Azimuthal and zenithal anchoring of nematic liquid crystals

Director anchoring on a simple edge dislocation at the surface of induced smectic-C_{A} films

We present a detailed analysis of c-director anchoring measurements on simple edge dislocations at the surface of smectic-C_{A} films (steps). Indications show that the c-director anchoring on the dislocations originates from a local and partial melting of the dislocation core that depends on the anchoring angle. The SmC_{A} films are induced on isotropic puddles of 1-(methyl)-heptyl-terephthalylidene-bis-amino cinnamate molecules by the surface field, while the dislocations are located at the isotropic-smectic interface. The experimental setup is based on the connection of a three-dimensional smectic film sandwiched between a one-dimensional edge dislocation on its lower surface, and a two-dimensional surface polarization spread over the upper surface. Applying an electric field produces a torque that balances the anchoring torque of the dislocation. The film distortion that results is measured under a polarizing microscope. Exact calculations on these data, anchoring torque versus director angle, yield the anchoring properties of the dislocation. A specificity of our sandwich configuration is to improve the measurement quality by a factor of N^{3/2}∼600, where N=72 is the number of smectic layers in the film. We fit a second-order Fourier series on the torque-anchoring angle data, which has the advantage of converging uniformly over the entire anchoring angle range, i.e., over more than 70^{∘}. The two corresponding Fourier coefficients, k_{a1}^{F2} and k_{a2}^{F2}, are anchoring parameters that generalize the usual anchoring coefficient. When changing the electric field E, the anchoring state evolves along paths in a torque-anchoring angle diagram. Two cases occur depending on the angle α_{∞} of E relative to the unit vector S, perpendicular to the dislocation and parallel to the film. When α_{∞}<130^{∘}, the operating point Q that represents the anchoring state in the diagram follows reversible and "at-equilibrium" paths. Its free displacement velocity is infinitely slow, so that we have to push it with electric torque steps smaller than the experimental error bar δΓ∼10^{-14}N. On the other hand, for α_{∞}>130^{∘}, Q describes a hysteresis loop similar to the usually encountered ones in solids. This loop connects two states that exhibit broken and nonbroken anchorings, respectively. The paths that join them in an out-of-equilibrium process are irreversible and dissipative. When coming back to a nonbroken anchoring state, both the dislocation and smectic film spontaneously heal back in the very same state they were before the anchoring broke. The process does not produce any erosion thanks to their liquid nature, including at the microscopic scale. The energy that is dissipated on these paths is roughly estimated in terms of the c-director rotational viscosity. Similarly, we can evaluate the maximum time of flight along the dissipative paths to be of the order of a few seconds, which is consistent with qualitative observations. In contrast, the paths located inside each domain of these anchoring states are reversible and can be followed in an "at equilibrium" manner all along. This analysis should provide a basis for understanding the structure of multiple edge dislocations in terms of parallel simple edge dislocations interacting with each other through pseudo-Casimir forces arising from c-director thermodynamic fluctuations between them.

Programming Solitons in Liquid Crystals Using Surface Chemistry

AC electric fields cause three-dimensional orientational fluctuations (solitons) to form and rapidly propagate in confined films of liquid crystals (LCs), offering the basis of a new class of active soft matter (e.g., for accelerating mixing and transport processes in microscale chemical systems). How surface chemistry impacts the formation and trajectories of solitons, however, is not understood. Here, we show that self-assembled monolayers (SAMs) formed from alkanethiols on gold, which permit precise control over surface chemistry, are electrochemically stable over voltage and frequency windows (<100 V; 1 kHz) that lead to soliton formation in achiral nematic films of 4'-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47). By comparing soliton formation in LC films confined by SAMs formed from hexadecanethiol (C₁₆SH) or pentadecanethiol (C₁₅SH), we reveal that the electric field required for soliton formation increases with the LC anchoring energy: surfaces patterned with regions of C₁₆SH and C₁₅SH SAMs thus permit spatially controlled creation and annihilation of solitons necessary to generate a net flux of solitons. We also show that solitons propagate in orthogonal directions when confined by obliquely deposited gold films decorated with SAMs formed from C₁₆SH or C₁₅SH and that the azimuthal direction of propagation of solitons within achiral LC films possessing surface-induced twists is not unique but reflects variation in the spatial location of the solitons across the thickness of the twisted LC film. Finally, discontinuous changes in LC orientation induced by patterned surface anchoring lead to a range of new soliton behaviors including refraction, reflection, and splitting of solitons at the domain boundaries. Overall, our results provide new approaches for the controlled generation and programming of solitons with complex and precise trajectories, principles that inform new designs of chemical soft matter.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Method for Tuneable Homeotropic Anchoring at Microstructures in Liquid Crystal Devices

A simple method for vapour-phase deposition of a silane surfactant is presented, which produces tuneable homeotropic anchoring in liquid crystals. Both the zenithal anchoring energy and surface slip are measured by fitting to the latching threshold versus pulse width characteristic of a zenithal bistable nematic liquid crystal device based on a deep, submicron grating. The method is shown to give microscopic anchoring strength between 5 × 10^-5 and 2 × 10^-4 J/m², with a surface slip of about 100 nm. The silanated surfaces are characterized using atomic force microscopy and X-ray photoelectron spectroscopy, which show a direct relationship between the surface coverage of silane groups and the resulting anchoring energy.

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Surface topography and rotational symmetry breaking

The surface electroclinic effect, which is a rotation of the molecular director in the substrate plane proportional to an electric field E applied normal to the substrate, requires both a chiral environment and C(2) (or lower) rotational symmetry about E. The two symmetries typically are created in tandem by manipulating the surface topography, a process that conflates their effects. Here we use a pair of rubbed polymer-coated substrates in a twist geometry to obtain our main result, viz., that the strengths of two symmetries, in this case the rub-induced breaking of C(∞) rotational symmetry and chiral symmetry, can be separated and quantified. Experimentally we observe that the strength of the reduced rotational symmetry arising from the rub-induced scratches, which is proportional to the electroclinic response, scales linearly with the induced topographical rms roughness and increases with increasing rubbing strength of the polymer. Our results also suggest that the azimuthal anchoring strength coefficient is relatively insensitive to the strength of the rubbing.

Macroscopic torsional strain and induced molecular conformational deracemization

A macroscopic helical twist is imposed on an achiral nematic liquid crystal by controlling the azimuthal alignment directions at the two substrates. On application of an electric field the director rotates in the substrate plane. This electroclinic effect, which requires the presence of chirality, is strongest at the two substrates and increases with increasing imposed twist distortion. We present a simple model involving a trade-off among bulk elastic energy, surface anchoring energy, and deracemization entropy that suggests the large equilibrium director rotation induces a deracemization of chiral conformations in the molecules-effectively "top-down" chiral induction-quantitatively consistent with experiment.

Temperature- and electric-field-induced inverse Freedericksz transition in a nematogen with weak surface anchoring

We report electric field dependence of the anchoring transition in a mesogen on cooling in a cell with perfluoropolymer treated surfaces. Below a crossover voltage V(co) the transition is discontinuous between planar and homeotropic alignments, and as the temperature is lowered, the transition temperature decreases quadratically with the field. Above V(co) the transition is continuous between planar and tilted alignments, the transition temperature decreasing essentially linearly with the rms field. We develop a simple model to account for these results and argue that the higher field regime corresponds to a temperature driven inverse Freedericksz transition in which the director orientation starts tilting at the weakly anchored surfaces while the tilt angle remains zero at the midplane of the cell.

Nematic liquid crystal in the wedge and edge geometry in the case of homeotropic alignment

Nematic liquid crystal confined to a wedge or edge is studied on the assumption that the confining surfaces provide strong and weak homeotropic anchorings, respectively. Both infinite and finite systems are considered. The model based on the Frank-Oseen and Rapini-Papoular formalisms predicts two textures of opposite rotations of the director as in the case of strong anchoring on both surfaces. However, the presence of weak anchoring results in a length scale lambda which characterizes the crossover between the regions close to the apex and far from it. The ratio lambda/b , where b is the extrapolation length, is a function of the opening angle alpha. Both stable and metastable textures are considered and the mechanism by which a texture loses its stability is found. It is related to the formation of a defect-like structure at the surface of weak anchoring whose distance from the apex is lambda(alpha) and the loss of stability is signalled by the divergence of lambda. Only in the limit alpha --> 2tau, the defect-like structure transforms into a defect of strength -1/2 located at a finite distance from the apex.

Quantitative methods based on twisted nematic liquid crystals for mapping surfaces patterned with bio/chemical functionality relevant to bioanalytical assays

We report methods for the acquisition and analysis of optical images formed by thin films of twisted nematic liquid crystals (LCs) placed into contact with surfaces patterned with bio/chemical functionality relevant to surface-based assays. The methods are simple to implement and are shown to provide easily interpreted maps of chemical transformations on surfaces that are widely exploited in the preparation of analytic devices. The methods involve acquisition of multiple images of the LC as a function of the orientation of a polarizer; data analysis condenses the information present in the stack of images into a spatial map of the twist angle of the LC on the analytic surface. The potential utility of the methods is illustrated by mapping (i) the displacement of a monolayer formed from one alkanethiol on a gold film by a second thiol in solution, (ii) coadsorption of mixtures of amine-terminated and ethylene glycol-terminated alkanethiols on gold films, which leads to a type of mixed monolayer that is widely exploited for immobilization of proteins on analytic surfaces, and (iii) patterns of antibodies printed onto surfaces. These results show that maps of the twist angle of the LC constructed from families of optical images can be used to reveal surface features that are not apparent in a single image of the LC film. Furthermore, the twist angles of the LC can be used to quantify the energy of interaction of the LC with the surface with a spatial resolution of <10 microm. When combined, the results described in this paper suggest nondestructive methods to monitor and validate chemical transformations on surfaces of the type that are routinely employed in the preparation of surface-based analytic technologies.

Effect of decoupled azimuthal and zenithal anchoring on smectic-C chevron structures

We present a study of the effect of decoupled azimuthal and zenithal weak anchoring on the transition between C1 and C2 chevron structures in smectic-C liquid crystals. We consider temperatures below the SmA-SmC transition and assume that the value of the smectic cone angle can be regarded as constant through the cell. By standard Euler-Lagrange minimization of the total energy we obtain a simple analytical expression for the equilibrium director twist angle in the C1 and C2 chevron states. Using this analytical form, we are able to compare the total energies of the C1 and C2 chevrons, and determine the globally stable chevron profile. We show that the C2 state is preferred when the azimuthal anchoring strength is relatively large, while C1 chevrons will dominate for strong zenithal anchoring.

Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers

The azimuthal anchoring energy of the nematic liquid crystal 4- n -pentyl- 4' -cyanobiphenyl (5CB) on a uv-aligned polyimide substrate with in-plane order parameter S'=0.2 is measured. The measurements are performed at temperature T=24 degrees C using simultaneously a high accuracy reflectometric method and a high accuracy transmitted light method. With both the methods, we observe an apparent surface director rotation opposite to the orienting torque that would correspond to a negative extrapolation length. It is shown that this unusual behavior is due to the relatively high birefringence of the uv-aligned polyimide layers. Taking into account for this birefringence, we find a small but positive extrapolation length. The experimental results are interpreted in terms of a simple mesoscopic model where the nematic molecules are assumed to be rigidly attached on the polymer surface and the measured extrapolation length is entirely due to the order parameter variation in a thin interfacial layer where the nematic order parameter passes from the surface value to the bulk value within a few nematic correlation lengths. Assuming the surface order parameter is S(0)=0.37 , the correlation length of the nematic liquid crystal is estimated to be xi'(c)=2.4+/-1 nm . The corresponding thermodynamic extrapolation length is de=2.8+/-1.2 nm that corresponds to a very strong azimuthal anchoring.

Anchoring of a nematic liquid crystal on a wettability gradient

We have studied the anchoring of the nematic liquid crystal 5CB (4'-n-pentyl-4-cyanobiphenyl) as a function of the surface wettability, thickness of the liquid crystal layer, and temperature by measuring the birefringence of a hybrid aligned nematic cell where the nematic material was confined between octadecyltriethoxysilane-treated glass surfaces, with one surface linearly varying in its hydrophobicity. A homeotropic-to-tilted anchoring transition was observed as a function of the lateral distance along the hydrophobicity gradient, typically in a region corresponding to a water contact angle of approximately 64 degrees. The effect of the nematic layer thickness was measured simultaneously by preparing a wedge cell where the thickness varied along the direction perpendicular to the wettability. The detailed behavior of the onset of birefringence was found to be consistent with a dual-easy-axis model that predicts a discontinuous anchoring transition from homeotropic to planar. The anchoring was independent of temperature, except within 1 degrees C of the nematic-to-isotropic transition temperature (T(NI)). As the temperature approached T(NI), the tendency for planar anchoring gradually increased relative to that for homeotropic anchoring.

Bend-induced melting of the smectic-A phase: analogy to a type-I superconductor

Using an atomic force microscope to nanopattern a substrate for liquid crystal alignment, a bend distortion is imposed on a liquid crystal. In regions of large bend the smectic-A phase melts into the nematic phase, and the width of the melted region is measured as a function of temperature. The results are consistent with type-I superconducting (nematic-smectic-A) behavior, wherein a large magnetic field (bend or twist distortion) induces an order to disorder transition. A model that accounts for non-mean-field behavior is presented.

Strong azimuthal anchoring energy at a nematic-polyimide interface

Some years ago we proposed an automated reflectometric method to measure the director azimuthal angle at the interface between a nematic liquid crystal and another medium. The method ensures a great accuracy and sensitivity and is virtually unaffected by the presence of a director bulk distortion. This latter property makes it possible to measure strong anchoring energies. In the present experiment, we use this method to measure the azimuthal anchoring energy at the interface between the nematic liquid crystal 4-pentyl-4-cyanobiphenyl (5CB) and a rubbed polyimide layer. This kind of interface is characterized by a strong azimuthal anchoring and, thus, it represents a good test for the proposed reflectometric method. An ac planar electric field is applied to a nematic layer and the consequent azimuthal rotation of the director at the interface is measured. The anchoring energy coefficient Wa at room temperature is strong (Wa=0.33 x 10(-3) J/m2) and decreases greatly as the clearing temperature is approached. The time response of the azimuthal surface director angle to a stepwise electric field evidences the characteristic slow dynamics which is currently observed for weak anchoring substrates.

Intrinsic torsional reorientations in a twisted nematic liquid crystal cell

The nature of the orientational relaxation process of the director n to its equilibrium orientation neq, in the twisted nematic cell, under the influence of an external electric field, is investigated. The influence of the electric, elastic, and viscous torques on the dynamics of the director is reflected in the relaxation of the director n to neq, with different relaxation times. It is shown that the relaxation time, both for the cases of a strong and weak anchoring, exhibits an anomalous increase with decreasing of an external electric field, whereas the influence of the azimuthal anchoring energy, in the case of the twisted nematic cell is characterized by a weak effect. It is also shown that these torques exerted on the director may excite the traveling wave spreading from one edge of the cell to their second edge. Calculations of the relaxation processes in the vicinity of a nematic-smectic- A (NA) phase transition temperature T(NA) , e.g., at a few tens of mK from T(NA) in the nematic phase, shows that the director distortion in the gap between two plates is maintained to be constant across the sample both in the case of a strong and weak anchoring.

Determination of liquid-crystal polar anchoring energy by electrical measurements

We propose a simple method for the determination of liquid-crystal (LC) polar anchoring energy by electrical measurements. The basic idea of this method is a two-channel scheme for capacitance measurements. The first channel uses one cell with a planar LC cell, while the second a LC cell with vertical alignment. One of the LC cells can have a high pretilt angle. The proposed method allows investigating anchoring properties of both planar and vertical aligned LC materials. Simultaneous measurements of the two cells compensate all volume effects in LC bulk and provide a good opportunity to study directly the LC-surface interaction. The method can be applied for LC cells, which do not have uniform azimuthal orientation. We used this method to investigate the polar anchoring properties of photoaligning material before and after illumination and for LC structures with a high pretilt angle.