Antiferroelectric Bent-Core Liquid Crystal for Possible High-Power Capacitors and Electrocaloric Devices

We present small-angle X-ray scattering, polarized optical microscopy and electric current measurements of a sulfur-containing bent-core liquid crystal material for characterization of the layer and director structures, thermally and electrically driven transitions between antiferroelectric and ferroelectric structures and switching properties. It was found that the material has polarization-modulated homochiral synclinic ferroelectric (SmCsPFmod), homochiral anticlinic antiferroelectric (SmCaPA) and racemic synclininc antiferroelectric (SmCsPA) structures that can be reversibly switched between each other either thermally and/or electrically. High switching polarization combined with softness of the liquid crystalline structure makes this compound a good candidate for applications in high-power capacitors and electrocaloric devices.


Introduction
Recent advances in wearable electronic devices drive the development of miniature chemical and electric sensors and miniature power and information storage devices. In particular, the personal health care industry requires reliable and robust pressure and voltage-specific sensors for monitoring blood circulation, heart activity and body temperature [1]. Electric energy storage is another area where soft organic ferroelectrics may find prospective applications for their flexibility and even semiconducting properties [2][3][4]. For instance, umbrella-shaped columnar liquid crystals have been shown to store information of unprecedented density due to the ability to address each molecular column separately [5]. Efficient and reliable energy storage is crucial in our society. Electrical energy can be stored either electro-chemically in batteries or electro-statically in capacitors. Batteries have high energy density (~50-200 Wh/kg) and low power density (~1-1000 W/kg), while electro-static capacitors, have energy densities less than 0.1 Wh/kg and power densities over 5000 W/kg [6]. The gap between batteries and capacitors has been partially bridged with super-capacitors, which are currently being utilized in power conditioning and electric transportation, although they still have an order of magnitude smaller energy densities than batteries and take longer time to charge and discharge than conventional capacitors [7][8][9]. Capacitors made of antiferroelectric materials that undergo a reversible thermal or electric-field-induced transition to a ferroelectric state have the potential to store as much energy as electrochemical capacitors while maintaining the advantages of traditional capacitors [10,11]. As shown in Figure 1b, between 150 °C and 125 °C, several rings appear in the 0.05-0.5 Å −1 qrange. The strongest temperature independent peak at q(10)~0.149 Å −1 and its two harmonics at q(20) = 2q (10) and q(30) = 3q(10) indicate a layer structure with periodicity d = 2π/q1 = 40.21 Å. Considering that the length of the symmetrically bent molecule is L = 54 Å, the tilt angle θ, assuming no intercalation between the terminal chains of the neighbor molecules, can be calculated as θ arccos 42°.
Allowing some interdigitation, this angle can be smaller, but considering the length of the terminal The broad peak at 0.4 Å −1 is due to the Kapton tape used as a window in the SAXS measurements.

Results and Discussion
The SAXS results are summarized in Figure 1a-d. No diffraction peaks were observed above 150 • C, showing its 3-D fluid nature.
As shown in Figure 1b, between 150 • C and 125 • C, several rings appear in the 0.05-0.5 Å −1 q-range. The strongest temperature independent peak at q (10)~0 .149 Å −1 and its two harmonics at q (20) = 2q (10) and q (30) = 3q (10) indicate a layer structure with periodicity d = 2π/q 1 = 40.21 Å. Considering that the length of the symmetrically bent molecule is L = 54 Å, the tilt angle θ, assuming no intercalation between the terminal chains of the neighbor molecules, can be calculated as θ = arccos d L ≈ 42 • . Allowing some interdigitation, this angle can be smaller, but considering the length of the terminal chains, it cannot be zero, even for complete interdigitation. Additionally, there are temperature Crystals 2020, 10, 652 4 of 11 dependent peaks in the 0.01 < θ < 0.06 Å −1 range. The main peak at q (01)~0 .015 Å −1 and its four harmonics show layer undulations with periodicities p m increasing from 330 Å at 147 • C to 420 Å at 127 • C (seen separately in Figure 1c). Such tilted smectic phases with undulated layers agree with the structural assignment of the B 7 phase [37,40]. The layer undulations disappear below 125 • C, where only the weakly temperature dependent peaks appear at q (10)~0 .128 Å −1 and at harmonics q (i,0) = i·q (10) (I = 2-4) corresponding to a layer spacing of d = 2π/q 1 = 48.8 Å (see Figure 1d). Such periodicity, assuming some degree of interdigitation between the terminal chains, indicates a fluid tilted smectic phase with tilt angle θ < 25 • . Such a structure is not compatible to the B 3 phase assignment with in-plane or crystalline order that would lead to peaks with other periodicities. Below 115 • C, with about a 5 • C overlap, another smectic phase without in-plane order is observed, as seen in Figure 1e. The peaks at q (10)~0 .122 Å −1 and its harmonics with q (i,0) = i·q (10) (I = 2-4) correspond to a layer periodicity of d = 2π/q 1 = 50.12 Å. Depending on the interdigitation by the terminal chains, this could correspond to a tilted smectic phase with a tilt angle of up to θ = 20 • or to an orthogonal (SmA) smectic phase. For the time being, we call it an SmX phase.
The temperature dependences of the layer spacing d and correlation length ξ are calculated from the first harmonic wavenumber peak q (10) , as d = 2p/q (10) and from the full width at half maxima (FWHM). The correlation length ξ is proportional to the inverse of FWHM. The order of magnitude and the temperature dependence of the correlation length is plotted against the right axis, assuming the proportionality constant is 1. The temperature dependence of the layer spacing is plotted against the left axis of Figure 2. The shaded area between the B 2 and SmX phases indicates phase overlap due to the first order nature of the transition. Although wide angle X-ray scattering would be needed to find out if the SmX phase has an in-plane order or not, the strongly first order transition between the B 2 and SmX phases indicate it has in-plane order. The inset shows the half periodicity of the layer undulation measured in the B 7 phase. While the layer periodicities d = 40.21, 48.8 and 50.12 Å and the correlation lengths ξ = 370, 483 and 502 nm are basically constant in the B 7 , B 2 and SmX phases, respectively, the periodicity of the in-layer modulation in the B 7 phase is clearly increasing on cooling.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 11 chains, it cannot be zero, even for complete interdigitation. Additionally, there are temperature dependent peaks in the 0.01 < θ < 0.06 Å −1 range. The main peak at q(01)~0.015 Å −1 and its four harmonics show layer undulations with periodicities pm increasing from 330Å at 147 °C to 420 Å at 127 °C (seen separately in Figure 1c). Such tilted smectic phases with undulated layers agree with the structural assignment of the B7 phase [37,40]. The layer undulations disappear below 125 °C, where only the weakly temperature dependent peaks appear at q(10) ~0.128 Å −1 and at harmonics q(i,0) = i . q(10) (I = 2-4) corresponding to a layer spacing of d = 2π/q1 = 48.8Å (see Figure 1d). Such periodicity, assuming some degree of interdigitation between the terminal chains, indicates a fluid tilted smectic phase with tilt angle θ < 25°. Such a structure is not compatible to the B3 phase assignment with inplane or crystalline order that would lead to peaks with other periodicities. Below 115 °C, with about a 5 °C overlap, another smectic phase without in-plane order is observed, as seen in Figure 1e. The peaks at q(10)~0.122Å −1 and its harmonics with q(i,0) = i . q(10) (I = 2-4) correspond to a layer periodicity of d = 2π/q1 = 50.12Å. Depending on the interdigitation by the terminal chains, this could correspond to a tilted smectic phase with a tilt angle of up to θ = 20° or to an orthogonal (SmA) smectic phase. For the time being, we call it an SmX phase. The temperature dependences of the layer spacing d and correlation length ξ are calculated from the first harmonic wavenumber peak q(10), as d = 2p/q(10) and from the full width at half maxima (FWHM). The correlation length ξ is proportional to the inverse of FWHM. The order of magnitude and the temperature dependence of the correlation length is plotted against the right axis, assuming the proportionality constant is 1. The temperature dependence of the layer spacing is plotted against the left axis of Figure 2. The shaded area between the B2 and SmX phases indicates phase overlap due to the first order nature of the transition. Although wide angle X-ray scattering would be needed to find out if the SmX phase has an in-plane order or not, the strongly first order transition between the B2 and SmX phases indicate it has in-plane order. The inset shows the half periodicity of the layer undulation measured in the B7 phase. While the layer periodicities d = 40.21, 48.8 and 50.12 Å and the correlation lengths ξ = 370, 483 and 502 nm are basically constant in the B7, B2 and SmX phases, respectively, the periodicity of the in-layer modulation in the B7 phase is clearly increasing on cooling.  Temperature dependence of the voltage threshold for switching, together with representative electric current waveforms (in inset) in the B 7 and B 2 phases are shown in Figure 3. At and above 125 • C, a ferroelectric type switching is seen with a threshold field of E th ≈ 10.5 V/µm (one current peak in each half period of the triangular wave voltage, as seen in the inset at 127 • C), which is basically constant in the entire B 7 phase range. Based on this and the SAXS results, we denote this as an SmCP Fmod phase, where SmC stands for tilted smectic phase, P refers to the polar nature of the phase and F in the subscript denotes ferroelectric switching and "mod" describes the modulated layer structure. Below 125 • C in the B 2 phase the electric current under triangular wave voltage has a double peak in each half period (see the time dependence of the electric current at 118 • C in the inset), corresponding to an antiferroelectric tilted smectic (SmCP A ) phase. In this phase the threshold field decreases continuously to E th ≈ 3.5 V/µm. Below 115 • C, no polarization peak can be observed even up to 20 V/µm fields, indicating a paraelectric or dielectric nature of the phase.
Crystals 2020, 10, x FOR PEER REVIEW 5 of 11 °C, a ferroelectric type switching is seen with a threshold field of Eth ≈ 10.5 V/µm (one current peak in each half period of the triangular wave voltage, as seen in the inset at 127 °C), which is basically constant in the entire B7 phase range. Based on this and the SAXS results, we denote this as an SmCPFmod phase, where SmC stands for tilted smectic phase, P refers to the polar nature of the phase and F in the subscript denotes ferroelectric switching and "mod" describes the modulated layer structure. Below 125 °C in the B2 phase the electric current under triangular wave voltage has a double peak in each half period (see the time dependence of the electric current at 118 °C in the inset), corresponding to an antiferroelectric tilted smectic (SmCPA) phase. In this phase the threshold field decreases continuously to Eth ≈ 3.5 V/µm. Below 115°C, no polarization peak can be observed even up to 20 V/µm fields, indicating a paraelectric or dielectric nature of the phase. Electric current measurements under rectangular voltage waveforms (see Figure 4) reveal two peaks in both the SmCPFmod and SmCPA phase ranges. The slow peak is in the 0.5-0.9 ms range, while the fast one with 5-6 µs range. The integral areas below these peaks, however, are very different in these two phases: the slow peak is dominating in the ferroelectric SmCPFmod range, while the fast peak area is much larger in the antiferroelectric SmCPA phase. These behaviors are very similar to that observed and explained for a Fluorine containing bent-core material [29]. The presence of two peaks indicates a coexistence of chiral and racemic domains in both phases. From the ratios of the integral areas (see Figure 5) we can see that about 80% of the material in the SmCPFmod state has synclinic chiral structure (SmCsPFmod). This ratio reverses as the material is cooled to the SmCPA phase, where over 80% of the material appears to be in the racemic synclinic SmCsPA state. It is known that switching the polarization while retaining homo-chirality requires rotation around the tilt cone, whereas in the racemic state it can be done by rotation around the long axis, which is much faster than the rotation around the tilt cone [14].
The temperature dependence of the polarization, as calculated from the areas below the current peaks, are shown in Figure 5. Triangular symbols indicate the values measured under triangular wave voltages and rectangular symbols correspond to data extracted from the measurements under rectangular voltage waveform. Open rectangles correspond to the areas of the slow (blue) and fast (red) peaks, while solid black rectangles are the sum of these two areas. The total polarization values in the Sm CPFmod phase increase weakly on cooling from 140n C/cm 2 to about 170n C/cm 2 , then jump up to 240n C/cm 2 in the B2 phase. The value of the polarization drops quickly upon the first-order Electric current measurements under rectangular voltage waveforms (see Figure 4) reveal two peaks in both the SmCP Fmod and SmCP A phase ranges. The slow peak is in the 0.5-0.9 ms range, while the fast one with 5-6 µs range. The integral areas below these peaks, however, are very different in these two phases: the slow peak is dominating in the ferroelectric SmCP Fmod range, while the fast peak area is much larger in the antiferroelectric SmCP A phase. These behaviors are very similar to that observed and explained for a Fluorine containing bent-core material [29]. The presence of two peaks indicates a coexistence of chiral and racemic domains in both phases. From the ratios of the integral areas (see Figure 5) we can see that about 80% of the material in the SmCP Fmod state has synclinic chiral structure (SmC s P Fmod ). This ratio reverses as the material is cooled to the SmCP A phase, where over 80% of the material appears to be in the racemic synclinic SmC s P A state. It is known that switching the polarization while retaining homo-chirality requires rotation around the tilt cone, whereas in the racemic state it can be done by rotation around the long axis, which is much faster than the rotation around the tilt cone [14]. transition to the Sm A phase. We note that each polarization measurements took only a few seconds and between two temperatures the material was cooled without field to prevent long-term structural transformations.  Although the dominating slow switching in the SmCPFmod phase and the mainly fast switching in the SmCPA phase have already indicated that the tilt is mainly synclinic in both phases, we also transition to the Sm A phase. We note that each polarization measurements took only a few seconds and between two temperatures the material was cooled without field to prevent long-term structural transformations.  Although the dominating slow switching in the SmCPFmod phase and the mainly fast switching in the SmCPA phase have already indicated that the tilt is mainly synclinic in both phases, we also The temperature dependence of the polarization, as calculated from the areas below the current peaks, are shown in Figure 5. Triangular symbols indicate the values measured under triangular wave voltages and rectangular symbols correspond to data extracted from the measurements under rectangular voltage waveform. Open rectangles correspond to the areas of the slow (blue) and fast (red) peaks, while solid black rectangles are the sum of these two areas. The total polarization values in the Sm CP Fmod phase increase weakly on cooling from 140n C/cm 2 to about 170n C/cm 2 , then jump up to 240n C/cm 2 in the B 2 phase. The value of the polarization drops quickly upon the first-order transition to the Sm A phase. We note that each polarization measurements took only a few seconds and between two temperatures the material was cooled without field to prevent long-term structural transformations.
Although the dominating slow switching in the SmCP Fmod phase and the mainly fast switching in the SmCP A phase have already indicated that the tilt is mainly synclinic in both phases, we also carried out electro-optical investigations to verify this independently. Representative POM textures and their schematic director and layer structures are summarized in Figures 6 and 7 for the SmC PFmod and SmCP A phases, respectively. and their schematic director and layer structures are summarized in Figures 6 and 7 for the SmCPFmod and SmCPA phases, respectively. Figure 6a shows the texture at 127 °C in the field-induced SmCPFstate under −80 V applied across the cell. The central area shows Maltese crosses rotated by about 30-35° with respect to the vertical and horizontal polarizers. The cross-section of the director and layer structure in the plane of the substrates is illustrated below the image. The smectic layers form concentric cylinders with a defect in the middle of the Maltese cross. The director is tilted uniformly (synclinic structure) with respect to the layer normal to the left by angle q; thus, it is parallel to the polarizers at an angle -θ.
The yellowish-green birefringence color corresponds to an optical path difference Δn ⋅ d ≈ 800nm , corresponding to a birefringence Δn ≈ 0.2. After turning the field OFF, the direction of the Maltese crosses remains unchanged, indicating bistability. Only the birefringence color shifts toward green with optical path difference Δn ⋅ d ≈ 750nm , corresponding to a birefringence Δn ≈ 0.188 . As illustrated in the director and layer structure below, this is due to the modulated layer structure both along and normal to the substrates. This causes the inhomogeneity of the director structure, explaining the decreased effective birefringence. On applying +80V, the Maltese crosses rotated by about 70°-i.e., by twice the tilt angle. This is the consequence of the switching of the polarization to the opposite direction, as shown in Figure 6c. The birefringence color again shifts to yellowish green, indicating the field induced SmCPFmod to SmCPF transition, as observed on other bent-core materials, as well. [41] Based on these observations, we verify that this layer-modulated tilted smectic phase is synclinic SmCsPFmod-i.e., homochiral [19]. After cooling to the antiferroelectric SmCPA phase at zero electric field, two different types of domains appear in Figure 7a. One is characterized by a turquoise ("Tiffany blue") birefringent color with Δn ⋅ d ≈ 700nm ( Δn ≈ 0.175), the other one has orange color with Δn ⋅ d ≈ 450nm( Δn ≈ 0.11).
The director and layer structure of these domains are shown below the texture. The turquoise domain in the center is synclinic antiferroelectric (SmCsPA)-i.e., racemic [19] as our switching time measurements indicated above, while the minority outside orange area is anticlinic (SmCaPA)-i.e., homochiral. In the approximation that the birefringence is much smaller than the ordinary refractive index (ns << no), the effective birefringence of an anticlinic state can be given as Δn a ≈ Δn s ⋅ cos 2 2θ ( ) [42], which with the synclinic Δn s ≈ 0.18 value gives the measured Δn a ≈ 0.11for θ~20°. This value agrees with the estimated θ < 25° tilt angle from the layer periodicities by SAXS measurements,  Figure 6a shows the texture at 127 • C in the field-induced SmCP F-state under −80 V applied across the cell. The central area shows Maltese crosses rotated by about 30-35 • with respect to the vertical and horizontal polarizers. The cross-section of the director and layer structure in the plane of the substrates is illustrated below the image. The smectic layers form concentric cylinders with a defect in the middle of the Maltese cross. The director is tilted uniformly (synclinic structure) with respect to the layer normal to the left by angle q; thus, it is parallel to the polarizers at an angle −θ. The yellowish-green birefringence color corresponds to an optical path difference ∆n · d ≈ 800 nm, corresponding to a birefringence ∆n ≈ 0.2. After turning the field OFF, the direction of the Maltese crosses remains unchanged, indicating bistability. Only the birefringence color shifts toward green with optical path difference ∆n · d ≈ 750 nm, corresponding to a birefringence ∆n ≈ 0.188. As illustrated in the director and layer structure below, this is due to the modulated layer structure both along and normal to the substrates. This causes the inhomogeneity of the director structure, explaining the decreased effective birefringence. On applying +80 V, the Maltese crosses rotated by about 70 • -i.e., Crystals 2020, 10, 652 8 of 11 by twice the tilt angle. This is the consequence of the switching of the polarization to the opposite direction, as shown in Figure 6c. The birefringence color again shifts to yellowish green, indicating the field induced SmCP Fmod to SmCP F transition, as observed on other bent-core materials, as well [41]. Based on these observations, we verify that this layer-modulated tilted smectic phase is synclinic SmC s P Fmod -i.e., homochiral [19].
Representative textures and schematics of the corresponding director and layer structure of the central circularly shaped domain after driving by 12 V/µm, f = 12 Hz square wave field for a few minutes, are shown in Figure 7b. The birefringence color is uniformly purple with Maltese crosses parallel to the crossed polarizers, indicating an anti-clinic antiferroelectric (homochiral) structure everywhere. Such a rectangular electric-field-induced racemic to chiral phase transformation is already found and explained for other bent-core materials. [43] The increased optical path difference n . d ≈ 550 nm means an effective birefringence of Δn a ≈ 0.138 , which with θ ≈ 20° gives Δn s ≈ 0.234 . This value is much larger than that observed after cooling at zero field, indicating that the smectic layers were tilted upon cooling at zero field and became upright after applying the large field. The birefringence of the SmCsPA structure with upright layers is also larger than of the field induced SmCsPF structure in the higher temperature phase range, which is consistent with the increasing birefringence (decreased director fluctuations) toward lower temperatures.

Conclusions
In this paper we have characterized the nanostructures, the thermally and electrically driven transitions, between antiferroelectric and ferroelectric structures and the switching properties of a sulfur containing bent-core liquid crystal material. It was found that the material has polarizationmodulated ferroelectric (SmCPFmod) and antiferroelectric (SmCsPA) structures that can be switched between one another either thermally and/or electrically. Fast sub-millisecond reversible switching between antiferroelectric and ferroelectric states with up to P = 2.4 mC/m 2 polarization provides a charging capacity with as high as a 30 kW/kg power density. Such power density makes this material comparable to state-of-the-art electronic double layer capacitors.
[9] The modulated structure of the ferroelectric phase (SmCsPFmod) allows for the stabilization of the polar domains at a modulation scale of 50 nm. Piezo and pyroelectric properties of ferroelectric bent-core liquid crystals also make them promising for sensor applications as touch and pressure sensors [44]. Although with the present materials these features can be achieved only at elevated temperatures, the recent development of After cooling to the antiferroelectric SmCP A phase at zero electric field, two different types of domains appear in Figure 7a. One is characterized by a turquoise ("Tiffany blue") birefringent color with ∆n · d ≈ 700 nm (∆n ≈ 0.175), the other one has orange color with ∆n · d ≈ 450 nm(∆n ≈ 0.11). The director and layer structure of these domains are shown below the texture. The turquoise domain in the center is synclinic antiferroelectric (SmC s P A )-i.e., racemic [19] as our switching time measurements indicated above, while the minority outside orange area is anticlinic (SmC a P A )-i.e., homochiral. In the approximation that the birefringence is much smaller than the ordinary refractive index (n s << n o ), the effective birefringence of an anticlinic state can be given as ∆n a ≈ ∆n s · cos 2 (2θ) [42], which with the synclinic ∆n s ≈ 0.18 value gives the measured ∆n a ≈ 0.11 for θ~20 • . This value agrees with the estimated θ < 25 • tilt angle from the layer periodicities by SAXS measurements, shown in Figure 2 and indicates some interdigitation between terminal chains of molecules in neighbor layers.
Representative textures and schematics of the corresponding director and layer structure of the central circularly shaped domain after driving by 12 V/µm, f = 12 Hz square wave field for a few minutes, are shown in Figure 7b. The birefringence color is uniformly purple with Maltese crosses parallel to the crossed polarizers, indicating an anti-clinic antiferroelectric (homochiral) structure everywhere. Such a rectangular electric-field-induced racemic to chiral phase transformation is already found and explained for other bent-core materials [43]. The increased optical path difference n·d ≈ 550 nm means an effective birefringence of ∆n a ≈ 0.138, which with θ ≈ 20 • gives ∆n s ≈ 0.234. This value is much larger than that observed after cooling at zero field, indicating that the smectic layers were tilted upon cooling at zero field and became upright after applying the large field. The birefringence of the SmC s P A structure with upright layers is also larger than of the field induced SmC s P F structure in the higher temperature phase range, which is consistent with the increasing birefringence (decreased director fluctuations) toward lower temperatures.

Conclusions
In this paper we have characterized the nanostructures, the thermally and electrically driven transitions, between antiferroelectric and ferroelectric structures and the switching properties of a sulfur containing bent-core liquid crystal material. It was found that the material has polarization-modulated ferroelectric (SmCP Fmod ) and antiferroelectric (SmC s P A ) structures that can be switched between one another either thermally and/or electrically. Fast sub-millisecond reversible switching between antiferroelectric and ferroelectric states with up to P = 2.4 mC/m 2 polarization provides a charging capacity with as high as a 30 kW/kg power density. Such power density makes this material comparable to state-of-the-art electronic double layer capacitors.
[9] The modulated structure of the ferroelectric phase (SmC s P Fmod ) allows for the stabilization of the polar domains at a modulation scale of 50 nm. Piezo and pyroelectric properties of ferroelectric bent-core liquid crystals also make them promising for sensor applications as touch and pressure sensors [44]. Although with the present materials these features can be achieved only at elevated temperatures, the recent development of wide temperature range (from −40 • C to +80 • C) antiferroelectric bent-core liquid crystal mixtures [45,46] may make such high power density storage devices a realm of the near future. An added advantage of the material studied here is the thermally induced antiferroelectric-ferroelectric transitions, that may offer their use in electro-caloric devices with over 100 Jkg −1 K −1 isothermal entropy change either at the Iso-SmCP s F mod or the SmCP A -SmCP s F mod phase transitions. This value is larger than those found in dielectric liquid crystals [47].