Anomalous diffusion, gigahertz, and terahertz spectroscopy of aliphatic ketones.

The experimental results of the complex dielectric permittivity of aliphatic ketones in dilute solutions of inert solvent cyclohexane in the gigahertz (GHz) and terahertz (THz) frequencies of the electromagnetic spectrum are examined in terms of the theory of inertial anomalous diffusion of polar molecules, considered as an assembly of molecules with interacting dipolar groups, in polar liquids. The theory is based on the generalization of the Debye rotational diffusion model of dielectric relaxation of polar molecules. The model comprises two interacting dipolar groups-one lighter and the other heavier; each has a finite moment of inertia and each experiences a finite friction with an extensive range of damping or drag coefficient and the dipole moment ratio of the two groups. The lighter group refers to the reference molecule, whereas the heavier group simulates the neighboring molecules, and the two groups interact with each other via the dipole-dipole interaction potential. The resulting approximate expression contains terms in both the Rocard form and the Сole-Сole form. The experimental data on aliphatic ketones are shown to fit extremely well with the theory, and parameters of the fit offer physical significance. An agreement of the plot of the experimental data on dielectric loss versus frequency to the formulas derived from the model offers a mathematical basis of the semiempirical equations used in the literature to fit the experimental data. Experimental results of the dielectric loss of neat polar liquid acetone in GHz and THz, as an example, are shown to fit the theory; however, the interaction potential parameter compared to its dilute solution counterpart is significantly increased, reflecting the increase in the dipole-dipole interaction energy.

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.

Distortions in structures of the twist bend nematic phase of a bent-core liquid crystal by the electric field.

The dielectric spectra of the twist bend nematic phase (N_{TB}) of an achiral asymmetric bent-core liquid crystalline compound are studied for determining the various relaxation modes. Dielectric measurements are also carried out under the bias field E up to 8 V/µm. Two molecular and two collective relaxation processes are observed. The orientational order parameters with respect to the local and the main directors determined using molecular modes are used to find the heliconical angle. The results also show that the order parameter with reference to the main director reverses its trend from increasing to decreasing at temperatures of a few degrees above the N_{TB} to N transition. The collective relaxation modes are assigned to (a) distortions of the local director by the electric field at a frequency of ∼100kHz while the periodic helical structure remains unaltered (mode attributed to flexoelectricity); (b) changes in the periodic structure arising from a coupling of the dielectric anisotropy with the electric field at the lowest frequency in the range of 100 Hz-10 kHz. Frequency of the higher frequency collective mode (∼100kHz) depends primarily on the heliconical angle and has anomalous softeninglike behavior at the N-N_{TB} transition. The lowest frequency mode is studied under the bias field E; the modulus of the wave vector gradually vanishes on increasing E (except for an initial behavior, E^{2}<0.1V^{2}/µm^{2}, which is just the opposite). The transition from the twist bend to splay bend structure is observed by a sudden drop in the frequency of this mode, followed by a linear decrease in frequency by increasing E. The results agree with the predictions made from the currently proposed models for a periodically distorted N_{TB} phase.

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.

Short bent-core molecules: X-ray, polarization, dielectricity, texture and electro-optics investigations.

Bent-core liquid crystals based on 1,2,4-oxadiazole as a central unit have been the first mesogens to exhibit a ferroelectric response in the nematic phase. This behavior has been widely recognized as due to the presence of smectic-like polar cybotactic clusters permeating the nematic phase. Unfortunately, these compounds exhibited rather high melting points, about 120 °C, due to the presence of four benzene rings in the molecules. Here we describe the synthesis and physical characterization of a new series of BC mesogens, featuring the same bent core as the previous compounds but shorter outer substituents. By keeping only two benzene rings, we were able to lower the melting points to about 70 °C. However, while X-ray diffraction and dielectric spectroscopy measurements confirm the cybotactic nature of the nematic phase of these compounds, polarization and electro-optical measurements ascribe their polar response to flexoelectricity rather than to spontaneous polarization. Finally, texture investigation suggests the biaxiality of the nematic phase, which is indicated also by conoscopic measurements. These results are important for recognizing size and rigidity limitations in designing bent-core liquid crystal molecules suitable for applications.

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}.

Flexoelectric polarization studies in bent-core nematic liquid crystals.

The flexoelectric polarization (Pf) of four bent-core nematic liquid crystals (LCs) has been measured using the pyroelectric effect. Hybrid aligned nematic cells are fabricated for measuring the pyroelectric response over the entire range of the nematic phase. It is found that the magnitude of flexoelectric polarization Pf and the sum of the flexoelectric coefficients |e1+e3| for the bent-core LCs studied here are three to six times higher than for the calamitics. Pf is found to depend on the transverse dipole moment of LC molecules. However, |e1+e3| values are by no means giant as |e3| alone had been reported for a bent-core nematic system previously. The dependence of the sum of "splay and bend flexoelectric coefficients" is discussed in terms of the shape of the molecule and of the dipole moment directed normal to the molecular axis.

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.

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals.

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter (S) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: S for the long axes and C for the ordering of the short axes of molecules. The temperature dependencies of S and C are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-AP(A)) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both S and C, particularly the temperature dependency of the latter, are being experimentally determined. Results show that S in the orthogonal smectic phase composed of bent cores is higher than in Sm-A calamatic LCs and C is also significantly large.

Gold nanorods embedded discotic nanoribbons.

It is shown that gold nanorods (GNRs) can be easily inserted into the supramolecular order of discotic liquid crystals (DLCs) along the director without disturbing their mesomorphism. GNRs embedded discotic nanoribbons, useful for constructing devices like thin film transistors, sensors, etc., are prepared by simple solution processing of GNR-DLC nanocomposites.

Biaxial order and a rotation of the minor director in the nematic phase of an organo-siloxane tetrapode by the electric field.

Biaxiality in the nematic phase for a liquid crystalline tetrapode made up of organo-siloxanes mesogens is investigated using polarized infrared spectroscopy. An ordering of the minor director for the homeotropically aligned sample is found to depend on the amplitude of the in-plane electric field. On increasing the in-plane electric field, the minor director, lying initially along the rubbing direction, rotates to the direction of the applied field. The scalar order parameters of the second rank tensor are found to depend significantly on the strength of the electric field. A most significant increase is found in the nematic order parameter and in the parameter that characterizes the phase biaxiality.

Effect of high hydrostatic pressure on the dielectric relaxation in a non-crystallizable monohydroxy alcohol in its supercooled liquid and glassy states.

The complex relative permittivity of a non-crystallizable secondary alcohol, 5-methyl-2-hexanol, is measured over a wide range of temperatures and pressures up to 1750 MPa (17.5 kbar). The data at atmospheric pressure (P = 0.101 MPa) are analyzed in terms of three processes, and the results are in complete agreement with that of O. E. Kalinovskaya and J. K. Vij [J. Chem. Phys. 112, 3262 (2000)]. Process I is of the Debye type and process II is of the Davidson-Cole type, whereas process III is identified as the Johari-Goldstein relaxation process. For pressures of ∼500 MPa and higher, processes I and II are seen to merge into each other to form a single dominant process which unambiguously cannot be resolved into more than one process. The dielectric relaxation strength of process I decreases slightly initially with pressure and when the two processes have merged at elevated pressures, the total relaxation strength increases with increase in pressure. Process III is better resolvable at higher pressures especially above T(g) in the supercooled liquid state for the reason that the separation in the time scales between the dominant and the JG relaxation process increases at elevated pressures. Surprisingly we find a change in the slope in the plot of log τ(JG) vs. 1/T for P = 1750 MPa. The results for the relaxation time of alcohols are compared with the Kirkwood correlation factor, g, and it is found that higher is the g, lower is the relaxation time for process I, and it is more of the Debye type. On a reduction in g brought about by an increase in pressure at lower temperatures, the dominant process becomes non-Debye though extensive hydrogen bonding is still present. The dielectric strength of the merged processes increases with increase in pressure. The values of the steepness index, m = |d log τ/d(T(g)/T)|(T = Tg) for processes I and II are different for P = 0.1 MPa. However the value of m, for the composite process, which is a merger of processes I and II, for P = 1750 MPa is almost the same for process II at P = 0.1 MPa. From the results of the activation volume, activation enthalpy, and a comparison of the relaxation times with the g factor, we conclude that both processes I and II are significantly affected by hydrogen bonding and both contribute to the structural relaxation.

Debye process and dielectric state of an alcohol in a nonpolar solvent.

To investigate the origin of the first order molecular kinetics of the most prominent, Debye-type polarization, a detailed dielectric relaxation study of 66.5, 40, and 20 mole% solutions of 5-methyl-2-hexanol in 2-methylpentane (2:1, 0.67:1, and 0.25:1 molar ratios) was performed. The Debye-type polarization remains prominent in the solutions, despite the extensive loss of intermolecular hydrogen bonds. At high temperatures, its contribution to permittivity extrapolates close to the statistically scaled values for the 2:1 solution. For others, the measured values of its contribution crossover the scaled values in a temperature plane. The faster relaxation process of about 4% magnitude has an asymmetric distribution of times in the solutions and, relative to those of the pure alcohol, their values decrease on heating more at high temperatures and less at low. This is attributed to an increase in the alcohol cluster size by consumption of monomers as well as the growth of smaller clusters as the solution is cooled. It is argued that structural fluctuation in solutions, as in the pure alcohol, is determined by the rates of both the Debye-type and the faster polarizations in the ultraviscous state.

Short-range correlations seen in the nematic phase of bent-core liquid crystals by dielectric and electro-optic studies.

Three bent-core nematic liquid crystals having the same core but with different terminal groups, short (C4) and long (C7,C9) tails, are investigated by dielectric and electro-optic contrast spectroscopic techniques. C4 shows sign reversal in the dielectric anisotropy Δε' as a function of both temperature and frequency, whereas C9 shows only negative Δε' in the entire mesophasic region. The behavior of C7 is intermediate of the two. Results of a dielectric study show that both C7 and C9 exhibit strong short-range polar correlations normal to the director. The correlation lengths of these interactions are found to be similar to those from the x-ray scattering. An increased hindered rotation for C9 compared to C4 moves the dielectric dispersion for ε(|') to much lower frequencies, such that C9 shows only negative Δε' over the entire temperature range.

Sequence of four orthogonal smectic phases in an achiral bent-core liquid crystal: evidence for the SmAP(α) phase.

The mesomorphic properties of an achiral bent-core liquid crystal derived from 4-cyanoresorcinol are studied by polarizing optical microscopy, x-ray diffraction, and second harmonic electro-optic response. It shows a novel sequence of four nontilted or orthogonal smectic phases on cooling: SmA-SmAP(R)-SmAP(X)-SmAP(A). Here SmAP(X) is the new orthogonal polar uniaxial smectic phase. The electric-field-induced transformations in the SmAP(X) phase give rise to two biaxial states separated by a uniaxial one. The second harmonic electro-optic response in this phase is interpreted in terms of the polar interaction with the electric field. A comparison of the experimental results with the next-nearest-neighbor model for the structure of the SmAP(X) phase shows it to be an SmAP(α) phase.