Resonant x-ray diffraction spectrum for possible structures of the smectic liquid crystal phase with a six-layer periodicity.

With the discovery of the smectic-C(d6)(*) (SmC(d6)(*)) phase showing six-layer periodicity [S. Wang et al., Phys. Rev. Lett. 104, 027801 (2010)] and a recent report of the observation of a possible alternative structure, the need for a reliable and accurate method for distinguishing different possible structures is more urgent than ever. Through simulations using the tensorial structure factor method, we present the resonant x-ray diffraction (RXRD) spectra for different possible structures as proposed in several theoretical studies. Subtle distinctions between models are shown. The ability and limitations of RXRD as a technique for determining the structure of this particular phase is discussed.

Spontaneous and field-induced mesomorphism of a silyl-terminated bent-core liquid crystal as determined from second-harmonic generation and resonant X-ray scattering.

The polarity and structure of the phases of a liquid crystal constituted by thiophene-based bent-core molecules is investigated by means of optical second-harmonic generation (SHG), and resonant and conventional X-ray diffraction. The material studied is representative of a wide family of mesogens that contain silyl groups at the ends of the chains. These bulky terminal groups have been reported to give rise to smectic phases showing ferroelectric switching. However, the analysis of the SHG signal before and after application of electric fields has allowed us to establish unambiguously that the reported ferroelectricity is not intrinsic to the material but stabilized by the cell substrates once an electric field has been applied. In addition, the results obtained from resonant X-ray diffraction indicate that virgin samples have antiferroelectric undulated synclinic smectic structures.

Resonant x-ray diffraction study of an unusually large phase coexistence in smectic liquid-crystal films.

The recent discovery of the new smectic-C(d6)(*) (SmC(d6)(*)) phase [S. Wang et al., Phys. Rev. Lett. 104, 027801 (2010)] also revealed the existence of a noisy region in the temperature window between the SmC(d6)(*) phase and the smectic-C(d4)(*) (SmC(d4)(*)) phase. Characterized by multiple resonant peaks spanning a wide region in Q(Z), the corresponding structure of this temperature window has been a mystery. In this Letter, through a careful resonant x-ray diffraction study and simulations of the diffraction spectra, we show that this region is in fact an unusually large coexistence region of the SmC(d6)(*) phase and the SmC(d4)(*) phase. The structure of the noisy region is found to be a heterogeneous mixture of local SmC(d6)(*) and SmC(d4)(*) orders on the sub-µm scale.

Polarization periodicity in the B(1) columnar phase determined by resonant x-ray scattering.

We report structural results that evidence the polarization distribution of the blocks in the columnar phase of an achiral bent-core liquid crystal. The study was performed using resonant x-ray diffraction at the sulfur K edge on oriented samples aligned on substrates. The extra periodicity is revealed through the violation of the systematic extinction rule of the structural symmetry group along the experimentally accessible diffraction direction. Further data obtained from the polarization analysis of a resonant reflection give information concerning the transition mechanism between B(1) and B(2) phases.

Characterization of a chiral phase in an achiral bent-core liquid crystal by polarization studies of resonant x-ray forbidden reflections.

The chiral antiferroelectric structure of an achiral bent-core liquid crystal is characterized by resonant x-ray scattering at chlorine K edge. The "forbidden" reflections resulting from the glide or screw symmetry elements are restored by the anisotropy of the tensor structure factor, which we calculate for two possible structural models. A careful analysis of the polarization states of the restored "forbidden" reflections enables an unambiguous identification of a chiral structure (i.e., the so-called anticlinic, antiferroelectric smectic-C or Sm-C(A)P(A)) coexisting with the achiral synclinic antiferroelectric smectic-C or Sm-C(S)P(A). The method proves to be quite powerful as it identifies the chiral structure within coexisting phases despite an imperfect orientation of the sample. The volume fraction of the chiral phase and the distribution of alignment are extracted from the data.

Effect of enantiomeric excess on the phase behavior of antiferroelectric liquid crystals.

Null transmission ellipsometry and resonant x-ray diffraction are employed to study the effect of enantiomeric excess (EE) on the phase behavior of antiferroelectric liquid crystal 10OTBBB1M7. Phase sequence, layer spacing, and pitch of the helical structures of the smectic-C(α)* and smectic-C* phases are studied as a function of temperature and EE. Upon reducing EE, a liquid-gas-type critical point of the smectic-C(α)* to smectic-C* transition is observed, as well as the disappearance of the smectic-C(d4)* and the smectic-C(d3)* phases. Results are analyzed in a mean-field model.

Discovery of a novel smectic-C{*} liquid-crystal phase with six-layer periodicity.

We report the discovery of a new smectic-C{*} liquid-crystal phase with six-layer periodicity by resonant x-ray diffraction. Upon cooling, the new phase appears between the SmC{alpha}{*} phase having a helical structure and the SmC{d4}{*} phase with four-layer periodicity. This SmC{d6}{*} phase was identified in two mixtures which have an unusual reversed SmC{d4}{*}-SmC{*} phase sequence. The SmC{d6}{*} phase shows a distorted clock structure. Three theoretical models have predicted the existence of a six-layer phase. However, our experimental findings are not consistent with the theories.

Recovery of a reversed phase sequence in one ternary liquid-crystal-mixture system.

The nOHFBBB1M7 (n=10) compound, 10OHF, shows a reversed SmC{FI2}-SmC phase sequence, unique among all known antiferroelectric liquid crystals. This reversed phase sequence is stabilized when 10OHF is doped with 9OTBBB1M7(C9) or 11OTBBB1M7(C11). In contrast, doping of the homologous members ( n=9 , 11, or 12) eliminates the SmC{FI2} phase. One 10OHF/11OHF mixture without the SmC{FI2} phase was selected for further studies. By adding C9 into this particular mixture, the reversed phase sequence is revived. To our surprise, even though 11OHF destabilizes the SmC_{FI2} phase in binary mixtures with 10OHF, it significantly increases the SmC_{FI2} temperature range in the 10OHF/11OHF/C9 ternary mixtures.

Effects of doping on an unusual smectic- C*alpha-smectic-C*FI2-smectic-C* phase sequence.

The compound 10OHF has a partially inverted phase sequence, unique among the series of nOHF homologous compounds and all other known liquid crystals, with the smectic-C*FI2 (SmC*FI2) phase occurring at higher temperature than the smectic-C* (SmC*) phase. We present ellipsometric data to identify the phase sequences of 9OHF, 10OHF, 11OHF, and 12OHF. Binary mixtures of 10OHF with C11, a compound with the typical phase sequence among the smectic phases, show that the unusual phase sequence of 10OHF stabilizes upon mixing and that SmC*FI2 predominates over SmC* throughout the entire mixing phase diagram. In thin films of some mixtures, surface interactions induce a reentrant SmC*FI2-SmC*-SmC*FI2 transition in the rest of the film.

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.

Unique pitch evolution in the smectic-C+alpha phase.

Employing resonant x-ray diffraction, we observed unique pitch evolutions in the smectic-C*(alpha) phase in mixtures of two antiferroelectric liquid crystals. Our results show that the pitch in this phase continuously evolves across 4 layers, contradicting a theoretical model that predicts that the smectic-C*(FI2) phase intervenes in the smectic-C*(alpha) phase. The phase sequences we found can be explained by another model that includes one type of long-range interaction among smectic layers.

Smectic-C*alpha phase with two coexistent helical pitch values and a first-order smectic-C*alpha to smectic-C* transition.

Previous results from Kundu using dielectric relaxation have suggested a reentrant antiferroelectric-ferroelectric-antiferroelectric transition in the compound LN36. Our comprehensive studies of this compound using differential optical reflectivity, nonadiabatic scanning calorimetry, null transmission ellipsometry, and resonant x-ray diffraction show that in fact LN36 exhibits the usual phase sequence for chiral smectic liquid crystals: SmA*-SmC*alpha-SmC*-SmC*FI1-SmC*A . Moreover, the SmC*alpha-SmC* transition is a first-order transition, characterized by a discontinuous change in the helical pitch. At temperatures just above the SmC*alpha-SmC* transition, two different values for the helical pitch are simultaneously observed for the first time.

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.

Polarization studies of resonant forbidden reflections in liquid crystals.

We report the results of resonant x-ray diffraction experiments performed on thick films of a biaxial liquid crystal made of achiral bent-core molecules. Polarization properties of forbidden reflections are observed as a function of the sample rotation angle phi about the scattering vector Q for the first time on a fluid material. The experimental data are successfully analyzed within a tensor structure factor model by taking the nonperfect alignment of the liquid crystal into account. The local structure of the B2 mesophase is hence determined to be SmC_{S}P_{A}.

Smectic-Calpha*-smectic-C* phase transition and critical point in binary mixtures.

We have investigated the smectic-Calpha*-smectic-C* (SmCalpha*-SmC*) transition in a series of binary mixtures with resonant x-ray diffraction, differential optical reflectivity, and heat capacity measurements. Results show that the phases are separated by a first-order transition that ends at a critical point. We report the observation of such a critical point. We have proposed the appropriate order parameter and obtained values of two critical exponents associated with this transition. The values of the critical exponents suggest that long-range interactions are present in the SmCalpha*-SmC* critical region.

Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal.

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC*FI2-SmC* phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the SmC*FI2 phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.

Experimental investigations of one liquid-crystal compound exhibiting the no-layer-shrinkage effect near the Sm-A-Sm- C(*) transition.

Three experimental probes have been employed to investigate the nature of the smectic- A -smectic- C ( Sm-A-Sm- C(*) ) phase transition of one liquid-crystal compound showing almost no layer-shrinkage effect through the transition. Results from both x-ray diffraction and optical studies indicate that the compound exhibits a crossover behavior of different molecular packing arrangements within the bulk Sm-A phase window. The calorimetry results show a significant critical anomaly near the Sm-A-Sm- C(*) transition, although it was found to be weakly first order.

In-line liquid-crystal microcell polarimeter for high-speed polarization analysis.

We report a type of high-speed microcell polarimeter that utilizes microelectrodes, liquid-crystal films, and ultrathin high-contrast polarizers, all integrated between the tips of two optical fibers. When combined with optimized nematic liquid-crystal materials, this compact (2.5 cm x 0.5 cm x 0.5 cm) device offers excellent optical properties and continuous, high-speed operation at > 2 kHz with moderately low operating voltages. It requires no bulk optical elements, and it shows excellent performance when implemented for the measurement of degree of polarization in 10-Gbit/s test systems. Polarimeters based on this design have promising potential applications in polarization analysis for high-speed optical communication systems.

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.

Orientational ordering in the chiral smectic-C*FI2 liquid crystal phase determined by resonant polarized x-ray diffraction.

High-resolution resonant polarized x-ray diffraction experiments near the sulfur K edge have been performed on free-standing liquid crystal films exhibiting the chiral smectic-C*FI2 phase. It is widely accepted that this phase has a four-layer repeat unit, but the internal structure of the repeat unit remains controversial. We report different resolved features of the resonant x-ray diffraction peaks associated with the smectic-C*FI2 phase that unambiguously demonstrate that the four-layer repeat unit is locally biaxial about the layer normal and that the measured angle, describing the biaxiality, is in good agreement with optical measurements.