Soft mode and related behaviour in the SmA and SmC* phases of a ferroelectric liquid crystalline polymer by dielectric spectroscopy

Anomalous dielectric relaxation behaviour is observed in the ferroelectric liquid crystalline polymer (viz. ferroelectric copolysiloxane (R)-COPS 11-10) around the ferroelectric SmC* to paraelectric SmA phase transition. Measurements have been performed on sample of thickness ～10 μm in indium-tin-oxide coated cell in the frequency range 10 Hz to 13 MHz. With increase of temperature, a gradual shift of the soft mode frequency towards the higher frequency side was observed, while a decrease in the relaxation strength was seen with the corresponding increase in temperature. The shifts of the soft modes in the SmC* and SmA phase are considered to be due to change in the viscosity of the polymer, as an increase in viscosity increases fluctuations of the coupling between the dipoles in the network even far from the paraelectric-ferroelectric phase transition. Application of a bias field causes a shift of the critical frequency towards the higher frequency side, while the dielectric strength (δε) decreases under the bias field. The Cole-Cole fitting parameters obtained from the best fit of the dielectric constant data are found to be consistent with other similar materials. Another relaxation mode (molecular mode) was also observed which comes into play in both the smectic phases (SmC% and SmA) and contributes to the dielectric permittivity.     

Dielectric spectroscopy of a smectic liquid crystal

Complex dielectric spectroscopy (frequency range 5 Hz–13 MHz) has been used to analyse the frequency, temperature and bias‐field dependences of the molecular dynamics of a very high‐spontaneous‐polarization ferroelectric liquid crystalline material exhibiting SmA, SmC* and unknown SmX smectic phases. Different smectic phase transition temperatures have been observed from the study of the temperature dependence of the dielectric strength and the relaxation frequency. The phase transition temperatures (crystalline to isotropic phases) have also been described very accurately from the temperature‐dependent symmetric and asymmetric shape parameters of the relaxation function and also the dc conductivity. In a planar aligned cell, two symmetric modes (Goldstone mode and domain mode) have been observed in both the SmX and SmC* phases. One asymmetric mode (X‐mode) observed in the SmC* and SmA phases could be related to the interaction of dipoles of the ferroelectric liquid crystals being affected by the surface of the cell. The soft mode, which usually appears very close to the SmC*–SmA phase transition was not observed until the bias field was applied. The second order nature of the SmC*–SmA phase transition was revealed.     

Dielectric spectroscopy of a smectic liquid crystal

Complex dielectric spectroscopy (frequency range 5 Hz-13 MHz) has been used to analyse the frequency, temperature and bias-field dependences of the molecular dynamics of a very high-spontaneous-polarization ferroelectric liquid crystalline material exhibiting SmA, SmC* and unknown SmX smectic phases. Different smectic phase transition temperatures have been observed from the study of the temperature dependence of the dielectric strength and the relaxation frequency. The phase transition temperatures (crystalline to isotropic phases) have also been described very accurately from the temperature-dependent symmetric and asymmetric shape parameters of the relaxation function and also the dc conductivity. In a planar aligned cell, two symmetric modes (Goldstone mode and domain mode) have been observed in both the SmX and SmC* phases. One asymmetric mode (X-mode) observed in the SmC* and SmA phases could be related to the interaction of dipoles of the ferroelectric liquid crystals being affected by the surface of the cell. The soft mode, which usually appears very close to the SmC*-SmA phase transition was not observed until the bias field was applied. The second order nature of the SmC*-SmA phase transition was revealed.     

Dielectric properties of four room temperature ferroelectric and antiferroelectric multi-component liquid crystalline mixtures

Dielectric properties of four recently formulated room temperature multi-component liquid crystalline mixtures with paraelectric (SmA*), ferroelectric (SmC*) and antiferroelectric (SmC*_A) phases have been studied as a function of temperature and frequency. Under planer anchoring condition, dielectric spectroscopy revealed all the characteristic modes: low frequency P_L and high frequency P_H mode in SmC*_A phase, Goldstone mode (GM) in SmC* phase and soft mode (SM) in SmA* phase. Dielectric behaviour has also been studied under the application of DC bias electric field. With bias electric field, we have been able to study the soft mode dielectric behaviour in the SmC* phase. An unknown high frequency mode (X-mode) with and without bias is also observed in SmC* phase. Dielectric results are explained in the light of generalised Landau theory. The mixtures show very high soft mode electroclinic coefficient in the SmA* phase in addition to fast switching in SmC*_A and SmC* phases [30].     

X-ray diffraction and dielectric spectroscopy studies on a partially fluorinated ferroelectric liquid crystal from the family of terphenyl esters

The fluorinated compound, (S)-4′′-(6-perfluoropentanoyoxyhexyl-1-oxy)-2′,3′-difluoro-4-(1-methylheptyloxycarbonyl)-[1,1′:4′,1′′]-terphenyl, which exhibits antiferroelectric SmC_A*, ferroelectric SmC* and paraelectric SmA* phases, has been investigated by polarising optical microscopy, differential scanning calorimetry, X-ray diffraction and frequency-dependent dielectric spectroscopy methods. X-ray studies have revealed that the layer thickness remains almost constant in the SmA* phase but within the SmC* and SmC_A* phases it decreases with decreasing temperature, a step jump being observed only at the SmA*–SmC* transition. The tilt angle in the SmC_A* phase decreases from 22.2° to 19.5°, and in the SmC* phase it decreases from 18.8° to 5.5°. Spontaneous polarisation is found to be quite high and varies between 74.1 and 118.7 nC cm^?2. The variation in ε′ and ε′′ with temperature shows a discontinuous change at the transition temperatures. Goldstone mode relaxation is only observed in the ferroelectric and antiferroelectric phases and is found to be of the Cole–Cole type. The soft mode is observed on application of a bias field near the SmC*–SmA* transition. Neither the soft mode nor the anti-phase azimuthal angle fluctuation mode is observed in SmC_A*. Rotational viscosity decreases quite rapidly with temperature but in a different manner in the ferroelectric and antiferroelectric phases. Activation energy for this process is found to be 48.14 kJ mol^?1 in the SmC* phase.     

Dielectric and electro-optical response of a room temperature tri-component antiferroelectric mixture

Frequency- and temperature-dependent dielectric and switching parameters of a room temperature tri-component antiferroelectric liquid crystal mixture W-287 have been determined. Dielectric, optical texture and thermodynamic studies show wide room temperature range antiferroelectric SmC*_a (?91.1°C to <–25°C) phase in addition to high temperature paraelectric SmA* (?2.6°C) and ferroelectric SmC* (?4.4°C) phases. The dielectric studies carried out in the frequency range of 1–35 MHz under planar anchoring condition of the molecules show five different relaxation modes appearing in the SmA*, SmC* and SmC*_a phases. Using Curie–Weiss law fit, ferroelectric SmC* to paraelectric SmA* transition temperature has been found to be 91.8°C. The dielectric response of SmC*_a phase exhibits unusually three relaxation modes due to collective as well as individual molecular processes in addition to phason mode in the SmC* phase and amplitudon mode in the SmA* phase. Spontaneous polarisation, switching time and rotational viscosity have also been determined. The maximum value of P_S is ?300 nC/cm², whereas viscosity is moderate. Switching time is of the order of few milli seconds.     

Molecular and collective modes in ferroelectric liquid crystals studied by dielectric spectroscopy

The complex dielectric permittivity has been measured for a ferroelectric liquid crystal in the range 102-109Hz. Six different relaxations have been obtained and characterized: soft mode (SmA* and SmC* phases), Goldstone mode (SmC* phase), rotation around molecular long axis, rotation around molecular short axis, ferroelectric domain mode (SmC* phase) and an internal motion associated with a polar group. Strengths and frequencies of these modes have been obtained for the different phases for different bias fields. Using these results together with spontaneous polarization and molecular tilt measurements we have also obtained the rotational viscosities associated with the soft mode and the Goldstone mode. We explain the results in the light of the so-called Landau extended model, concluding that the biquadratic coupling between polarization and tilt is quite important with regard to the bilinear coupling. This fact has been used to explain the noticeable increase of the activation energy of the frequency of the mode related to the rotation around the molecular long axis at the SmA*-SmC* phase transition.     

Dielectric characterisation of a ferroelectric liquid crystalline material having SmA*–SmC*–SmBh* phase sequence

Thermodynamical, optical and dielectric characterisation of a material possessing ferroelectric SmC* and hexatic SmB* phases has been carried out. Phase identification has been done by miscibility studies. From the dielectric studies, a relaxation mechanism is observed in the low MHz region of the SmA* phase, which is related to the tilt fluctuation (soft mode) of the directors. In the SmC* phase, another collective relaxation mechanism has been observed in the kHz region, which is related to the phase fluctuation (Goldstone mode) of the directors. In the SmB_h* phase, 2-weak relaxation modes are observed in the kHz and MHz frequency range, respectively, due to individual molecular rotations.     

Alpha sub-phase in a new ferroelectric fluorinated compound

Dielectric and DSC methods were used to study a new fluorinated liquid crystalline compound exhibiting ferroelectric and paraelectric phases as well as an intermediate alpha sub-phase. Two dielectric relaxation processes were revealed in the SmC* phase: a typical Goldstone mode over the whole temperature range and a soft mode in the pre-transition region on both sides of the SmC*–SmA* transition. From the temperature dependencies of the dielectric increments and critical frequencies for the dielectric relaxation processes observed in all the liquid crystalline phases, as well as from texture observations, it was shown that there is a SmC*_α sub-phase between the ferroelectric SmC* and paraelectric SmA* phases.     

Effect of chain length and fluorination on the dielectric and electro-optic properties of three partially fluorinated biphenylyl benzoate rigid core based ferroelectric liquid crystals

Three partially fluorinated ferroelectric liquid crystals (4F4R, 4F5R and 7F3R) with biphenylyl benzoate rigid core have been investigated by frequency-dependent dielectric spectroscopy and electro-optic methods. Molecular structures of the compounds differ only by the length of the carbon chain and the number of oligomethylene spacers. 4F4R and 4F5R exhibit ferroelectric SmC* phase over a considerable temperature range and directly melts into isotropic phase, 4F4R also shows a ferroelectric type subphase. Only Goldstone mode (GM) relaxation is observed in these compounds, but no soft mode (SM). 7F3R exhibits both the SmC* and SmA* phases, has higher stability of SmC*. Both the GM and SM relaxations are observed in this case, signifying that SM relaxation is possible only when SmC* is formed on cooling from SmA*. Increase of dielectric strength and critical frequency with temperature, in all cases, has been explained in the light of generalised Landau model. Spontaneous polarisation is found to decrease with increasing flexibility, and optical tilt depends more on fluorination than on chain length.     

Electroclinic effect in the chiral smectic A and cholesteric phases at the proximity of a N*–SmA–SmC* multicritical point

We studied the electro-optic and dielectric properties of three pure ferroelectric liquid crystal materials (C10, C11 and C12) of the same series exhibiting cholesteric (N*), smectic A (SmA) and chiral smectic C (SmC*) phases. From electro-optic investigations, the tilt angle and spontaneous polarisation were determined as a function of temperature. In the dielectric measurements carried out without a dc bias field, we studied the soft-mode relaxation in the SmA phase. From experimental data and using the results of a Landau model, we evaluated the soft-mode rotational viscosity and the electroclinic coefficient in the SmA phase. A soft-mode like mechanism was also observed in the N* phase for compounds with shorter chains (C10 and C11). This relaxation process is not detected for the homologue with a longer chain (C12). The observation of this mechanism is related to smectic order fluctuations within N* phase whose amplitude is increased when approaching the SmC*–SmA–N* multicritical point.     

Dielectric and electro-optic properties of two biphenylyl benzoate-based ferroelectric mesogens with tilted hexagonal phases

ABSTRACT

Two partially fluorinated ferroelectric liquid crystals (2F3R, 3F3R) with biphenylyl benzoate core have been investigated by frequency domain dielectric spectroscopy and electro-optic method. Both the compounds exhibit SmC* phase over a wide range of temperature along with tilted hexatic phase SmF* and soft crystal phases SmJ* (in 2F3R) and SmG* (in 3F3R) and one coexistence phase of (SmF*+SmC*). Both BOO phason and tilt phason relaxations are observed in SmF* phase and cooperative relaxation behaviour is also observed in crystal-like smectic phases. Goldstone mode relaxation is observed in SmC* phase and Maxwell Wagner mode is observed in all the phases. In 2F3R soft mode is detected in both SmC* and SmA* phases but not in 3F3R which melts directly to isotropic phase from SmC* phase. Compounds possess moderate values of spontaneous polarisation and exhibit quite sharp electrical response especially in 2F3R. Rotational viscosities, pitch and elastic constant are also measured. Effect of chain length and fluorination on various physical parameters has been discussed.     

Amplitude and phase fluctuation modes in the smectic Cα* phase of an antiferroelectric compound

Dielectric measurements have been carried out on the chiral smectic C_α (SmC_α*) phase of a MHPOBC analogous compound. Two relaxation modes have been observed in this phase for planar orientation of the molecules. One process has been observed at frequency lower than that of the soft mode of the chiral smectic A (SmA*) phase. This relaxation process is connected with the helicity of the SmC_α* phase. In the high‐frequency region, another relaxation process has been observed in the SmC_α* phase for which bias field dependence is similar to that of the soft mode at the SmA*–SmC* phase transition. The experimental observations are in agreement with a recently proposed dielectric theory for the SmC_α* phase and theoretical dielectric results obtained by numerical simulations. Thus, we report here experimental verification of two theoretically predicted dielectric modes in the SmC_α* phase.     

Systematic study of the chiral smectic phases of a fluorinated compound

ABSTRACT

Physical properties of the partially fluorinated compound 3F5FPhF, with hockey stick-like molecules, were studied by complementary methods. Apart from the already reported paraelectric SmA*, ferroelectric SmC* and antiferroelectric SmC*_A phases, the presence of the smectic C*_α subphase in the phase sequence was proved by differential scanning calorimetry, polarising optical microscopy, electro-optic and dielectric spectroscopy methods. The temperature dependence of the smectic layer thickness and correlation length of the lateral short-range order was determined by X-ray diffraction. Based on dielectric measurements three relaxation processes were revealed in the antiferroelectric SmC*_A phase (two collective: P_L, P_H and one molecular: s-process), two collective ones (Goldstone and soft modes) were found both in the ferroelectric SmC* phase and SmC*_α subphase while one relaxation process (soft mode) in the paraelectric SmA* phase. The results were compared with that obtained for other structurally similar compounds, and it was shown that even addition of one methylene group to the side chain influences much on the physical properties.     

Switching and electrical properties of ferro‐ and antiferroelectric phases of MOPB(H)PBC

Switching and dielectric relaxation phenomena were investigated for an antiferroelectric liquid crystal, 4,4‐(1‐methyloctyloxycarbonyl)phenyl]‐4′‐[3‐(butanoyloxy)prop‐1‐oxy]biphenyl carboxylate, exhibiting chiral smectic A (SmA*), smectic C (SmC*) and antiferroelectric (SmC_A*) phases. Spontaneous polarisations, rotational viscosities, relaxation frequencies, dielectric strengths and distribution parameters were determined as a function of temperature. The electric field required for saturation of the spontaneous polarisation increased with a decrease in temperature. In the SmA* phase, only one relaxation mechanism was observed that behaves as soft mode. Two relaxation processes were detected in the SmC* phase. A high‐frequency relaxation process invariant at 2.2 kHz was due to a Goldstone mode, but the origin of low‐frequency relaxation process (1–20 Hz) is unclear; however, it may belong to an X‐mode. The dielectric spectrum of the SmC_A* phase exhibits two absorption peaks separated by two decades of frequency. The low‐frequency peak is related to the antiferroelectric Goldstone mode, whereas the high‐frequency peak originates from the anti‐phase fluctuation of the directors in the anti‐tilt pairs of the SmC_A* phase.     

The dielectric relaxation processes in an antiferroelectric liquid crystal under cylindrical confinement

In the cylindrical pore geometry of inorganic Anopore membranes the collective relaxation processes observed in a bulk antiferroelectric liquid crystal change considerably under confinement. The frequency degeneration of the soft and Goldstone modes present at the smectic A* (SmA*)-chiral smectic C (SmC*) phase transition in the bulk phase is removed under geometrical restrictions. The relaxation rate of the soft mode is strongly modified due to the deformation of the smectic layers in the curved geometry of the pores and is superimposed by the molecular relaxation process in the SmA* and SmC* phases. The soft mode in confinement splits into two relaxation processes, which are present through all other mesophases (SmC* and SmC_a*). One of them is nearly temperature independent and slightly decreases in frequency in the SmC_a* phase. This Goldstone-like process can be assigned to the highly deformed helical structure fluctuations. The second one exhibits the characteristic features for the molecular and soft mode relaxation processes depending on the temperature range. The biquadratic and the piezoelectric coupling between the tilt angle and spontaneous polarization are revealed in their temperature dependence.     

Temperature and bias-field dependences of dielectric behaviour in the antiferroelectric liquid crystal, (R)-MHPOBC

Temperature and bias-field dependences of dielectric behaviour in the antiferroelectric liquid crystal, R-MHPOBC, were investigated (see also previous paper). There are mainly two relaxation modes in the SmC*alpha and SmC* phases: one behaves as the soft-mode, which shows significant slowing down in the SmA* and SmC*alpha phases; the other one appears at lower frequencies and changes the dielectric strength remarkably, especially in the SmC* phase, which is considered to relate to the azimuthal phase-fluctuation of molecules in the parallel tilt sequences of the smectic layers. These two modes show different bias field dependences in different C* subphases. In the SmC*A phase, two other types of relaxation mode were observed, which are probably due to the in-phase and anti-phase azimuthal angle fluctuations of molecules in the anti-tilt pairs.     

Dielectric investigation of the liquid crystal compound with the directSmA*–SmCA* phase transition

New compound showing a direct SmA*–SmC_A* phase transition was synthesised. As far as authors know there are a few pure compounds showing para- and antiferroelectric phases without SmC* between them. Direct current (DC) field applied into a planar-oriented cell induces ferroelectric SmC* phase in an investigated compound. Typical for SmC*, Goldstone mode starts to be detectable. DC field also shifts down the temperature of a SmC_A* phase creation. Moreover, modes in the appearing antiferroelectic phase are enhanced by DC field. This paper shows and discusses relations between modes detected in SmA*, SmC_A* and SmC* (SmC* phase – nucleated by DC field) phases. Parameters of observed modes are calculated using the Cole–Cole relaxation model and a calculation procedure useful especially for high frequency relaxations (higher than 200 kHz).     

Evidence for a tilted smectic phase in Anopore membranes by dielectric spectroscopy

Collective relaxation processes are completely undetectable in a ferroelectric liquid crystal confined in porous Anopore membranes, as a result of perfect orientation of the smectic layers perpendicular both to the long axis of the pores and the direction of the measuring electric field. In the ferroelectric liquid crystal – Anopore composite only one relaxation process, assigned to rotation of the molecule around the molecular short axis, appears throughout all smectic phases. The temperature dependence of the relaxation frequency and of the dielectric strength of this process also shows no irregularity at the point of polarization sign reversal. The temperature dependence of the relaxation frequency follows the Arrhenius law with an activation energy slightly higher in the ferroelectric SmC* phase. Analysis of the non‐linear changes of temperature dependence of the dielectric strength at the SmA–SmC* phase transition enables one to obtain the temperature dependence of the tilt angle of the molecules in the SmC* phase in the Anopore membrane. Dielectric measurements confirm the existence of the tilted smectic phase in Anopore cylindrical channels with no tilt anomaly at the point of polarization sign reversal.     

Polarization and dielectric properties of an antiferroelectric liquid crystal

The spontaneous polarization and dielectric properties of a new antiferroelectric liquid crystal (AFLC) exhibiting several intermediate phases between the SmCA and SmC* phases are investigated. A low frequency ferri Goldstone mode and a higher frequency ferro Goldstone mode have been observed over a certain range of temperatures. The effect of d.c. bias voltage on these modes is examined. The results confirm the existence of an FiLC phase with q 1/2 between SmCgamma and SmC*. These also show the co-existence of the FiLC phase with SmC* over a narrow range of temperatures above the FiLC phase. The phase sequence for this material is found to contain SmCA, SmCgamma, FiLC, (FiLC coexisting with SmC*), SmC*, SmA phases on heating and SmA- SmC* SmCgamma- SmCA- phases on cooling.