Non-linear dielectric spectra of ferroelectric liquid crystals

Abstract

The non-linear dielectric relaxation spectroscopy has been recently developed and applied to soft materials such as polymers. We have applied this new method to the S*_C phases of some ferroelectric liquid crystals. Under a weak AC electric field, the original and third order harmonic frequency components of electric displacement are proportional to the first and third powers of the applied electric field, respectively. The linear spectrum obtained from the original frequency component shows the relaxation of Debye type and the third order non-linear spectrum shows the relaxation with an extended form of Debye type to the non-linear case. The third order non-linear dielectric increment is found to be negative, which implies that the dielectric non-linearity of the liquid crystal in the S*_C phase is due to the saturation of molecular dipole moments induced by the applied electric field. The temperature dependence of the linear and third order non-linear spectra in the S*_C phase are also studied. Both spectra do not change their forms much through the whole temperature range of the S*_C phase. In the vicinity of the S_A–S*_C transition temperature, the critical behaviour is more remarkable in the third order spectrum than in the linear one.     

Low and high frequency dielectric spectroscopy on a liquid crystal with the phase sequence N*-SA-S*c

Abstract

Broadband dielectric measurements on a multicomponent ferroelectric liquid crystal mixture have been performed. The alignment was homeotropic and the cell and sample holder were the same in the whole frequency range. Two relaxation processes have been observed in all liquid crystal phases with shapes given by the Havriliak-Negami and inverted Havriliak-Negami functions. Strengths and frequencies of both modes have been obtained for the different phases. The values of the latter and their activation energies allowed us to assign the low and high frequency mechanism to the molecular reorientation around the transversal axis and around the longitudinal axis, respectively. The behaviour of this high frequency mode does not show any jump in the S_A-S*_c phase transition, neither in the amplitude nor in the frequency, indicating that the appearance of the spontaneous polarization in the S*_c phase is not the consequence of the freezing of this mode.     

The characteristic dielectric behaviour in ferroelectric liquid crystals at a phase transition and the contribution of the soft mode

The characteristic dielectric behaviour of ferroelectric liquid crystals with a large spontaneous polarization has been studied as functions of the D.C. bias field, frequency, cell thickness and applied pressure. Under the condition in which the contribution of the Goldstone mode is suppressed, a sharp peak in the temperature dependence of the dielectric constant is clearly observed at the transition between S_A and S*_C phases T _{S C *s A}. The relaxation of the soft mode is observed both in the S_A and S*_C phases by eliminating the contribution of the Goldstone mode under a D.C. bias field. Another relaxation is also observed in the S*_C phase around several kHz in addition to that of the soft mode and the Goldstone mode. The pressure effect on the soft mode was also studied.     

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.     

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.     

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].     

The existence of four dielectric modes in the planar oriented S*c phase of a fluorinated substance

Abstract

Soft mode and Goldstone mode properties have been studied for a fluorinated substance. The dielectric spectra have been measured on the planar oriented samples, in the frequency range from 10 Hz to 10 MHz. The thickness of the sample was 10 μm and two kinds of capacitors were used: (i) a low resistance EHC cell and (ii) gold coated electrodes. A bias field up to 10kV cm^?1 has been applied to show the existence of both the soft mode and domain mode in the S*_c phase below T _c. In the S*_c phase a strong Goldstone mode has been observed with a low critical frequency (v ^G _C = 15 Hz). The high frequency side at the Goldstone mode spectrum is accompanied by a shoulder which consists of the soft mode and domain mode as well. In the vicinity of the S*_A-S*_C transition the dielectric parameters of the soft mode obey a Curie-Weiss law. The slope ratio is equal to ?1·62 for the inverse of dielectric increments (Δ∈^?1) and ?1·73 for the critical frequencies (v _c) obtained by using gold electrodes. The respective values received for the EHC cell are ?4·14 and ?2·1. The dielectric parameters of the domain mode have been obtained versus temperature and bias field. We can qualitatively show that a high frequency molecular relaxation is present in the S*_A and S*_C phases as the high frequency limit of dielectric permittivity is distinctly higher than the refractive index squared.     

Hindered reorientation of chiral molecules around their long axes in the S*C phase

Abstract

In this work, the high frequency dielectric relaxation process has been studied for the N*, S*_A and S*_C phases of the mixture ZLI 3654. To this end, time domain spectroscopy (TDS) was used to cover the frequency range from 10⁷ to 10¹⁰ Hz. The dielectric parameters obtained show that the high frequency spectrum is mostly influenced by the reorientation of molecules around their long axes. In addition, the latter process seems to be strongly hindered in the S*_C phase, because the necessary relaxation time is of the order of 1 ns, whereas for the N* and S*_A phases, the relaxation time is remarkably shorter and equal to 0.3 and 0.4 ns, respectively.     

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.     

Phase transitions in ferroelectric liquid crystals in a restricted geometry

Abstract

Using a wedge type cell, we have studied the S_A–S*_c, S*_c–S_c and S_A–S_c phase transition lines in the ferroelectric liquid crystals 4-(2-methylbutyl)phenyl 4′-n-octylbiphenyl-4-carboxylate (CE-8) and 2-methylbutyl 4-(4-decyloxy-benzylidene)aminocinnamate (DOBAMBC) as a function of cell thickness in the planar geometry. The phase diagram is similar to the one observed using an external magnetic field. A surface induced re-entrant-like phenomenon is also observed. The experimental results are compared with the predictions of a Landau model with surface anchoring and a qualitative agreement was found. The results show that whereas disclination lines are not important for the S_A–S*_c and S_A–S_c transition lines, these defects have to be taken into account when evaluating the S*_c→S_c transition line. The form of the phase diagram has some important implications for the performance of surface stabilized ferroelectric liquid crystal cells used in electrooptic devices.     

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.     

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.     

The influence of finite dimensions on the static ordering of the S*C phase in an electric field

Abstract

A ferroelectric liquid-crystalline sample of a finite length along the helical axis is studied in an external electric field applied perpendicular to the helical axis. By taking into account the linear coupling to the field, the equilibrium state is found for the case of free boundary conditions. Just below the critical field which induces the transition into the homogeneous S*_C phase the domain-like structure appears as in the case of an infinite sample. The helical period in a finite sample is not a continuous function of the field, but it increases in finite jumps. We show that the finiteness of the sample has also an influence on the dielectric response at zero field.     

Dielectric studies of a ferroelectric liquid crystal

Measurements of the complex dielectric permittivity in the frequency range 30 Hz-13MHz have been made for the chiral smectic C and smectic A phases of the mixture ZLI-3654. In the S*_C phase a large contribution to the electric permittivity coming from the Goldstone mode was found. For the pretransitional region S*_C-S_A, only the soft mode has been detected. It is found that the molecular relaxation originating from the reorientation around the short axis is well separated from the soft mode even in the pretransitional region. The influence of different relaxation modes on the dielectric anisotropy is presented.     

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 mum 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.     

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.     

Broadband dielectric relaxation study on a diluted solution of a ferroelectric liquid crystal by time domain reflectometry

Abstract

In this work, complex permittivity measurements on a diluted solution of the ferroelectric liquid crystal, 4-[(S,S)-2,3-epoxyhexyloxy]-phenyl 4-(decyloxy)-benzoate, which shows ferroelectric smectic C phase (S*_C), have been performed. Using time domain reflectometry, at frequencies between 10 MHz and 10 GHz, in the temperature range from 50°C down to 10°C for every 10°C, at 5, 10 and 30 wt.% in benzene we observe two independent relaxation processes around 150 MHz and 2 GHz. It is shown that the high frequency process is due to the internal molecular reorientations while the low frequency one is due to molecular orientation around the long molecular axis. It is concluded that the reorientation around the long axis is hindered and leads to a resultant macroscopic polarization.     

Liquid Crystalline Properties of Side-chain Polymers Bearing the Same Mesogenic Group

The synthesis and properties of a series of new ferroelectric liquid crystal side-chain polymers with the same mesogenic side group but different polymer backbones (polyacrylate, polymethacrylate and polysiloxanes) are described. The polymorphism is studied by optical microscopy, differential scanning calorimetry and X-ray diffraction. All the monomers exhibit at least an S_A and a ferroelectric S*_C phase, as the polymethacrylate and the copolysiloxane. These two polymers and the polyacrylate exhibit also an S*_F phase. © 1997 John Wiley & Sons, Ltd.     

Low and high frequency dielectric spectroscopy on a liquid crystal with the phase sequence N*-SA-S*c

Broadband dielectric measurements on a multicomponent ferroelectric liquid crystal mixture have been performed. The alignment was homeotropic and the cell and sample holder were the same in the whole frequency range. Two relaxation processes have been observed in all liquid crystal phases with shapes given by the Havriliak-Negami and inverted Havriliak-Negami functions. Strengths and frequencies of both modes have been obtained for the different phases. The values of the latter and their activation energies allowed us to assign the low and high frequency mechanism to the molecular reorientation around the transversal axis and around the longitudinal axis, respectively. The behaviour of this high frequency mode does not show any jump in the S_A-S*_c phase transition, neither in the amplitude nor in the frequency, indicating that the appearance of the spontaneous polarization in the S*_c phase is not the consequence of the freezing of this mode.