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The recent discovery of the new smectic-C{sub d6}* (SmC{sub 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{sub d6}* phase and the smectic-C{sub d4}* (SmC{sub d4}*) phase. Characterized by multiple resonant peaks spanning a wide region in Q{sub 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{sub d6}* phase and the SmC{sub d4}* phase. The structure of the noisy region is found to be a heterogeneous mixture of local SmC{sub d6}* and SmC{sub d4}* orders on the sub-{micro}m scale.

A state-of-the-art calorimetric system has been established. The system enables us to measure simultaneously heat capacity and optical reflectivity of free-standing liquid-crystal films from many hundreds down to only two molecular layers in thickness. Our experimental results on the smectic-A-hexatic-B and smectic-C-smectic-I transitions cannot be described solely in terms of the creation of bond-orientational order, indicating that additional molecular order must be present in the hexatic phases of liquid crystals.

Calorimetric and optical reflectivity studies on free-standing partially fluorinated liquid-crystal films have revealed novel melting phenomena. The smectic-$A$-isotropic transition occurs through a series of layer-thinning transitions, causing the films to thin in a stepwise manner as the temperature is increased. The temperature dependence of the film thickness has been found to be well fitted by a simple power law. These results are discussed in the context of present theory and the effects of fluorination are addressed.

High-resolution heat-capacity data near the smectic-C--smectic-I transition in free-standing p-decyloxybenzylidene-p-amino-2-methylbutylcinnamate (DOBAMBC) films down to only two molecular layers in thickness have been obtained. The data reveal preferential surface ordering phenomena and surface transitions localized to individual smectic layers. Moreover, the data from two-layer films are not consistent with existing theory, and indicate that the present understanding of the liquid-crystal hexatic phases is not complete.

High-resolution specific-heat data as a function of temperature and applied magnetic field have been obtained on an untwinned ${\mathrm{LuBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$ single crystal near its normal-superconducting transition. The magnitude of the specific-heat anomaly has been found to depend on the magnetic-field strength and the orientation of magnetic field relative to all three crystallographic axes. The implications of this anisotropy, specifically along the a and b axes, will be discussed.

Experimental results from extremely thin free-standing liquid-crystal films have been found to exhibit divergent heat-capacity anomalies in the vicinity of the smectic-A-hexatic-B (SmA-HexB) transition. In fact, the data can be successfully fit to a power-law expression yielding the critical exponent α =0.30±0.04. The results clearly indicate that the transition cannot be described solely in terms of hexatic order and that some additional molecular order must be created in the SmA-HexB transition in these liquid crystals. This transition is therefore not the simple liquid-hexatic transition as had been suggested previously. In light of x-ray diffraction studies indicating the existence of herringbone order in some liquid-crystal samples, Bruinsma and Aeppli formulated a coupled XY hamiltonian as a possible explanation for the anomalous experimental data obtained on the SmA-HexB transition in three dimensions (i.e. bulk samples). Based on our novel calorimetric and optical reflectivity results from thin liquid-crystal films, we have conducted extensive Monte Carlo simulations to explore this model in two-dimensional lattices. These studies have resulted in a number of novel discoveries that reveal important aspects of both the SmA-HexB transition in thin liquid-crystal films and two-dimensional melting phenomena in general.

We describe a simple method and device design that enables fast in-plane electro-optic modulation in conventional nematic liquid crystal (NLC) devices. When combined with optimized NLC materials, this approach yields rotational speeds of 1°/μs (independent of rotation angle, over a wide range) at a moderately low voltage. The observed rotational dynamics indicate that even these high speeds may not represent fundamental physical limits. We demonstrate these ideas in a compact tunable NLC waveplate that uses microelectrodes patterned directly on the tips of optical fibers. These devices offer fast, continuously tunable optic axis with low insertion loss and good performance in the near infrared. Modulators that use this design have promising potential applications for polarization control and analysis in optical communication systems.

Null transmission ellipsometry was employed to study the field induced transition of the surface arrangements in freestanding films of smectic liquid crystals. The interlayer interaction between the two surfaces obtained from the threshold voltage for the transition is found to be antiferroelectric and is quasilong ranged. The possible microscopic origins of the measured interaction and its relevance to the interlayer interaction in antiferroelectric liquid crystal materials are discussed.

Two modified mean-field ${J}_{1}\ensuremath{-}{J}_{2}$ models are studied to explain the surface reduction of twisting power in the helical smectic-${C}_{\ensuremath{\alpha}}^{*}$ phase in free-standing liquid crystal films. Profiles of the surface interlayer interaction are calculated from the experimental results. The calculations reveal the existence of a strong surface field and indicate that the surface field is the reason for the observed reduced twisting power near the surface region. Our results provide a quantitative study of the interlayer interactions through surface effects in smectic liquid crystals.

5 pages; International audience; 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-Cor Sm-CAPA) coexisting with the achiral synclinic antiferroelectric smectic-C or Sm-CSPA. 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.

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.

Null transmission ellipsometry was employed to study the temperature evolution of the helical structure of the smectic-$C$${}_{\ensuremath{\alpha}}^{*}$ phase. Free-standing films with thickness ranging from 31 to more than 400 layers were prepared and studied. The experimental results show a reduced twisting power in thin films. A simple model was constructed to explain the results. Surface effects were found to be the key reason for this phenomenon. Our findings are consistent with the theoretical studies of helically ordered magnetic films.

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$${}_{\ensuremath{\alpha}}^{*}$ and smectic-$C$${}^{*}$ phases are studied as a function of temperature and EE. Upon reducing EE, a liquid-gas-type critical point of the smectic-$C$${}_{\ensuremath{\alpha}}^{*}$ to smectic-$C$${}^{*}$ 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.

Employing the Monte Carlo simulation technique, we have investigated several phase transitions exhibited by a coupled XY model in two dimensions. The model is based on the Hamiltonian proposed by Bruinsma and Aeppli [Phys. Rev. Lett. 48, 1625 (1982)]. The simulation results demonstrate the existence of a new type of phase transition in which two different orderings are simultaneously established through a continuous transition. The unique nature of this phase transition provides a plausible explanation for our recent high-resolution heat-capacity data near the smectic- A-hexatic-B transition of two-layer free-standing films

Susceptibility and specific-heat data for a low-molecular-weight polymer blend near its critical point of unmixing are compared with a match-point renormalization-group theory which describes the crossover from classical mean-field to fluctuation-dominated behavior near the critical temperature. Using the Flory-Huggins form of the bare free-energy density, the crossover function requires only two free parameters.

Ever since the hexatic phase was proposed more than 14 years ago in the context of two-dimensional melting theory, the concept of hexatic order has offered unique insight into the nature of several liquid-crystal phases, namely the hexatic-B, smectic-I and smectic-F phases. Moreover, these liquid-crystal phases have offered numerous opportunities to explore and investigate the nature of hexatic order and the related phase transitions. In this paper we present an extensive review of the thermal properties associated with the phase transitions related to these liquid-crystal hexatic phases. Although both electron-beam and X-ray diffraction studies have indicated the importance of hexatic ordering in understanding these phases, the existing experimental data from numerous thermal measurements fail to demonstrate that hexatic order, which can be represented by a complex variable and therefore belongs to the XY universality class, is the only symmetry-breaking field associated with the hexatic-B—smect...

High-resolution specific-heat measurements have been performed on an untwinned single crystal of LuBa[sub 2]Cu[sub 3]O[sub 7[minus][ital y]] in an applied magnetic field, along the [ital c] axis, of up to 5 T. The zero-field data near the normal-superconducting transition temperature ([ital T][sub [ital c]]=92.5 K) display a very large and sharp specific-heat anomaly. Among various models for scaling the magnetic field and temperature-dependent specific-heat data, a model which incorporates the two-dimensional nature of this transition provides the best description of our data. A narrow region of crossover to three-dimensional behavior is also observed.

Our recent heat-capacity measurements on four-layer free-standing liquid-crystal films near the smectic-A-hexatic-B transition of n-heptyl-4'-n-pentyloxybiphenyl-4-carboxylate (75OBC) exhibit separate heat-capacity anomalies associated with the distinct ordering of the interior and surface layers. Employing the Metropolis Monte Carlo technique, we have simulated these transitions in a layered system with finite thickness (for example, 30×30×4). Comparison between our experimental and simulation results indicates that the anisotropy between inter- and intralayer interactions plays an important role in our experimental findings. Furthermore, the ratio of intra- to interlayer interactions strength should be more than 100.

A null transmission ellipsometer was employed to study the uniaxial to biaxial smectic-A phase transition of a bent core liquid crystal material. Free-standing films of thicknesses ranging from 5 molecular layers to more than 300 were prepared and studied. Critical exponents for both the surface and interior biaxiality were obtained. The results were discussed in the general framework of phase transition in lower dimensions.

In free-standing smectic films, layers near the surfaces of the film often contain molecules tilted away from the layer normal, while in the bulk of the film the magnitude of the tilt decays exponentially with distance from the surface. We have identified the detailed molecular tilt orientations in the surface layers of films for one antiferroelectric liquid crystal compound. A series of five surface structures exists with different nonplanar tilt arrangements for each structure. The molecular orientations in the surface layers evolve with temperature. The polarization of the film also evolves with temperature, corresponding to the tilt arrangements. Using ellipsometric data, we reconstruct the changes in the magnitude and azimuthal direction of the tilt as functions of temperature. We have also studied films of several different thicknesses. We present a phase diagram for the five surface structures showing the dependence on temperature and film thickness.

Detailed heat-capacity measurements have been carried out on free-standing liquid-crystal films of n-heptyl-4'-n-pentyloxybiphenyl-4-carboxylate to investigate the nature of transitions related to surface crystal-E order. Distinct thermal hystereses are observed. Upon heating from the temperature range exhibiting surface crystal-E order and interior hexatic order, anomalous effects on the interior smetic-A-hexatic-B transition, which strongly depend on the film thickness, are evident

A high-resolution differential ac free-standing film calorimeter has been constructed in our laboratories. We have employed this unique calorimeter to investigate the evolution of the temperature dependence of heat-capacity anomalies through the smectic-A-hexatic-B-crystal-E transition sequence of one liquid crystal compound as the film thickness is reduced from a few hundred to just three molecular layers. The existence of free surfaces in the free-standing liquid-crystal films has a very strong effect on the development of the molecular order through the smectic-A-hexatic-B transition and other unexpected results related to the crystal-E order.

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.

Free standing films of a liquid crystal compound with simple surface enhanced order were studied. The resultant phase diagram demonstrates that (1) the short helical pitch smectic-C(alpha)* phase disappears below a film thickness of 10 layers, and (2) the temperature window of a distorted 4 layer smectic-C(FI2)* phase increases dramatically upon decreasing film thickness. The experimental findings were attributed to the reduced dimensionality and enhanced surface effects in thin films. The results of the smectic-C(alpha)* phase are consistent with what have been reported for helically ordered magnetic thin films, with a noticeable difference due to the opposite effect of the surface on ordering in the two systems.

Using differential scanning calorimetry, the transition enthalpies and temperatures for the bulk smectic-isotropic phase transition have been measured for a series of liquid-crystal compounds. For five compounds, those values were used as parameters in a microscopic mean-field model to predict the temperature dependence of the difference in free-energy density between a sample of material in a free-standing smectic film and that in the bulk. The model predicts a weak temperature dependence below the bulk clearing point and a pronounced monotonic increase with temperature above the transition temperature. The compounds used in this study were chosen specifically because they were also the subject of a previous independent experimental study [M. Veum et al., Phys. Rev. E 74, 011703 (2006)] that demonstrated a sudden monotonic increase in the free-standing film tension with temperature, which is qualitatively consistent with the predictions of the above-mentioned mean-field model. This study presents a direct and quantitative comparison between the predictions of the mean-field model and the results from previous tension experiments.

Surface effects cause tilted molecular arrangements in smectic layers near the surface of a free-standing liquid-crystal film in which the bulk of the film is in the smectic- A phase. One recent work has shown that the tilt directions in adjacent surface layers may be nonplanar. In this paper we study films with thicknesses of two to six smectic layers. Surface effects dominate in these very thin films. We show that the molecular tilts are nonplanar even in these very thin films.

A unique ac calorimeter for measuring the heat capacity of free‐standing liquid‐crystal films has been developed. A theory of the measurement method used is presented and the experimental setup is discussed. The calorimeter has been used to study the nature of the smectic‐A‐hexatic‐B transition of several liquid‐crystal compounds. The evolution of the heat‐capacity anomaly associated with this transition has been studied for films ranging from three to a few thousand smectic layers in thickness.

The $n\text{OHFBBB}1\text{M}7$ $(n=10)$ compound, 10OHF, shows a reversed $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}\text{-Sm}{C}^{\ensuremath{\ast}}$ 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 $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}$ phase. One 10OHF/11OHF mixture without the $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}$ 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 $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}$ phase in binary mixtures with 10OHF, it significantly increases the $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}$ temperature range in the 10OHF/11OHF/C9 ternary mixtures.

Null transmission ellipsometer was employed to study the surface-induced tilt transition of an antiferroelectric liquid crystal compound in the bulk smectic- A (SmA) temperature range. The data of the surface tilt transition can be fitted with an extended mean-field model. These results indicate the transition is near a mean-field tricritical point. The surface layers' tilt directions are found to be in different planes several degrees above the bulk SmA-SmC_{alpha};{ *} transition.

The compound 10OHF has a partially inverted phase sequence, unique among the series of $n\text{OHF}$ homologous compounds and all other known liquid crystals, with the smectic-${C}_{FI2}^{\ensuremath{\ast}}$ $(\text{Sm}{C}_{FI2}^{\ensuremath{\ast}})$ phase occurring at higher temperature than the smectic-${C}^{\ensuremath{\ast}}$ $(\text{Sm}{C}^{\ensuremath{\ast}})$ 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 $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}$ predominates over $\text{Sm}{C}^{\ensuremath{\ast}}$ throughout the entire mixing phase diagram. In thin films of some mixtures, surface interactions induce a reentrant $\text{Sm}{C}_{FI2}^{\ensuremath{\ast}}\text{-Sm}{C}^{\ensuremath{\ast}}\text{-Sm}{C}_{FI2}^{\ensuremath{\ast}}$ transition in the rest of the film.

Temperature variations of heat capacity, optical tilt angle, polarization, and helical pitch have been measured in the vicinity of the smectic-A (SmA)-chiral-smectic-C (SmC*) transition of one liquid-crystal compound which exhibits an unusual reversal behavior in polarization at about 25°C while the SmA-SmC* transition occurs at 50°C. Unexpectedly, from our detailed calorimetric and optical microscopy studies, we have found that the recrystallization also occurs around 25°C during a reasonably slow cooling experimental run

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{sub 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.

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.

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.

Infrared spectroscopy was used to study the optical responses of ferromagnetic Ga1−xMnxAs samples and heavily p‐doped GaAs:Be samples to clarify whether the optical response of the Ga1−xMnxAs is related to the presence of the magnetic ions in the sample. Absorption dips are observed for both Ga1−xMnxAs and GaAs:Be samples and could be attributed to the intervalence band transition. The temperatures dependence of the absorption spectra for the two samples shows similar behavior and it is concluded that the optical response of the Ga1−xMnxAs is not related to the presence of the magnetic ions in the samples.

4 pages; International audience; 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 ' 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 SmCSPA.

An unexpected three-stage melting transition has been observed in two-dimensional (2D) free-standing liquid-crystal films by in situ electron-diffraction and optical-reflectivity measurements. These data suggest the existence of two phases between the 2D solid and liquid: a hexatic phase and, at a higher temperature, an intermediate liquid phase with hexatic-like positional correlations (∼40 angstroms) but no long-range orientational order. Previous high-resolution heat-capacity measurements have revealed a divergent-like anomaly at the hexatic-liquid transition that sharply contradicts the predictions of 2D melting theories. The observation of an intermediate isotropic phase may alter our understanding of 2D melting and lead to reconciliation between current experiments and theories.

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.

Null transmission ellipsometry has been employed to study the molecular arrangements in freestanding films of two no-layer-shrinkage liquid crystal homologous compounds above the bulk smectic $A$--smectic ${C}^{*}$ (Sm ${C}^{*}$) transition temperature. An unusual nonplanar-parallel or nonplanar-antiparallel-parallel transition has been observed in both compounds under a proper electric field. With the addition of one ${\mathrm{CH}}_{2}$ group, while the $\mathrm{Sm}{C}^{*}$ phase is more stable thermally, the magnitude of the critical field needed to induce a parallel-antiparallel transition decreases dramatically.

Differential optical reflectivity (DOR) was used to study the temperature dependence of the short helical pitch in freestanding films of a liquid crystal compound. The experimentally measured DOR signal was fitted using Berreman's 4 x 4 matrix method to get the pitch value in the smectic-C*alpha (sMC*alpha) phase. The results show continuous evolution of the pitch between the smectic-C*alpha and sMC*alpha phases. In sMC*alpha, the pitch decreases as temperature increases and is found to level off at 16+/-1 smectic layers at the sMC*alpha to smectic-A* transition.

We have studied tilted surface layers in the bulk SmA temperature window of one liquid crystal using null transmission ellipsometry. Five distinct nonplanar surface structures were observed. We present analyses of the tilt and azimuthal profiles of the structures and examine the transitions between the structures. The transitions are identified as a double reentrant synclinic-anticlinic-synclinic-anticlinic transition. Meanwhile, the transitions also display reentrant ferroelectric-antiferroelectric-ferroelectric behavior.

Building upon our previous report [Veum, Phys. Rev. E 17, 020701(R) (2005)] involving two compounds, we have performed a systematic study of the temperature variation of film tension above the bulk isotropic transition in freestanding films to include a total of six smectic liquid-crystal compounds. Consistent with the previous results, the tension increases sharply with temperature above the transition, the tension-temperature slope is proportional to the film's thickness, and the data can be interpreted in the context of theoretical models for layer thinning. Our data suggest that both molecular weight and bulk phase appearing below its isotropic phase play important roles in the slope values.

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC{sub F12}{sup *}-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{sub F12}{sup *} phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.

High-resolution surface tension measurements have been conducted on free-standing films of selected liquid-crystal compounds containing different combinations of flexible tails. The tail combinations studied were two hydroalkyl tails, one hydroalkyl tail and one fluoroalkyl tail, and two fluoroalkyl tails, respectively. Comparisons of the results with existing data obtained from other measurement techniques are made.