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Depolarized reflected light microscopy and high resolution optical reflectivity measurements have been conducted on free-standing films of an achiral four-ring hockey stick shaped liquid crystal exhibiting SmA-B2–SmX* transition sequence. A layer thinning transition above the bulk isotropic-SmA phase transition has been observed. This behaviour was highly irreproducible, indicating an irregular layer thinning transition. From optical reflectivity data, both thickness of the free-standing films and the smectic interlayer spacing were determined. This is the first report of the layer thinning transition in a hockey stick shaped liquid crystal.

Calorimetric measurements have been done to investigate the smectic-C*α(SmC*α)- smectic-C*(SmC*) transition using high sensitivity differential scanning calorimetry. It was found that the SmC*α−SmC* transition for a liquid crystalline compound 11OHFBBB1M7 shows a first-order transition with a clear thermal hysteresis while other two compounds, LN36 and 12OTBBB1M7, exhibit continuous behaviors which support the existence of the critical point and also the slow relaxation dynamics encountered with the change in the helical pitch.

Measurements of dielectric dispersion have been carried out on two liquid crystal compounds 8422[2F3] and 8O23[7F8-], showing non-layer-shrinkage (NLS) behavior through the smectic-A(Sm-A)-smectic-C (Sm-C) transition. The critical exponent γ determined from the data lies 1.5–1.9 for 8422[2F3], and 1.1–1.2 for 8O23[7F8-]. These results indicate that the Sm-A-Sm-C transition with NLS behavior can exhibit quasi two-dimensional Ising critical behavior under a certain condition.

International audience; In 2006, employing ellipsometry and resonant x-ray diffraction, our research group discovered a liquid crystal mesophase having a six-layer periodicity in a ternary mixture (mixture A) as well as in a binary mixture (mixture B). This phase showsantiferroelectric-like properties. Subsequently, J. K. Vij’s group used field-induced birefringence to explore the physical properties of various binary mixtures similar to mixture B. Recently, Y. Takanishi et al. obtained dielectric responses and twodimensional microbeam resonant x-ray diffraction profiles as a function of temperature from a different binary mixture with one compound of the mixture containing a central bromine atom. They discovered another new mesophase which shows a six-layer structure and displays ferrielectric-like responses along with a different phase sequence. This article will review the sequence of events leading up to the discovery of the new phases with a six-layer periodicity and highlight differences in conclusions about the new phases and an ongoing debate about the existence of a phase with five-layer periodicity.

International audience; For more than one decade, SmC∗d4, SmC∗d3, andSmC∗ A were the only three confirmed commensurate SmC* variant phases with periodicities less than or equal four layers. In 2006, employing ellipsometry and resonant X-ray diffraction (RXRD), our research team first discovered a new liquid crystal mesophase having a six-layer periodicity in one ternary mixture which includes one sulfur-containing compound. From our ellipsometric results, this phase showed antiferroelectric-like optical response. This novel discovery inspired renewed interest to search for liquid crystal mesophases with commensurateperiodicities greater than four layers. Soon after, another mesophase having a six-layer structure and showing a ferrielectric-like dielectric response, instead, was uncovered by RXRD measurements on a different binary mixture which has one bromine-containing compound. Meanwhile mesophases having a 5-, 8-, 12- or 15-layer periodicity were reported. However, numerous questions remain to be addressed associated with these unusual reported phases. Theoretical models giving rise to mesophases with periodicities greater than four layers have been developed; but, to date, none of them haveprovided satisfactory explanations of all the physical phenomena related to the mesophases exhibiting a six-layer structure. Moreover, the question “what is the source of long-range interactions between liquid-like smectic layers, which are responsible for establishing mesophases with long periodicities and mean-field behavior of the smectic-A–smectic-C transition?” remains unanswered for more than three decades.

High-resolution resonant X-ray diffraction experiments have been performed on free-standing films of two selenium-containing antiferroelectric liquid-crystal mixtures. Optical studies had indicated that both mixtures exhibit exceptionally wide intermediate phases, over a total range of > 9 K. Through the structural information obtained from the resonant scattering data, we confirm that the intermediate phases of these mixtures show both 3-layer and 4-layer structural periodicities. Moreover, due to the stability of these phases, we report for the first time the temperature dependence of both the helicoidal pitch and distortion angle in the 3-layer phases deduced using the resonant X-ray technique. Analysis using an extension of the theory set out by Levelut and Pansu (Levelut A-M. and Pansu B., Phys. Rev. E, 60 (1999) 6803) shows that over the temperature ranges measured, the pitch changes linearly as a function of temperature whilst the distortion angle remains constant.

Null transmission ellipsometry and depolarized reflected light microscopy have been performed on freestanding films of two achiral meta‐substituted three‐ring compounds. These compounds exhibit two different tilted smectic phases, SmC1 and SmC2. Our studies confirmed previous results obtained from another achiral meta‐substituted three‐ring compound that the SmC1 and SmC2 phases are SmC and SmCA, respectively.

High-resolution heat-capacity and optical-reflectivity measurements have been conducted near the smectic-A to hexatic-B transition in thin free-standing films of the liquid-crystal compound 64COOBC. We find an unexpected dependence on film thickness of the integrated magnitude of the heat-capacity anomalies as the films undergo layer-by-layer transitions. We measure the penetration depths of the ordering from the surface and next-to-surface layers which are pertinent to the highly correlated thermal behavior.

Three experimental measurements have been conducted to investigate the nature of the SmA–SmCα*–SmC* phase transitions of two liquid crystal compounds. The SmA-SmCα* transition shows a continuous transition with XY-like critical exponents. The SmCα*-SmC* transition displays a rapid variation of the incommensurate helical pitch. One of the compounds shows a small jump in the helical pitch, which signals a first order transition and is consistent with high resolution calorimetric results.

We observe, in free-standing films of a chiral smectic liquid crystal, a series of discrete transitions in the relative orientation of the tilt of the interior and surface layers. These transitions include a remarkable reentrant synclinic-anticlinic-synclinic ordering sequence of the film surfaces in the presence of an electric field upon cooling. The profiles of the associated heat-capacity anomalies are found to be strongly thickness-dependent and exhibit a novel crossover behavior in reduced dimensions.

We have measured the temperature variation of surface tension, σ, in freestanding films of three liquid-crystal compounds. To do so, we have constructed a curvature-pressure tensiometer that uses a feedback loop to hold constant the curvature of a film while the temperature of the system is smoothly ramped. The apparatus enables us to obtain the temperature variation of σ in a continuous manner with resolution in σ of ∼0.2%. We interpret reproducible features of our data in terms of phase transitions.

A high resolution null-transmission ellipsometry system has been developed for measurement of the optical properties of liquid crystal free-standing films. The ellipsometric parameters are measured to within a resolution of 0.002° from samples held in a sealed, temperature-controlled environment. By measuring the ellipsometric parameters as a function of applied electric field orientation, the optical symmetry and molecular orientations of free-standing liquid crystal films can be determined in some cases. Three carefully selected applications of this technique are presented.

We have performed resonant X-ray scattering on two bent-core liquid crystal compounds exhibiting the B2 phase using three sample geometries: free-standing film and two others with free surface arrangements. The results conclusively demonstrate the two-layer orientational periodicity in this phase suggested by optical studies. We have performed the first resonant scattering experiments on liquid crystals at the chlorine K-edge, opening up a new class of compounds for resonant X-ray scattering studies. Furthermore, we have achieved an excellent alignment of the B2 phase with a free surface.

This article has no abstract. Keywords: liquid crystals; thermal study; mesophase; phase transition; AC calorimetry; critical exponent

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.

High-resolution heat-capacity and optical-reflectivity measurements have been conducted on thin free-standing films of n-hexyl-4′-n-pentanoyloxy-biphenyl-4-carboxylate (64COOBC). The data suggest incomplete layer-by-layer liquid-hexatic transitions. The transition in extremely thin films shows a diverging heat-capacity anomaly. The results are compared with those reported in other compounds, and discussed in the context of the theory of two-dimensional melting.

A differential optical reflectivity measurement technique for freestanding films is presented. The system is highly sensitive to changes in the polarization state of the reflected light. The method is used to study the evolution of an optically anisotropic liquid crystalline structure with temperature. In addition we present a reflectivity method for determining the film thickness for films consisting of two to hundreds of layers.

We present a new high energy resonant x-ray scattering study of a brominated chiral liquid crystal material exhibiting antiferro, ferri and ferroelectric smectic C phases. The absorption K-edge of bromine is at much higher energy (13.49 keV) than the sulfur K-edge (2.47 keV) which should enable a wider variety of experimental geometries. A weak resonant signal is detected on free standing films in the SmCA* phase only. Interestingly, the signal is stronger in binary mixtures with a bromine free thiobenzoate compound. This observation suggests that most chiral liquid crystal structures could be studied by resonant scattering after incorporation of a molecule bearing a resonant atom as a probe. Resonant x-ray diffraction profiles are also calculated for some recently proposed distorted clock models of the 4-layer ferrielec- tric phases. Finally, the influence of defects is investigated.

We describe a model for the layer-thinning transition in free-standing liquid-crystal films based on the successive, spontaneous formation of dislocation loops. As the film temperature increases and the smectic order and layer compressional modulus decrease, the condition for creating a dislocation loop of critical radius is met and a thinning is nucleated. The resulting equation for N, the number of smectic layers, as a function of temperature yields good fitting results to the thinning transitions obtained from several fluorinated compounds.

We have recorded the angular dependence of the ellipsometric signal of bulkisotropic dodecylcyanobiphenyl (12CB) as a function of temperature in the pre-smectic temperature region. Using a simple model, the order parameter of the discontinuously growing smectic surface layer has been determined approaching the isotropic-smectic phase transition temperature. Also the pretransitional isotropic region of the isotropic-smectic transition of the liquid crystal compound 2-(4-(1,1-dihydro-2-(2-perfluorobutoxy)perfluoroethcxy) phenyl-5-octyl pyrimidine (H8F(4,2,1)MOPP) has been investigated.

The liquid crystal (-)7S5 spreads as a two-terraced droplet on an oxide covered (100) Si wafer. The thickness of the upper and lower terraces are respectively approximately 200 and approximately 40 A. This is the simplest system for which the de Gennes and Cazabat (dGC) terraced spreading model [C. R. Acad. Sci. II 310, 1601 (1990)] is applicable. We find that soon after the upper terrace acquires a flat top a hole develops in the center of this terrace. The hole propagates down to the depth of the first terrace. In this contribution we demonstrate that the dGC model is unstable to the formation of a hole in the center of the upper terrace for a two-terraced droplet. Our extended dGC model, which includes a hole in the upper terrace, provides a reasonable description of the average spreading dynamics for this system. However, this model has difficulties quantitatively accounting for all of the features exhibited by the dynamics, perhaps because experimentally the inner and outer borders of the upper terrace become irregular with time. These irregularities in the borders have not been included within the model.

A high resolution a.c. calorimetric study of a phenyl pyrimidine derivative with one alkyl and one perfluorinated end group shows that the excess heat capacity associated with the smectic A-smectic C transition exhibits critical fluctuation behaviour that is consistent with the three-dimensional XY universality class. This is in contrast to the usual mean-field SmA-SmC behaviour and the near tricritical fluctuation behaviour reported recently in several other compounds. It is speculated that smaller than usual correlation lengths are the cause for the wide fluctuation region in this compound.

We report the results of resonant x-ray diffraction at the sulfur $K$-edge performed upon free-standing films of a thiobenzoate liquid-crystal compound. Our data provide the first direct structural evidence of distinct periodicities in several chiral Sm-C phases, including 2-layer, 3-layer, and 4-layer superlattices in $\mathrm{Sm}\ensuremath{-}{C}_{A}^{*}$, $\mathrm{Sm}\ensuremath{-}{C}_{\mathrm{FI}1}^{*}$, and $\mathrm{Sm}\ensuremath{-}{C}_{\mathrm{FI}2}^{*}$, respectively. In $\mathrm{Sm}\ensuremath{-}{C}_{\ensuremath{\alpha}}^{*}$, periodicity incommensurate with the layer spacing was detected. The racemic compound version was also studied. The results are consistent with a ``clock model'' of the $\mathrm{Sm}\ensuremath{-}{C}^{*}$ variant structures.

High-resolution surface tension measurements have been carried out on the free-standing films of more than 30 selected liquid-crystal compounds in their smectic phases. Surface tension (γ) values falling into major categories of 27, 24, 21, 13, and 11.5 dyn/cm have been obtained. The dependence of γ on specific terminal groups or molecular structures will be discussed. Our results provide important information about the molecular origin of surface tension.

We report ellipsometric measurements on freely suspended films of chiral liquid-crystal compounds near their smectic-A-smectic-C transition. The temperature difference between the surface and the bulk transition is found to vary considerably within a homologous series. In two compounds possessing a fluorinated alkyl chain an unexpected sign inversion of the spontaneous polarization in the ferroelectric smectic-C phase is observed which occurs only in thin but not in thick films.

High-resolution surface tension measurements have been conducted on free-standing films of a specially selected series of liquid-crystal compounds. We have discovered a dramatic change in the surface tension of liquid-crystal compounds by replacing a single fluorine atom in the molecular tail with a hydrogen atom. The implication of this finding will be discussed.

10 pages; International audience; 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.

Large negative thermal-expansion coefficients of a partially perfluorinated liquid-crystal compound as a function of temperature and number of layers have been obtained from free-standing films. Exploiting this behavior, as well as novel layer-by-layer thinning transitions, we have demonstrated the existence of an anomalous layer compression. For a 3-layer film, the magnitude of total compression was found to be as large as 3 A.

We have successfully prepared stable one-layer films of 54COOBC $[n$-pentyl-${4}^{\ensuremath{'}}\ensuremath{-}n$-pentanoyloxy biphenyl-4-carboxylate] in a small film hole $(\ensuremath{\approx}0.7$ mm in diameter) and conducted high-resolution optical reflectance measurements near the smectic-$A$\char21{}hexatic-$B$ transition. The stability of these films is contrary to experiences with all other compounds and also to heuristic understanding. We propose a modification to such understanding. Within the resolution of our measurements, data are in good agreement with those of two-layer films. The result gives a confirmation of two-dimensional behavior of two-layer films.

Calorimetric, optical reflectivity, and electron-diffraction measurements have revealed several unique features near the smectic-A-hexatic-B transition of thin freestanding films of nmOBC (n-alkyl-4′-n-alkyoxy-biphenyl-4-carboxylate). Our recent Monte-Carlo simulations of a coupled XY model offer important insight into the nature of this transition.

Liquid crystals are soft materials that combine the fluidity of disordered liquids and the long range orientational or positional order of crystalline solids along one or two directions of space. X-ray scattering is widely and generally successfully used to investigate and characterize the microscopic structure of most liquid crystals. In many cases however, the Bragg reflections are forbidden by special symmetries of the unit cell and the low dimensional structure of the liquid crystalline phases are out of reach of conventional X-ray experiments. We show in this paper that this problem can be overcome by resonant scattering of X-rays as it reveals the anisotropy of the tensor structure factor. We review various examples in which the restored forbidden reflections reveal unambiguously the hidden structure of liquid crystalline phases. Moreover, we show that in some cases, a fine analysis of the polarization of the Bragg reflections enables one to discriminate between different structural models. These studies solved long standing questions about biaxial liquid crystal structures and provided new insights into physical phenomena such as supercritical behaviour or commensurate-incommensurate transitions.

To address the issue of the pairing state in high-temperature superconductors, four different experimental investigations have been carried out on a single high-quality, untwinned single crystal of ${\mathrm{LuBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. These include measurements of the specific heat in magnetic fields, both near the transition temperature and at low temperatures, investigations of the angular dependence of the transverse magnetic moment in the nonlinear Meissner regime, and the measurement of microwave properties leading to the temperature dependences of the penetration depth and the surface resistance at low temperatures. Some of the results raise questions relating to the existence of a pairing state with line nodes in the energy gap, whereas others appear to be consistent with this picture. The results taken together suggest that studies of the pairing state be examined critically for possible alternative explanations. \textcopyright{} 1996 The American Physical Society.

Utilizing our high-resolution ac calorimeter, optical reflectivity, and electron diffraction, we have found a few very interesting phenomena associated with the free-standing films of the N-(4-n-butyloxybenzylidene)-4-n-octylaniline (4O.8) compound. Upon cooling from the smectic-A phase, the outer surface layers display a distinct hexatic-B order and subsequently transforms into crystal-B phase through a two-stage transformation. Each stage is found to be first order. The film exhibits a layer-by-layer ordering transitions developed from the film/vapor interface inwardly.

Motivated by the defect-mediated two-stage melting theory, extensive experiments have been concluded on free-standing films of a liquid-crystal sample which exhibits the isotropic-smectic-A–hexatic B-crystal-B bulk phase sequence. For a two-layer film, which is virtually two-dimensional, our calorimetric measurement shows an apparently divergent anomaly near the smectic-A-hexatic-B transition. Its anomaly has a dominant fluctuation contribution and can be fitted to a power law with an exponent α≈0.37±0.05, in disagreement with the theoretical prediction. Thicker films exhibit surface-initiated layer-by-layer (LBL) wetting transition upon cooling. Moreover, these films also exhibit interesting LBL thinning transitions above the bulk clearing temperature.

Free-standing liquid-crystal films constitute a unique and phenomenally rich system in which a number of physical phenomena may be carefully studied. In particular, they provide an ideal system in which the novel theories of defect-mediated melting in two-dimensions (2D) may be tested. Calorimetric data is presented that indicate that such theories cannot adequately account for phase transitions in effectively 2D free-standing liquid-crystal films only two molecular layers in thickness. Extensive Monte Carlo simulation studies have therefore been performed on a trial Hamiltonian that couples herringbone order to the hexatic order. In a relatively large region of parameter space, the simulation yields heat-capacity consistent with our calorimetric data. These results are discussed in the context of existing data on the structural, optical, and mechanical properties of free-standing films.

After implementing a computer-enhanced imaging system in our newly estab- lished apparatus, we have achieved much higher resolution in measuring the surface tension of free-standing films in the smectic-A or smectic-Ad phase of seven different liquid-crystal com- pounds. The experimental results reveal two salient features: the relation of surface tension to thickness and the difference in surface tension between the smectic-A and smectic-Ad phases

By utilizing our state-of-the-art ac differential freestanding film calorimetric system, three remarkable surface enhanced layer-by-layer transitions in several liquid-crystal compounds have been investigated. Each of these transitions can be well-described by the simple power-law expression: L = Lo t−ν. This demonstrates that these surface enhanced transitions occur on the smooth “substrate” with long-range interactions.

Employing our free-standing film calorimetric system. we have identified three remarkable layer-by-layer transitions in several liquid crystal compounds. Each of these transitions can be well described by the simple power-law form:L = L 0 t. The layering transitions liMind near the smectic-A- hexatic-B and smectic-A crystal-B transitions are well characterized by the exponent v≈ 1 3. This value is consistent with models based on a van der Wads-like dominant intermolecular interaction. Another novel layer-by-layer thinning transition has been discovered above the hulk smectic-A isotropic transition of a perfluorinated liquid crystal compound. The value of the exponent obtained, v ≈ 3 4. cannot he easily explained using familiar models.

This letter describes classes of tunable microfluidic fiber (μFF) devices that use specially designed long-period gratings in which the phase matching condition is satisfied over a wide spectral range. Dynamic tuning is achieved by electrowetting-based pumping of microfluidic plugs back and forth over the gratings. As specific examples, we demonstrate dynamically tunable broadband attenuators and filters with adjustable profiles by using fluids with different refractive indices. These devices have attractive features that include in-fiber design and polarization-independent behavior together with low-power, nonmechanical, fully reversible, and latchable tuning.

We carried out an improved characterization of phase transitions among chiral smectic-C subphases observed for various antiferroelectric liquid crystals by precise heat capacity measurements. It was found that the phase transitions are intrinsically first order exhibiting a remarkable heat anomaly which involves little pretransitional thermal fluctuation and a finite thermal hysteresis. On the other hand, we also noticed that the critical point of the smectic-C(α)(*)-smectic-C* transition is induced by the destabilization of the smectic-C(α)(*) phase which couples with the fluctuation associated with the smectic-A-smectic-C(α)(*) phase transition.