted with respect to the layer normal already in the SmA* phase but the tilting directions are there randomly distributed, giving the phase its uniaxial characteristics. At the transition to the SmC* phase, the distribution is biased such that the molecular tilt already present in SmA* now gives a contribution to the macroscopic tilt angle. In addition, there is a certain increase of the average tilt angle, leading to a slightly smaller layer thickness in the tilted phases. Analysis of the wide angle scattering data show that the molecular tilt in SmC_a* is about 20° larger than in SmA*. The large optical tilt (45°) in the SmC_a* phase thus results from a combination of an increased average molecule tilt and a biasing of tilt direction fluctuations.     

A microscopic model considering the effect of molecular biaxiality on ferroelectric ordering of liquid crystalline smectic C* phases

On the basis of a mean-field approach, a microscopic model is presented to explain some ferroelectric properties of induced smectic C* phases of chiral dipolar guest molecules in an achiral smectic C host phase. The molecular biaxiality of the chiral dopants has been taken into account, resulting in a polar and quadrupolar ordering of the molecular short axes in the rotational distribution function of the guest molecules. This model explains the dependence of the magnitude and sign of the spontaneous polarization on the molecular structure of a series of cyclo-hexanone derivatives used as chiral dopants, as well as the effect of a local field at higher dopant concentrations.     

Polar and quadrupolar order in smectic liquid crystals

In several smectic phases the long molecules are tilted towards the layer planes. The molecules in the layers of smectic C phases have a preferred tilt direction with a C2 rotation axis perpendicular to the tilt plane. If the molecules have a brick-like shape, a configuration possessing the D2h symmetry is also possible. For molecules shaped like chevrons or bananas, the existence of a smectic phase with the symmetry Cv was recently reported. We consider different in-plane configurations of smectics using a geometrical approach based on the 'scaled particle theory'. Varying the geometrical parameters of hard rod particles, a phase diagram for several smectic configurations is predicted. Depending on the particle shape, phases with dipolar order (C2,Cv) and quadrupolar order (D2h) can be stable.     

On the origin of high optical director tilt in a partially fluorinated orthoconic antiferroelectric liquid crystal mixture

We have investigated the orthoconic antiferroelectric liquid crystal mixture W107 by means of optical, X-ray and calorimetry measurements in order to assess the origin of the unusally high tilt angle between the optic axis and the smectic layer normal in this material. The optical birefringence increases strongly below the transition to the tilted phases, showing that the onset of tilt is coupled with a considerable increase in orientational order. The layer spacing in the smectic A* (SmA*) phase is notably smaller than the extended length of the molecules constituting the mixture, and the shrinkage in smectic C* (SmC*) and smectic C_a* (SmC_a*) is much less than the optical tilt angle would predict. These observations indicate that the tilting transition in W107 to a large extent follows the asymmetric de Vries diffuse cone model. The molecules are on average considerably tilted with respect to the layer normal already in the SmA* phase but the tilting directions are there randomly distributed, giving the phase its uniaxial characteristics. At the transition to the SmC* phase, the distribution is biased such that the molecular tilt already present in SmA* now gives a contribution to the macroscopic tilt angle. In addition, there is a certain increase of the average tilt angle, leading to a slightly smaller layer thickness in the tilted phases. Analysis of the wide angle scattering data show that the molecular tilt in SmC_a* is about 20° larger than in SmA*. The large optical tilt (45°) in the SmC_a* phase thus results from a combination of an increased average molecule tilt and a biasing of tilt direction fluctuations.     

Polar and quadrupolar order in smectic liquid crystals

In several smectic phases the long molecules are tilted towards the layer planes. The molecules in the layers of smectic C phases have a preferred tilt direction with a C2 rotation axis perpendicular to the tilt plane. If the molecules have a brick-like shape, a configuration possessing the D2h symmetry is also possible. For molecules shaped like chevrons or bananas, the existence of a smectic phase with the symmetry Cv was recently reported. We consider different in-plane configurations of smectics using a geometrical approach based on the 'scaled particle theory'. Varying the geometrical parameters of hard rod particles, a phase diagram for several smectic configurations is predicted. Depending on the particle shape, phases with dipolar order (C2,Cv) and quadrupolar order (D2h) can be stable.     

A study of the electroclinic effect in the smectic A* phase of mixtures with strongly chiral alkoxybiphenyl-phenyl carboxylate dopants

A detailed investigation has been reported of the electroclinic behaviour in the smectic A* phase of eleven mixtures made up of a commercial achiral smectic C host and strongly chiral alkoxybiphenyl-phenyl carboxylate dopants. A new technique was used to measure the induced tilt angle as a function of electric field and temperature. For all the mixtures, the electroclinic response followed a Curie-Weiss type temperature dependence for measurements performed well away from the smectic A* to smectic C* phase transition temperature. The strength of the electroclinic response was evaluated for each mixture by determining the temperature independent ratio k/a (i.e. the electroclinic coupling susceptibility, k divided by the susceptibility coefficient controlling the induced tilt, a). Analysis of the results showed that k/a of the mixtures was dependent on the type and position of the electronegative or polar substituents that affected the net dipole moment of the chiral dopants. In fact, the value of k/a was largest when fluorine was replaced by hydrogen in the lateral position and at the chiral centre. Furthermore, relatively short alkyl chains (e.g. C₆H₁₃) at the chiral centre were preferred to longer ones (e.g. C₁₀H₂₁) for a larger electroclinic response.     

Molecular dynamics study of the ferroelectric liquid crystal CI IPNOC by proton spin-lattice relaxation

Proton spin-lattice relaxation studies were carried out in the S_A and S*_C phases of the liquid crystal CI IPNOC using both conventional and fast field cycling NMR techniques. T₁ dispersion curves were obtained at two different temperatures for each mesophase covering frequencies from 10² to 3 × 10⁸ Hz. In both mesophases the T₁ data can be described assuming the presence of three different relaxation mechanisms, namely local molecular rotations, molecular self-diffusion and collective motions. The self-diffusion constant D₁ was evaluated for several temperatures and the activation energy associated with the diffusion process was obtained. The expected contribution of the soft-mode for the spin-lattice relaxation could not be separated from the contribution of other collective motions. The correlation times associated with the rotations around the molecular long axis and with the fluctuations of this axis were evaluated for both the S_A and the S*_C phases.     

2H NMR spectroscopy of liquid crystals: structure and orientational order of a chiral smectogen in its A, C* and J* phases

²H NMR spectroscopy is employed to investigate the orientational order, molecular structure and phase transitions of the chiral smectic liquid crystal 1-methylheptyl 4'-(4-n-decyloxybenzoyloxy)biphenyl-4-carboxylate (10B1M7), showing smectic A, C* and J phases, as well as several sub-smectic C* phases. Two optically pure, differently deuteriated isotopomers have been purposely synthesized and studied.     

Invited Article Experimental techniques for the investigation of ferroelectric liquid crystals

A review is given of several experimental methods for the measurement of the performance parameters of ferroelectric liquid crystals. We discuss (a) the technique for measuring the spontaneous polarization, the elastic modulus and dielectric susceptibility for the tilt of the director (the pyro-electric method), (b) the measurement of the tilt angle and the optical anisotropy (the electro-optical method) and (c) the determination of the non-linear susceptibility of the chiral smectic C* phase (the optical second harmonic generation technique).     

Evidence for a tilted smectic phase in Anopore membranes by dielectric spectroscopy

Collective relaxation processes are completely undetectable in a ferroelectric liquid crystal confined in porous Anopore membranes, as a result of perfect orientation of the smectic layers perpendicular both to the long axis of the pores and the direction of the measuring electric field. In the ferroelectric liquid crystal – Anopore composite only one relaxation process, assigned to rotation of the molecule around the molecular short axis, appears throughout all smectic phases. The temperature dependence of the relaxation frequency and of the dielectric strength of this process also shows no irregularity at the point of polarization sign reversal. The temperature dependence of the relaxation frequency follows the Arrhenius law with an activation energy slightly higher in the ferroelectric SmC* phase. Analysis of the non‐linear changes of temperature dependence of the dielectric strength at the SmA–SmC* phase transition enables one to obtain the temperature dependence of the tilt angle of the molecules in the SmC* phase in the Anopore membrane. Dielectric measurements confirm the existence of the tilted smectic phase in Anopore cylindrical channels with no tilt anomaly at the point of polarization sign reversal.     

Evidence for a tilted smectic phase in Anopore membranes by dielectric spectroscopy

Collective relaxation processes are completely undetectable in a ferroelectric liquid crystal confined in porous Anopore membranes, as a result of perfect orientation of the smectic layers perpendicular both to the long axis of the pores and the direction of the measuring electric field. In the ferroelectric liquid crystal - Anopore composite only one relaxation process, assigned to rotation of the molecule around the molecular short axis, appears throughout all smectic phases. The temperature dependence of the relaxation frequency and of the dielectric strength of this process also shows no irregularity at the point of polarization sign reversal. The temperature dependence of the relaxation frequency follows the Arrhenius law with an activation energy slightly higher in the ferroelectric SmC* phase. Analysis of the non-linear changes of temperature dependence of the dielectric strength at the SmA-SmC* phase transition enables one to obtain the temperature dependence of the tilt angle of the molecules in the SmC* phase in the Anopore membrane. Dielectric measurements confirm the existence of the tilted smectic phase in Anopore cylindrical channels with no tilt anomaly at the point of polarization sign reversal.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Shear flow and magnetic field effects on smectic C,C*, CM and C*M liquid crystals

Abstract

The continuum equations of Leslie et al. [1] for smectic C, and the extension of this theory for chiral smectic C* [2], are applied to problems involving simple planar layer configurations which accommodate uniform layer thickness constraints. The chiral smectic C*_M and non-chiral smectic C_M [3] are considered as either biaxial smectic A phases or antiferroelectric smectic C phases and are therefore included as interesting degenerate cases of the smectic C* and C phases, respectively. The effects of static and time dependent magnetic fields on these materials are compared with related deformations occurring in nematics [4] and cholesterics [5,6]. Their reaction to applied shears is also investigated yielding examples of flow alignment, induced secondary flows and unwinding of the chiral helix and testing the validity of enforcing a constant layer thickness.     

Molecular dynamics of a ferroelectric smectogen in its smectic phases by means of 2H NMR spectroscopy

In this work the dynamic behaviour of the ferroelectric liquid crystal (-)-(S )-[4-(2-methylbutyloxycarbonyl)phenyl] 4-n-heptylbiphenylcarboxylate (MBHB) in its smectic A (SmA), unwound chiral smectic C (uSmC*) and chiral smectic C (SmC*) phases has been studied by means of ²H NMR spectroscopy. Zeeman (T _1Z) and quadrupolar (T _1Q) spin-lattice relaxation times have been analysed to extract dynamic parameters (diffusion coefficients and activation energies). The small step rotation diffusion model in the uniaxial approximation has been used to describe overall spinning and tumbling motions, and the strong collision model to describe the internal reorientations of the aromatic fragment. Relaxation data in the SmC* phase have been analysed by using a theoretical approach. The dynamic features obtained in the smectic phases of this mesogen are here presented and discussed in comparison with the results obtained in other ferroelectric liquid crystals, focusing on the fast regime of motions.