Collective Relaxation Processes in Nonchiral Nematics

Abstract

Nematic–nematic transitions in a highly polar nematic compound are studied, in thick cells in which the molecules are aligned parallel to the substrates but perpendicular to the applied electric field, using dielectric spectroscopy in the frequency range 1 Hz to 10 MHz over a wide temperature range. The studied compound displays three nematic phases under cooling from the isotropic phase: ubiquitous nematic N; high polarizability N_X; and ferroelectric nematic N_F. Two collective processes were observed. The dielectric strength and relaxation frequency of one of the processes P₂ showed a dependence on the thickness of the cell. The process P₁ is the amplitude mode, while the process P₂ is the phason mode.

1. Introduction

During the last few decades, both chirality and the polarization have been detected in liquid crystalline (LC) systems consisting of nonchiral mesogens such as the bent-core molecules under certain confinement conditions and the dimers with odd methylene spacers in between the two mesogens [1]. In these systems, achiral mesogens may lead to the so-called “chiral phases”, exhibiting spontaneous polarization or the optical activity. Finally, the Ferroelectric Nematic phase was discovered in 2017, over a century after its prediction made by P. Debye [2] and M. Born [3]. Nishikawa et al. [4] reported extremely large dielectric permittivity ~10⁴, and they also observed huge spontaneous polarization of ~4.4 µC cm⁻² in the ferroelectric nematic phase of a compound DIO. DIO exhibits a variety of nematic phases on cooling from the isotropic phase termed as the conventional nematic (M1 or N), high polarizability nematic (M2 or N_X), and the ferroelectric nematic (MP or N_F) phases [5,6] in order of decreasing temperature. Initially, Mandle et al. synthesized compounds with large dipole moments: RM230, RM734 and their homologues; these exhibited two nematic mesophases, termed N and N_X, and these phases were separated by a weak first-order transition [7,8,9,10]. The polar N_X formed a splay nematic (N_S) phase [11,12,13]. The latter arose presumably from the wedge shape of the molecules having a splay modulation period of 5–10 microns. The N-N_S phase transition bears semblance to the ferroelectric–ferro-elastic transition that occurs via flexoelectric coupling [13]. Chen et al. demonstrated ferroelectricity for the first time in a previously labelled N_X (or N_S) phase of the nitro compound RM734, thus confirming the discovery of the ferroelectric nematic (N_F) phase that displayed intriguing electro-optical properties [14]. The compound DIO was also visited by the Boulder group in 2021 [15]. They found that the intermediate (M2 or N_X) is a density-modulated biaxial phase (existing between the paraelectric, uniaxial N, and the ferroelectric, phase, N_F), antiferroelectric and has a period of 8.8 nm. They labelled this phase the smectic Z_A (SmZ_A) antiferroelectric phase. These previously unknown phases displayed fascinating properties, which motivated researchers internationally to understand the peculiar and interesting characteristics [16] of the new nematic phases.

It is important to understand such rarely observed novel nematic–nematic phase transitions to underpin its physics as well as harness the enormous potential of the ferroelectric nematics for applications in super capacitors as energy storage devices, non-linear optics, sensors, and photonics. The origin of the mechanism/s for the formation of the multiple nematic phases is not yet fully understood. It is worth remarking that nematic–nematic transitions have been observed so far only in a few compounds. Though a large dipole moment of a molecule is an important prerequisite, the spatial arrangement of dipoles, however, in a molecule is also an extremely important requirement. Undoubtedly, the lack of understanding of the properties of the nematic variant phases is a barrier to their use in new technologies. The library of the compounds showing the N_F phase needs to be expanded to predict the structure–property (N_F phase) characteristics.

Dielectric spectroscopy (DS) [17] is a powerful methodology for studying the dipolar response to a weak electric field without causing much disturbance to the material, and for exploring the relaxation phenomena in the liquid crystalline nematic phase under investigation. Dielectric spectroscopy has been used for investigating ferroelectric nematics: in investigating fluoro compounds with the objective of making a preliminary assignment of the processes in DIO [18]. DS has successfully been used to explore the various LC phases such as the columnar hexagonal [19,20], ferrielectric [21], ferroelectric SmC* [22], SmCP [23], and antiferroelectric SmC_A* [24], de Vries phase [25], and the bent core nematics [26].

In this paper, we investigate the dielectric properties of a compound DIO, including the study of its high-temperature paraelectric N phase. Specifically, we present a detailed analysis of the relaxation mechanisms detected in this compound in a thick cell and compare the results from a thin cell. The molecular structure and the phase transition temperatures recorded using polarizing optical microscopy at a scanning rate of 2 °C/min on cooling are given in Figure 1.

2. Materials and Methods

The compound, DIO, was resynthesized at the University of Hull, Hull, UK. The real and imaginary parts of complex dielectric permittivity values are measured as a function of frequency for different temperatures using a high-resolution broadband dielectric spectrometer manufactured by Novo-control, GmbH, Germany. The LC cells for the experiments were made by gluing together of the two indium tin oxide (ITO)-coated glass substrates, separated by a spacer of thickness ~25 µm. The ITO substrates are selected to have a low sheet resistance of 10 Ω/□. The latter enables a shift in the parasitic mode to higher frequencies beyond the window of the experiment. Commercial cells procured from EHC Ltd., Japan were used for planar alignment, having a coating of the polyimide (LX-1400, Hitachi-Kasei) of ~20 nm thickness. Thick homeotropic samples were made by coating the glass plates with a polymer, AL6072. The sample was filled at a lower temperature (150 °C) in the nematic phase by capillary action and then heated quickly to its isotropic state. The dielectric permittivity measurements were made using planar and homeotropic aligned liquid crystalline sample under cooling. A low probe voltage of 0.1 V was applied across the cell and temperature was changed slowly in steps of 1 °C.

3. Results and Discussions

The variation of the permittivity and of the dielectric loss with temperature were recorded for a planarly aligned cell with a thickness of 25 µm in the frequency range of 0.1 Hz to 10 MHz. The three-dimensional spectra for permittivity and loss for a cell with planar alignment having a cell-spacing of 25 μm are shown in Figure 2. Prior to making these measurements, the samples in liquid crystal cells were placed under a polarizing optical microscope to check the quality of alignment of the mesogens in the planar configuration. Figure 3 depicts the textures captured for the planar-aligned sample in all phases. The snapshots show perfect alignment in the paraelectric nematic phases, which are the focus of the present study. In the N_X phase, numerous small domains start emerging which convert into bigger domains covering the entire area of the cell in the N_F phase. Figure 4 presents the dielectric permittivity and the dielectric loss spectra at different temperatures in the three phases: (N) 160 °C, 120 °C; (N_X) 80 °C, 70 °C; and (N_F) at 60 °C.

The recorded dielectric spectra were analyzed using WINFIT software, supplied by Novocontrol GmbH, Germany, and fitted to three relaxation processes with the objective of determining the origin of these three processes. The Havriliak–Negami Equation (1) was used to fit the experimental dielectric data on the real and the imaginary parts of the complex permittivity:

$${\epsilon }^{\mathrm{*}}={\epsilon }_{\mathrm{\infty }}+\sum _{j=1}^n\frac{\mathsf{\Delta }{\epsilon }_j}{{\left[1+{\left(i\omega {\tau }_j\right)}^{{\alpha }_j}\right]}^{{\beta }_j}}-\frac{i\sigma }{{\epsilon }_0\omega }$$

(1)

The fitting of the data to Equation (1) led to the dielectric parameters of the various processes as well as the infinite frequency permittivity denoted by ${\epsilon }_{\infty }$. The latter permittivity is dependent on the atomic and electronic polarizabilities, ε₀ is the permittivity of free space, ω = 2πf is the angular frequency of the applied field, σ is the dc conductivity, τ_j is the relaxation time, Δε_j is the dielectric amplitude or the dielectric strength, and α_j and β_j are the symmetric and asymmetric broadening parameters determining the distribution of relaxation times of the jth relaxation process. The experimental data were fitted to the three relaxation processes; i.e., n = 3. The symmetrical stretching parameter of the lowest frequency relaxation process P₀ is α₀ < 1. Hence, the mechanism is of ‘the Cole–Cole type’. This process (blue curve in Figure 5a) is strongly dependent on the LC cell parameters, especially on the thickness of the alignment layer/s. We identify this process as arising from the mobility of ions since this also exists in a generic nematic LC, 5CB, where no collective relaxation processes are observed. However, the LC cells used in practice do need to incorporate alignment layers for achieving the defined orientations: planar or homeotropic. The alignment layer limits the conductivity, i.e., on the application of the external electric field, the ions in the medium (though initially distributed uniformly in the entire volume of the cell) start to migrate in the direction of the electric field, and the ionic charge continues accumulating on the surfaces of the alignment layers. On applying an AC electric field, ions in the medium respond to the alterations of the field leading to a relaxation process in the dielectric spectra. This process depends on the ionic mobility (and hence on the temperature) and the thickness of the alignment layer/s. The dielectric strength also depends on the ion’s mobility, concentration, electric conductivity, thickness and the type of alignment layer/s. There are two opposite scenarios: (i) finite conductivity and (ii) zero conductivity of the material. For the first case, we can expect only a low-frequency exponential conductivity term $\left(\frac{i\sigma }{{\epsilon }_0\omega }\right)$ in Equation (1). For the second case, this conductivity term should be absent, though a strong pseudo-relaxation process does arise from a separation of the ions and from the accumulation of charge on the alignment layers. This is confirmed by our experiments using a generic nematic 5CB in two cells, one without conducting layers and the second with a high resistivity SiO dielectric layer. This parasitic pseudo-process is mistakenly reported in the literature as a collective relaxation process. This in turn leads to an incorrect conclusion for the occurrence of the spontaneous polarization in an ordinary nematic phase of liquid crystals. Therefore, the lowest frequency process is mainly due to the conductivity arising from a separation of the charges and from the deposition of the ions on the polymer layers. It disappears on cooling to the N_F phase.

For the other two relaxation processes, P₁ and P₂, the fitting parameters are: α_j = 1 and β_j = 1. These correspond to the Debye relaxation processes. The temperature dependencies of the relaxation processes in terms of the dielectric strength and the relaxation frequencies for the 25 μm and 4 μm thick planar-aligned cells are shown in Figure 5a,b. A comparison of Figure 2, Figure 3, Figure 4 and Figure 5 shows numerous peculiar but interesting features.

• Two collective relaxation processes are observed in the high-temperature paraelectric nematic phases in contrast to those in an ordinary nematic phase. The relaxation processes are termed as P₁ and P₂ in order of the increase in the relaxation frequency and specified by the subscripts 1 and 2.
• The DC conductivity (mode P₀ in Figure 5a) in a planar-aligned cell is predominant. This gives the impression to the readers that the permittivity in the paraelectric nematic phases is also very high. However, on a careful examination and from subtracting the conductivity term from the spectra, the real value of the permittivity obtained is less in the paraelectric phases and it jumps to a higher value in the N_F phase (Figure 5a). Additionally, it is pertinent to mention here that ‘dielectric parameters of the two main relaxation processes’ are not affected by the conductivity.
• An extremely large value of the permittivity (~3000) was deduced from the fitting of the dielectric spectra to Equation (1) (Figure 4, parametersplotted in Figure 5a). Generally, the spectra are recorded using LC cells fabricated by sandwiching two glass substrates, having an ITO layer on each inside surface of the substrate and each surface coated by different polymers, depending on the alignment needed. The surface treatment by an aligning agent, which is polymerized on keeping the substrates in the oven for a fixed time, is a crucial step in obtaining an almost perfect alignment. Without it, one cannot be certain of the molecular alignment achieved, especially in an opaque cell, with electrodes made from a metal. In cells with the surface treatment, the total capacitance of the experimental cell depends on the relative values of the capacitance of the liquid crystalline sample (C_LC) and of the two alignment layers (C_P). For details on the extremely large dielectric permittivity of the confined material, see Clark et al. [28]; for C_LC > C_P, the measured capacitance is the capacitance of the two polymer layers connected in series with C_LC. The measured value approximates to the capacitance of the aligning layers if C_LC >> C_P, and hence, the measured value of the permittivity in the N_F phase is erroneous. Nevertheless, in the present study, as stated above, we focus on to the collective relaxation processes in the higher temperature paraelectric phases, where the dielectric permittivity is reasonably low, and is therefore not limited by the capacitance of the alignment layers.

The variation in the dielectric strength and the relaxation frequency of the mid-frequency process P₁ with temperature is represented in Figure 5a,b (marked black). The relaxation process starts off from the isotropic phase and gradually continues increasing, under cooling, in the N_F phase in a thick cell, but it disappears in a thin cell. In the isotropic state, this mode arises from the flip-flop rotation of the mesogens around their short axes. Permittivity in the iso phase is related to ε_iso = (ε_|| + 2ε_┴)/3. Hence, at the isotropic (Iso)-N phase transition temperature, the strength of the relaxation process should decrease when the molecules are planarly aligned, in agreement with the results presented in Figure 5b, for a 4 µm-thick cell This trend also agrees with the assignment as the flip-flop mode given by Sebastian et al. [13]. The dependencies of the dielectric parameters (Δε, f) on temperature show intriguing features in the paraelectric nematic phases in thin and thick cells. In general, the dependence of the relaxation frequency on the temperature should obey the Arrhenius equation given by:

f(T) = A exp((−E_a)/RT)

(2)

According to the above equation, the log of the frequency f(T) with respect to 1/T should be a straight line with a negative slope equal to the activation energy, E_a. The thick cell follows Arrhenius behavior in the N phase, but the sample aligned in a thin cell exhibits a different behavior, as seen for f(T) for P₁, Figure 5b. Instead, a soft mode-like behavior is displayed by the temperature-dependent curve of the frequency; i.e., the relaxation frequency shows a large decrement as the N_XtoN_F phase transition temperature is approached in a thin cell. This peculiar behavior is reminiscent of the soft mode relaxation observed at the SmA−SmC* phase transition temperature. This is attributed to an increase in the correlation length or to an increase in the tilt angle fluctuations with a decrease in temperature. On approaching the ferroelectric nematic phase, the relaxation process is due to an increase in the correlation length (hence to the correlation volume) which persists from the N_X−N_F phase transition temperature. This process can be identified as the amplitude mode. The dielectric strength in the N phase demonstrates the soft mode-like trend in a thin cell but is a straight line (as a function of 1/T) in thick cells. The soft mode-like behavior in the N phase is found to be similar to that in the SmA phase [29]. However, in the N_F phase, the Goldstone mode dominates in the N_F phase, and it would be a challenge to find the soft mode in the N_F phase. It may be that the two modes, Goldstone and the soft in the N_F phase, cannot be easily separated. This is suggested as a problem that need to be solved in future.

The process P₂ shows almost similar behavior in both thick and thin cells. However, P₂ is not observed in the isotropic phase but it first emerges in the paraelectric nematic phase. There can be a possibility that the process P₂ is too weak in strength to be visible at higher temperatures. This explains why Brown et al. [18] observed this process only in the N_X phase, where this process is prominent and is distinguishable from the parasitic ITO peak. In our study, as mentioned before, the low sheet resistance ITO electrodes were used such that the ITO peak is moved outside the frequency range of the experiment, and the process P₂ becomes noticeable both in the thin and thick cells. The process is assigned to the phason mode.

Another interesting feature of the processes P₁ and P₂ is found from drawing a comparison of their relaxation parameters in thick and thin [27] planar cells. The dielectric parameters of P₁ are almost independent of the cell thickness, while the parameters of P₂ are dependent on the cell thickness, and hence as a thickness mode, the dielectric strength is proportional to the cell thickness, and the relaxation frequency is a reciprocal of the cell thickness, which reminds us of the so-called “thickness mode” in SSFLCs [22]. This leads to a conclusion that that relaxation process P₁ can be an amplitude mode, while the process (P₂) is a phason mode.

Furthermore, a homeotropic cell fabricated with a cell thickness of 28 µm was also studied in a temperature range of 45–120 °C. Figure 6a represents the three-dimensional dielectric loss spectra, the corresponding dielectric parameters are plotted in Figure 6b. The dielectric relaxation strength Δε₁ decreases in the N_X phase. The behavior of the two relaxation modes in N_X is similar to that observed by Brown et al. [18], while in thin cells [27], the process P₁ does not show any decrease in strength in the N_X phase but exhibits a sharp decrease in the N_F phase only. A comparison between thin (refer Figure 3a and Figure 4a of [27]) and thick homeotropic cells (Figure 6a,b) shows a similar dependence on the thickness of the cell. This demonstrates that the dielectric response especially for the homeotropic aligned cell is strongly dependent on the thickness of the cell used and the conditions of molecular anchoring on the two surfaces.

4. Conclusions

In conclusion, two collective relaxation modes are observed experimentally in the paraelectric nematic phases of an achiral compound aligned both in thick planar and homeotropic cells in contrast to those seen in a conventional nematic. A decrease in Δε₁ in the N_X phase followed by in N_F is observed in thick homeotropic cells. A sudden increase in Δε₂ at the N_X−N_F transition signifies that the two phases, N_X and N_F, are different in nature. The dielectric parameters for the process P₂ show a variation with an increase in thickness of the cells. It is shown that the thickness of the cells and the surface anchoring conditions have profound effect on the dielectric response in nematic phases of a ferroelectric nematic compound.