Coincident molecular auxeticity and negative order parameter in a liquid crystal elastomer.

Auxetic materials have negative Poisson's ratios and so expand rather than contract in one or several direction(s) perpendicular to applied extensions. The auxetics community has long sought synthetic molecular auxetics - non-porous, inherently auxetic materials which are simple to fabricate and avoid porosity-related weakening. Here, we report, synthetic molecular auxeticity for a non-porous liquid crystal elastomer. For strains above ~0.8 applied perpendicular to the liquid crystal director, the liquid crystal elastomer becomes auxetic with the maximum negative Poisson's ratio measured to date being -0.74 ± 0.03 - larger than most values seen in naturally occurring molecular auxetics. The emergence of auxeticity coincides with the liquid crystal elastomer backbone adopting a negative order parameter, QB = -0.41 ± 0.01 - further implying negative liquid crystal ordering. The reported behaviours consistently agree with theoretical predictions from Warner and Terentjev liquid crystal elastomer theory. Our results open the door for the design of synthetic molecular auxetics.

Graphene electrodes for adaptive liquid crystal contact lenses.

The superlatives of graphene cover a whole range of properties: electrical, chemical, mechanical, thermal and others. These special properties earn graphene a place in current or future applications. Here we demonstrate one such application - adaptive contact lenses based on liquid crystals, where simultaneously the high electrical conductivity, transparency, flexibility and elasticity of graphene are being utilised. In our devices graphene is used as a transparent conductive coating on curved PMMA substrates. The adaptive lenses provide a + 0.7 D change in optical power with an applied voltage of 7.1 Vrms - perfect to correct presbyopia, the age-related condition that limits the near focus ability of the eye.

Understanding the unusual reorganization of the nanostructure of a dark conglomerate phase.

The dark conglomerate (DC) phase exhibited by a bent-core liquid crystal shows remarkable properties including an electric-field tunable chiral domain structure and a large (0.045) reduction of refractive index, while maintaining an optically dark texture when observed under crossed polarizers. A detailed investigation of the system is presented, leading to a model that is fully consistent with the experimental observations. It reports the observation of two distinct regimes in the DC phase: a higher temperature regime in which the periodicity measured by small angle x-ray scattering decreases slightly (0.5%) and a lower temperature regime where it increases considerably (16%). Also, the paper discusses the unusual electric-field-induced transformations observed in both the regimes. These changes have threshold fields that are both temperature and frequency dependent, though the phenomena are observed irrespective of device thickness, geometry, and the alignment layer. The electro-optic behavior in the DC phase corresponds to a number of structural changes leading to unusual changes in physical properties including a small (1%) increase in periodicity and a doubling of the average dielectric permittivity. We propose a model of the DC phase where in the ground state the nanostructure of the phase exhibits an anticlinic antiferroelectric organization. Under an electric field, it undergoes a molecular rearrangement without any gross structural changes leading to an anticlinic ferroelectric order while keeping the overall sponge-like structure of the DC phase intact.

Field-induced refractive index variation in the dark conglomerate phase for polarization-independent switchable liquid crystal lenses.

Liquid crystal lenses are an emerging technology that can provide variable focal power in response to applied voltage. Many designs for liquid-crystal-based lenses are polarization dependent, so that 50% of light is not focused as required, making polarization-independent technologies very attractive. Recently, the dark conglomerate (DC) phase, which is an optically isotropic liquid crystalline state, has been shown to exhibit a large change in refractive index in response to an applied electric field (Δn=0.04). This paper describes computational modeling of the electrostatic solutions for two different types of 100 µm diameter liquid crystal lenses, which include the DC phase, demonstrating that it shows great potential for efficient isotropic optical switching in lenses. A feature of the field dependence of the refractive index change in the DC phase is that it is approximately linear in a certain range, leading to the prediction of excellent optical quality for driving fields in this regime. Interestingly, a simulated microlens is shown to exhibit two modes of operation: a positive lens based upon a uniform bulk change in refractive index at high voltages, and a negative lens resulting from the induction of a gradient index effect at intermediate voltages.

Understanding the distinctive elastic constants in an oxadiazole bent-core nematic liquid crystal.

The splay and bend elastic constants of the bent-core oxadiazole material [C5-Ph-ODBP-Ph-OC12] have been investigated as a function of temperature across the nematic phase. The bend constant K(33) is found to take values of ~3.0 pN and to be almost temperature independent, whereas, the splay constant K(11) increases monotonically from ~3.5 pN close to the isotropic phase transition to values of ~9 pN deep in the nematic phase. No pretransitional divergence is observed in either K(11) or K(33) at temperatures approaching the underlying phase. This behavior of the elastic constants is distinct from that observed in rodlike liquid crystal systems but appears to share characteristics with the few other bent-core nematic systems studied to date. We discuss the interdependence of the elastic constants, the birefringence, and the order parameter to allow a comparison of the observed behavior with theory. We show that calculations of the elastic constants via molecular-field theory and atomistic modeling are in excellent qualitative as well as good quantitative (within 2 pN) agreement with the measurements across the temperature range, offering a deeper understanding of the elasticity in bent-core nematic materials than has been, hitherto, available.

Nonstandard electroconvection in a bent-core oxadiazole material.

Electroconvection (EC) phenomena have been investigated in the nematic phase of a bent-core oxadiazole material with negative dielectric anisotropy and a frequency dependent conductivity anisotropy. The formation of longitudinal roll (LR) patterns is one of the predominant features observed in the complete frequency and voltage range studied. At voltages much above the LR threshold, various complex patterns such as the "crisscrossed" pattern, bimodal varicose, and turbulence are observed. Unusually, the nonstandard EC (ns-EC) instability in this material, is observed in a regime in which we measure the dielectric and conductivity anisotropies to be negative and positive respectively. A further significant observation is that the EC displays distinct features in the high and low temperature regimes of the nematic phase, supporting an earlier report that EC patterns could distinguish between regions that have been reported as uniaxial and biaxial nematic phases.

Cholesteric pitch divergence near smectic phase transitions.

The critical behavior of the pitch divergence of cholesteric liquid crystals in the vicinity to smectic-A∗ (SmA∗) and smectic-C∗ (SmC∗) phases is studied experimentally and compared with conflicting theoretical interpretations. Members of two homologous series were studied with varying polymorphism from N∗-SmC∗ to N∗-SmA∗. A modified functionality of the temperature dependence of the pitch is introduced to determine the critical exponent, and it is shown that the latter is independent of sample geometry. In contrast to several earlier investigations aiming to determine the critical exponent, which were inconclusive, the results of our critical exponents for the pitch divergence provide evidence for the model by Chen and Lubensky which predicts a critical exponent of ν=1/2 for the N∗-SmA∗ and ν=1 for the N∗-SmC∗ transition. This specifically implies that fluctuations cannot be neglected in the consideration of the nature of the phase transition.

Dielectric spectroscopy of Polymer Stabilised Ferroelectric Liquid Crystals.

Dielectric measurements were carried out in the frequency range from 20 Hz to 500 kHz on Polymer Stabilised Ferroelectric Liquid Crystals (PSFLCs). Polymerisation in the Smectic A* (Sm A*) and the Smectic C* (Sm C*) phase at equal polymer concentration results in a dielectric strength which is nearly twice the value in the latter case. An increase of the polymer concentration results in a decrease of the dielectric strength and an increase in relaxation frequency. The textural morphology and transmission intensity due to the residual birefringence of the polymer network in the isotropic phase, revealed a correlation between the interactions of the liquid crystal molecules with the polymer network. Results for polymerizing in the tilted Sm C* phase with a large bias field are also reported which show that the structure of the phase in which the system was polymerised affects the dielectric properties. The observed differences in dielectric behaviour can be explained by the polymer network morphology formed due to the interplay of phase and temperature on the stabilised ferroelectric liquid crystal materials.

Time-resolved x-ray studies of the dynamics of smectic- A layer realignment by magnetic fields.

While the rotation of smectic layers under an applied field may at first appear to be a relatively simple problem, the dynamic processes involved are rather complex. An applied field produces a torque on the liquid crystal director, but has no direct influence on the smectic layers. If the director is reoriented significantly, however, the layers must also reorient in order to accommodate this (the layered structure is produced by short-range molecular interactions). Indeed, if the liquid crystalline order is not maintained during the realignment then matters become even more complex. In this paper we use time-resolved x-ray scattering to investigate the realignment of smectic- A layers in thin-film devices using a magnetic field. No evidence is found for continuous rotation of the smectic layers under any circumstances in such devices, a result that is not found when using bulk samples. No evidence indicating the formation of the nematic phase is observed during realignment. A molecular-dynamics technique is used to model the system which indicates that the sample becomes significantly disorganized during the realignment process when large angular rotations are induced.

Continuously rotating chiral liquid crystal droplets in a linearly polarized laser trap.

The transfer of optical angular momentum to birefringent particles via circularly polarized light is common. We report here on the unexpected, continuous rotation of chiral nematic liquid crystal droplets in a linearly polarized optical trap. The rotation is non-uniform, occurs over a timescale of seconds, and is observed only for very specific droplet sizes. Synchronized vertical motion of the droplet occurs during the rotation. The motion is the result of photo-induced molecular reorganization, providing a micron sized opto-mechanical transducer that twists and translates.

Unexpected field-induced phase transitions between ferrielectric and antiferroelectric liquid crystal structures.

Liquid crystals are intriguing electrically responsive soft matter systems. We report previously unexplored field-induced changes in the structures of some frustrated liquid crystal phases and describe them theoretically. Specifically, we have discovered using resonant x-ray scattering that the four-layer intermediate smectic phase can undergo either a transition to the ferrielectric (three-layer) phase or to the ferroelectric phase, depending on temperature. Our studies of intermediate phases using electric fields offer a way to test theories that describe ferroelectricity in self-assembling fluids.

Molecular models for ferroelectric liquid crystals with conventional and anomalously weak layer contraction.

A molecular theory of the ferroelectric smectic C* phase has been developed using the simple model of a chiral molecule composed of a uniaxial core and a pair of off-center nonparallel dipoles which determine molecular chirality and polarity. The interaction between uniaxial cores is modeled by a rather general effective potential which can be used to describe smectic materials with both conventional and anomalously weak layer contraction in the smectic C* phase. Spontaneous polarization, tilt, and layer spacing are calculated numerically as functions of temperature, and it is shown that the variation of the polarization generally deviates from that of the tilt angle. It is shown that this deviation is more pronounced in smectic materials tilting with low layer contraction which corresponds to existing experimental data. The model has been used to reproduce qualitatively the experimental data for polarization, tilt and layer spacing for two similar mixtures exhibiting conventional and anomalously weak layer contraction. The polarization and the tilt are also calculated in the case when the smectic A-smectic C* transition is characterized by the biaxial primary order parameter.

Using the full Raman depolarisation in the determination of the order parameters in liquid crystal systems.

The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range, and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly polarised light was incident normally on a homogeneously aligned sample and a chi(2) minimisation routine performed on the 360 degrees depolarisation ratio profile. The order parameters (P(200)) and (P(400)), together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging from -0.032 + or - 0.008 in the isotropic phase through to -0.245 + or - 0.015 at the nematic-to-smectic A phase transition. The measured order parameters (P(200)) and (P(400)) varied from 0.35-0.55 + or - 0.02 and 0.180-0.245 + or - 0.02, respectively, across the 8 degrees C wide nematic phase range. The values of both (P(200)) and (P(400)) are in excellent agreement with theory, but it is noteworthy that (P(400)) shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of r is shown to be a contributing factor in the low (P(400)) values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically biaxial materials, is discussed.

Deduction of the temperature-dependent structure of the four-layer intermediate smectic phase using resonant X-ray scattering.

A binary mixture of an antiferroelectric liquid-crystal material containing a selenium atom and a highly chiral dopant is investigated using resonant X-ray scattering. This mixture exhibits a remarkably wide four-layer intermediate smectic phase, the structure of which is investigated over a temperature range of 16K. Analysis of the resonant X-ray scattering data allows accurate measurement of both the helicoidal pitch and the distortion angle as a function of temperature. The former decreases rapidly as the SmC* phase is approached, whilst the latter remains constant over the temperature range studied at 8 degrees +/-3 degrees. We also observe that the senses of the helicoidal pitch and the unit cell of the repeating four-layer structure are opposite in this mixture and that there is no pitch inversion over the temperature range studied.

Nanofabricated media with negative permeability at visible frequencies.

A great deal of attention has recently been focused on a new class of smart materials--so-called left-handed media--that exhibit highly unusual electromagnetic properties and promise new device applications. Left-handed materials require negative permeability micro, an extreme condition that has so far been achieved only for frequencies in the microwave to terahertz range. Extension of the approach described in ref. 7 to achieve the necessary high-frequency magnetic response in visible optics presents a formidable challenge, as no material--natural or artificial--is known to exhibit any magnetism at these frequencies. Here we report a nanofabricated medium consisting of electromagnetically coupled pairs of gold dots with geometry carefully designed at a 10-nm level. The medium exhibits a strong magnetic response at visible-light frequencies, including a band with negative micro. The magnetism arises owing to the excitation of an antisymmetric plasmon resonance. The high-frequency permeability qualitatively reveals itself via optical impedance matching. Our results demonstrate the feasibility of engineering magnetism at visible frequencies and pave the way towards magnetic and left-handed components for visible optics.

The absorption of polarized light by vertebrate photoreceptors.

A physiologically realistic model has been constructed for a theoretical study of the mechanisms by which the vertebrate visual system absorbs linearly polarized light. Using a 4 x 4 matrix technique, analytic solutions to Maxwell's equations have been deduced for rod and cone photoreceptors, allowing calculation of the absorbance as a function of wavelength for a variety of illumination geometries. With the use of experimentally measured optical parameters, the calculated absorbance spectra show excellent agreement in both magnitude and form with microspectrophotometric data. Moreover, failing to correct for the true nature of reflection or scattering in the sample, results in the elevated absorbance commonly seen at shorter wavelengths in experimental measurements. Finally, calculated dichroic ratios also accurately predict experimental results, mirroring the differences seen between rods and cones.

Theory of layer structure in ferroelectric liquid crystal devices in applied electric fields.

We propose a model for the free energy of a ferroelectric liquid crystal formed by cooling a sample from the smectic-A phase between parallel substrates. Under these circumstances the smectic layers may deform into V-shaped structures known as chevrons. Application of a strong electric field causes the layers to return to a flat shape, but this can occur in a number of ways. In the model presented here, it is a parameter related to the layer compression modulus that is the principal factor in determining the nature of the field-induced transition from chevrons to flat layers. When this parameter is large, the transition is sudden, but when it is small the chevron first takes on a rounded form before flattening. At intermediate values the tip of the chevron first flattens, and then this flat region gradually grows to encompass the entire layer.

Interlayer structures of the chiral smectic liquid crystal phases revealed by resonant X-ray scattering.

The structures of the liquid crystalline chiral subphases exhibited by several materials containing either a selenium or sulphur atom have been investigated using a resonant x-ray scattering technique. This technique provides a unique structural probe for the ferroelectric, ferrielectric, antiferroelectric, and SmC(*)(alpha) phases. An analysis of the scattering features allows the structural models of the different subphases to be distinguished, in addition to providing a measurement of the helical pitch. This paper reports resonant scattering features in the antiferroelectric hexatic phase, the three- and four-layer intermediate phases, the antiferroelectric and ferroelectric phases and the SmC(*)(alpha) phase. The helicoidal pitch has been measured from the scattering peaks in the four-layer intermediate phase as well as in the antiferroelectric and ferroelectric phases. In the SmC(*)(alpha) phase, an investigation into the helical structure has revealed a pitch ranging from 5 to 54 layers in different materials. Further, a strong resonant scattering signal has been observed in mixtures of a selenium containing material with as much as 90% nonresonant material.

Influence of electric fields on the smectic layer structure of ferroelectric and antiferroelectric liquid crystal devices.

The electric-field-induced structural rearrangement of smectic layers in the antiferroelectric and ferroelectric phases of three different materials is reported. The materials all have high optical tilt angles (around 30 degrees ), compared with the steric tilt angles deduced from layer spacing measurements (around 18 degrees ). The chevron angles observed in devices agree well with values found for the steric tilt angle across the tilted mesophase range. Electric fields were applied to liquid crystal devices while the smectic layer structures, in both the depth and in the plane of the device, were probed using small angle x-ray scattering. Two separate aspects of the influence of the field on the layer structure were studied. First, the organization of the smectic layers in the antiferroelectric phase is described before, during, and after the application of an electric field of sufficient magnitude to induce a chevron to bookshelf transition. Second, the evolution of the field-induced layer structure change has been investigated as the field was incrementally increased in both the antiferroelectric and ferroelectric phases. It was found that the chevron to bookshelf transition has a distinct threshold in the antiferroelectric phase, but shows low or zero threshold behavior in the ferroelectric phase for all the materials studied.