An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data.     

Particle tracking microrheology of lyotropic liquid crystals

We present comprehensive results on the microrheological study of lyotropic liquid crystalline phases of various space groups constituted by water-monoglyceride (Dimodan) mixtures. In order to explore the viscoelastic properties of these systems, we use particle tracking of probe colloidal particles suitably dispersed in the liquid crystals and monitored by diffusing wave spectroscopy. The identification of the various liquid crystalline phases was separately carried out by small-angle X-ray scattering. The restricted motion of the particles was monitored and identified by the decay time of intensity autocorrelation function and the corresponding time-dependent mean square displacement (MSD), which revealed space group-dependent behavior. The characteristic time extracted by the intersection of the slopes of the MSD at short and long time scales, provided a characteristic time which could be directly compared with the relaxation time obtained by microrheology. Further direct comparison of microrheology and bulk rheology measurements was gained via the Laplace transform of the generalized time-dependent MSD, yielding the microrheology storage and loss moduli, G'(ω) and G'(ω), in the frequency domain ω. The general picture emerging from the microrheology data is that all liquid crystals exhibit viscoelastic properties in line with results from bulk rheology and the transition regime (elastic to viscous) differs according to the specific liquid crystal considered. In the case of the lamellar phase, a plastic fluid is measured by bulk rheology, while microrheology indicates viscoelastic behavior. Although we generally find good qualitative agreement between the two techniques, all liquid crystalline systems are found to relax faster when studied with microrheology. The most plausible explanation for this difference is due to the different length scales probed by the two techniques: that is, microscopical relaxation on these structured fluids, is likely to occur at shorter time scales which are more suitably probed by microrheology, whereas bulk, macroscopic relaxations occurring at longer time scales can only be probed by bulk rheology.     

Hydrogen catalysis of alkyl radical decay in single crystalline polyethylene

Although hydrogen gas is about tenfold more soluble in hot-filtered mats of polyethylene (PE) single crystals (SC) than in bulk linear PE, we found that no hydrogen solubility at all could be measured in freeze-dried SC. Despite this, hydrogen gas still exerts a catalytic effect on alkyl radical decay on both the fast and slow first-order decay reactions in the freeze-dried samples. Above 40°C the first-order decay constants of the slowly decaying component decrease with increasing fold period.     

Invited Lecture. Studies of liquid crystal monolayers and films by optical second harmonic generation

It is shown that optical second harmonic generation can be used to probe a number of important properties of liquid crystals: second order non-linearity of liquid crystal molecules, polar ordering and orientation of liquid crystal monolayers at various interfaces, and bulk alignment of molecules in supported and freely suspended films. Surface effects on bulk alignment can also be investigated.     

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.     

Role of surface anchoring and geometric confinement on focal conic textures in smectic-A liquid crystals

A high surface area-to-volume ratio in microchannels increases the importance of surface interactions within them. In layered liquids, such as smectic liquid crystals, surface interactions play an important role in the formation of defect textures. We use 8CB liquid crystal, which is in the smectic-A phase at room temperature, as a model layered liquid. PDMS surfaces can be tuned to be hydrophilic or hydrophobic, and due to the nature of liquid crystalline molecules, we show that this results in planar or homeotropic anchoring conditions, respectively. In a confined system, contrary to the bulk, generated defects cannot grow freely. In the present work, we show that the confinement offered by PDMS microchannels along with the capability of creating mixed anchoring conditions within them results in the formation of particular ordered defect textures through increased surface interactions in smectic-A liquid crystals. Our observations imply that microscale confinement is useful for controlling the size, size distribution, and packing structure of microscale defect structures within these materials. In addition, we show that by placing a droplet of smectic-A liquid crystal on a PDMS surface containing microscale parallel cracks, ordered focal conic defects form between two adjacent cracks. The distance between two adjacent cracks dictates the size of the defects. These observations could lead to useful ideas for exploring new technologies for flexible optical devices or displays that utilize smectic-A liquid crystals.     

Elastic properties of bent-core nematic liquid crystals: the role of the bend angle

ABSTRACT

The nematic phase formed from bent-core liquid crystals has been the focus of intensive research for more than a decade. With the potential of biaxial nematic phase and other interesting features, such as high Kerr constants, large flexoelectric coefficients and anomalous elastic constants, these bent-core materials have been in the limelight of research. This paper presents a mini-review of the interesting elastic behaviour reported in various bent-core compounds. The review further focusses on two different types of bent-core compounds as exemplars: one derived from an oxadiazole and other a thiadiazole, highlighting the importance of bend angle in bent-core compounds. The universality of the unique behaviour of bend elastic constants via molecular field theory and atomistic modelling has also been summarised.     

Elastic properties of the (001) face of xenon crystals

In this work we investigated the elastic properties of the (001) face of xenon crystal. The slabs (twodimensional crystals) defined by (001) planes are generated, their structures are optimized and the slabs thermodynamic functions in excess to the crystal bulk calculated. The calculations are based on the Lennard-Jones 6?12 force field, classical elasticity theory and surface thermodynamics. In this work, the number of planes undergoing relaxation is not a priori constrained but it follows from the minimization of the free energy of the slabs and of the bulk, in respect to atomic positions. The value of the surface free energy is calculated as a function of the homogeneous strain of the 2D (001) cell measured relatively to the cell of the stable 3D crystal. At 0 K, when strain is not applied, the specific surface free energy is about 0.064 Jm^-2 and decreases by about 6% at 50 K. The surface stress is positive amounting to 0.010 Jm^-2 at 0 K, and it decreases by about 50% at 50 K. We find that the surface stress can be released by a reorganization of the interatomic distances at the crystal surfaces. The surface excess mean value of the slab elastic constants at 0 K is small (0.012 GPa) and it decreases by about 35% at 50 K. The method proposed can be alternative to molecular dynamics simulations in order to assess the excess surface properties of materials having a complex structure.     

Modelling of microstructure in mesophases

Small-molecule liquid crystals show textures which are readily studied at low magnification in the optical polarizing microscope. In polymeric liquid crystals, however, the textures are often much finer, taxing the microscope's resolution. Nevertheless, studies of microstructure in such polymers have been made and it is apparent that they can differ widely both from small-molecule liquid crystals and, indeed, from polymer to polymer. This paper sets out to account for these variations by exploring the effect on microstructure of the marked differences between the magnitudes of the splay, twist and bend elastic constants which are a characteristic of many liquid crystalline polymers. We report a computer model which simulates the development of microstructure for different ratios of the elastic constants. When these are approximately equal, textures characteristic of small-molecule liquid crystals result, such as those involving escape into the third dimension with the degeneration of line defects into points. When the splay energy is high in comparison with bend and twist, as is the case for many thermotropic liquid crystalline copolyesters, escape does not occur and half integral disclination lines predominate. For simulations involving planar boundary conditions, layered microstructures result, frequently with little matching of the orientation from layer to layer. Within the layers the trajectory of the orienting units is sinuous. This simulated microstructure resembles textures observed in thermotropic copolyesters, studied both in this laboratory and elsewhere. The computer model uses a lattice approach which is similar in some respects to that developed by Lebwohl and Lasher. It should not be thought of as a molecular scale model, however, but rather as one based on assemblies of molecules which share a common director.     

Biaxial phases in mineral liquid crystals

A review is given of liquid crystals formed in colloidal dispersions, in particular those consisting of mineral particles. Starting with the historical development and early theory, the characteristic properties related to the colloidal nature of this type of liquid crystals are discussed. The possibility to find biaxial nematic and smectic phases is described for mixtures of rods and plates and recent examples are given of biaxial liquid crystal phases of mineral particles with inherent biaxial shape.     

New Lutetium Silicate Scintillators

Cerium-doped lutecium orthosilicate (LSO) is the most promising scintillator discovered in almost five decades. It exhibits a unique combination of important properties for x and gamma-ray spectroscopy: high density, fast decay, and large light yield. However, the practical use of LSO is hindered by difficulties related to its fabrication as a single crystal by the Czochralski method. We report on the usefulness of the sol-gel process in obtaining lutecium silicate scintillators. Upon appropriate drying and firing, lutetium silicate crystals can be grown in a silica matrix. The bulk, polycrystalline transparent scintillators are characterized by XRD, optical absorption, light decay measurement and gamma-ray spectral response. Their properties are comparable to that of traditional LSO single crystals.     

Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.     

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.     

State of the art of the sphere method, a unique characterization technique for non-linear crystals

We report the sphere method as a unique characterization technique for the complete study of non-linear optical properties for frequency conversion in new materials belonging to the uniaxial or biaxial optical class. It relies on the use of a single crystal with millimetre dimensions cut as a sphere, combined with a tuneable laser source. With the sphere method we perform direct measurements of phase-matching angles and associated conversion efficiencies for second harmonic, sum- and difference-frequency generation. Furthermore, we follow the orientation of the dielectric frame as a function of the wavelength for monoclinic and triclinic crystals. It also allows the determination of the magnitude of the principal refractive indices in biaxial crystals based on the study of the double refraction affect at the exit of a sphere. By combining the analysis of all these data simultaneously, we determine Sellmeier equations reliable over the whole transparency domain and we are able to get the non-zero elements of the second-order susceptibility tensor of uniaxial or biaxial crystals. Finally, the sphere method is completely self-sufficient for the study of biaxial crystals.     

Towards the biaxial nematic phase through molecular design

In this article, the search for the elusive biaxial nematic phase (NB) in liquid crystals is considered. The structure of the phase is described along with theoretical and computational work which suggests how it might be realised. An overview of the work of the Exeter group in this area is then given showing the different approaches adopted and illustrating how one of these has led to a new type of amphiphilicity based on shape.     

Dual quartz crystal microbalance compensation using a submerged reference crystal. Effect of surface roughness and liquid properties

Absolute resonant frequency measurements were made on gold-coated AT-cut quartz crystals with one face in contact with a series of liquids. The effect of surface roughness and liquid properties (viscosity and density) was analyzed in terms of a “trapped liquid” model. In this model, liquid present in surface imperfections is viewed as rigidly coupled mass. In some of the literature this density-dependent, but not viscosity-dependent, term is viewed as being additive to the hydrodynamic shift seen for a smooth surface. Data obtained using 1 μm and 5 μm surface finish crystals are inconsistent with the predictions of the trapped liquid model. This suggests hydrodynamic coupling between liquid internal and external to the crevices. Despite the lack of a theoretical model for the liquid motion, it is possible to compensate for frequency variations resulting from changing liquid properties and for roughness effects by making direct measurements of the resonant frequency difference between two crystals exposed to the same solution. This novel procedure works to the extent that the two crystals have similar surface topographies. Compensation is excellent for 1 μm finish crystals and good for 5 μm finish crystals.     

A metastable prerequisite for the growth of lumazine synthase crystals

Dense liquid phases, metastable with respect to a solid phase, form in solutions of proteins and small-molecule materials. They have been shown to serve as a prerequisite for the nucleation of crystals and other ordered solid phases. Here, using crystals of the protein lumazine synthase from Bacillus subtilis, which grow by the generation and spreading of layers, we demonstrate that within a range of supersaturations the only mechanism of generation of growth layers involves the association of submicrometer-size droplets of the dense liquid to the crystal surface. The dense liquid is metastable not only with respect to the crystals, but also with respect to the low-concentration solution: dynamic light scattering reveals that the droplets' lifetime is limited to several seconds, after which they decay into the low-concentration solution. The short lifetime does not allow growth to detectable dimensions so that liquid-liquid phase separation is not observed within a range of conditions broader than the one used for crystallization. If during their lifetime the droplets encounter a crystal surface, they lower their free energy not by decay, but by transformation into crystalline matter, ensuring perfect registry with the substrate. These observations illustrate two novel features of phase transformations in solutions: the existence of doubly metastable, short-lifetime dense phases and their crucial role for the growth of an ordered solid phase.     

Determination of several thermophysical properties of toluene using a single experimental setup

Dynamic light scattering can be used for the determination of several thermophysical properties of interest using one single experimental setup. Light scattering from bulk fluids allows the measurement of thermal diffusivity and sound velocity. Results are presented for toluene, an important reference fluid, over a wide temperature range up to the critical point at saturation conditions for both the liquid and the vapour phase. Furthermore, it is demonstrated that the same setup can be used for the determination of surface tension and kinematic viscosity of the liquid phase from light scattering by surface waves on a vertical liquid layer. All experiments are based on a heterodyne detection scheme and signal analysis by photon correlation spectroscopy. The results are discussed in comparison with literature data.     

Imaging of affinity microcontact printed proteins by using liquid crystals

This paper reports the design of surfaces on which thermotropic liquid crystals can be used to image affinity microcontact printed proteins. The surfaces comprise gold films deposited onto silica substrates at an oblique angle of incidence and then functionalized with a monolayer formed from 2-mercaptoethylamine. Ellipsometric measurements confirm the transfer of anti-biotin IgG to these surfaces from affinity stamps functionalized with biotinylated bovine serum albumin (BSA), while control experiments performed using anti-goat IgG confirmed the specificity of the IgG capture on the stamp. On these surfaces, anti-biotin IgG caused nematic phases of 4-cyano-4'-pentylbiphenyl (5CB, Delta epsilon = epsilon(parallel) - epsilon(perpendicular) > 0) to assume orientations that were parallel to the surfaces (planar anchoring) but with azimuthal orientations that were distinct from those assumed by the liquid crystals on the amine-terminated surfaces not supporting IgGs. Following incubation of these samples for >8 h at 36 degrees C, we observed that the amine-terminated regions of the surface not supporting IgG cause 5CB to undergo a transition from planar to perpendicular (homeotropic). Because N-(4-methoxybenzylidene)-4-butylaniline (MBBA) (Delta epsilon < 0) does not undergo a similar transition in orientation, this transition is consistent with the effects of an electrical double layer formed at the amine-terminated surface on the liquid crystal. Following the transition to homeotropic anchoring, the liquid crystals provide high optical contrast between regions of the surface supporting and not supporting IgG. We conclude that amine-terminated surfaces (I) uniformly align liquid crystals when not supporting proteins and (II) have sufficiently high surface free energy to capture proteins delivered to the surface from an affinity stamp, and thus they form the basis of a useful class of surfaces on which affinity microcontact printed proteins can be imaged using liquid crystals.