Low-frequency Relaxation Mode Research Articles

Linear and Nonlinear Electro-optic Response of MHPOCBC

This study investigated the linear and second-order electro-optic responses in chiral smectic liquid crystal 4-(1-methylheptyloxycarbonyl) phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). The result revealed a single Debye-type relaxation in the linear electro-optic frequency dispersion, with a relaxation frequency extending up to one hundred kHz. Conversely, the second-order electro-optic response exhibited intricate temperature-dependence, accurately depicted by a phenomenological Landau theory around the SmA–SmCa* phase transition point. Notably, in the SmCa* phase, critical slowing down of the amplitude mode occurred near the transition to the SmA phase, while at lower temperatures of the SmCa* phase, a distinct low-frequency relaxation mode emerged. Furthermore, the relaxation frequency of the antiferroelectric Goldstone mode in the SmCA* phase remained constant across the entire temperature range. These findings should significantly contribute to the understanding of dynamic behaviors in chiral smectic liquid crystals, shedding light on their complex phase transitions and electro-optic properties.

Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies

The formation of the nematic to twist-bend nematic (NTB) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular interactions drive the complex twist-bend modulation observed in the NTB. The study employs broadband dielectric spectroscopy spanning frequencies from 10 to 2 × 109 Hz to investigate the molecular orientational dynamics within the glass-forming thioether-linked cyanobiphenyl liquid crystal dimers, namely, CBSC7SCB and CBSC7OCB. The experimental findings align with theoretical expectations, revealing the presence of two distinct relaxation processes contributing to the dielectric permittivity of these dimers. The low-frequency relaxation mode is attributed to an “end-over-end rotation” of the dipolar groups parallel to the director. The high-frequency relaxation mode is associated with precessional motions of the dipolar groups about the director. Various models are employed to describe the temperature-dependent behavior of the relaxation times for both modes. Particularly, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics in accordance with findings from infrared (IR) spectroscopy. Here, as the longitudinal correlations of dipoles intensify, the m1 mode experiences a sudden upsurge in enthalpy, while the m2 mode undergoes continuous changes, displaying critical mode coupling behavior. Interestingly, both types of molecular motion exhibit a strong cooperative interplay within the lower temperature range of the NTB phase, evolving in tandem as the material’s temperature approaches the glass transition point. Consequently, both molecular motions converge to determine the glassy dynamics, characterized by a shared glass transition temperature, Tg.

Dielectric and thermodynamic investigation of heterocyclic compound Indole-3-Carbinol (I3C) using time domain reflectometry

The present work aims at the study of dielectric relaxation spectroscopy, which involves the measurement of dielectric loss and dielectric permittivity of Indole-3-carbinol in (Dimethyl Sulfoxide) DMSO over the frequency range of 10 MHz to 50 GHz. Two relaxation modes were observed for the studied system. Low-frequency relaxation mode is observed at the frequency of about 80–100 MHz, which is attributed to Indole-3 Carbinol (I3C) molecules, and high-frequency relaxation is observed at about 6–7 GHz, which is due to DMSO molecules. The structural properties of I3C have been studied through dielectric parameters such as dielectric constant (εi), relaxation time (τi), distribution parameters, dipole moment, Kirkwood correlation factor (g), and number of DMSO molecules irrotationally bound to I3C molecules (Zib), and the results have been expressed in terms of molecular interaction between solute–solute and solute solvent (I3C and DMSO) molecules. The results obtained using dielectric spectroscopy are corroborated by the thermodynamic parameters.

Dielectric and electrooptical properties of hockey-stick-shaped liquid crystal with a negative dielectric anisotropy

We investigated dielectric properties of a hockey-stick-shaped liquid crystal (HLC). Two dielectric relaxation modes were observed at 0.91 kHz and 4.51 MHz. The low frequency relaxation modes in isotropic, smectic, and nematic phases are related to the motion of ions, collective tilt fluctuation, and rotation around the long molecular axis, respectively. Meanwhile, the high frequency relaxation modes in nematic and smectic phases was due to the rotation around the short axis of the molecules and hindered by the resistance of the ITO layers. We also examined the electrooptical response of the 5.0 wt% HLC-doped commercial nematic liquid crystal (LC) mixtures. The birefringence of the LC mixture was slightly increased, while the falling time and the rotational viscosity was decreased in the nematic phase.

Low-frequency relaxation modes in ferroelectric liquid crystal/gold nanoparticle dispersion: impact of nanoparticle shape

ABSTRACTLow-frequency (1 mHz–100 Hz) dielectric relaxation modes were experimentally studied in ferroelectric liquid crystal (FLC)/gold nanoparticles (nanospheres and nanorods) dispersion. It was demonstrated that the dielectric spectra of nanodispersion are strongly influenced by the shape of nanoparticles. Using different formalisms of the impedance spectroscopy, three possible low-frequency relaxation processes were found in the dispersions and the pure FLC. Due to the electrical double layers (EDLs) near nanoparticles and the alignment layers, one can observe the relaxation of the EDL polarisation around the nanoparticles (Schwarz’s relaxation) and near the driving indium tin oxide (ITO) electrodes (electrode polarisation). The other possible relaxation process is interfacial polarisation (Maxwell–Wagner mode) in which the frequency is unaffected by the nanoparticles. It was shown that Schwarz’s relaxation frequency strongly depended on the shape and size of the nanoparticles. Moreover, dispersion of nanoparticles significantly reduced direct current conductivity of the FLC mixture.

Core/shell quantum dots in ferroelectric liquid crystals matrix: effect of spontaneous polarisation coupling with dopant

ABSTRACTIn order to fabricate efficient and superior performance liquid crystal (LC) devices, the physical parameters of the LC mesogens can be duly altered by incorporating non-mesogenic materials like quantum dots (QDs), graphene and polymers. In the present work, the effect of adding core/shell QDs in two ferroelectric liquid crystals (FLCs), along with the change in their physical properties, has been investigated. A small concentration of QDs is dispersed into the two FLCs and temperature variations of vital parameters like spontaneous polarisation (Ps), rotational viscosity, response time, relative permittivity and relaxation strength have been measured for both the FLC materials. The contrast ratio, UV–near visible absorbance as well as photoluminescence (PL) of both the mesogens have also been determined and compared. A faster electro-optical response and the induced phenomenon of PL with a temperature-dependent low-frequency relaxation mode have been observed in Felix 17/100 after the addition of QDs. The present study also provides valuable information about the interaction between QDs and the two FLC systems depending upon polarisation–field (P–E) coupling. The same dopant can interact with FLCs in dissimilar fashion if the intrinsic properties of both the FLCs are different thereby producing different modifications in their respective physical parameters.

Analysis of physical parameters and collective dielectric relaxations in core/shell quantum dot ferroelectric liquid crystal composite

The effect of doping of Cd1−xZnxS/ZnS core/shell quantum dots (QDs) on the physical parameters and dielectric relaxations of ferroelectric liquid crystal (FLC) with the variation of dopant concentration, temperature and frequency has been examined in the present study. Fourier transformed infrared spectroscopy reveals that the QDs interact with FLC molecules and affect their molecular dynamics. The UV absorbance of pure FLC material has diminished in the presence of QDs according to the dopant concentration in FLC. A substantial change has been observed in tilt angle, spontaneous polarization and relative permittivity with the addition of QDs. A faster optical response for FLC, when doped with 0.25wt.% quantum dots, is one of the interesting finding of the present study. In the SmC⁎phase, a low frequency relaxation mode at 20Hz along with the characteristic Goldstone mode has been observed. The occurrence of new low frequency relaxation mode is accredited to the ionization–recombination assisted diffusion of slow ions present in the FLC material. These results would certainly be helpful in the fabrication of low charge consumable and faster liquid crystal systems.

Dielectric spectroscopy of T-shaped blue-phase-III liquid crystal

Dielectric relaxation spectra of a liquid crystalline (LC) material showing blue-phase-III (BPIII) for a considerably large temperature regime consisting of T-shaped molecules are investigated. A low frequency relaxation mode is observed in the isotropic phase (I) as well as in BPIII of the investigating material which is attributed to the short axis rotation of the T-shaped molecules. The outcome of the temperature and dc bias field variation of dielectric strength (Δε) and relaxation frequency (ν(c)) in the vicinity of the I-BPIII transition is also discussed. The temperature dependence of ν(c) in BPIII with a minor deviation from Arrhenius activities in the fluctuation-dominated nonlinear region (FDNLR) is found to follow the unusual thermal behavior of the activation energy (E(A)). The growth of pretransitional fluctuations is found to be nonlinear in the vicinity of the I-BPIII transition. A moderate growth of transition fluctuation commences from the value of the exponent α(eff)=0.38/°C, which is obtained by an exponential variation of ν(c) with respect to temperature in BPIII. Observed dynamic phenomenon in the vicinity of the I-BPIII transition regions is explained on the basis of the Landau-de Gennes and Maier-Saupe Theories.

Disentangling molecular motions involved in the glass transition of a twist-bend nematic liquid crystal through dielectric studies

Broadband dielectric spectroscopy spanning frequencies from 10(-2) to 1.9 × 10(9) Hz has been used to study the molecular orientational dynamics of the glass-forming liquid crystal 1",7"-bis (4-cyanobiphenyl-4'-yl)heptane (CB7CB) over a wide temperature range of the twist-bend nematic phase. In such a mesophase two different relaxation processes have been observed, as expected theoretically, to contribute to the imaginary part of the complex dielectric permittivity. For measurements on aligned samples, the processes contribute to the dielectric response to different extents depending on the orientation of the alignment axis (parallel or perpendicular) with respect to the probing electric field direction. The low-frequency relaxation mode (denoted by μ(1)) is attributed to a flip-flop motion of the dipolar groups parallel to the director. The high-frequency relaxation mode (denoted by μ(2)) is associated with precessional motions of the dipolar groups about the director. The μ(1)-and μ(2)-modes are predominant in the parallel and perpendicular alignments, respectively. Relaxation times for both modes in the different alignments have been obtained over a wide temperature range down to near the glass transition temperature. Different analytic functions used to characterize the temperature dependence of the relaxation times of the two modes are considered. Among them, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics on approaching the glass transition.

Tuning of dielectric properties of SrTiO3in the terahertz range

Tuning of the dielectric permittivity spectra of strontium titanate (SrTiO${}_{3}$) single crystals in an external electric field is investigated between 90 and 300 K by means of terahertz time-domain spectroscopy. Application of the electric bias leads to an appreciable tuning of the permittivity observed up to room temperature both in the parallel and perpendicular directions to the bias field. The observed behavior is interpreted in terms of soft-mode hardening due to the anharmonic character of its potential. No additional low-frequency relaxation mode was observed. A weak temperature dependence of the anharmonic coefficients was found in agreement with previously published low-temperature data.

Screening and Fundamental Length Scales in Semidilute Na-DNA Aqueous Solutions

The fundamental length scales in semidilute Na-DNA aqueous solutions have been investigated by dielectric spectroscopy. The low- and the high-frequency relaxation modes are studied in detail. The length scale of the high-frequency relaxation mode at high DNA concentrations can be identified with the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution, whereas at low DNA concentrations and in the low added salt limit the length scale shows an unusual exponent reminiscent of semidilute polyelectrolyte chains with hydrophobic backbone. The length scale of the low-frequency relaxation mode corresponds to a Gaussian chain composed of correlation blobs in the low added salt limit, and to the Odijk-Skolnick-Fixman value of the single chain persistence length in the high added salt limit.

Low-Frequency Relaxation Modes of Surface-Stabilized Ferroelectric Liquid Crystal

Very broad low-frequency dielectric data of a surface-stabilized ferroelectric liquid crystal (SSFLC) sample in the frequency (ω) domain was analyzed by the Tikhonov regularization method to derive three distinctive modes of relaxation in time (τ) domain spectra corresponding to the X-, D- and L-modes.

Dielectric and high-pressure investigations on a thermotropic cubic mesophase.

Optically isotropic cubic mesophases, which are commonly exhibited by lyotropic materials, have been observed in a few thermotropic liquid crystalline systems also. Although the first thermotropic cubic mesophase was reported about 40 years ago, its existence in diverse systems is only a recent finding. Moreover, the investigations on this mesophase have mainly concentrated on the structural aspects. While the effect of pressure has not been reported, only one dielectric measurement seems to have been carried out. In this paper we present the results of our dielectric and high pressure investigations on a compound exhibiting a thermotropic cubic mesophase. Two salient results are (i) a low frequency relaxation mode is observed with a large dielectric strength with appreciable changes across the columnar-cubic and cubic-smectic C transitions; and (ii) the cubic phase ceases to exist when the applied pressure exceeds about 400 bar.

Dielectric relaxation behaviour of protonated and deuterated betaine arsenate

This work reports the study of the dielectric relaxation of betaine arsenate (BA) and of strongly deuterated betaine arsenate (DBA92) below room temperature for different values of d.c. electric fields, in the frequency range of 50 Hz-13 MHz. The main contributions for dielectric constant come from low-frequency relaxation modes. Some evidence for the existence of a new antiferroelectric phase in BA was found, stable in a short range of temperatures.

Thickness dependent low frequency relaxations in ferroelectric liquid crystals with different temperature dependence of the helix pitch

A low frequency relaxation mode 1 has been detected in ferroelectric phases of three materials. The relaxation frequency and the dielectric strength of this mode depend strongly on the sample thickness, but their temperature dependences are qualitatively different in the materials studied, reflecting the behaviour of the helicoidal structure of these materials. This mode has been attributed to a superposition of the Goldstone and thickness modes when the helicoidal structure exists and to the thickness mode only, when the helix is unwound. In addition, with one material, mode 2 has been detected at still lower frequencies, and this also exhibits a strong sample thickness dependence. It was attributed to fluctuations of the director field modified by a non-homogeneous ionic charge distribution across the sample. As both modes 1 and 2 are strongly sample thickness dependent, they do not represent bulk properties of the materials studied, but reflect the structure in real samples, which is determined by surface conditions.

Dielectric and esr behaviour of the first mesogenic iron complex: Local ordering of dipole moments in the mesophase

Abstract The dielectric and ESR behaviour of the smectic liquid-crystal of iron (III) Schiff base (L) complex FeClL2 was investigated. A variation of the real part of the dielectric permittivity typical for a smeared ferroelectric phase transition was observed in the temperature region of a S A - S x phase transition. Anomalies of dielectric behaviour were caused by local ordering of Fe-Cl dipole moments along the chains in smectic layers. The activation energy E=0.09 eV of the low-frequency relaxation mode, determined from time-domain dielectric spectroscopy data, coincides with the activation energy of the process defining the ESR line broadening. The observed relaxation is probably connected with the chlorine intra Fe—Cl…Fe bond jumps (between two sites in the double-minimum potential), which are correlated along the chains.

Dielectric Degrees of Freedom in Chiral Smectic C Liquid Crystals

Abstract We show that there are only three low frequency relaxation modes in the dielectric spectrum of smectic C* liquid crystals due to the symmetry of that phase. Two additional symmetry violating dielectric modes may exist at very high frequencies. We refute a recent criticism of that picture expressed in this journal.

A theory of the strongly pinned Fr�hlich mode

The extended Fukuyama-Lee-Rice theory of phase dynamics in quasi one-dimensional charge density wave systems is worked out for the pinned Frohlich mode in the strong pinning limit and for three spatial dimensions. The ac conductivity δ(ω) is expressed in terms of a self energy function Σ(ω) which is evaluated self consistently within the single sitet-matrix approximation. A case of hard momentum cut-off is shown to be inconsistent for reasons of analyticity breaking. A conserving theory for δ(ω) is worked out for a soft Lorentz cut-off and discussed in detail. Analytical results for the low frequency relaxation mode, for the “second dielectric constant”, for the high frequency pinned mode, and for the conductivity step at the frequency of the longitudinal optical phason are given in the descreened limit of low temperatures. The limit of very strong pinning is shown to be isomorphic to the case of the weakly pinned Frohlich mode ind=3, but with different parameters. Finally, a comparison is made between measurements of Re δ(ω) for two semiconducting charge density wave systems and the theories of both weak and strong pinning. The results are inconclusive with weak pinning slightly in favour over strong pinning.

A theory of the weakly pinned Fr�hlich mode

Extending earlier work of Littlewood (1987) a theory for the collective mode (“Frohlich mode”) response of weakly pinned charge density waves (CDW) is given. Long range Coulomb interaction is incorporated in both a proper definition of the measured ac conductivity σCDW(ω) and in the Fukuyama-Lee-Rice treatment of phason dynamics. The frequency and wave number dependent quasi particle resistivity is shown to appear only in the internal phason lines in the perturbation expansion of the impurity averaged phason propagatorD ren. Quantitative results for σCDW(ω) are evaluated within the self-consistent Born approximation toD ren in three spatial dimensions taking anisotropy into account. Besides the low frequency relaxation mode we find a significant effect of the longitudinal optical phason ωLO on the Frohlich mode pinning frequency when descreening sets in at low temperatures. This is yet another manifestation of selection rule breaking by inhomogeneous pinning and establishes the special role that ωLO plays in the dynamics of CDW. An explicit analytical formula for σCDW(ω) is given and discussed in some detail including the important analyticity properties. Available measurements of the linear ac response in a wide range of frequencies and conductivities are compared with the theory and found to agree with the theoretical predictions supporting the concept of weak pinning in CDW.

Low-frequency relaxation modes and structural disorder in KTa1-xNbxO3.

A light-scattering study of the low-frequency excitations in single crystals of cubic and tetragonal KTa{sub 1{minus}{ital x}}Nb{sub {ital x}}O{sub 3} ({ital x}=0.26 and 0.28) has been carried out by employing a technique which uses an Iodine filter to remove elastically scattered light. Low-frequency Raman and Fabry-Perot components related to structural disorder in the mixed-crystal tantalate-niobate system were observed. The spectral shape, symmetry properties, and thermal behavior of these components are consistent with an eight-site order-disorder model of the sequence of structural phase transitions observed in ferrodistortive perovskites.