Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.     

Liquid crystal orientation in elliptic droplets in nematic emulsions

Elliptic droplets of nematic liquid crystal dispersed in a fluid organic monomer were obtained by phase separation from an isotropic mixture consisting of an organic monomer and a nematic liquid crystal contained in a poly(ethylene terephthalate) cell with inner surfaces treated with rubbed polyimide. The elliptic shape is a consequence of the constraint upon droplet growth along the direction perpendicular to the cell surfaces owing to the small thickness. Then, the resulting droplets will have a contact area with the inner surfaces of the cell treated with polyimide, which will impart a planar orientation on the liquid crystal in the droplet. By means of an optical microscope, using a simple pin hole of 5 μ m, we have selected single droplets for a series of samples having different contact areas. By polarized infrared spectroscopy we have also studied the liquid crystal orientation in selected areas of the droplets. We then report the dependence of the order parameter of the liquid crystal on different contact areas with the alignment surface of the cell. The good degree of planar alignment of the liquid crystal in the elliptic droplets allows the use of such a technique for realizing electro-optical films operating in the reverse mode. We report the electro-optical transmission of reverse mode films with different sizes of elliptic droplet.     

Liquid crystal orientation in elliptic droplets in nematic emulsions

Elliptic droplets of nematic liquid crystal dispersed in a fluid organic monomer were obtained by phase separation from an isotropic mixture consisting of an organic monomer and a nematic liquid crystal contained in a poly(ethylene terephthalate) cell with inner surfaces treated with rubbed polyimide. The elliptic shape is a consequence of the constraint upon droplet growth along the direction perpendicular to the cell surfaces owing to the small thickness. Then, the resulting droplets will have a contact area with the inner surfaces of the cell treated with polyimide, which will impart a planar orientation on the liquid crystal in the droplet. By means of an optical microscope, using a simple pin hole of 5 μm, we have selected single droplets for a series of samples having different contact areas. By polarized infrared spectroscopy we have also studied the liquid crystal orientation in selected areas of the droplets. We then report the dependence of the order parameter of the liquid crystal on different contact areas with the alignment surface of the cell. The good degree of planar alignment of the liquid crystal in the elliptic droplets allows the use of such a technique for realizing electro-optical films operating in the reverse mode. We report the electro-optical transmission of reverse mode films with different sizes of elliptic droplet.     

Graphene and liquid crystal mediated interactions

ABSTRACT

The two-dimensional graphene-honeycomb structure can interact with the liquid crystal’s (LC) benzene rings through π–π electron stacking. This LC–graphene interaction gives rise to a number of interesting physical and optical phenomena in the LC. In this paper, we present a combination of a review and original research of the exploration of novel themes of LC ordering at the nanoscale graphene surface and its macroscopic effects on the LC’s nematic and smectic phases. We show that monolayer graphene films impose planar alignment on the LC, creating pseudo-nematic domains (PNDs) at the surface of graphene. In a graphene-nematic suspension, these PNDs enhance the orientational order parameter, exhibiting a giant enhancement in the dielectric anisotropy of the LC. These anisotropic domains interact with the external electric field, resulting in a non-zero dielectric anisotropy in the isotropic phase as well. We also show that graphene flakes in an LC reduce the free ion concentration in the nematic media by an ion-trapping process. The reduction of mobile ions in the LC is found to have subsequent impacts on the LC’s rotational viscosity, allowing the nematic director to respond quicker on switching the electric field on and off. In a ferroelectric LC (smectic-C* phase), suspended graphene flakes enhance the spontaneous polarisation by improving the tilted smectic-C* ordering resulting from the π–π electron stacking. This effect accelerates the ferroelectric-switching phenomenon. Graphene can possess strain chirality due to a soft shear mode. This surface chirality of graphene can be transmitted into LC molecules exhibiting two types of chiral signatures in the LCs: an electroclinic effect (a polar tilt of the LC director perpendicular to, and linear in, an applied electric field) in the smectic-A phase, and a macroscopic helical twist of the LC director in the nematic phase. Finally, we show that a graphene-based LC cell can be fabricated without using any aligning layers and ITO electrodes. Graphene itself can be used as the electrodes as well as the aligning layers, obtaining an electro-optic effect of the LC inside the cell.     

Liquid crystal nanoparticles prepared as miniemulsions

Liquid crystal nanoparticles using the low molecular weight liquid crystal E7 are prepared by a miniemulsion approach with a droplet size between 180 and 630 nm. The sizes of liquid crystal droplets prepared in this work are one of the smallest sizes ever reported for liquid crystals, and they are considerably dependent on the type and amount of the surfactant used, as well as on the amount of hexadecane. Furthermore, the behavior of a liquid crystal confined to small droplets is investigated. DSC measurements reveal a large shift in the nematic-isotropic phase transition temperature. Further investigations on liquid crystal droplets are carried out using AFM measurements showing that these particles have an order of the liquid crystal molecules within the droplets. Light scattering measurements yield the temperature dependence of the anisotropy and the temporal stability of the droplets. An effect of the director fluctuations within the droplets on dynamic depolarized scattering was found.     

Diffusion of brownian particles in the isotropic phase of a nematic liquid crystal

Abstract

We report a light scattering study of the translational diffusion of a suspension of silica spheres in the liquid crystal, 4-n-pentyl-4'-cyanobiphenyl. We observe a small but significant increase of the effective hydrodynamic radius of the colloidal particles as the transition to the nematic phase is approached. This effect can be understood in terms of orientational pre-wetting of the silica spheres.     

Diffusion of brownian particles in the isotropic phase of a nematic liquid crystal

We report a light scattering study of the translational diffusion of a suspension of silica spheres in the liquid crystal, 4-n-pentyl-4'-cyanobiphenyl. We observe a small but significant increase of the effective hydrodynamic radius of the colloidal particles as the transition to the nematic phase is approached. This effect can be understood in terms of orientational pre-wetting of the silica spheres.     

Nanoconfined heliconical structure of twist-bend nematic liquid crystal phase

We produced controlled heliconical structures of a twist-bend nematic (N_TB) liquid-crystal (LC) phase in nanoconfinement in a porous anodic aluminium oxide (AAO) film. The structural parameters of the N_TB phase such as conical angle and helical pitch can be modulated by varying the surface energy of the inner surface of the porous AAO film, done by using different self-assembled monolayers (SAMs). The LC molecules tend to be more freely packed, thus forming a larger conical angle, when placed on the tri-deca-fluoro-1,1,2,2-tetrahydrooctyl-trichlorosilane (FOTS)-treated substrate, which has a relatively low surface energy. In contrast, the molecules form a more tightly packed structure, and thus a smaller conical angle, when placed on the 2-(methoxy(polyethyleneoxy)-propyl)trimethoxysilane (PEG 6/9)-treated substrate, which has higher surface energy. This work improves our collective understanding of self-assembled heliconical structures in the N_TB phase.     

Complete phase diagrams of mixtures of a nematic liquid crystal with n-alkanes

The full experimental phase diagrams of mixtures of the nematic liquid crystal 4.4'-azoxyanisole, (PAA), and n-tetracosane and of PAA and n-octadecane are given. Equilibria of a nematic phase with an isotropic phase, of two isotropic phases, and a reentrant isotropic phase could be observed directly. The experimental phase diagram is in qualitative agreement with the result derived from the Flory lattice model adopted for thermotropic systems.     

Cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of several members of the 1,ω-bis(4-cyanobiphenyl-4′-yl) alkane (CBnCB) and the 1-(4-cyanobiphenyl-4′-yloxy)-ω-(4-cyanobiphenyl-4′-yl) alkane (CBnOCB) homologous series are reported. The new odd members described CB5CB, CB13CB, CB4OCB, CB8OCB and CB10OCB all exhibit twist-bend nematic and nematic phases. The members of these series already reported in literature, CB7CB, CB9CB, CB11CB and CB6OCB, were also prepared in order to allow for a direct comparison of their transitional properties. The properties of these dimers are also compared to those of the corresponding members of the 1,ω-bis(4-cyanobiphenyl-4,-yloxy) alkanes (CBOnOCB). For any given total spacer length, for odd members of these series, the nematic–isotropic transition temperatures and associated entropy changes are greatest for the CBOnOCB dimer and lowest for the CBnCB dimer. These trends are understood in terms of molecular shape. For short spacer lengths, the twist-bend nematic–nematic transition temperature (T_NTBN) is higher for the CBnOCB series than for the CBnCB series but this is reversed as the spacer length increases. Of the CBOnOCB dimers, a virtual value of T_NTBN was estimated for CBO3OCB and T_NTBN was measured for CBO5OCB. These values are considerably lower than those observed for the corresponding members of the CBnCB or CBnOCB series. The dependence of T_NTBN on molecular structure is discussed not only in terms of the molecular curvature but also in the ability of the molecules to pack efficiently. As the temperature range of the preceding nematic phase increases, so the twist-bend nematic–nematic transition entropy change decreases and the transition approaches second order for the longer spacers. For comparative purposes, the transitional behaviour of the even-membered dimers CB6CB, CB5OCB and CBO4OCB is reported and differences accounted for in terms of molecular shape.     

Azobenzene-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of two new sets of non-symmetric liquid crystal dimers is reported, the 1-(4-substitutedazobenzene-4′-yloxy)-6-(4-cyanobiphenyl-4′-yl)hexanes (CB6OABX) and 1-(4-substitutedazobenzene-4′-yloxy)-6-(4-cyanobiphenyl-4′-yloxy)pentanes (CBO5OABX). The terminal substituents are methyl, methoxy, butyl, butyloxy, nitrile and nitro. All the CB6OABX dimers exhibit twist-bend nematic (N_TB) and nematic (N) phases. The CBO5OABX dimers also all show an N phase but only the butyl and butyloxy homologues exhibit the N_TB phase. The transitional behaviour of the non-symmetric dimers is compared to that of the corresponding symmetric dimers, the 1,5-bis(4-substitutedazobenzene-4′-yloxy)pentanes (XABO5OABX) and either 1,7-bis(4-cyanobiphenyl-4′-yl)heptane or 1,5-bis(4-cyanobiphenyl-4′-yloxy)pentane. The XABO5OABX dimers all show a nematic phase and in addition, the butyl homologue exhibits a smectic A phase. The difference in transitional behaviour between the CB6OABX and CBO5OABX dimers is attributed to the difference in their molecular shapes arising from different bond angles between the para axis of the cyanobiphenyl unit and the first bond in the spacer. Specifically, the all-trans conformation of a CBO5OABX dimer is more linear than that of the corresponding CB6OABX dimer. Differences within each set of dimers are attributed to changes in the average molecular shape and the strength of the mixed mesogen interaction on varying the terminal group. Crystal structures are reported for CB6OABOMe, CBO5OABNO₂ and MeOABO5OABOMe.     

Modelling a nematic liquid crystal

The bulk phase liquid crystalline behaviour of a cyclic siloxane with a pentamethylcyclosiloxane core and biphenyl-4-allyloxybenzoate mesogens (BCS) was studied using molecular dynamics (MD) and wide angle X-ray analysis. This material exhibits partial crystallinity at room temperature and liquid crystalline behaviour above 120° C. For the MD simulations an ensemble of 27 molecules with 135 mesogenic units was simulated and a molecular mechanics force field was used to model the structural anisotropy of the siloxane molecules. Simulations were carried out both at room temperature and at an elevated temperature (425 K). Room temperature simulations showed that, contrary to our initial assumptions, the low energy molecular conformations were not cylindrical but splayed in shape. During the simulation a smectic-like, tilted layer structure was found to evolve for the cluster when full atom potentials were used, while no such development was observed when electrostatic interactions were neglected. The presence of a tilted layered structure was also suggested by the X-ray data. These results indicate that long range electrostatic interactions are significant for the molecular system under study. In order to calculate the orientational order parameter, the orientation of the molecular axis had to be determined. This was achieved by describing the mesogen shapes to be ellipsoidal and defining the principal axis of the ellipsoids to be the molecular directors. By sampling over 200 ps of simulation at 425 K, the time averaged order parameter (S) was calculated. The calculated S of 0.36 was comparable to the value of 0.4-0.45 found from the experimental data. Apart from providing insight into the relative importance of the various competing forces in the formation of the liquid crystalline phase, these simulations are also expected to be useful in predicting the mesophase behaviour of liquid crystalline systems.     

Textures in polygonal arrangements of square nanoparticles in nematic liquid crystal matrices

A systematic analysis of defect textures in faceted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform alignment in the outer boundaries. Defect and textures are analyzed as functions of temperature T, polygon size R, and polygon number N. For nematic nanocomposites, the texture satisfies a defect charge balance equation between bulk and surface (particle corner) charges. Upon decreasing the temperature, the central bulk defects split and together with other -1/2 bulk defects are absorbed by the nanoparticle's corners. Increasing the lattice size decreases confinement and eliminates bulk defects. Increasing the polygon number increases the central defect charge at high temperature and the number of surface defects at lower temperatures. The excess energy per particle is lower in even than in odd polygons, and it is minimized for a square particle arrangement. These discrete modeling results show for first time that, even under strong anchoring, defects are attached to particles as corner defects, leaving behind a low energy homogeneous orientation field that favors nanoparticle ordering in nematic matrices. These new insights are consistent with recent thermodynamic approaches to nematic nanocomposites that predict the existence of novel nematic/crystal phases and can be used to design nanocomposites with orientational and positional order.     

Forces between cylindrical nanoparticles in a liquid crystal

Using classical density functional theory, the forces between two cylindrical nanoparticles in a liquid crystal solvent are calculated. Both the nematic and isotropic phases of the solvent are considered. In the nematic phase, the interaction is highly anisotropic. At short range, changes in the defect structure around the cylinders leads to a complex interaction between them. In the isotropic phase, an attractive interaction arises due to overlap between halos of ordered fluid adsorbed on the surfaces of the cylinders.     

Optical phase grating diffraction in a quasistatic electric field biased nematic liquid crystal film

Abstract

It is known that an optical phase grating can be obtained when two mutually coherent laser beams overlap in a nematic liquid crystal. This is mainly due to director reorientation which contributes to a large optical non-linearity. It has been suggested by Herman and Serinko that a phase grating could be obtained in nematic liquid crystals if a D.C. field is used to bias it near the critical orientational Freedericksz transition. A homeotropic MBBA film biased by an electric field at 1 kHz has been studied. Two weak Ar⁺ laser beams were incident normally to the film with a small intersection angle (?0·4?). Using the picture of a director reorientation mechanism and a degenerate four wave mixing scheme, we have obtained the dependence of the diffraction beam intensity on that of the incident beam and the strength of the biased electric field. The theoretical prediction and experimental results both show that the phase grating diffraction can be dramatically enhanced by the coupling of the electric field to the optical field in the Freedericksz transition region. This is due to the critical behaviour of the sample at that transition. The prominently improved signal-to-noise ratio is discussed.     

NMR relaxation of rigid molecules in the nematic phase of a discotic liquid crystal

Abstract

Frequency and temperature dependent NMR relaxation measurements were performed on deuteriated benzene, pyrene and triphenylene dissolved in the nematic phase of a discotic liquid crystal. The results show a strong frequency dependence of the spectral densities. Based on the symmetries of the system and the usual model for director fluctuations this frequency dependence should be equal for J ₁ and J ₂. From fitting the commonly used model of rotational diffusion and director fluctuations to the data we see that this is not the case for benzene and triphenylene, even though the fits themselves are satisfactory. Values for the elastic constants, effective viscosity and translational diffusion in similar discotic liquid crystals do not account quantitatively for the frequency dependence of benzene. For both pyrene and triphenylene quantitative comparison was impossible due to lack of translational diffusion data. We also find that the so-called cut-off wave-length is of the order of the dimensions of the liquid crystal molecules, just as in ordinary nematics.     

NMR relaxation of rigid molecules in the nematic phase of a discotic liquid crystal

Frequency and temperature dependent NMR relaxation measurements were performed on deuteriated benzene, pyrene and triphenylene dissolved in the nematic phase of a discotic liquid crystal. The results show a strong frequency dependence of the spectral densities. Based on the symmetries of the system and the usual model for director fluctuations this frequency dependence should be equal for J₁ and J₂. From fitting the commonly used model of rotational diffusion and director fluctuations to the data we see that this is not the case for benzene and triphenylene, even though the fits themselves are satisfactory. Values for the elastic constants, effective viscosity and translational diffusion in similar discotic liquid crystals do not account quantitatively for the frequency dependence of benzene. For both pyrene and triphenylene quantitative comparison was impossible due to lack of translational diffusion data. We also find that the so-called cut-off wave-length is of the order of the dimensions of the liquid crystal molecules, just as in ordinary nematics.     

Liquid crystal composites with a high percentage of gold nanoparticles

We have reported in our previous work that doping low concentrations (up to 10% by weight) of gold nanoparticles (GNP) in a polar nematic 4’-hexyl-4-biphenylcarbonitrile (HBPCN) increases the dielectric anisotropy, while the switching voltage and times, and the nematic–isotropic liquid (IL) transition point of the mixtures are not affected by doped nanoparticles. In the current work we extend our study of the behaviour of HBPCN doped with higher than 10% GNP. We show that at certain gold concentrations – 35% and 45% – the nematic–IL phase transition point increases by 15°C in comparison with the pure nematic value. At the same concentrations the dielectric anisotropy increases from its value for the pure nematic by about 2.2 times for 35% and twice for 45%. Also, the threshold voltage increases by 0.2 V for 35% and decreases by 0.15 V for 45%. However, the switching-off times decrease for both concentrations: 7 ms for 35% and 12 ms for 45%. We propose that the described effects of doped GNP on the properties of the nematic are due to the formation of different kinds of aggregations between two components of the mixtures.     

Dielectric properties of a strongly polar nematic liquid crystal compound doped with gold nanoparticles

This study focuses on the electrical characteristics of a strongly polar nematic liquid crystal, Hexyloxy-cyanobiphenyl (6OCB), doped with a low concentration (2% by weight) of citrate buffer stabilised gold nanoparticles (GNPs) at low frequencies between 20 Hz and 35 MHz. The doped samples have lower values of nematic–isotropic transition temperature, permittivity (both parallel and perpendicular to the field direction) and dielectric anisotropy; however, relaxation time and activation energy were increased. The observed results could be explained on the basis of weakly anisotropic nature of GNPs and a local rearrangement of liquid crystal molecules surrounding the nanoparticles. Moreover, a complimentary suggestion on a possible change in the dipole–dipole correlation is made to explain the difference in changes (qualitative and quantitative) observed for permittivity of the host nematic liquid crystal doped with GNP. Temperature dependent dielectric relaxation studies indicate an increase in viscosity and potential barrier; and hence a change in strength of inter-molecular and intra-molecular interactions is suggested.