Liquid crystalline derivatives exhibiting smectic phases with ferro- and antiferro-electric properties

Abstract

Chiral liquid crystalline molecules can self-assemble and generate ferroelectricity (FE) or antiferroelectricity (AF) in tilted lamellar smectic C phases. In previous studies, lactic acid has been repeatedly employed as an effective source of chirality. In this study, we synthesized several mesogens with the aim to establish the role of chiral chains and reveal their influence on the mesogenic and polar properties. For the first studied mesogen, we utilized a methylbutyl group in the chiral chain. The second mesogen differed from the first one in incorporated (S)-lactate group added to prolong the chain terminated with a methylbutyl. In the third homologue, two (S)-lactates and one methylbutyl group form the chiral chain. To establish their optical purity by high-performance liquid chromatography (HPLC), additional derivatives were prepared with a racemic methylbutyl chain. We compared all the homologues with respect to the effect of the chiral chain modification. Among them, the third derivative with two lactates in its chiral chain exhibited an AF smectic phase, which was stable and enantiotropic in a broad temperature range, including the room temperature, which could be attractive for various applications.

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1. Introduction

Liquid crystals (LCs), as self-assemblies of organic molecules, belong to partially ordered soft matter systems. They can form various mesophases with specific properties. The introduction of chirality into the molecular structure of LCs can induce effects such as helicity or ferroelectricity.^1,2 Since the discovery of ferroelectricity in the tilted smectic C phase (SmC*) of chiral rod-like molecules, researchers have concentrated on investigating their electro-optical properties,^3–9 which are highly desirable for various applications due to their fast response and high contrast ratio. The antiferroelectric SmC_A* phase differs from the SmC* phase in the anticlinic ordering of the tilt angle in neighbouring layers and it shows greater relevance and potential in modern technological applications. Chiral liquid crystalline compounds have been intensively studied and analysed for various aspects of their molecular structure and the relationship between their molecular chirality and mesomorphic behaviour.¹⁰

Chirality can be introduced into molecular structures via a chiral part, and various chiral centres can be utilized for achieving this.^11–13 A lactate group is a promising source of chirality and its numerous derivatives have been synthesized to date.^14–20 In the previous design of lactate derivatives, (S)-lactate has been repeatedly utilized as a natural source of chirality. It has been demonstrated that these derivatives are thermally and chemically stable.^17–29 This type of chiral chains can enhance the chirality of liquid crystalline systems, which can be proved by the presence of various frustrated mesophases such as twist-grain boundary phases (TGB), smectic Q phase or blue phases.^25–27 The cholesteric phase, a chiral version of the nematic phase, with an unusually short pitch in the range of 120–250 nm, was described.²¹ The pitch was detected by AFM analysis and confirmed by a resonant X-ray technique.²⁸ In several cases, it was found that the combination of two (S)-lactates in the chiral chain led to the presence of an antiferroelectric phase.^23–26

For the estimation of the role of the molecular core, several series with (S)-lactate in the chiral chain have been investigated. Molecular cores with phenyls and biphenyls connected via ester linkages in various modifications and lateral substitutions have been prepared and studied.^17–20 The preference of smectic phases and the formation of ferroelectricity in SmC* has been described; nevertheless, very often there is a delicate balance between the SmC and orthogonal smectic A (SmA) phases, and a re-entrant SmA phase below the SmC phase has also been described.^29,30 In the previous study, we tried to establish how this effect can be influenced by chirality and prepared enantiomers with both (S)-lactate and (R)-lactate groups. A detailed study confirmed that the mesomorphic properties do not vary when comparing enantiomers or their racemic mixtures and the re-entrant phenomenon is not connected with the chirality of the molecules.³⁰

Herein, we concentrate on a molecular core based on phenyl–biphenyl connected via an ester linkage. This molecular structure was successfully applied previously and broadening of the mesophase range down to room temperature was achieved.³¹ We investigated the effect of the chain length on the mesomorphic properties, and for this type of molecular core, we found that adding one more lactate into the chiral chain can induce antiferroelectricity.²³ Based on the same type of molecular core, we modified the chiral chain and varied it, starting from a simple methylbutyl and adding one or two (S)-lactate units. The chemical formulae of the studied compounds are presented in Fig. 1.

Fig. 1 Chemical formulae of the studied compounds: Z12(S), ZL12(S,S) and ZLL12(S,S,S).

We synthesised three chiral compounds, namely, Z12(S), containing an (S)-methylbutyl group; ZL12(S,S), containing an (S)-lactate group and (S)-methylbutyl group, and ZLL12(S,S,S), containing two (S)-lactate groups and an (S)-methylbutyl group. In addition, we prepared three analogous materials, in which methylbutyl was used in its racemic form: Z12(rac), ZL12(S,rac) and ZLL12(S,S,rac). These materials allowed us to identify the HPLC peaks corresponding to the opposite methylbutyl-containing (R) enantiomer, which is present in the Z12(rac), ZL12(S,rac) and ZLL12(S,S,rac) compounds. Molecules of Z12(R), ZL12(S,R) and ZLL12(S,S,R) could have been present in small amounts as impurities in the target substances Z12(S), ZL12(S,S) and ZLL12(S,S,S). Enantioselective HPLC methods were developed, and the separation conditions were optimized for each studied molecule. A detailed analysis and comparison allowed us to establish the optical purity of all the studied compounds.

2. Experimental

2.1. Synthesis of the Z12, ZL12 and ZLL12 materials

New liquid crystalline materials with multiple chiral centres were synthesised as shown in Scheme 1. The synthesis of the materials with one lactate unit ZL12(S,S) was analogous to that described previously.³¹ Both types of materials, ZL12(S,S) and ZL12(S,rac), were prepared in one step from 4′-(dodecyloxy)biphenyl-4-carboxylic acid (1), according to the general procedure described previously,³² using an N,N′-dicyclohexylcarbodiimide (DCC)-mediated esterification reaction with chiral hydroxybenzoates 2 or 3. Multichiral hydroxybenzoates 2 and 3 were synthesised in their pure enantiomeric forms as described earlier,³³ and their diastereomeric forms were synthesised in an analogous way. The detailed synthetic procedures are given in the SI.

Scheme 1 Synthesis routes of the target materials.

2.2. Optical purity analysis

The optical purity of the materials was analysed using a high-performance liquid chromatography (HPLC) system on two chiral columns. The separation behaviour of Z12(S) was described and published previously.^34,35 For the materials with two and three chiral centres, ZL12(S,rac) and ZLL12(S,S,rac), we developed new procedures for their analysis by enantioselective HPLC. For ZL12(S,rac), we applied a chiral Lux i-Amylose-3 column (i.d. 4.6. and length 150 mm) from Phenomenex (USA) with amylose tris(3-chloro-5-methylphenylcarbamate) as a chiral selector. For the ZLL12(S,S,rac) material, we utilized a Lux Amylose-2 column (i.d. 4.6. and length 150 mm) from Phenomenex (USA) with amylose tris(5-chloro-2-methylphenylcarbamate) as a chiral selector. After enantiomer separation of the racemic materials, (R)-enantiomers were unambiguously identified only as a very small amount in the corresponding (S)-materials. Thus, all the compounds were confirmed to be optically highly pure, with purity higher than 98.2%, as shown in Table S1 in the SI.

2.3. Set-up and measurements

A polarized light optical microscope (POM), Nikon Eclipse E-600 (Nikon, Tokyo, Japan), equipped with a heating stage, Linkam LTSE350 (Linkam, Tadworth, UK), and a digital camera, Canon EOS 700D, were applied for textural observations and all electro-optical measurements. The temperature was changed at a rate of about 5 K min⁻¹ and stabilized for texture acquisition with an accuracy ±0.1 K. We mostly studied our compounds in commercial cells (WAT, Warsaw, Poland), with glasses covered by transparent indium tin oxide (ITO) electrodes and surfactant coating to ensure a homogeneous geometry (HG). We filled the cells in the isotropic phase by means of capillary action.

We studied thermal properties by means of differential scanning calorimetry (DSC), utilizing a Pyris Diamond 7 calorimeter (PerkinElmer, Shelton, CT, USA). 1–3 mg of compounds were weighed and hermetically sealed in aluminium pans. The heating and cooling runs were conducted at 10 K min⁻¹. Analysis of the calorimetric results supplies information on the phase transition temperature, T_tr, and the corresponding enthalpy value, ΔH.

The spontaneous polarisation, P_S, and the tilt angle, θ, were studied under an applied electric field. The θ values were calculated from the angular difference between the extinction positions under the opposite sign of the applied DC electric field of about ±10 V µm⁻¹. The P_S values were obtained by integration of the polarisation current detected under the applied electric field of a triangular profile (with the magnitude of 10–20 V µm⁻¹) at a frequency of 10 Hz.

For dielectric spectroscopy, we utilized a Schlumberger 1260 impedance analyser and measured the frequency dispersion of the complex permittivity, ε*, in the frequency range of 1 Hz–1 MHz. The temperature was stabilized within ±0.1 K during the frequency sweeps. We analysed the measured data using the Cole–Cole equation, as follows:

Formula (1) contains additional terms corresponding to the low frequency contribution from conductivity, σ, and the high frequency contribution due to the resistance of the ITO electrodes, respectively. The parameter α lies between 0 and 1 and describes the distribution of relaxation, ε₀ is the permittivity of vacuum, ε_∞ the high frequency permittivity, and n, m, and A are other supporting fitting parameters. We fitted the real, ε′, and imaginary, ε″, parts of the complex permittivity ε*(f) = ε′ − iε″ simultaneously to formula (1) to obtain information on the relaxation frequency, f_r, and the dielectric strength, Δε.

The small-angle X-ray scattering (SAXS) technique was applied to determine the structural properties of the studied compounds. The Bruker D8 Discover (Bruker AXS, Karlsruhe, Germany) was used, equipped with ceramic X-ray tube as a radiation source (Cu anode, wavelength λ = 1.5418 Å), parabolic mirror monochromator and scintillation counter. An Anton Paar DCS 350 chamber (Anton Paar, Graz, Austria) was used for temperature control with an accuracy of ±0.1 K. The samples were prepared in the form of thin films, and the measurements were performed in the reflection mode. The smectic layer thickness, d, was calculated using Bragg's law from the position of the diffraction angle peak.

3. Results

3.1. DSC measurements and texture observations

Differential scanning calorimetry (DSC) measurements allowed us to establish the phase transition temperatures and the corresponding enthalpies. The results obtained from the second run of DSC measurements are collected in Table 1. The DSC thermographs are shown in Fig. 2 for illustration. Firstly, the mesophases were identified based on the observations under a polarizing microscope. We concluded that all the studied compounds show two smectic mesophases. During the POM studies in planar (HG) cells, we observed fan-shaped and broken fan-shaped textures in the SmA and SmC phases, respectively. For illustration, the fan-shaped textures observed for the ZL12(S,S) compound in the SmA and SmC* phases are presented in Fig. 3. The textures for several other compounds could be found in the SI (Fig. S1–S4). In the SmC* phase, we detected a defect pattern (Fig. 3(b)), which can be ascribed to dechiralization lines, which exist in the SmC* phase due to anchoring at the cell surfaces.³⁶ However, the dechiralization lines were not regular, which prevented the measurement of the helical pitch of the SmC* phase. Nevertheless, we assume that the helical pitch is small because after the application of an electric field, dechiralization lines started appearing within the texture, depicting the helical structure unwinding (see Fig. S2 for ZLL12(S,S,rac)). For the compounds with two lactates, ZLL12(S,S,S) and ZLL12(S,S,rac), there is a direct phase transition from the Iso to the SmC* phase on cooling. An additional tilted phase appeared during the cooling process, which is recognized as a transformation between two broken fan-shaped textures (Fig. S3). It is interesting to note that for the racemic compound Z12(rac), twisted domains were observed (Fig. S4), which evidences the separation of molecular conformers with different sense of axial chirality.³⁷

Table 1 DSC data for the Z12, ZL12 and ZLL12 compounds, taken during the 2nd heating and cooling runs at a rate of 10 K min⁻¹. The melting point (m.p.), phase transition temperature (T_tr), temperature of crystallization (T_cr), and temperature of the isotropic-mesophase phase transition (T_iso) are presented in °C, and the corresponding enthalpy values (ΔH) are presented in kJ mol⁻¹ in square brackets. M1 and M2 are the subsequent mesophases obtained upon cooling

Compounds	m.p. [ΔH]	Tcr [ΔH]	M2	Ttr [ΔH]	M1	Tiso [ΔH]
Z12(S)	75 [+18.16]	32 [−8.79]	SmC*	133 [−0.40]	SmA	175 [−3.58]
Z12(rac)	67 [+22.72]	30 [−19.62]	SmC	132 [−0.10]	SmA	175 [−5.81]
ZL12(S,S)	52 [+18.96]	35 [−17.86]	SmC*	115 [−0.33]	SmA	127 [−2.24]
ZL12(S,rac)	49 [+19.56]	38 [−16.68]	SmC*	114 [−0.25]	SmA	129 [−2.86]
ZLL12(S,S,S)	54 [+15.84]	35 [−12.26]	SmCA*	91 [−0.06]	SmC*	98 [−0.88]
ZLL12(S,S,rac)	60 [+24.30]	37 [−17.71]	SmCA*	91 [−0.08]	SmC*	99 [−0.61]

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Fig. 2 DSC plots for the (a) Z12(S), (b) ZL12(S,S) and (c) ZLL12(S,S,rac) compounds detected during the second heating (red) and cooling (blue) runs. Phase transitions with small enthalpy changes are presented in enlarged views in the insets.

Fig. 3 Textures in the (a) SmA phase and (b) SmC* phase of ZL12(S,S) in a 7-µm planar cell.

3.2. Mesomorphic properties

For compound Z12 with a methylbutyl, we prepared and studied a chiral version, Z12(S), and its racemic mixture, Z12(rac). We observed that both compounds show an SmA–SmC phase sequence. In the case of Z12(S), the SmC* phase reveals ferroelectricity, and we established its polar properties. We measured polarization, P_s, by integrating the switching current. The tilt angle, θ, was detected optically in an applied DC field. The temperature dependence of P_s(T) and θ(T) is presented in Fig. 4 in comparison with other materials.

Fig. 4 Temperature dependence plots of the (a) spontaneous polarisation, P_s, and (b) tilt angle, θ, for the Z12(S), ZL12(S,S) and ZLL12(S,S,S) compounds.

The compounds ZL12(S,S) and ZL12(S,rac) are both chiral and differ only in the terminal methylbutyl part. ZL12(S,rac) represents a molecular mixture of two chiral compounds, ZL12(S,S) and ZL12(S,R), both of which we were able to distinguish by HPLC and establish their optical purity (for details, see SI). The mesomorphic properties of both compounds, ZL12(S,S) and ZL12(S,rac), are similar, where the same SmA–SmC* phase sequence was detected on cooling from the isotropic phase. The comparison of the physical properties will be shown below.

The results for the two-lactate derivatives ZLL12(S,S,S) and ZLL12(S,S,rac) evidence that adding an additional lactate substantially decreases the phase transition temperature to the isotropic phase, T_iso. While compounds Z12(S), ZL12(S,S) and ZL12(S,rac) exhibit the SmA–SmC* phase sequence and paraelectric-ferroelectric phase transition, for ZLL12(S,S,S) and ZLL12(S,S,rac), we detected a direct phase transition from the isotropic phase to the SmC* phase at T = 98–99 °C on cooling. Then a transformation to the antiferroelectric SmC*_A phase took place at the temperature T = 91 °C.

3.3. Polarization and tilt angle measurements

In the ferro- and antiferro-electric smectic mesophases, we measured the polarization and the tilt. The temperature dependence of these parameters is shown in Fig. 4 for Z12(S), ZL12(S,S) and ZLL12(S,S,S). One can see that the polarization values are much lower for the Z12(S) compound in comparison with the other two materials containing additional lactate groups. The polarization values of the racemic compounds ZL12(S,rac) and ZLL12(S,S,rac) do not differ much from their chiral counterparts ZL12(S,S) and ZLL12(S,S,S), respectively. Explicitly, the P_s values for Z12(S) do not exceed 12 nC cm⁻², and for ZL12(S,S) and ZL12(S,rac) these values moderately saturate at about 120 nC cm⁻². For ZLL12(S,S,S) and ZLL12(S,S,rac), their P_s values continuously increase and reach 160 nC cm⁻² when approaching their crystallization temperature. Similarly, the tilt angle of Z12(S) does not extend 20°, while for the lactate derivatives ZL12(S,S) and ZLL12(S,S,S), the value of θ approaches 40°. It is necessary to point out that for ZLL12(S,S,S) and ZLL12(S,S,rac), no peculiarities are observed at the SmC*–SmC_A* phase transition in their P_s(T) and θ(T) dependence. This can be explained by the high measuring applied electric field (20 V µm⁻¹) exceeding the threshold, which is necessary to unwind the helical structure and transform the sample from the anticlinic to synclinic state.³⁸ Moreover, this phase transition is not recognizable in the current profile during the polarization measurements. We were able to measure the non-zero polarization and tilt angle values at temperatures slightly exceeding the phase transition temperatures to the SmC* phase (Table 1) due to the electroclinic effect.

A more complicated situation is if we compare the polarization and the tilt values between ZL12(S,S) and ZL12(S,rac). As was mentioned above, the polarization values do not show measurable differences between ZL12(S,S) and ZL12(S,rac). On the contrary, we detected smaller tilt values for the racemic Z12(rac) in comparison with Z12(S), and for ZL12(S,rac) in comparison with ZL12(S,S), which is demonstrated in Fig. 5. Alternatively, for the longest derivatives ZLL12(S,S,S) and ZLL12(S,S,rac), their tilt values jump up to 30° at the Iso-SmC* phase transition, and within the SmC* and SmC_A* phases, the tilt values increase up to 35° continuously on cooling of the sample, without a recognizable difference between these two derivatives. We can claim that the molecular shape of the ZLL12 derivatives with very long and complicated chiral chains is complex and the racemization at the terminal part only partially influences their molecular packing.

Fig. 5 Temperature dependence plot of the tilt angle, θ, for the Z12(S), Z12(rac), ZL12(S,S) and ZL12(S,rac) compounds.

3.4. Dielectric spectroscopy

Dielectric spectroscopy is a powerful tool to describe molecular dynamics, mainly in the vicinity of the paraelectric-ferroelectric SmA–SmC* phase transition. Due to molecular fluctuations, various modes can be observed with different characteristic behaviours.³⁹ A soft mode is detectable in the SmA phase, with a steep linear decrease in the relaxation frequency during cooling when approaching the SmA–SmC* phase transition. A phason type of mode, which is a Goldstone mode, can be detected in a ferroelectric phase, reflecting the vibrations of tilted molecules. For an antiferroelectric phase, the dynamics is even more complex in tilted smectics due to the opposite orientation of the tilted molecules in the neighbouring layers, and other modes can be detected.^40,41

We performed dielectric spectroscopy measurements for all the studied derivatives. For Z12(rac), which does not reveal a ferroelectric phase, its dielectric signals do not show any dispersion (see Fig. S5). For all the ferroelectric compounds, we detected one dielectric mode in their frequency scans. By fitting the complex permittivity, ε*, to eqn (1), we obtained the temperature dependence of the dielectric strength, Δε(T), and the relaxation frequency, f_r(T). For Z12(S), the soft mode is observed at the SmA–SmC* transition, the Goldstone mode in the SmC* phase is rather weak and the value of the dielectric strength, Δε, does not exceed 10 (see Fig. S6 in SI). For the lactate derivatives ZL12(S,S) and ZL12(S,rac), in the SmC* phase, the Goldstone mode is much stronger in comparison with Z12(S). The dielectric strength Δε(T) reaches a value of about 160 for ZL12(S,S). Fig. 6 presents the temperature dependence of the fitted values of the dielectric strength, Δε, and the relaxation frequency, f_r, for ZL12(S,S). When we compared the fitting results for ZL12(S,S) and ZL12(S,rac), there are only small differences.

Fig. 6 Temperature dependence plot of the fitted values of the dielectric strength, Δε, and the relaxation frequency, f_r, for ZL12(S,S), measured in a 5-µm cell without a surfactant.

For ZLL12(S,S,S) with the SmC*–SmC_A* phase sequence, the Goldstone mode in SmC* is very strong and the Δε(T) values are very high, more than 300. Unfortunately, for frequencies higher than 100 kHz, there is a limitation in studying high-frequency modes due to the conductivity of ITO electrodes. Accordingly, to extend the frequency range of the dielectric measurements and achieve better accuracy, we utilized cells with more conductive gold electrodes. The measurements in cells with gold electrodes allowed us to extend the frequency range of the dielectric spectroscopy up to 10 MHz. For ZLL12(S,S,S) in a 7-µm gold cell, the 3D plots of the real, ε′, and imaginary, ε″, parts of permittivity versus temperature and frequency are shown in Fig. 7(a) and (b), respectively. Due to the presence of a Goldstone mode, the permittivity values are very high in the SmC* phase and decrease at the SmC*–SmC_A* phase transition. In the SmC_A* phase, two very week modes are present. We fitted these modes and the results are presented in Fig. 8(a) and (b) for the dielectric strength, Δε, and the relaxation frequency, f_r, respectively. This dielectric spectroscopy behaviour is characteristic for the antiferroelectric ordering of the observed smectic mesophase.⁴¹

Fig. 7 (a) Real part of the complex permittivity, ε′, and (b) imaginary part of the permittivity, ε″, in the SmC* and SmC_A* phases of ZLL12(S,S,S). Dielectric spectroscopy was performed in a 7-µm cell with gold electrodes. Numbers mark the two modes in the SmC_A* phase, namely, 1: a lower-frequency mode and 2: a higher-frequency mode.

Fig. 8 Fitted values of (a) dielectric strength, Δε, and (b) relaxation frequency, f_r, for the two modes detected in the SmC_A* phase, where the red colour indicates the higher-frequency mode and the black colour indicates the lower-frequency mode.

3.5. X-ray diffraction measurements

The phase identification was confirmed by XRD measurements. In the X-ray profile, there are commensurate peaks reflecting the lamellar character of the smectic phases. According to the peak maximum position, we can obtain information about the layer spacing value, d. Fig. 9 shows the temperature dependence of d(T) for Z12(S), ZL12(S,S) and ZLL12(S,S,S), with the corresponding intensity of their X-ray peak. For compounds Z12(S) and ZL12(S,S), the d(T) values continuously increase within the SmA phase during the cooling process, as shown in see Fig. 9(a) and (b), respectively. A negative thermal expansion coefficient is typical for the SmA phase for rod-like molecules, which can be explained by stretching of their terminal chains and growth of orientational order of molecules upon cooling. When entering the tilted SmC* phase from the SmA phase, the layer spacing decreased gradually, which reflects the tilting of the molecules in layers. During the cooling of the sample within the SmC* phase, the decrease in d(T) became slower and finally the layer spacing was slightly increasing till the crystallization temperature. This effect can be explained by the continuous stretching of the terminal molecular chains and extension of the molecules. This increase in molecular length compensates for the changes in layer thickness due to the tilt, which tends to a gradual saturation (Fig. 4 and 5).

Fig. 9 Temperature dependence plots of the layer spacing, d, and the corresponding intensity of the X-ray diffraction signal for (a) Z12(S), (b) ZL12(S,S) and (c) ZLL12(S,S,S).

For the ZLL12 compounds with the SmC* phase forming directly below the isotropic phase, the layer spacing decreases within the SmC* phase until the phase transition to SmC_A*, where d(T) slightly jumps down, as shown in Fig. 9(c) for ZLL12(S,S,S). This small decrease is usually attributed to the better molecular ordering in the anticlinic phase. Simultaneously, an increase in diffracted intensity is observed (Fig. 9(c)), which is usually explained by an increase in smectic order due to the enhanced packing efficiency of the anticlinic arrangement.^26,33,42 The profile of d(T) continuously changes within the SmC_A* phase, but it is not monotonous. Below the SmC*–SmC_A* phase transition, the layer spacing continues decreasing, and after reaching a local minimum, starts growing deeper in the SmC_A* phase. Concerning the effect of racemization on the layer spacing values, there is a negligible change when comparing ZL12(S,S) with ZL12(S,rac) or ZLL12(S,S,S) with ZLL12(S,S,rac).

We can linearly extrapolate the layer spacing from the SmA phase and calculate the tilt angle from the temperature dependence, d(T), in the SmC* phase, θ_X. The tilt obtained from the layer spacing is usually lower than that determined from the orientation of the optical axis under a microscope. The reason for this is that the optical axis relates to the orientation of the molecular core, while the layer spacing reflects the overall molecular shape. As the terminal chains are very long, they can be inclined from the molecular core, which results in a smaller calculated molecular tilt.¹⁸ Fig. S8 in the SI presents the temperature dependence of the tilt angle measured optically, θ, and the tilt calculated from the temperature dependence of the layer spacing measured by SAXS, θ_X, for Z12(S) and ZL12(S,S).

3.6. DFT and ab initio calculations

To obtain detailed information about the studied molecules, we optimized their molecular structures using ab initio calculations at the B3LYP 6-31Gd level of theory.⁴³ The resulting molecules in their global minimum potential energy conformation are shown in Fig. 10. We established the length of the molecule, l, with extended terminal chains to be about 37.4 Å for Z12(S) and Z12(rac). For ZL12(S,S) and ZL12(S,rac), their l values were calculated to be about 39.6 Å. These values are slightly higher than the values of the layer spacing in the SmA phase, which evidences that in the mesophase, molecular shape does not correspond to the fully extended conformation. For ZLL12(S,S,S) and ZLL12(S,S,rac), with the most conformationally complicated chiral chain, we evaluated their molecular length to be l ∼39.2 Å. Nevertheless, we cannot compare l with the layer spacing, as there are only tilted SmC phases present in the phase sequence. We can speculate that the large bend in the chiral terminal chain obtained by DFT optimisation will be lower in the condensed fluid state within the smectic layers as the molecules experience lateral collisions.

Fig. 10 Visualization of the molecular structures of the studied molecules of (a) Z12(S), (b) ZL12(S,S) and (c) ZLL12(S,S,S) generated using the Chem3D program.

4. Discussion and conclusions

Chiral rod-like molecules represent a vivid and attractive topic in liquid crystals from many aspects, spanning basic research to applications. In this contribution, we aimed to shed more light on the effect of the chiral chain and its partial racemization in the methylbutyl terminal part. We prepared and studied chiral mesogens with an equivalent molecular core and modified only their chiral chain. We applied a methylbutyl chain, S-lactate methylbutyl and two lactates with a methylbutyl in the chiral chain, respectively, in three molecular structures. Additionally, we prepared analogous compounds with racemic methylbutyl to prove the effect of the racemization at this position.

Firstly, we compared the mesomorphic properties with respect to the molecular length and shape. We found a large reduction in the phase transition temperature, T_iso, with the molecular elongation. This effect has been observed previously for various compounds. For multilactate derivatives, it has been established that adding one more lactate to a molecular structure can drop the temperatures by even more than 30 °C.^17,23 Alternatively, for all the studied compounds herein, the crystallization temperatures and melting points are similar, which means that the width of the liquid crystalline phases decreases with the incorporation of an additional lactate group into the chain. We observed an antiferroelectric phase (SmC_A*) only for the compounds with two lactates with a methylbutyl in the chiral chain. We identified this phase based on the decrease in permittivity at the SmC*–SmC_A* transition and the emergence of two weak modes. The anticlinicity of the SmC_A* phase was supported by POM observations, in which only a sufficiently high electric field causes the helices to unwind and switching to be detected. In addition, the slight jump-like decrease in the temperature dependence of the layer spacing d(T) at the SmC*–SmC_A* phase transition and the simultaneous increase in the diffracted intensity, which are probably connected with an increase in the smectic order, support the synclinic-anticlinic transformation.

We applied DFT calculations to shed more light on the molecular structure. When comparing the molecular shape and the overall length, we must consider the tendency of molecular chains to crimp. For the shortest molecules Z12(S) and Z12(rac), the layer spacing approximately corresponds to the molecular length, l, of their most extended conformation. However, this is not true for the longer molecules ZL12(S,S) and ZL12(S,rac), for which their layer spacing is smaller than their l value. For compounds ZLL12(S,S,S) and ZLL12(S,S,rac), we cannot compare the data, as there is no orthogonal SmA phase in the phase sequence.

We tried to compare the polarization values of the three basic molecular structures. Unambiguously, it turned out that Z12(S) shows much lower P_s values than lactic acid derivatives ZL12 and ZLL12. This necessarily leads to the conclusion that (S)-lactate is actually very effective in supporting strong ferroelectric behaviour. When comparing ZL12(S,S) with ZL12(S,rac) and ZLL12(S,S,S) with ZLL(S,S,rac), one can see that their polarization values are similar and the effect of racemization in the methylbutyl part is not pronounced enough. We can conclude that the replacement of S-methylbutyl with methylbutyl racemate does not play an important role in polarization and dielectric properties.

Conversely, the tilt values for Z12(rac) and ZL12(S,rac) show slightly smaller values than their counterparts Z12(S) and ZL12(S,S), respectively. This fact can be explained by the lower degree of ordering in the presence of various enantiomeric versions, which imply a greater diversity of molecular conformations, which necessarily leads to worse packing. We can conclude that racemization at methylbutyl only slightly influenced the ferroelectric properties of the lactate derivatives and lactate seems to be a driving force to enhance their ferroelectric properties.

Author contributions

NP – Data curation, formal analysis, investigation, validation, visualisation, and writing – original draft, review and editing; VN – conceptualisation, data curation, funding acquisition, project administration, supervision, visualisation, and writing – original draft, review and editing; TJ – formal analysis, investigation, validation, and writing – original draft; VH – conceptualization, methodology, project administration, and supervision; DP – formal analysis, investigation, validation, visualisation, and writing – original draft; and MC – formal analysis, resources, validation, and writing – original draft.

Conflicts of interest

No potential conflict of interest was reported by the authors.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: includes the synthesis procedures, NMR spectra, chemical and optical purity (Table S1), and further experimental details. See DOI: https://doi.org/10.1039/d6sm00028b.

Acknowledgements

This work was supported by the Czech Ministry of Education, Youth and Sports through the international project 8I23001 FerroFluid (EIG Concert Japan – 9th Call, “Design of Materials with Atomic Precision”).

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