Elucidation of the de Vries behavior in terms of the orientational order parameter, apparent tilt angle, and field-induced tilt angle for smectic liquid crystals by polarized infrared spectroscopy.

We report experimental results of the orientational order parameter, the apparent tilt angle, and the field-induced tilt angle for three chiral smectic liquid crystalline materials investigated using infrared (IR) polarized spectroscopy. The common feature in these materials is use of the core 5-methyl-2- pyrimidine benzoate as the central part of the mesogen. This core is terminated by siloxane or carbosilane chains on one of the ends and by the chiral alkoxy chains on the opposite. These compounds exhibit low concomitant layer shrinkage at the smectic A^{*} (SmA^{*}) to smectic C^{*} (SmC^{*}) transition temperature and within the SmC^{*} phase itself. The maximum layer shrinkage in SmC^{*} is observed as ∼1.5%. We calculate the apparent orientational order parameter, S_{app} in the laboratory reference frame from the observed IR absorbance for homeotropic aligned samples, and the true order parameter, S, is calculated using the measured tilt angle and is also interpolated from Iso-SmA^{*} transition temperature closer to SmC^{*} phase. The apparent tilt angle in the SmA^{*} phase calculated from a comparison of order parameters S and S_{app} is found to be significantly large. A low magnitude of S_{app} found for homeotropic aligned samples in the SmA^{*} phase indicates that the order parameter plays a vital role in determining the de Vries characteristics, especially of exhibiting larger apparent tilt angles. Furthermore there is a significant increase in the true order parameter at temperatures close to SmA^{*} to SmC^{*} transition temperature in all three compounds. The planar-aligned samples are used to study the dependence of induced tilt angle on the applied electric field. The generalized Langevin-Debye model given by Shen et al. reasonably fits the experimental data on the field-induced tilt angle. The results show that the dipole moment of the tilt correlated domain in SmA^{*} diverges as temperature is lowered to the SmA^{*}-SmC^{*} transition temperature. The generalized Langevin-Debye model is also found to be extremely effective in confirming some of the conclusions of the de Vries behavior.

Molecular orientational distribution function of a chiral de Vries smectic liquid crystal from birefringence measurements.

An alternative method for determining the orientational distribution function and the order parameter from the electric field-induced birefringence measurements of a chiral liquid crystal compound in its Smectic A* is being introduced. A chiral mesogen based on a 5-phenyl-pyrimidine benzoate core terminated by a trisiloxane group on one side and the chiral alkyloxy chain on its opposite side is designed and synthesized to exhibit the "de Vries" smectic characteristics. The compound exhibits first order Smectic A*-Smectic C* phase transition, evidenced by the results of differential scanning calorimetry. The material is being investigated by electro-optical experiment in its smectic phases. We present a model that incorporates the generalised Langevin-Debye model which includes the Maier-Saupe effective mean-field potential term in order to explain the change in birefringence with the electric field. A good agreement between the experimental results and the predictions from the model leads to the determination of the molecular orientational distribution function in Smectic A phase. Furthermore, the temperature dependency of the Saupe orientational order parameter ⟨P2⟩ is obtained using the parameters of the model. Based on the experimental and theoretical results, we show that de Vries Smectic A* phase exhibits a broad volcano-like tilt angle distribution with the two maxima occurring at finite tilt angles closer to the Smectic A*-Smectic C* transition temperature, and a sugarloaf-like distribution occurs in the tilt for temperatures close to the Isotropic-Smectic A* phase transition.

Observation of the de Vries behavior in SmA* phase of a liquid crystal using polarised Raman scattering and infrared spectroscopy.

Two approaches exist in the literature for describing the orientational distribution function (ODF) of the molecular directors in SmA* phase of liquid crystals, though several models are recently proposed in the literature for explaining the de Vries behaviour. These ODFs correspond to either the conventional unimodal arrangements of molecular directors arising from the mean field theory that leads to the broad or sugar-loaf like distribution or to the "diffuse-cone-shaped" type distribution proposed by de Vries. The hypothesis by de Vries provides for a realistic explanation as to how at a molecular level, a first-order SmA* to SmC* transition can occur where the uniform molecular director azimuthal distributions condense to values lying within a narrow range of angles; finally these condense to a single value while at the same time ensuring a little or no concomitant shrinkage in the layer spacing. The azimuthal distribution of the in-layer directors is probed using IR and polarized Raman spectroscopic techniques. The latter allows us to obtain the ODF and the various order parameters for the uniaxial and the biaxial phases. Based on the results of these measurements, we conclude that the "cone-shaped" (or volcano-shaped) de Vries type of distribution can most preferably describe SmA* where "a first-order phase transition from SmA* to SmC*" and a low layer shrinkage can both be easily explained.

Chiral smectic-A and smectic-C phases with de Vries characteristics.

Infrared and dielectric spectroscopic techniques are used to investigate the characteristics of two chiral smectics, namely, 1,1,3,3,5,5,5-heptamethyltrisiloxane 1-[4^{'}-(undecyl-1-oxy)-4-biphenyl(S,S)-2-chloro-3-methylpentanoate] (MSi_{3}MR_{11}) and tricarbosilane-hexyloxy-benzoic acid (S)-4'-(1-methyl-hexyloxy)-3'-nitro-biphenyl-4-yl ester (W599). The orientational features and the field dependencies of the apparent tilt angle and the dichroic ratio for homogeneous planar-aligned samples were calculated from the absorbance profiles obtained at different temperatures especially in the smectic-A* phase of these liquid crystals. The dichroic ratios of the C-C phenyl ring stretching vibrations were considered for the determination of the tilt angle at different temperatures and different voltages. The low values of the order parameter obtained with and without an electric field applied across the cell in the Sm-A^{*} phase for both smectics are consistent with the de Vries concept. The generalized Langevin-Debye model introduced in the literature for explaining the electro-optical response has been applied to the results from infrared spectroscopy. The results show that the dipole moment of the tilt-correlated domain diverges as the transition temperature from Sm-A^{*} to Sm-C^{*} is approached. The Debye-Langevin model is found to be extremely effective in confirming some of the conclusions of the de Vries chiral smectics and gives additional results on the order parameter and the dichroic ratio as a function of the field across the cell. Dielectric spectroscopy finds large dipolar fluctuations in the Sm-A^{*} phase for both compounds and again these confirm their de Vries behavior.

Phase behavior and characterization of heptamethyltrisiloxane-based de Vries smectic liquid crystal by electro-optics, x rays, and dielectric spectroscopy.

A heptamethyltrisiloxane liquid crystal (LC) exhibiting I-SmA^{*}-SmC^{*} phases has been characterized by calorimetry, polarizing microscopy, x-ray diffraction, electro-optics, and dielectric spectroscopy. Observations of a large electroclinic effect, a large increase in the birefringence (Δn) with electric field, a low shrinkage in the layer thickness (∼1.75%) at 20 °C below the SmA^{*}-SmC^{*} transition, and low values of the reduction factor (∼0.40) suggest that the SmA^{*} phase in this material is of the de Vries type. The reduction factor is a measure of the layer shrinkage in the SmC^{*} phase and it should be zero for an ideal de Vries. Moreover, a decrease in the magnitude of Δn with decreasing temperature indicates the presence of the temperature-dependent tilt angle in the SmA^{*} phase. The electro-optic behavior is explained by the generalized Langevin-Debye model as given by Shen et al. [Y. Shen et al., Phys. Rev. E 88, 062504 (2013)10.1103/PhysRevE.88.062504]. The soft-mode dielectric relaxation strength shows a critical behavior when the system goes from the SmA^{*} to the SmC^{*} phase.

Design and investigation of de Vries liquid crystals based on 5-phenyl-pyrimidine and (R,R)-2,3-epoxyhexoxy backbone.

Calamitic liquid crystals based on 5-phenyl-pyrimidine derivatives have been designed, synthesized, and characterized. The 5-phenyl pyrimidine core was functionalized with a chiral (R,R)-2,3-epoxyhexoxy chain on one side and either siloxane or perfluoro terminated chains on the opposite side. The one involving a perfluorinated chain shows SmA^{*} phase over a wide temperature range of 82 °C, whereas the siloxane analog exhibits both SmA^{*} and SmC^{*} phases over a broad range of temperatures, and a weak first-order SmA^{*}-SmC^{*} transition is observed. For the siloxane analog, the reduction factor for the layer shrinkage R (relative to its thickness at the SmA^{*}-SmC^{*} transition temperature, T_{AC}) is ∼0.373, and layer shrinkage is 1.7% at a temperature of 13 °C below the T_{AC}. This compound is considered to have "de Vries smectic" characteristics with the de Vries coefficient C_{deVries} of ∼0.86 on the scale of zero (maximum-layer shrinkage) to 1 (zero-layer shrinkage). A three-parameter mean-field model is introduced for the orientational distribution function (ODF) to reproduce the electro-optic properties. This model explains the experimental results and leads to the ODF, which exhibits a crossover from the sugar-loaf to diffuse-cone ODF some 3 °C above T_{AC}.

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.

Dielectric and electro-optic studies of a bimesogenic liquid crystal composed of bent-core and calamitic units.

A bimesogen, BR1, composed of a bent-core and calamitic unit, linked laterally via a flexible spacer is investigated by dielectric and electro-optic techniques. X-ray results show the presence of clusters in the nematic phase, and the cluster size is of the order of the thickness of a single layer. The splitting of the small-angle scattering Δχ/2 is about 50°, which indicates SmC like clusters with a significant tilt of the molecules in the quasilayers. The sign reversal of the dielectric anisotropy Δε' is observed as a function of frequency; the behavior is rather similar to that exhibited by the conventional dual frequency nematics, composed of a calamitic mesogen, with the exception that it occurs at much lower frequencies in this material. Interestingly, as the bimesogen enters its nematic phase, the average permittivity decreases as the temperature is lowered. This indicates the onset of antiparallel association of some of the dipoles in the system, and this type of association is much more prominent in BR1 in comparison to other bent-core liquid crystalline systems composed of the same bisbenzoate core unit. The analysis of the dielectric spectra using the Maier-Meier model confirms the onset of an antiparallel correlation of dipoles occurring at the isotropic to nematic phase transition temperature. Additionally these results support a model of the cluster where the transverse dipole moments in the neighboring layers are antiparalleled to each other.

Nematic twist-bend phase with nanoscale modulation of molecular orientation.

A state of matter in which molecules show a long-range orientational order and no positional order is called a nematic liquid crystal. The best known and most widely used (for example, in modern displays) is the uniaxial nematic, with the rod-like molecules aligned along a single axis, called the director. When the molecules are chiral, the director twists in space, drawing a right-angle helicoid and remaining perpendicular to the helix axis; the structure is called a chiral nematic. Here using transmission electron and optical microscopy, we experimentally demonstrate a new nematic order, formed by achiral molecules, in which the director follows an oblique helicoid, maintaining a constant oblique angle with the helix axis and experiencing twist and bend. The oblique helicoids have a nanoscale pitch. The new twist-bend nematic represents a structural link between the uniaxial nematic (no tilt) and a chiral nematic (helicoids with right-angle tilt).

Effect of cybotactic clusters on the elastic and flexoelectric properties of bent-core liquid crystals belonging to the same homologous series.

We report results of the splay (K_{11}) and bend (K_{33}) elastic constants and the effective flexoelectric coefficient of three bent-core liquid crystals belonging to a homologous series of 4-cyanoresorcinol bisbenzoates with varying chain lengths. Based on the results of x-ray scattering studies, one of the three compounds with a shorter chain length (C4) has few, if any, clusters present in its nematic phase and behaves quite normally, whereas the others two with longer chain lengths (C6 and C7) show the presence of cybotactic nematic phase with smectic C type clusters. These grow in size with a reduction in temperature. K_{33} is found to be the least for C7, whereas it is weakly dependent on temperature. K_{33} is somewhat higher for C4 and C6 and is almost independent of temperature. K_{11} for C6 and C7 is higher by 20% to 50% than C4 depending on the temperature. K_{11} increases linearly with a reduction in temperature for the three compounds. For C6 K_{11}>K_{33} by a factor up to ∼2 depending on the temperature, for C4 it is greater by a factor up to 1.3, and for C7 it is greater by a factor of ∼2.5. These results suggest that the clusters do not have any effect on K_{11}. The magnitude of the effective flexoelectric coefficient e=(|e_{1}-e_{3}|) is measured by creating a uniform lying helix (ULH) configuration in a planar cell. By doping the bent-core system with a small wt% of a chiral dopant, the ULH is obtained by cooling planar cells to the cholesteric phase under weak electric field. The effective flexoelectric coefficient is greater for the bent-core systems than for calamatics but it is much lower than would otherwise have been expected for such systems. |e_{1}-e_{3}| for C4 > C6 ≈ C7 is greater by 20% to 25% than C6 and C7 at the same reduced temperature. These differences in the effective flexoelectric coefficient can easily arise from a difference in the chain lengths among the members of the series but if the presence of clusters were to have an influence on |e_{1}-e_{3}|, then these would reduce it, contrary to the expectations for the bent-core systems.

Spontaneous periodic deformations in nonchiral planar-aligned bimesogens with a nematic-nematic transition and a negative elastic constant.

Hydrocarbon linked mesogenic dimers are found to exhibit an additional nematic phase below the conventional uniaxial nematic phase as confirmed by x-ray diffraction. The phase produces unusual periodic stripe domains in planar cells. The stripes are found to be parallel to the rubbing direction (in rubbed cells) with a well-defined period equal to double the cell gap. The stripes appear without external electromagnetic field, temperature or thickness gradients, rubbing or hybrid alignment treatments. Simple modeling proposes a negative sign for at least one of the two elastic constants: splay and twist, as a necessary condition for the observed pattern.

Experimental study of de Vries properties in antiferroelectric smectic liquid crystals.

Results of the experimental study on different antiferroelectric liquid crystal (AFLC) materials are presented using a number of techniques such as the optical birefringence, electro-optics and the measurements of optical thickness of free-standing films. Despite differences in the molecular structures of the various AFLC materials studied, these are found to exhibit a de Vries type of smecticA (SmA) properties in a temperature range higher than SmC. This correlation leads to the conclusion that these two classes of liquid crystals are related to each other. Furthermore, we suggest that these arise from the same physical mechanism, namely the existence of the weak synclinic (or reduced anticlinic) correlations between the neighbouring molecular tilt directions.

Discontinuous change in the smectic layer thickness in ferrielectric liquid crystals.

The temperature dependence of the thickness of thick free-standing films is studied using a high-resolution film thickness measurement technique. A small discontinuity in the temperature dependence of the smectic layer thickness at every phase transition between ferro-, ferri-, and antiferroelectric phases is observed. We show that the major contribution to it arises from a change in the smectic tilt angle.

Investigations of nanoscale helical pitch in smectic-C*alpha and smectic-C* phases of a chiral smectic liquid crystal using differential optical reflectivity measurements.

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.

Surface-induced multiple reentrant transitions.

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.

Discrete flexoelectric polarizations and biaxial subphases with periodicities other than three and four layers in chiral smectic liquid crystals frustrated between ferroelectricity and antiferroelectricity.

The subphase for the temperature range that lies in between Sm-C(A)* and the three-layer Sm-C(A)* (1/3)subphase has been confirmed to exist using the measurements of electric-field-induced birefringence, optical rotation, and the characteristic reflection bands in the antiferroelectric liquid-crystalline compound, 1-trifluoromethylundecyl-4-(4'-dodecyloxybiphenyl-4-yl-carbonyloxy)-3-fluorobenzoate (12BIMF10). The measurements of electric-field-induced birefringence and optical rotatory power are made on -thick homeotropic cells, and the characteristic reflection bands are observed in free-standing films of thicknesses ranging from 30 to 50 microm. Several binary mixtures have been prepared by mixing (S)-12BIMF10 with (S)-4-(1-methylheptyloxycarbonyl)-phenyl-4'-octylbiphenyl-4-carboxylate (MHPBC), and the effect of racemization of the compound on the character of the biaxial subphase (other than three and four layers) is also discussed. The results are interpreted in terms of the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)]; the effective long-range couplings between the director orientations in separated smectic layers emerge after the minimization of free energy with respect to the total (ordinary spontaneous and discrete flexoelectric) polarizations, lifting the degeneracy and producing the nonplanar structures of the subphases.

Self-assembled uniaxial and biaxial multilayer structures in chiral smectic liquid crystals frustrated between ferro- and antiferroelectricity.

With a view to obtain a molecular model for the subphases produced by the frustration between ferro- and antiferroelectricity in chiral smectic liquid crystals, we report results on two compounds and observe (i) the staircase character of uniaxial Sm C(*)(alpha) itself in the bulk and (ii) the multipeaked characteristic reflection bands due to the modulated helical structures just above the Sm C(*)(A) temperature range. We suggest the emergence of several uniaxial and biaxial subphases. The results show that both types of subphases can be specified by q(T) = [F] / ( [A] + [F] ) in the zero-order approximation; [A] and [F] are the numbers of antiferroelectric and ferroelectric orderings in the unit cell. We consider the basis of both types of subphases, particularly the description of the short-pitch helical structure of Sm C(*)(alpha), in terms of the molecular models so far proposed and emphasize the important role played by the discrete flexoelectric polarization.

Optical rotatory power, biaxiality, and models of chiral tilted smectic phases.

Among the chiral tilted smectics, the stable existence has been confirmed in numerous investigations of SmC(*)(A), (antiferroelectric smectic-C(A)) SmC(*)(F11) (SmC(*)(gamma)), SmC(*)(F12) (antiferroelectric, AF) and SmC* phases. The structures of the ferrielectric SmC(*)(F11) and SmC(*)(F12) phases suggested by different models are essentially different although all the models use the three-layer and four-layer periodicity for them. The structures of the phases were investigated using the optical rotatory power (ORP) measurements technique. The ORP was simulated using Berreman's 4 x 4-matrix method. The compound under investigation (S)-1-methylheptyl 4-(4(')-n-undecyloxy-biphenyl-4-yl-carbonyloxy) [acronym (S)-11OF1M7] clearly provides SmC(*)(F11) and SmC(*)(F12) phases, the temperature range for the existence of these phases is about 5 degrees C each. This had not been achieved for the earlier investigated antiferroelectric liquid crystal (AFLC) samples. The results obtained confirm that the unit cell of the molecular structure of these subphases is highly biaxial. Due to the biaxiality the texture of the homeotropic cell under a polarizing microscope appears nonuniform. This requires a special approach to the measurements and a simulation of the ORP, which is discussed in detail. A technique has been designed where the transmitted intensity through a polarizing microscope is measured as a function of the angle of polarization of the incident light. From the observed output, which is a biased sine wave, the ORP is being determined. In the same scan, the wavelength of light is also being automatically altered. Comparing the simulated and measured data, we can conclude that in the SmC(*)(F12) phase the distortion angle of the directors in the Ising model is lower than 10 degrees. Using the Ising model, the pitch in SmC(*)(F11) has been determined and this is found to have a strong temperature dependence.

Dependence of the molecular orientational states on the surface conditions for the "V-shaped switching" in a ferroelectriclike liquid crystal sample.

The three-component mixture showing the V-shaped switching in a rubbing cell is investigated using a temperature gradient cell (TGC) where the epitaxial method of alignment, but without an alignment layer, is used. The molecular alignment and the switching characteristics in a TGC are compared with the rubbing sandwich and the open cells. The uniform or the twisted state is observed in the TGC, depending on the surface condition whether indium-tin oxide (ITO) or glass, while the uniformlike state with the average optical axis parallel to the smectic layer normal emerges only in the rubbing cell. The cancellation of the surface polarization charges by the surface free charges on the ITO surfaces determines the molecular alignment state in the TGC. From these results, we conclude that the nonpolar in-plane anchoring plays an important role in giving a uniformlike state in the rubbing cell.