Ferroelectric smectic A-phase materials, devices including same, and methods of forming and using same

Abstract

Devices including volumes comprising ferroelectric smectic A (SmAF) liquid crystal forming fluids are disclosed, as well as methods of forming and using these devices. An example apparatus includes one or more surfaces and one or more electrodes on the one or more surfaces for applying an electric field to the electric field.

Description

[0001] Cross - Reference to Related Applications

[0002] This application claims priority to U.S. Provisional Application Serial No. 63 / 354,991, filed on June 23, 2022, entitled "FERROELECTRIC SMECTIC A PHASE MATERIALS, DEVICES INCLUDING THE MATERIALS, AND METHODS OF FORMING AND USING SAME", the content of which is hereby incorporated by reference in its entirety.

[0003] Statement Regarding Federally Sponsored Research or Development

[0004] This invention was made with government support under Grant Nos. DMR2005170 and DMR1710711 awarded by the National Science Foundation. The government has certain rights in the invention. Technical Field

[0005] This disclosure generally relates to devices including ferroelectric liquid crystal materials. More specifically, this disclosure relates to devices including ferroelectric smectic A liquid crystal - forming materials. Background Art

[0006] In the 1910s, P. Debye and M. Born predicted ferroelectricity in liquids by applying the ferromagnetic Langevin - Weiss model to the orientation ordering of molecular electric dipoles. More recently, there has been increasing interest in nematic ferroelectrics. Due to the unique combination of macroscopic polar ordering and fluidity in nematic ferroelectricity, it presents opportunities for new liquid crystal science and technology. In addition, new phases of ferroelectric nematics can also provide additional desirable properties for devices and applications. Thus, improved devices and methods using ferroelectric nematic materials are desired.

[0007] Any discussion of problems and solutions set forth in this section has been included in this disclosure solely for the purpose of providing context for the disclosure and should not be taken as an admission that any or all of the discussion was known at the time the invention was made. Summary of the Invention

[0008] The Summary of the Invention is provided to introduce a series of concepts. The Summary of the Invention is not necessarily intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

[0009] Liquid crystal science becomes richer and more applicable with each newly discovered or created phase. The recently discovered ferroelectric nematic is exciting and unexpected because it appears in new molecules that do not differ greatly in structure from many similar materials studied over the past 100 years. Clearly, important and sometimes seemingly magical secrets remain to be discovered in the complex organic molecular structures and interactions. A fundamental question after the discovery of the ferroelectric nematic is whether there also exists a ferroelectric smectic A, a nematic-associated phase obtained when molecules spontaneously slide to form planar fluid layers normal to their molecular long axes. Here, we report such a phase and disclose devices comprising such a phase and methods of using such a phase.

[0010] Embodiments of the present disclosure relate to devices comprising a smectic A F that is a new liquid crystal phase in the field of ferroelectric nematic phases. The smectic A F is a phase of small polar rod-like molecules that form two-dimensional fluid layers spaced approximately an average molecular length apart. The phase is uniaxial, has a director normal to the layer plane, a local average major axis orientation, and has a spontaneous polarization ferroelectric parallel to the director. As discussed in more detail below, polarization measurements indicate that a ~10 Debye longitudinal molecular dipole is almost completely polar ordered, and a coercive field of ~2 × 10 F V / m for hysteretic polarization reversal is observed. The SmA 5 phase appears upon cooling in two binary mixtures of partially fluorinated mesogens: 2N / DIO, which exhibits a nematic (N) – smectic Z F (SmZ A )-ferroelectric nematic (N A )-SmA F phase sequence; and 7N / DIO, which exhibits an N–SmZ F –SmA A –SmA F phase sequence.

[0011] Various embodiments of the present disclosure relate to devices comprising a ferroelectric smectic A (SmA F ) liquid crystal forming fluid, and methods of forming and using these devices. Examples of the present disclosure may be listed below, including in the originally filed claims, and these claims are incorporated herein by reference.

[0012] According to an exemplary embodiment of the present disclosure, a device comprises: comprising a ferroelectric smectic A (SmA F)The volume of the liquid crystal-forming fluid and the device for containing the fluid. The fluid includes molecules organized in layers. The molecules have one or more electric dipoles. The molecules have (e.g., spontaneously) formed a ferroelectric polarization density, which includes a non-zero local unidirectional average orientation of the dipoles. The polarization density includes a magnitude and a vector direction in the volume, and the vector direction is locally normal to the layer. According to an exemplary embodiment of the present disclosure, the device includes one or more electrodes for applying an electric field to the volume. As described herein, the electrodes can be formed of any suitable conductive material (such as gold, copper, aluminum, indium tin oxide (ITO), etc.). In some cases, an electromagnetic field can propagate in the volume, and the electric field causes a change in the magnitude of the polarization density, thereby generating a change in the electromagnetic field. In some cases, the electric field can cause a change in the vector direction of the polarization density, thereby generating a change in the electromagnetic field. In some cases, the electric field can cause a change in the polarization density in the vector direction and / or the magnitude, thereby generating a change in the shape or physical movement of the volume. According to a further example, the device can include one or more electrodes for measuring the electric potential or current within the volume, and the electric potential and / or current are generated by a change in the polarization density, which is caused by a change in the stress within the volume or a change in the shape of at least a part of the volume. In some cases, the device can thermally generate a charge density, where the device includes one or more electrodes for measuring the electric potential within the volume or obtaining the current within the volume, and the electric potential and / or current are generated by a change in the polarization density, and the change in the polarization density is generated by a change in the temperature of the volume. The volume can be contained between parallel surfaces. The electric field can be applied parallel to the surfaces. The polarization density and / or the electromagnetic field can be parallel to the surfaces. According to various examples of the present disclosure, the volume includes two or more different molecules. According to these or other embodiments of the present disclosure, the molecules include stable characteristics suitable for the ferroelectric smectic A phase, including one or more of the following characteristics: (1) a rod-shaped shape with a molecular major axis suitable for smectic A liquid crystal ordering; (2) a substantial molecular net dipole parallel to the molecular major axis, which stabilizes the head-to-tail chains of the rod-shaped molecules; (3) an alternating signal distributed along the molecular major axis gives molecular sub-components along the molecular length with local charges; (4) a minimum flexible tail for enabling the dipole charges to interact, but providing sufficient flexibility to inhibit crystallization; and (5) a lateral group for controlling the relative positions of adjacent molecules along the director to promote their polar order.

[0013] According to a further example of the present disclosure, a device includes: a volume, the volume including ferroelectric smectic A (SmA F ) liquid crystal-forming molecules, the volume containing SmA F liquid crystal phase, the SmAF The liquid crystal phase includes a vector orientation field of the polarization density throughout the volume; and one or more materials, the one or more materials including one or more surfaces in contact with the volume, wherein the one or more surfaces are configured to impart a favorable surface polarity to the molecules, and the favorable surface polarity controls the vector orientation at the interface with the one or more surfaces. The one or more materials may include a first material and a second material, the first material including a first surface in contact with the volume, and the second material including a second surface in contact with the volume. The favorable surface polarity of the molecules may include, for example, a component that is locally normal to and points away from at least one of the one or more surfaces, a component that points toward at least one of the one or more surfaces, a component that is locally tangent to at least one of the one or more surfaces. The favorable surface polarity of the molecules may include a component created by photo-degradation caused by illumination of one or more of the surfaces, a component created by depositing a material onto the surface of one or more of the surfaces, a component created by depositing a material onto the surface of one or more of the surfaces (wherein the deposition is inclined), a component created by etching a material from one or more materials. An exemplary device may further include one or more electrical connections for applying an electric field to the volume and / or means for applying an electromagnetic field to the volume. The device may further include dopant molecules in the SmA F phase. The dopant molecules may have a dipole moment, which is preferably aligned by the vector orientation field of the SmA F adjacent to or near the dopant molecules. According to an example, the SmA F phase is a mixture of two or more different molecular species; the SmA F phase may be a smectic mixture.

[0014] According to yet a further example of the present disclosure, a method is provided for controlling the favorable vector orientation of the three-dimensional polarization field of SmA F liquid crystal at the interface surface with one or more materials. The method includes: providing a volume that includes SmA F liquid crystal-forming molecules; providing a first material having a first surface in contact with the volume; and using the first surface to impart a favorable surface polarity to the molecules, the favorable surface polarity controlling the favorable vector orientation of the molecules in the volume. The method may further include: providing a second material having a second surface in contact with the volume. The favorable surface polarity of the molecules may include a component that is locally normal to the surface and points toward the surface, a component that is locally normal to the surface and points away from the surface, a component that is locally tangent to the first surface (e.g., a unique favorable azimuthal orientation around the surface normal). An exemplary method may further include applying an electric field to the SmAF Phase steps. As described above and elsewhere, dopant molecules can be dissolved in the SmA F phase. According to an example, the SmA F phase is a mixture of two or more different molecular species; the SmA F phase can be a smectic mixture.

[0015] According to a further example of the present disclosure, a device includes: a volume that includes SmA F liquid crystal-forming molecules; and a first material that includes a first surface in contact with the volume, wherein the first surface is configured to impart a favorable surface polarity to the molecules to control the vector orientation of the molecules within the volume at the interface with the first surface. The volume can include SmA F phase.

[0016] According to a further example of the present disclosure, a material including a ferroelectric smectic A (SmA F ) material includes: two or more molecular components. The material can include a mixture of a first molecule and a second molecule.

[0017] According to a further example of the present disclosure, a method of forming a material having a tunable SmA F phase includes: mixing a plurality of molecules to form a mixture having a SmA F phase, wherein some of the molecules cause a polar orientation order in one or more of the other molecules.

[0018] According to a further additional example of the present disclosure, a device includes: a volume that contains a ferroelectric smectic A (SmA F ) liquid crystal material; a dielectric layer that covers a portion of the volume; and a charge-carrying substrate that covers at least a portion of the dielectric layer, wherein the volume includes a polarization charge near the dielectric layer, and the polarization charge is controllable by the charge on the charge-carrying substrate and / or the charge applied to the charge-carrying substrate. The device can include one or more additional dielectric layers that cover the volume. In such cases, the device can include one or more additional charge-carrying substrates that cover the one or more additional dielectric layers. In some cases, each surface that defines the SmA F liquid crystal includes a dielectric layer adjacent to the liquid crystal and a neighboring charge-carrying substrate, and each surface has a finite capacitance and thus acts as a capacitor. According to aspects of these embodiments, the polarization charge and molecular orientation of the SmA F liquid crystal on the inner side (liquid crystal side) of the capacitor are controlled by changing the charge on the outer side (substrate side) of the capacitor. According to a further aspect, the charge on the boundary surface and the resulting SmAF The molecular orientation of a liquid crystal responds to an external field or other stimuli, which include an external electromagnetic field or optical field, a chemical or electrochemical reaction, a biomolecular binding event, mechanical strain or shear, and liquid flow. The response to the external field or other stimuli is detected electrically and / or optically. A sensor, actuator, and / or energy conversion device may include a device as described in this paragraph and elsewhere in this document. In some cases, including SmA F The volume of the liquid crystal is at least partially bounded by a surface having a spatially varying capacitance, wherein the SmA F The molecular orientation in the material exhibits an analog response to the spatial variation of the applied voltage. According to a further example, including SmA F The volume of the liquid crystal is at least partially bounded by a surface having a spatially varying capacitance and has patterned electrodes on the bounding substrate, wherein the molecular orientation in the ferroelectric nematic material exhibits an analog response to the spatial variation of the voltage applied to the patterned electrodes.

[0019] According to yet a further example of the present disclosure, a composite material includes: a first porous material, the volume of the pores of the material containing ferroelectric smectic A (SmA F ) liquid crystal. The volume of the pores of the porous material is substantially filled with SmA F liquid crystal. A semiconductor structure may include a porous solid material, the volume of the pores of the material containing SmA F liquid crystal. A dielectric structure may include a porous, solid, electrically insulating material, the volume of the pores of the material containing SmA F liquid crystal. A capacitor may include electrodes and a dielectric medium, the dielectric medium including a porous, solid, electrically insulating material, the volume of the pores of the material containing SmA F liquid crystal. The porosity of the porous material 104 may be in the range of about 0.05 to about 0.4 or about 0.5 to about 0.95. The pore size or average pore size of the pores of the porous material 104 may be in the range of about 2 nm to about 50 nm or about 0.1 micron to about 10 microns. According to a further example, a dielectric medium includes: SmA F liquid crystal and a solid material, the solid material being dispersed as fine particles in the liquid crystal. The dielectric constant of the dielectric medium may be greater than 10 or between about 2 and about 5000.

[0020] According to a further example, a dielectric medium includes: SmA F liquid crystal and a solid material, the solid material being composed of ferroelectric or ultra-flat electric nanoparticles.

[0021] According to yet a further example, a dielectric medium includes: SmA FDispersion of liquid crystal and solid materials, the dispersion being formed by phase separation.

[0022] According to a further example, a dielectric medium comprises: SmA F Dispersion of liquid crystal and solid materials, the dispersion being formed by photopolymerization.

[0023] According to a further example, a dielectric medium comprises: SmA F Dispersion of liquid crystal and solid materials, the dispersion being stabilized by an amphiphilic molecular component.

[0024] According to a further example, a dielectric medium comprises: SmA F Emulsion of liquid crystal and fluid materials, the emulsion being stabilized by an amphiphilic molecular component. Exemplary suitable fluid materials include ionic liquids, dielectric liquids, and conductive liquids.

[0025] As described herein, the device may comprise a composite material or a dielectric medium. The device may include, for example, an energy storage device (e.g., an energy conversion device), an information storage and processing device, an actuator, a sensor, an electrothermal device, or a device for converting electrical energy into mechanical energy through an electromechanical effect, etc.

[0026] According to a further example herein, a device comprises: a volume that includes ferroelectric smectic A (SmA F ) liquid crystal-forming molecules, the volume containing SmA F liquid crystal phase, the SmA F liquid crystal phase includes a vector orientation field of dipolar SmA F liquid crystal-forming molecules throughout the volume, the dipolar molecules having a finite first hyperpolarizability β; and one or more electrical connections for applying an electric field to the SmA F liquid crystal-forming molecules.

[0027] According to a further additional example, a device comprises: a volume that includes ferroelectric smectic A (SmA F ) liquid crystal-forming molecules, the volume containing SmA F liquid crystal phase, the SmA F liquid crystal phase includes a vector orientation field of dipolar SmA F liquid crystal-forming molecules throughout the volume, the dipolar molecules having a finite first hyperpolarizability β; one or more electrical connections for applying an electric field to the SmA F liquid crystal-forming molecules; and one or more materials that include one or more surfaces in contact with the volume, wherein the one or more surfaces are configured to impart SmA FA favorable surface polarity of the liquid crystal-forming molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0028] According to a further additional example, the volume includes ferroelectric smectic A (SmA F ) liquid crystal-forming molecules, the volume containing SmA F liquid crystal phase, the SmA F liquid crystal phase includes a dipole SmA F vector orientation field of the liquid crystal-forming molecules, the dipole molecules having a finite first hyperpolarizability β; one or more electrical connections for applying an electric field to the SmA F liquid crystal-forming molecules; and one or more materials including one or more surfaces in contact with the volume, wherein the one or more surfaces are configured to impart a favorable surface polarity to the SmA F liquid crystal-forming molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0029] The various devices described herein can be used, for example, for electro-optic phase, amplitude, or polarization modulation of electromagnetic fields, non-linear optical mixing of electromagnetic fields including second harmonic generation and sum and difference frequency generation, non-linear optical terahertz (THz) electromagnetic field generation and / or sensing, non-linear optical conversion frequency, as components of a photonic integrated circuit, and the like.

[0030] According to a further additional example, the material can include SmA F fibers of liquid crystal and / or SmA F thin films of liquid crystal. These materials can be incorporated into composite materials including polymeric, amphiphilic, and / or solid components. These materials can be functional textiles or fabrics. Electro-optic devices can be formed using such materials. Exemplary fibers can have a length of about 20 μm to about 100 μm or about 1 mm to about 20 mm and / or a cross-sectional dimension (e.g., diameter) of about 5 μm to about 40 μm or about 100 μm to about 300 μm.

[0031] According to a still further example, the material including SmA F liquid crystal includes bipolar molecules having a large first hyperpolarizability β, wherein the bipolar molecules have a polar orientation order that controls the second-order non-linear optical properties of the material.

[0032] These and other embodiments will become apparent to those skilled in the art from a detailed description of certain embodiments with reference to the accompanying drawings; the present disclosure is not limited to any particular embodiment(s) disclosed. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] A more complete understanding of the embodiments of the present disclosure can be derived by reference to the detailed description and the claims when considered in conjunction with the following illustrative drawings.

[0034] Figure 1 Schematic diagrams showing the structures, phase sequences, and liquid crystal phase behaviors of the 2N, 7N, and DIO single components and their indicated mixtures.

[0035] Figure 2 Showing the N in a 50:50% 2N / DIO mixture F and SmA F X-ray scattering and polarized microscopy textures of the phases.

[0036] Figure 3 Showing the N in a 50:50% 7N / DIO mixture F and SmA F X-ray scattering and polarized microscopy textures of the phases.

[0037] Figure 4 Showing the X-ray diffraction of the periodic density modulation in the SmA phase of the 7N / DIO mixture F phase.

[0038] Figure 5 Showing the response of the SmA texture to the field and frustration in the C and D diagrams (cells with a d = 3.5 μm spacing and anti-parallel surface friction) in the SmA domain (wide normal band) that replaces the π-twisted N F phase (needle-like normal domains in Figures A - C, bright blocks in D, and triangular regions in F). F domain (wide normal band), SmA F texture pair Figure 2 to the field and frustration in the C and D diagrams (cells with a d = 3.5 μm spacing and anti-parallel surface friction).

[0039] Figure 6 Showing the I(t)–V(t) characteristics of the 2N / DIO mixture as a function of temperature, where a 30 V peak amplitude, 8 Hz triangular wave voltage (white, triangular trace) is applied to an ITO sandwich cell with d = 17 μm, the cell having a bookshelf-like stratification in the smectic phase, and the polarization value P(T) [hollow circles] is obtained by integrating the current.

[0040] Figure 7 Showing devices according to various examples of the present disclosure.

[0041] Figure 8 Showing devices according to various embodiments and examples of the present disclosure.

[0042] Figure 9 Showing the unit deformation modes for electromechanical energy conversion.

[0043] It will be understood that the elements in the drawings are shown for simplicity and clarity and are not necessarily drawn to scale. For example, the dimensions of some of the elements in the drawings may be enlarged relative to other elements to assist in improving the understanding of the illustrated embodiments of the present disclosure. Detailed Description

[0044] Although certain embodiments and examples are disclosed below, it will be understood that the invention extends beyond the specifically disclosed embodiments and / or uses of the invention and their obvious modifications and equivalents. Thus, the scope of the invention disclosed herein is not intended to be limited by the specific embodiments described below.

[0045] The present disclosure generally relates to devices comprising a ferroelectric smectic A (SmA F ) liquid crystal forming fluid, and methods of forming and using such devices.

[0046] In the present disclosure, any two digits of a variable can constitute a viable range of that variable, and any range indicated can include or exclude endpoints. Additionally, in some embodiments, any value of a variable indicated (whether or not it is indicated with "about") can refer to an exact value or an approximate value and include equivalents, and can refer to an average value, a median value, a representative value, a majority, etc. Any value (such as a percentage) can include + / - 10% or + / - 5% or + / - 2% of that value. Directions (such as normal or tangent) can include, for example, within + / - 10 degrees or + / - 5 degrees or + / - 2 degrees of that direction. Further, in the present disclosure, in some embodiments, the terms "including", "constituted by", and "having" and corresponding words can independently refer to "typically or broadly comprising", "comprising", "consisting essentially of", or "consisting of". According to various aspects of the present disclosure, any defined meaning of these terms does not necessarily exclude their ordinary and customary meanings.

[0047] Turning now to the drawings, Figure 1 Schematic diagrams showing the structures, phase sequences, and liquid crystal phase behaviors of the 2N, 7N, and DIO single components and their indicated mixtures are shown. As described more specifically below, the relevant phases of rod-like molecules having an axial electric dipole moment are shown, where the dipole direction of the schematic molecules is indicated by their normal shading. (A) Sketches of phase textures, divided into macroscopically non-polar and polar types. The experiments reported below confirm the previously described paraelectric nematic (N), antiferroelectric smectic Z (SmZ A) and ferroelectric nematic (N F ) phase as well as the new SmZ A phase. These phases appear upon cooling, and the approximate sequence relationship with T is shown by the shaded area. Note that the N F phase is missing in the 7N / DIO mixture, which allows a direct transition from smectic Z to smectic A F . The thick solid line depicts the smectic layering. The SmA F phase is a spontaneous ferroelectric phase with polarization P ~ 6 μC / cm 2 and polar order parameter p ~ 0.9, and these values are comparable to those of the N F phase of DIO and RM734. The polarization reversal is caused by the motion of pure polarization reversal domain walls. In the SmZ A phase, the antiferroelectric layer-by-layer polarization alternation causes a twist modulation of the director, but in the ferroelectric N F phase and SmZ A phase, the twist is suppressed.

[0048] Figure 2 shows the X-ray scattering and polarized microscopy textures of the N F and SmA F phases in a 50:50% 2N / DIO mixture. (A) Typical non-resonant SAXS and WAXS obtained upon cooling from N F to SmA F . In the N F phase at 57.9 °C, there is a nematic-like diffuse scattering arc that peaks along , and this diffuse scattering arc comes from the head-to-tail correlation of the mixture molecules. (B) Radial intensity scans along the n, q z direction (the white line in (A)) at different temperatures. In the case shown, due to the texture reorganization in the capillary, the azimuthal rotation of the scattering pattern is up to 10° as the smectic layers form. The initially diffuse smectic peak sharpens upon cooling, and at T ≈ 56 °C, a distinct, resolution-limited SmA F Bragg reflection appears in the n direction (as shown in the inset), which indicates a smectic ordering with the layer plane normal to n. The scattering vector corresponds to the SmA F layer spacing close to the wt% average molecular length of DIO and 2N . The SmA FThe peak position is very close to that of the nematic peak, which is also the peak expected for the orthorhombic smectic phase. Polarized light microscopy images show 50:50 wt% 2N / DIO mixtures in (C, D) antipolar cells with d = 3.5 μm thick (with antiparallel surface friction) and (E) homopolar cells with d = 3.5 μm thick (with parallel surface friction), both lacking the applied field. (C) SmA F After slow cooling to T ≈ 55 °C, irregular polygonal domain layers n and layer P grow from the top of the cell region. These layers are oriented parallel to the cell plates and are uniformly aligned throughout the volume. The existing N F is in a surface-induced π-twisted state, and P is polished along (antiparallel) at the surface. This twisted state does not bring a preferred bulk polarization orientation. Thus, the advancing SmA F domains are ambivalent in their choice of polar alignment. As shown, P is locally aligned along +z or along -z. (D) Different parts of the cell are observed when heating from SmA F to N F phase. As shown in D1, SmA F domains typically extend along z in the steady state to minimize the polarization space charge. These domains are separated by molten grain boundaries and polarization-stabilized kinks (PSK) (as shown in the inset of (E)), and these polarization-stabilized kinks mediate small changes in the orientation of P along z. In contrast, non-zero does not generate polarization charge, so that the direction of P in adjacent domains alternates with the change of y. When heating to N F , the boundaries between these adjacent domains transform into splay-bend walls (bright lines in D2, D3), and then expand into π-twisted domains that eventually cover most of the cell (D4, D5). (E) In homopolar cells, a uniform single domain is formed upon cooling. Its n in the N F and SmA F phases is usually along the polishing direction, providing excellent extinction, while P is along the preferred polar orientation in the N F phase. The image shows the texture around the bubbles that extend through the entire thickness of the cell. The preferred orientation of P on the bubble boundary is tangential. On the bubble meridian, this boundary condition is compatible with the preferred uniform polarization on the cell surface. But elsewhere, n and P are distorted inside the cell to adapt to this boundary condition, and the cell has a non-extinguishing yellow-green transmission color. This non-uniform state persists until the curved dashed line above the bubble, where the director field returns to the preferred uniform state. The lines of these polarization-stabilized kinks are overall parabolic, which have a local structure that minimizes the polarization charge (as shown in the inset), while mediating the change in the direction of P. Once SmA FGrowth, exclusion of layer distortions and bending forces more area around the bubble into a homogeneous state, with the inhomogeneous regions confined to small areas near the bubble. Residual transmission in the regions near the bubble may be due to dislocations in the SmA F stratification. Scale bars: (C) 500 μm; (D) 200 μm; (E) 100 μm.

[0049] Figure 3 Shows X-ray scattering and polarization microscopy textures of the N F and SmA F phases in a 50:50% 7N / DIO mixture. (A) Typical non-resonant SAXS obtained on cooling from SmZ A to SmA F . In the SmZ A phase at 43.6 °C, the SAXS shows a diffuse scattering arc that peaks along n , from head-to-tail correlations of the molecules in the mixture, and these features are also observable in the diffraction pattern of DIO. (B) Radial intensity scans along the n, q z direction (white line in (A)) at different temperatures. As with the 2N mixture, reorganization of the texture within the capillary due to replacement of the SmZ A layers by SmA F layers causes the scattering pattern to rotate and broaden. Scattering from the SmZ A stratification is not visible here but is shown in Figure 4 . On cooling, the diffuse peak sharpens, the SmZ y stratification along q A weakens and disappears, and at T ≈ 31 °C, a clearly resolution-limited Bragg reflection appears along q z (as shown in the inset), which indicates a smectic ordering with the layer planes normal to n. The scattering vector corresponds to the SmA F layer spacing close to the wt% average molecular length of DIO and 7N . The position of the SmA F diffuse peak is very close to the position of the diffuse nematic peak, which is also the peak expected for an orthorhombic smectic phase. (C, D) Polarization microscopy images of antipolar cells with d = 3.5 μm and electrode spacing of 1 mm (white dashed line) for applying an in-plane field normal to the polished direction z. The planar-aligned SmZ A texture shows only subtle changes on transition to SmA F (C1, C2). This is because the antiparallel polishing, while orienting the director, does not bias either antiferroelectric polarization direction, such that in the transition, the nanoscale antiferroelectric SmZ normal to yA The layer is only coarsened into a SmA that extends in z along the new layer normal F domain, and is alternately polarized along y. The director remains consistent during this change, making these two phases look very similar. However, applying a small electric field (C3 - C6) along the y direction causes the directors in the stripes of opposite P to rotate away from extinction in opposite directions, thus generating optical contrast and confirming their opposite polarities. The circular black regions are bubbles, which effectively shield the applied electric field in the adjacent liquid crystal, leaving the original texture undisturbed. (D) Annealing after such field treatment produces an inhomogeneous fan-shaped texture (D1, D2). In the applied field, these domains reorient, bend, and coarsen in a sufficiently large applied field to form large domains where n, z, and P are all oriented along the field, normal to the polishing direction (D3 to D5). Therefore, during field-induced reorientation, n, z, and P remain coupled together, and this threshold stems from the elasticity and plasticity of the smectic layering. This threshold also results in a coercive field in the polarization hysteresis ( Figure 6 ). N F phase is easily reoriented by the weak stray applied field on the electrodes. However, in the SmA F phase, there is a field threshold for such reorientation, so the field effect is confined to the electrode gap. Scale: The electrode gap (white dashed line in C) is 1 mm wide.

[0050] Figure 4 Shows X-ray diffraction of the periodic density modulation of the SmZ A phase in 7N / DIO and 2N / DIO mixtures. Panels (A) to (C) use the color scale as shown in (C) and show the full SAXS images of the scattering intensity I(q) respectively. The rectangular overlay shows the histogram stretching and I(q) after using the color scale in (B), thus revealing weak scattering peaks from the SmZ y layer modulation along q A . Aligning by the magnetic field B in the nematic phase, but the rearrangement of the sample in the capillary during cooling results in some inhomogeneity in the orientation of the SmZ A and SmA F layers. (A) At T = 36 °C, the 7N / DIO mixture is in the SmZ A phase, as evidenced by the scattering along q y . Along q z , the diffuse peak parallel to the director comes from short-range, end-to-end molecular correlations. The SmZ A peak position is at , corresponding to the layer spacing, which is essentially independent of T. (B) Cooling to T = 31 °C triggers a weak first-order phase transition to SmA F , and SmZ A and SmAF layers simultaneously produce intense scattering, thus indicating SmZ A / SmA F phase coexistence. The SmZ A peak appears as an extended arc at this temperature. The SmZ A scattering disappears approximately 0.5 °C after the start of the SmZ A -SmA F transition (i.e., there is a narrow temperature range where both the SmZ A peak and the SmA F peak exist), which we attribute to the two-phase coexistence during a first-order transition. (C) Diffraction of the 2N / DIO mixture at T = 71 °C, located in the middle of the SmZ A phase region. (D) Radial scan of the scattering intensity along q z obtained by averaging I(q) within the q z range (white line in C and D) around q y = 0, which includes the SmZ A peak (B)'s low-temperature sweep shows the SmZ peak at A , as well as the SmA scattering at F . Although making the SmZ A peak small, its intensity is several orders of magnitude smaller than the SmA z peak along q F .

[0051] Figure 5 shows that in the SmA F domains (wide normal bands) that replace the π-twisted N F phase (needle-like normal domains in A - C, bright blocks in D, triangular regions in F), Figure 2 the SmA F texture in the cells of C, 2D (cells with d = 3.5 μm spacing having anti-parallel surface friction) responds to fields and frustration. The twisted N F does not bias the polarization preference, so domains of either of the two P's appear spontaneously. (A - C) This can be tested by applying an in-plane electric field E (essentially normal to n and P) in the transverse plane to the area of a domain with a generally oriented director. The opposite-induced rotations in (A) and (C) verify the macroscopically uniform polarization within the domain. (D, E) Inclusions of the rhombic twisted N F mediate the inversion (D) or termination (E) of the up-down pair of SmA F domains. The white domain boundaries in E are polarization-stabilized kinks (PSKs), which stabilize the local reorientation of P by the attraction of sheets of polarization charges with opposite signals, as Figure 2as shown in (E).

[0052] Figure 6 shows the temperature-dependent I(t)–V(t) characteristics of the (A) 2N / DIO mixture, where a 30 V peak amplitude, 8 Hz triangular-wave voltage (white triangular trace) is applied to an ITO intercalation cell with d = 17 μm, and the intercalation cell has a bookshelf-like stratification in the smectic phase. The curve shows N→SmZ A →N F →SmA F current response during the cooling scan. In the N phase (T > 84 °C), the current shows an ionic peak only after the sign change of V(t). In the SmZ A phase (84 °C > T > 68 °C), during this half cycle of the applied voltage, the areas of two polarization peaks can be seen to continuously expand and appear at a smaller voltage upon cooling. This is typical antiferroelectric behavior, and these peaks mark the transition at a finite voltage between the field-induced ferroelectric state and the equilibrium antiferroelectric state. In the N F phase, the reorientation mediated by the Goldstone mode appears to be “thresholdless”, and the reversal of P generates a current peak at the zero crossing of V(t), followed by an ionic peak at t > 0. The polarization measured in this phase is comparable to that of pure DIO. In the SmA F phase, the ionic current disappears and a polarization reversal peak appears at the positive voltage corresponding to the coercive field E c as shown, taking 34 °C as an example (the normal arrow starts from the right peak of the 34 °C curve, resulting in the horizontal arrow terminating on the right side of the applied field axis). The temperature sequence of the I(t) curves is 135 °C, 130 °C, 125 °C, 120 °C, 115 °C, 110 °C, 105 °C, 100 °C, 95 °C, 93 °C, 91 °C, 89 °C, 87 °C, 85 °C, 83 °C, 81 °C, 79 °C, 77 °C, 75 °C, 73 °C, 71 °C, 69 °C, 67 °C, 65 °C, 63 °C, 61 °C, 59 °C, 57 °C, 55 °C, 53 °C, 51 °C, 49 °C, 47 °C, 45 °C, 43 °C, 41 °C, 39 °C, 38 °C, 37 °C, 35 °C, and 34 °C. (B) The polarization value P(T) [open circles] is obtained by integrating the current. In the SmZ A phase, the polarization current generated by each zero crossing of V(t) overlaps with the ionic current, so in this case, P(T) is obtained by doubling the area of the current peak generated before the zero crossing. The coercive field E c is also shown as a function of T [solid symbols]. Note that in the N F and SmA F phases, due to the screening of the polarization charge, the electric field in the ferroelectric phase is usually very small, so ionic peaks are not observable.

[0053] In the 1910s, P. Debye and M. Born predicted the correct ferroelectricity in liquids. They applied the ferromagnetic Langevin - Weiss model to propose a liquid - phase transition, where the order - transition is the spontaneous polarization orientation of molecular electric dipoles. A century later, in 2017, two groups independently reported new nematic phases in strongly dipolar mesogens in addition to the typical nematic (N) phase, namely the "flat - on nematic" in molecule RM734 and the "ferroelectric - like nematic" phase in molecule DIO, as shown in Figure 1 (B). These nematic phases were subsequently shown to be ferroelectric in both RM734 and DIO and are the same phase in these two materials. This new phase, ferroelectric nematic (N F ) is a uniaxially symmetric, spatially homogeneous nematic liquid that has polar ordering of longitudinal molecular dipoles. A related new phase recently observed is the helical ferroelectric N F obtained by chiral doping of RM734, DIO, or their homologues, or by introducing a chiral tail into the molecular structure. DIO also exhibits an additional phase found between N and N F , which we recently characterized and named smectic Z A , and showed that it is also new: a density - modulated antiferroelectric that exhibits a lamellar ordering with a repeat of about 18 nm, consists of layers about 9 nm thick with alternating polarization, and the director and polarization orientation are parallel to the layer plane. It should be noted that although specific molecules are pointed out in this article, unless otherwise stated, the present invention is not limited to these examples.

[0054] Here, we introduce another new phase in the field of ferroelectric nematics, smectic A F , a uniaxial lamellar phase whose director is normal to the layer and has spontaneous polarization along the director. Figure 1 Sketches the schematic diagrams of the phases discussed here, divided into macroscopically non - polar and polar types, and shows the molecular structure and phase sequence of the mesogenic molecules used in the mixtures. Figure 1 (A) Sketches the macroscopically non - polar, paraelectric nematic (N) and smectic A (SmA) phases, ferroelectric nematic (N F ) and ferroelectric smectic A (SmA F ) phases and antiferroelectric SmZ A phase. The light and dark shading of the schematic molecules indicates their dipole symmetries. The SmA F phase can be observed in 50:50 wt% AUQU2N / DIO (2N / DIO) and AUQU7N / DIO (7N / DIO) mixtures; other weight ratios may also be applicable. Figure 1 The shaded area in (A) shows the general phase sequence (Iso → N → SmZ observed upon cooling in the mixture.A →N F →SmA F →X), note that some phases may be missing in a given component or mixture. For example, no single component exhibits the SmA F phase, and the 7N / DIO mixture does not have the N F phase. The first mesophase that appears upon cooling either a component or a mixture from the isotropic state is the conventional dielectric nematic (N) phase, which is also considered paraelectric in the present case. They all cool from N to the antiferroelectric smectic Z (SmZ A ) phase.

[0055] Then, the 2N / DIO mixture first transforms to the N F phase and then to the SmA F upon further cooling, while the 7N / DIO transforms directly to the SmA F . This allows for a comparative study of the N F →SmA F and SmZ A →SmA F transformations. The latter is characterized by the disappearance of the SmZ parallel to the director without any reorientation of the director / polarization and the formation of the SmA normal to the director. A stratification while disappearing and the formation of the SmA normal to the director. F stratification.

[0056] In contrast to the conventional dielectric smectic A phase, the ferroelectric smectic A phase exhibits a macroscopic polarization P, with the polarization in each layer pointing in the same direction along the director n normal to the layer plane. The phase is uniaxial and has a high degree of polar order (polar order parameter p > 0.9). In regions with continuous smectic stratification, domains of opposite polarization separated by polarization reversal walls ( Figure 1 (sketched in (A)) can be observed.

[0057] This ferroelectric phase is different from several previously described uniaxial "polar smectics", including the monolayer paraelectric SmA1 phase, the partially bilayer SmA d phase, the antipolar bilayer SmA2 phase, and the polarization modulation phases of multiple dipole molecules (Sm, Sm, etc.), as they all have a zero net average polarization. Tournilhac and colleagues initially claimed that, based on evidence of piezoelectricity and nonlinear dielectric behavior, a macroscopic polarization normal to the layers in a small molecule, smectic A phase had been observed, but their subsequent X-ray scattering studies revealed a cell-doubling of the smectic unit cell, leading to the conclusion that the relevant phase was a bilayer smectic phase of the SmA d type and that the observed electrical effects were indicative of bilayer antiferroelectricity. SmA FIt is also different from the orthogonal polar smectic phases exhibited by some bent-core mesogens, which form biaxial smectics with a spontaneous polarization oriented parallel to the smectic layers.

[0058] Exemplary embodiments

[0059] X-ray scattering - We have previously performed Figure 1 (B) X-ray diffraction, polarized microscopy, and polarization measurements on the single-component DIO and 2N, 7N shown. Here we focus on the binary mixtures 2N / DIO and 7N / DIO. All our observations indicate that the N, N F SmZ A and SmA F phases exhibit common experimental features and each appears as the same phase in different materials: the N phase is a homogeneous, uniaxial nematic phase, the N F phase is a homogeneous, uniaxial nematic phase with a macroscopic polarization along the nematic director, and SmZ A is the same bilayer antiferroelectric phase in all components and mixtures, with a layer spacing in DIO of in the 2N / DIO mixture of in the 7N / DIO mixture of The period of the alternating antiferroelectric polarization layer by layer is 2d M .

[0060] Here, we describe the LC behavior of 50:50% 2N / DIO and 7N / DIO mixtures, both of which exhibit SmA F . We find that these mixtures show: (i) similar SAXS from the SmA F layering, with a smectic layer spacing close to the average molecular length; (ii) similar uniaxial birefringence; (iii) similar SmA-like optical textures; (iv) similar SmA F response to surface alignment conditions and the applied electric field; and (v) similar SmZ A and SmA F polarization reversal kinetics. Since SmA F expands differently upon cooling, 2N / DIO comes from the N F phase and 7N / DIO comes from the SmZ A phase, we describe the two mixtures separately because this condition strongly affects the texture morphology of SmA F .

[0061] In the SAXS and WAXS experiments, the mixture was filled into a thin-walled capillary with a 1 mm diameter and aligned the director n by an external magnetic field B (arrow) ( Figure 2 (double-headed arrow in (A)). The SAXS and WAXS were non-resonant, and the diffraction images of the samples were obtained in transmission at the SMI beamline (12-ID) at NSLS II, with a microbeam energy of 16.1 keV and a beam size of 2 μm × 25 μm.

[0062] 2N / DIO—Typical SAXS and WAXS images obtained upon cooling a 50:50% 2N / DIO mixture from the N F phase to the SmA F phase are shown in Figure 2 (A). In the N phase at T = 57.9 °C, we observed a nematic-like diffuse scattering arc that peaks in the azimuthal orientation of the scattering vector q along n, which comes from the head-to-tail correlation of the molecules along n. F Figure 2 (B) shows a line scan of the scattering intensity through these peaks. As visible in the inset of Figure 2 (B), the SmA F phase is heralded by new, resolution-limited peaks along q z , and the SmA F phase first appears at at T ≈ 56 °C, with the wavevector very close to that of the diffuse nematic peak at . This behavior indicates a first-order phase transition from N F to SmA F , which is consistent with our polarized light microscopy observations. The corresponding layer spacing is , which is comparable to the concentration-weighted average molecular length of and . The absence of the half-order peaks at q z = q zAF / 2 in the SAXS image indicates that no bilayer fluctuations or ordering tendencies in the SmA F phase were observed in this mixture. Figure 2 (A) The WAXS diffraction image shows second-harmonic scattering of the layers at . In the magnetically aligned samples, the full-width at half-maximum mosaic distribution of the azimuthal angle of n was initially about 5°. Due to the dynamic texture rearrangement in the capillary, the scattering pattern rotates upon cooling into the SmA F phase, and at lower temperatures, due to the magnetic torque not being strong enough to maintain the alignment of the increasingly rigid smectic layers, some detectable scattering from the layering is present at all azimuthal angles.

[0063] 7N / DIO—Cooling a 50:50% 7N / DIO mixture from the SmZ A phase to the SmA F phase yields the typical SAXS diffraction images shown in Figure 3 (A) and Figure 4 . The SmA F scattering is qualitatively similar to that of the 2N / DIO mixture. In the SmZ A phase at T = 43.6 °C, SAXS shows a diffuse, nematic-like scattering arc that peaks at the scattering vector q along n, which arises from the head-to-tail correlations of the molecules along n||z. Figure 3 (B) shows a radial line scan of the scattering intensity along n ( Figure 3 the white line depicted in (A)).

[0064] As Figure 3 shown in the inset of (B), like the 2N / DIO mixture, the SmA F phase is characterized by new, resolution-limited peaks along q z . This SmA F phase first appears at ≈ 31 °C, at the maximum of the scattering nematic peak. The corresponding layer spacing is which is comparable to the concentration-weighted average molecular length of and . The absence of the half-order peaks at q z = q zAF / 2 in the SAXS images again indicates no tendency to form bilayers. As in the DIO / 2N mixture, due to the dynamic texture rearrangement caused by the varying temperature in the capillary, the scattering pattern in the SmA F phase rotates. In the SmA F phase, the scattering arc becomes broader due to the reduced effectiveness of magnetic field alignment upon cooling.

[0065] Finally, Figure 4 shows the equatorial Bragg spots at q y = q yM which arise from density modulations due to the smectic layering of the SmZ A . These are observed in both the 2N / DIO and 7N / DIO mixtures but are not visible in Figure 2 (A) or Figure 3 (A) due to their relative weakness.

[0066] Polarized optical transmission microscopy enables the direct visualization of the director field, n(r), and P(r) except for the sign. These observations provide insights into the SmA of the 2N / DIO and 7N / DIO mixtures FThe macroscopic ferroelectric ordering of the phase, the uniaxial optical texture, and the fluid layer structure provide key evidence.

[0067] 7N / DIO—The 50:50% 7N / DIO mixture was studied in d = 3.5 μm cells (antipole cells) with antiparallel surface friction, which had planar electrodes separated by a 1 mm gap on one surface. In the N phase, the LC formed a uniform alignment single domain with n along the polishing direction, which was the same as previously observed in the N phase of DIO. As Figure 3 (C1, C2) shows, in the 7N / DIO mixture without an applied field, the appearance of the sample changed little with the temperature in these cells, and the nematic texture remained unchanged upon cooling to the SmZ A and SmA F phases. During the SmZ A to SmA F transition, the SmZ A layers parallel to n disappeared, while new SmA F layers normal to n formed. During the N→SmZ A →SmA F cooling sequence, the birefringent colors were uniform throughout the cell and changed only slightly, providing evidence that the phase was uniaxial or only weakly biaxial and that the optical anisotropy in all three phases was nearly the same. The uniaxiality of the N phase and the weak biaxiality of the SmZ A have been demonstrated previously.

[0068] The SmZ A layers adopt a bookshelf geometry, with the smectic layers normal to the plates and the Rapini - Papoular type anchoring of the molecules aligning the director along the friction direction. The antiferroelectric SmZ A (whose P values alternate layer by layer) to the ferroelectric SmA F phase transition is achieved through a coarsening process in which layers with the same sign of P coalesce into wider, uniformly polarized stripes extending along z, thus forming irregular, needle - shaped, alternately polarized ferroelectric domains in the SmA F . In the absence of an applied field, this process only produces subtle changes in the texture (compare Figure 3 (C1 and C2)), while applying an in - plane electric field normal to n causes the P to rotate in opposite directions in domains with opposite polarizations, thus promoting and inducing the coarsening of the domain pattern ( Figure 3 (C3 to C6)). This electric - field response becomes increasingly drastic as the stripes coarsen from the nanoscale to the microscale.

[0069] As Figure 3 (D1, D2) shows, after a long - time application of a weak electric field, the SmA FThe cell is annealed without any further applied field and becomes long, rectangular bookshelf domains with uniform birefringence and excellent extinction, which is typical of a weakly oriented smectic A texture. A sufficiently large transverse DC field can fully reorient the SmA F layer such that P and n are aligned along E (normal to the polishing direction) ( Figure 3 (D5)). In the N F phase, this global, field-induced reorientation is essentially thresholdless and thus easily reversible upon reversal of the applied field, but in the SmA F phase, there is a distinct threshold for the switching and hysteresis of the response, which is evident in the Figure 5 polarization data. This behavior can be understood by considering that a spatially uniform field-induced reorientation of SmA F can only be achieved by generating a group of glide edge dislocations (an inherently nonlinear process). The effect of this threshold is immediately obvious in the electro-optic behavior of cells with in-plane electrodes. In the applied field, these domains reorient, bend, and coarsen in a sufficiently large applied field to form large domains in which n, z, and P are all oriented along the field, normal to the polishing direction Figure 3 (D3 to D5). Thus, during field-induced reorientation, n, z, and P remain coupled, and this threshold arises from the elasticity and plasticity of smectic layering. This threshold also results in a coercive field in the polarization hysteresis ( Figure 6 ). N F typically responds readily to an in-plane applied electric field present anywhere in the cell, including above metal or ITO electrodes, even to a small fringe field far from any electrode. In contrast, in the SmA F phase, this response becomes subthreshold and is eliminated from these peripheral areas, and the electro-optic effect is limited to the designated active area of the cell where the field is strongest, as seen in Figures D3 to D5.

[0070] An interesting side observation is the lack of field response in the left and right regions of the bubble in Figure 3 (C3 to C6). This "shadow" effect is a direct consequence of the ferroelectric nature of the SmA F phase. The bubble in the middle of the gap between the electrodes becomes a series of impedance connections: the left / right electrodes and right / left boundaries of the bubble filled with SmA F and the bubble filled with air. Due to the reorientation of the large polarization density, the region filled with SmA F has a lower electrical impedance, while the bubble capacitance is smaller, thus losing most of the applied voltage and having little field response in the adjacent LC.

[0071] 2N / DIO—The 50:50% 2N / DIO mixture was studied in antipolar d = 3.5 μm cells (with antiparallel surface polishing) and homopolar d = 5 μm cells (with parallel surface rubbing).

[0072] In the antipolar cells, the surface anchoring is in the N F phase where a twisted structure is imposed, in which the director / polarization field n(r), P(r) rotates by β through the thickness of the cell. Figure 2 (C) shows the transition from the first-order N F to SmA F upon cooling of the cell. The twisted N F state (shown as broad, scattered domains in the lower part of these images) has a somewhat rough texture, while the SmA F domains with uniform birefringence expand as smooth dark and bright bands or rectangular blocks in the upper part of the field of view. The uniformity of the birefringence color and the SmA F domains can be observed to rotate extinction between crossed polarizers, indicating that the twist has been expelled and that the director is locally uniform throughout the cell along the main optical axis of n, with n(r) uniformly parallel to the plates. The expanded SmA F domains are not initially strongly aligned in orientation by the cell surface, most likely due to the conflict of these polar domains towards the antipolar surface. F Figure 5 (A - C) show the results of the application of a weak probe electric field normal to the director, thus confirming that each domain is internally uniformly polarized (black / white arrows), with its orientation along the local director, some pointing upward and some downward. Since the smectic A F layering precludes bending and twisting of n(r), and precludes flattening of n(r) in order to eliminate polarization charges, resulting in a steady-state texture of uniformly oriented SmA F blocks, as shown in Figure 2 (D), in which there are distinct domain boundaries parallel or perpendicular to n. As sketched in the inset of Figure 2 (E), the boundaries parallel to n (roughly vertical in these images) are polarization reversal walls, as found in the N F phase, while those perpendicular to n are molten grain boundaries, this type of grain boundary being commonly found in the SmA phase but not fully aligned due to weak rubbing, or polarization-stabilized kinks (PSKs). The change in the signal of P(r) across the horizontal boundaries would generate maximum space charge and is therefore avoided, where the jump in the orientation of P(r) at these positions should be limited to 10° or less. As visible in Figure 2 (D) and Figure 3 (D), generally, there are formed long SmA F ​Trends in the domain. The internal variation of the orientation within the block is typically a few degrees and tends to be curved in orientation, which must be mediated by edge dislocations in the SmA F layered system.

[0073] Figure 5 (D - F) show a more detailed structure of the transition mechanism that mediates the expansion of the uniform SmA F domain into the distorted region. Here, a PSK domain boundary with a polarization direction is formed in the mid - plane of the sample indicated in Figure 5 (E), and the remaining rhombic N F distorted domains are connected to the surrounding uniform SmA F domains. A similar structure constitutes the zig - zag SmA F –N F boundary line.

[0074] If the SmA F is heated back to the N F phase, the elimination of the layer confinement enables the polarization - reversal walls to reorganize into nematic splay - bend walls extending along the director and separated by areas of uniform polarization (as shown in Figure 2 (D2), Figure 3 ). In the absence of layering, the horizontal melting grain boundaries disappear, while the horizontal PSK lines can persist into the N F phase but then also melt, leaving only the splay - bend walls (the bright lines in Figure 2 (D2), Figure 3 ). Due to the anti - parallel boundary conditions, the initially uniform N F state is only relatively stable, and the intrinsic twist core of the splay - bend walls acts as nucleation points for the formation of low - energy distorted domains that eventually spread over the entire area ( Figure 2 (D5)).

[0075] In the homochiral cell, the surface treatment stabilizes a single domain in which n is uniformly aligned along the polishing direction. As visible in Figure 2 (E), during the cooling of the N–SmZ A –N F –SmA F phases, the texture and birefringence of these single domains hardly change, showing excellent extinction between the crossed polarizers in the N F and SmA F phases (except near the bubbles). The first image shows a uniform background N FHow the director field is distorted to accommodate the non-uniform n(r) orientation imposed by the boundary conditions at the bubble boundary, where the n(r) field is tangential, this configuration only requires bending of the director and minimizes the amount of space charge deposited at the LC / air interface. On the sides of the bubble, the distortion of the director field relaxes continuously with distance, and the director field eventually becomes indistinguishable from the surrounding uniform state. However, at the top and bottom of the bubble, the 90° angle mismatch of the circumference P(r) with the uniform background is accommodated by a "break" in P(r) in the form of a polarization-stabilized kink in the inset. The PSK has the minimum energy discontinuity in P(r), and its internal structure is determined by the balance of Frank elasticity and electrostatic interactions, the latter manifested as attraction between sheets of polarization charges of opposite signs (as shown just above and below the wall in the inset), thus stabilizing the wall. The kink orientation locally bisects the angle of the incoming and outgoing P(r) directions, thus forming a global parabolic boundary with the minimum bulk polarization charge between regions with uniform and circularly bent director fields. This 2D parabolic texture is easily observed in the N F cells, which is the typically preferred orientation of P(r).

[0076] In the N F –SmA F transition, due to the emergence of SmA stratification, the area of the uniform director orientation expands. In the absence of edge and screw dislocations, in a non-polar smectic A with non-uniform alignment, the smectic can exclude the bending and distortion of n(r), thus allowing the layered defects only in the form of focal conic domains, because these defects only require the flattening of n(r). However, in the polar SmA F phase, due to the associated polarization charges, the flattening is also suppressed, resulting in a strong tendency to form uniform n(r) domains. As shown in the second image of Figure 2 (E), as the smectic layers form upon cooling, the size of the bent director region near the bubble (where n(r) has both bending and distortion) also decreases accordingly. The remaining bent and distorted director regions near the bubble must be accommodated by edge and screw dislocations in the SmA stratification.

[0077] Polarization dynamics and field-induced phase transitions—Polarization is measured in a d = 17 μm ITO intercalated cell with bookshelf stratification using a triangular wave with a low frequency (8 Hz) and a peak amplitude of 30 V. The electrical response of the 2N / DIO mixture is summarized in Figure 6 In Figure 6 (A), at the beginning of the current-voltage cycle shown, the applied voltage is large and negative (V(t) ≈ -30 V), at which time any ions have been pulled to the cell surface. In the N phase (T > 84 °C), the current shows an increase after the sign change of V(t). At this time any ions have been pulled to the cell surface. In the SmZA In the phase (84 °C > T > 68 °C), an LC repolarization peak appears when the voltage decreases, its area continuously expands, and the peak center voltage V FA becomes smaller upon cooling, and the behavior is very similar to that of pure DIO. This is typical antiferroelectric behavior, and these peaks mark the return to the antiferroelectric ground state at a finite voltage of the field-induced ferroelectric state. In SmZ A phase, the polarization current interacts with the ionic current in a complex manner after each sign change of V(t), so P(T) is obtained by doubling the area of I(t) to the left of the t = 0 axis (before the zero crossing of the applied voltage), when there is no ionic current. In N F phase, the reorientation mediated by the Goldstone mode and the inversion of P generate a current peak at the zero crossing of V(t), followed by an ionic peak at t > 0. The P(T) as the area of the large peak is found to be comparable to that of pure DIO. In SmA F phase, at a finite voltage corresponding to the coercive field E c , the ionic current completely disappears and the polarization inversion occurs after the zero crossing, as shown by the solid symbols in Figure 6 (B) and schematically shown in the adjacent hysteresis loop.

[0078] The ferroelectric smectic A phase adds an exciting new dimension to the field of ferroelectric nematics. Ferroelectric nematics, chiral ferroelectric nematics, and antiferroelectric smectic Z A have already opened unexpected doors for new soft matter science and technology, and here smectic A F joins this development. SmA F is a layered spontaneously polar fluid, the long-sought-after proper ferroelectric smectic A liquid, and its macroscopically reorientable spontaneous polarization is now clearly demonstrated. The transition to SmA F , whether from N F to SmA F or from SmZ A to SmA F , is first-order and quite subtle in cells with parallel polar surface anchoring, and its texture and many phase properties show continuity in the transition. In N F , the polarization remains about 90% saturated, so in SmA F , this is related to the long-range side-by-side molecular alignment implied by the smectic A layer ordering. This is something of a puzzle because side-by-side is the highest energy arrangement of similarly oriented dipoles.

[0079] Materials and methods

[0080] The mixtures were studied using standard liquid-crystal phase analysis techniques, including observation of the LC texture by polarized transmission optical microscopy and its response to an electric field, X-ray scattering (SAXS and WAXS), and techniques for measuring polarization and determining the electro-optic response.

[0081] Materials— Figure 1 The DIO shown was synthesized for these experiments. Figure 1 AUUQU2N and AUUQU7N in were synthesized in a manner analogous to that of AUUQU3N.

[0082] X-ray scattering—For SAXS and WAXS, the LC samples were filled into thin-walled capillaries with a 1-mm diameter. The director n was aligned with an external magnetic field normal to the beam. The diffraction data presented here were obtained at the SMI beamline at NSLSII with a photon energy of 16 keV. At this wavelength, the desired range of scattering vectors covers a small range of scattering angles (θ < 3°), such that the Ewald sphere can be approximated by an Ewald plane (q y 、q z ), which is normal to the beam, where z is along the magnetic field B direction and the director n is oriented. The SAXS and WAXS images of 2N, 7N, and their mixtures with DIO obtained by cooling from Iso to the nematic phase show that there are strong diffraction scattering features at and respectively, which arise from end-to-end and side-by-side molecular position pair correlations characteristic of such polar media.

[0083] Electro-optic—For electro-optic measurements, the mixtures were filled into a planar-switching test cell with planar alignment, with unidirectionally polished alignment layers on both plates. Cells with antiparallel polishing on plates with a spacing d = 3.5 μm and cells with parallel polishing on plates with a spacing d = 5 μm were used. The in-plane ITO electrodes were spaced 1 mm apart, and the polishing was parallel to this gap. Such surfaces align the N and SmZ A directors quadrupole-wise along the polishing axis and polarize the N F polarity-wise on each plate. Antiparallel polishing stabilizes the twisted configuration in the N F phase, generating a director / polarization field parallel to the plates and undergoing a π twist between the plates. Parallel polishing generates a polar single domain in the N F and SmA F phases.

[0084] Polarization measurements—We measured the temperature dependence of the I(t)-V(t) characteristics of a 50:50 wt% 2N / DIO mixture with an AC electric field applied along n. During the N→SmZ A →N F →SmA F cooling scan, the current in response to a triangular wave of 8 Hz, 30 V peak amplitude was measured in a d = 17 μm ITO sandwich cell with a bookshelf stratification.

[0085] Figure 7 Device 1300 according to various examples of the present disclosure is shown. Device 1300 includes a volume 1302 containing a ferroelectric smectic A (SmA F ) liquid crystal-forming fluid and means (e.g., plates or surfaces 1304, 1306, etc.) for containing the fluid. For example, the plates or surfaces may include glass, polymers (such as PET, polycarbonate, etc.). In the example shown, device 1300 also includes one or more polymer layers 1310, 1312 and / or electrodes. Exemplary polymers for layers 1310, 1312 include polyimide. Surfaces 1311 and / or 1313 may be polished using, for example, flannel.

[0086] Figure 8 Another device 500 according to various embodiments and examples of the present disclosure is shown. Device 500 includes a volume 502, one or more materials 504, 506, the one or more materials 504, 506 including one or more surfaces 508, 510 in contact with the volume 502. Device 500 also includes one or more electrical connections 512, 514 that can be coupled to electrodes (such as electrode 1308 or the electrodes described below) for applying an electric field to the volume and means 516 for applying an electromagnetic electric field to the volume.

[0087] Figure 9Shows the deformation modes of a cell for electromechanical energy conversion. The ferroelectric smectic A material 906 is filled between the planar electrodes 902, 904 on the surfaces 901, 903, and the smectic layers 908 - 914 are parallel to this surface. (A, B) In - plane shear of the smectic layer generates current. In (A), the polarization is normal to the layer. The polarization charges at the surface are balanced by the free charges on the electrodes. (B) Shearing parallel to the electrodes causes re - orientation of the polarization, thereby reducing the surface polarization charge density and resulting in a potential difference between the electrodes. In such a periodic shear system, a dynamic current can be generated through an external circuit. (C - E) Bending of the smectic layer generates current. In (C), there are three parallel electrodes at each surface. In the absence of mechanical deformation, the smectic layer is strain - free and the free charges are uniformly distributed along the electrodes. Bending of the layer (D, E) causes the bound charges and free charges to accumulate in the central region of the bend. The imbalance of free charges between adjacent electrodes can be used to generate a current through the external circuit.

[0088] There are three main types of deformations of the director field of liquid crystals: splay, bend, and twist. In conventional (non - polar) smectic A materials, the bend and twist of the director field vector are largely suppressed because these deformations disrupt the preferred uniform layering. However, splay of the director is allowed, and this deformation corresponds to bending of the layer and is largely achieved without affecting the layer spacing.

[0089] In the ferroelectric smectic A phase, the presence of a large, macroscopic, ferroelectric polarization P can give rise to new electromechanical effects, thus laying the foundation for new types of electromechanical devices. Any splay of the polarization P generates polarization space charge whose associated electrostatic energy is proportional to the square of the polarization (E P ∝P 2 ). The electric field generated by the polarization charge increases the bulk electrostatic energy by an amount:

[0090]

[0091] where k=(1 / 4π∈) and ∈ is the dielectric constant of the liquid crystal. Since the director n and P are collinear, this results in an effective rigidity of the director field in response to splay deformation. Assuming an amplitude δP y (r) of the polarization δP y (r) and a wave vector q y for a periodic transverse modulation such that in our geometry we have an elastic energy density:

[0092]

[0093] where K Sis the Frank splay elastic constant of the liquid crystal. This expression has the usual form of the Frank free energy density, which has an effective splay elastic constant K eff , given by:

[0094]

[0095] The inverse-square dependence of the wave vector of the contribution of polarization to the effective elastic constant means that the polarization term will be dominant in , where is the polarization self-penetration length. Since for P = 6 μC / cm 2 , we have ξp ∼ 0.1 nm, this dominance will persist up to the molecular length scale.

[0096] Thus, in the SmA F phase, in addition to suppressing bending and twisting, splay can also be expelled, resulting in a "soft crystal". However, by applying sufficient mechanical stress, we can introduce a deformation of the director field and convert the work done into electrostatic energy that can drive a current in an external circuit. Figure 9 Two examples of such applications are shown below.

[0097] First, as Figure 9 (A), in a cell with a parallel-plate capacitor geometry and a smectic layer initially oriented parallel to the electrodes, the surface depolarization charges at the cell boundaries will be balanced by the free charges on the electrodes. As Figure 9 (B), the liquid-like nature of the smectic layer ensures that when the cell is sheared along a direction parallel to the layer, the shear viscosity is small. This shear action couples to the director field and causes a tilt of the polarization, which results in a reduction of the surface depolarization charges. The mismatch between the free charges and the surface depolarization charges introduces a voltage V = P d(1 - cosθ) across the electrodes, where d is the cell thickness and θ is the tilt angle caused by the shear. This electrokinetic signal is unique to the SmA F phase and does not exist in conventional SmA without ferroelectric polarization. The signal of the induced voltage alternates with the shear direction, and the response can be used for a dynamic electromechanical energy converter.

[0098] In the second example, the liquid crystal material is again filled into a cell with a parallel-plate capacitor geometry, and the smectic layer is parallel to the electrodes. In this case, there are multiple electrodes at each surface, but as Figure 9 (C) shows, the surface depolarization charges are similarly uniformly distributed along the cell boundaries and are balanced by the free charges on the electrodes. If sufficient stress is applied to bend the layer, as Figure 9As shown in (D) and 9(E), polarization space charge appears in the liquid crystal, while the density of surface depolarization charge near the boundary electrode changes, thus breaking the balance between free charge and depolarization charge at the cell surface and causing a potential difference between adjacent electrodes (902, 904) on the same surface. The signal of the induced voltage alternates with the bending direction and can be used again for dynamic electromechanical energy conversion.

[0099] Piezoelectricity is a well-known and studied electromechanical effect in solid ferroelectric crystals. In crystal materials, mechanical deformation is resisted by the rigidity of the lattice: even a small deformation of the material requires a huge stress to achieve. Therefore, most of the work done on the material is stored as elastic energy in the crystal rather than being converted into electrostatic energy by coupling to polarization. SmA F Liquid crystals in the SmA F phase have a spontaneous polarization that is close in magnitude to the spontaneous polarization of solid ferroelectrics and have the fundamental advantage that they are much less rigid. The effective stress modulus associated with generating a voltage by flattening the polarization in the SmA F phase is much smaller than the stress modulus associated with generating a comparable piezoelectric response in a solid. This means that electromechanical energy conversion in SmA

[0100] Specific examples of the present disclosure

[0101] A: relates to examples of SmA F devices:

[0102] 1. A device comprising a volume containing a ferroelectric smectic A (SmA F ) liquid crystal-forming fluid and means for containing the fluid, the fluid comprising molecules that are organized into layers, the molecules having one or more electric dipoles, the molecules having spontaneously formed a ferroelectric polarization density, the polarization density comprising a non-zero local unidirectional average orientation of the dipoles, the polarization density comprising a magnitude and a vector direction in the volume, the vector direction being locally normal to the layers.

[0103] 2. The device for the electrical control of an electromagnetic field according to example 1, wherein the device comprises one or more electrodes for applying an electric field to the volume, and the electromagnetic field propagates in the volume, the electric field causing a change in the magnitude of the polarization density, thereby generating a change in the electromagnetic field.

[0104] 3. The device according to example 1, for the electrical control of an electromagnetic field, wherein the device comprises one or more electrodes for applying an electric field to the volume, and the electromagnetic field to be controlled propagates in the volume, the electric field causing the polarization density to change in vector direction, thereby generating a change in the electromagnetic field.

[0105] 4. The device as described in Example 1, which is used to generate an electrically driven motion, wherein the device includes one or more electrodes for applying an electric field to the volume, and the electric field causes the polarization density to change in the vector direction and / or the magnitude, thereby generating a change in the shape or physical motion of the volume.

[0106] 5. The device as described in Example 1, which is used to perform mechanical sensing, wherein the device includes one or more electrodes for measuring the electric potential or current within the volume, and the electric potential and / or current are generated by a change in the polarization density, and the change is caused by a change in the stress within the volume or a change in the shape of at least a part of the volume.

[0107] 6. The device as described in Example 1, which is used to generate a thermal charge density, wherein the device includes one or more electrodes for measuring the electric potential within the volume or obtaining the current within the volume, and the electric potential and / or current are generated by a change in the polarization density, and the change in the polarization density is caused by a change in the temperature of the volume.

[0108] 7. The device as described in any one of Examples 1-6, wherein the volume is contained between parallel surfaces.

[0109] 8. The device as described in Example 7, wherein the electric field / the electric field is applied parallel to the surface.

[0110] 9. The device as described in Example 7, wherein the polarization density is parallel to the surface.

[0111] 10. The device as described in any one of Examples 7 or 8, wherein the electromagnetic field has a polarization parallel to the surface.

[0112] 11. The device as described in Example 2 or Example 3, wherein the polarization components of the electric field, the polarization density, and the electromagnetic field are along the same straight line.

[0113] 12. The device as described in any one of Examples 2, 3 or 7, wherein the electromagnetic field includes one or more of microwaves, infrared rays, visible light, ultraviolet rays, and X-rays that propagate within the device or are reflected from the device.

[0114] 13. The device as described in Example 1, which is used to perform molecular dipole scavenging, wherein the polarization density generates local molecular-scale cavities that bind the molecules with dipoles in the volume.

[0115] 14. The device as described in any one of Examples 1-13, wherein the ferroelectric smectic A liquid crystal forming fluid includes dimers, oligomers or polymer materials.

[0116] 15. The device according to any one of Examples 1-13, wherein the ferroelectric smectic A liquid crystal forming fluid comprises an elastomeric material.

[0117] 16. The device according to any one of Examples 1-13, wherein the ferroelectric smectic A liquid crystal forming fluid comprises glass.

[0118] 17. The device according to any one of Examples 1-16, wherein the molecules comprise stabilizing features suitable for the ferroelectric smectic A phase, including one or more of the following: (1) a rod-like shape having a molecular major axis suitable for smectic A liquid crystal alignment; (2) a substantial molecular net dipole parallel to the molecular major axis, the dipole stabilizing the head-to-tail chains of the rod-like molecules; (3) local charges of alternating signals distributed along the molecular major axis giving molecular sub-components along the molecular length; (4) a minimum flexible tail for enabling the dipole charges to interact but providing sufficient flexibility to inhibit crystallization; and (5) lateral groups for controlling the relative positions of side-by-side molecules along the director to promote their polar order.

[0119] 18. A method of using the device according to any one of Examples 1-17.

[0120] B: Examples related to substrate pole calibration:

[0121] 19. A device comprising:

[0122] a volume that includes ferroelectric smectic A (SmA F ) liquid crystal forming molecules, the volume including an SmA F liquid crystal phase, the SmA F liquid crystal phase including a vector orientation field of the polarization density throughout the volume; and

[0123] one or more materials that include one or more surfaces in contact with the volume, wherein the one or more surfaces are configured to impart a favorable surface polarity to the molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0124] 20. The device according to Example 19, wherein the one or more materials include a first material and a second material, the first material including a first surface in contact with the volume, and the second material including a second surface in contact with the volume.

[0125] 21. The device according to Example 20, wherein the second surface is configured to impart a favorable surface polarity to the molecules at the interface with the second surface to control the vector orientation of the molecules within the volume.

[0126] 22. The device according to any one of Examples 19 - 21, wherein the favorable surface polarity of the molecule comprises a component that is locally normal to and points away from at least one of the one or more surfaces.

[0127] 23. The device according to any one of Examples 19 - 21, wherein the favorable surface polarity of the molecule comprises a component that is locally normal to and points towards at least one of the one or more surfaces.

[0128] 24. The device according to any one of Examples 19 - 21, wherein the favorable surface polarity of the molecule comprises a component that is locally tangential to at least one of the one or more surfaces.

[0129] 25. The device according to Example 24, wherein the component comprises a unique favorable azimuthal orientation around a surface normal to at least one of the one or more surfaces.

[0130] 26. The device according to any one of Examples 19 - 25, wherein the favorable surface polarity of the molecule comprises a component created by photo - degradation caused by illumination of one or more of the surfaces.

[0131] 27. The device according to any one of Examples 19 - 25, wherein the favorable surface polarity of the molecule comprises a component created by depositing a material onto a surface of one or more of the surfaces.

[0132] 28. The device according to any one of Examples 19 - 25, wherein the favorable surface polarity of the molecule comprises a component created by depositing a material onto a surface of one or more of the surfaces, wherein the deposition is inclined.

[0133] 29. The device according to any one of Examples 19 - 25, wherein the favorable surface polarity of the molecule comprises a component created by etching a material from the one or more materials.

[0134] 30. The device according to any one of Examples 19 - 25, wherein the favorable surface polarity of the molecule comprises a component created by etching a material from the one or more materials, wherein the etching is inclined.

[0135] 31. The device according to any one of Examples 19 - 30, further comprising: one or more electrical connections for applying an electric field to the volume.

[0136] 32. The device according to any one of Examples 19 - 30, further comprising:

[0137] An apparatus for applying an electromagnetic field to the volume.

[0138] 33. A method for controlling the favorable vector orientation of a three-dimensional polarization field of a SmA F liquid crystal at the interfacial surface with one or more materials, the method comprising: providing a volume including SmA F liquid crystal forming molecules; providing a first material having a first surface in contact with the volume; and using the first surface to impart a favorable surface polarity to the molecules, the favorable surface polarity controlling the favorable vector orientation of the molecules in the volume.

[0139] 34. The method according to example 33, further providing a second material having a surface in contact with the volume.

[0140] 35. The method according to example 33 or example 34, wherein the favorable surface polarity of the molecules includes a component that is locally normal to the surface and points towards the surface.

[0141] 36. The method according to example 33 or example 34, wherein the favorable surface polarity of the molecules includes a component that is locally normal to the surface and points away from the surface.

[0142] 37. The method according to example 33 or example 34, wherein the favorable surface polarity of the molecules includes a component that is locally tangential to the first surface.

[0143] 38. The method according to example 37, wherein the component includes a unique favorable azimuthal orientation about the surface normal.

[0144] 39. The method according to examples 33 - 38, further comprising applying an electric field to the SmA F phase.

[0145] 40. The device and method according to any one of examples 19 - 39, further comprising dopant molecules dissolved in the SmA F phase.

[0146] 41. The device and method according to example 40, wherein the dopant molecules have a dipole moment that is preferably aligned by the vector orientation field of the SmA F adjacent to or near the dopant molecules.

[0147] 42. The device and method according to examples 19 - 41, wherein the SmA F phase is a mixture of two or more different molecular species.

[0148] 43. The device and method as described in Example 42, wherein the SmA F phase is a smectic mixture.

[0149] 44. A device comprising:

[0150] a volume that includes a SmA F liquid crystal-forming molecule; and

[0151] a first material that includes a first surface in contact with the volume,

[0152] wherein the first surface is configured to impart a favorable surface polarity to the molecules to control the vector orientation of the molecules within the volume at the interface with the first surface.

[0153] 45. The device as described in Example 44, wherein the volume includes a SmA F phase.

[0154] 46. The device as described in Example 44 or Example 45, including any of the limitations in the limitations of Examples 20 - 28 and Examples 40 - 43.

[0155] C: Examples related to mixtures:

[0156] 47. A material comprising a ferroelectric smectic A (SmA F ) material, comprising:

[0157] two or more molecular components.

[0158] 48. The material as described in Example 47, comprising:

[0159] a mixture of a first molecule and a second molecule.

[0160] 49. A method of forming a material having a tunable SmA F phase, the method comprising:

[0161] mixing a plurality of molecules to form a mixture having a SmA F phase, wherein some of the molecules cause a polar orientation order of one or more other molecules.

[0162] D: Examples related to charge control devices:

[0163] 50. A device comprising:

[0164] a volume that contains a ferroelectric smectic A (SmA F ) liquid crystal material;

[0165] a dielectric layer that covers a portion of the volume; and

[0166] A charge-carrying substrate that covers at least a portion of the dielectric layer, wherein the volume includes polarization charges adjacent to the dielectric layer, and the polarization charges can be controlled by charges on the charge-carrying substrate and / or charges applied to the charge-carrying substrate.

[0167] 51. The device according to Example 50, further comprising one or more additional dielectric layers covering the volume.

[0168] 52. The device according to Example 51, further comprising one or more additional charge-carrying substrates covering the one or more additional dielectric layers.

[0169] 53. The device according to any one of Examples 50-52, wherein each surface defining the SmA F liquid crystal includes a dielectric layer adjacent to the liquid crystal and an adjacent charge-carrying substrate, and each surface has a finite capacitance and thus acts as a capacitor.

[0170] 54. The device according to any one of Examples 50-53, wherein the SmA on the inner side (liquid crystal side) of the capacitor is controlled by changing the charges on the outer side (substrate side) of the capacitor. F The polarization charges and molecular orientation of the liquid crystal.

[0171] 55. The device according to any one of Examples 50-54, wherein the charges on the boundary surface and the resulting SmA F liquid crystal molecular orientation respond to an external field or other stimuli, including an external electromagnetic field or light field, a chemical or electrochemical reaction, a biomolecular binding event, mechanical strain or shear, and liquid flow.

[0172] 56. The device according to Example 55, wherein the response to the external field or other stimuli is electrically detected.

[0173] 57. The device according to Example 55, wherein the response to the external field or other stimuli is optically detected.

[0174] 58. A sensor comprising the device according to any one of Examples 50-57.

[0175] 59. An actuator comprising the device according to any one of Examples 50-57.

[0176] 60. An energy conversion device comprising the device according to any one of Examples 50-57.

[0177] 61. The device according to any one of Examples 50 - 57, including SmA F The volume of the liquid crystal is at least partially bounded by a surface having spatially varying capacitance, wherein the SmA F The molecular orientation in the material exhibits a spatially varying analog response to the applied voltage.

[0178] 62. The device according to any one of Examples 50 - 57, including SmA F The volume of the liquid crystal is at least partially bounded by a surface having spatially varying capacitance and has patterned electrodes on the bounding substrate, wherein the molecular orientation in the ferroelectric nematic material exhibits a spatially varying analog response to the voltage applied to the patterned electrodes.

[0179] E: Examples related to composite materials:

[0180] 63. A composite material, the composite material comprising a first porous material, the volume of the pores of the material containing ferroelectric smectic A (SmA F ) liquid crystal.

[0181] 64. The composite material according to Example 63, wherein the volume of the pores of the porous material is substantially filled with SmA F liquid crystal.

[0182] 65. A semiconductor structure, the semiconductor structure comprising a porous solid material, the volume of the pores of the material containing SmA F liquid crystal.

[0183] 66. A dielectric structure, the dielectric structure comprising a porous, solid, electrically insulating material, the volume of the pores of the material containing SmA F liquid crystal.

[0184] 67. A capacitor, the capacitor comprising electrodes and a dielectric medium, the dielectric medium comprising a porous, solid, electrically insulating material, the volume of the pores of the material containing SmA F liquid crystal.

[0185] 68. A dielectric medium, the dielectric medium comprising SmA F liquid crystal and a solid material, the solid material being dispersed as fine particles in the liquid crystal.

[0186] 69. A dielectric medium, the dielectric medium comprising SmA F liquid crystal and a solid material, the solid material being composed of ferroelectric or superflat nano - particles.

[0187] 70. A dielectric medium, the dielectric medium comprising SmA FA dispersion of liquid crystal and solid materials, the dispersion being formed by phase separation.

[0188] 71. A dielectric medium, the dielectric medium comprising SmA F A dispersion of liquid crystal and solid materials, the dispersion being formed by photopolymerization.

[0189] 72. A dielectric medium, the dielectric medium comprising SmA F A dispersion of liquid crystal and solid materials, the dispersion being stabilized by an amphiphilic molecular component.

[0190] 73. A dielectric medium, the dielectric medium comprising SmA F An emulsion of liquid crystal and fluid materials, the emulsion being stabilized by an amphiphilic molecular component.

[0191] 74. A device, the device comprising a composite material or a dielectric medium according to any one of Examples 63, 64 and 66 - 73.

[0192] 75. The device according to Example 74, wherein the device is an energy storage device.

[0193] 76. The device according to Example 74, wherein the device is an energy conversion device.

[0194] 77. The device according to Example 74, wherein the device is an information storage and processing device.

[0195] 78. The device according to Example 74, wherein the device is an actuator, a sensor, an electrothermal device or a device for converting electrical energy into mechanical energy by electromechanical effects.

[0196] F: Other examples:

[0197] 79. A device, comprising:

[0198] A volume, the volume comprising ferroelectric smectic A (SmA F ) liquid crystal - forming molecules, the volume containing SmA F liquid crystal phase, the SmA F liquid crystal phase comprising a vector orientation field of dipolar SmA F liquid crystal - forming molecules, the dipolar molecules having a finite first hyperpolarizability β; and

[0199] One or more electrical connections for applying an electric field to the SmA F liquid crystal - forming molecules.

[0200] 80. A device, comprising:

[0201] A volume, the volume comprising ferroelectric smectic A (SmAF ) Liquid crystal forming molecules, the volume comprising SmA F Liquid crystal phase, the SmA F The liquid crystal phase includes a dipole SmA throughout the volume F A vector orientation field of liquid crystal forming molecules, the dipole molecules having a finite first hyperpolarizability β; and

[0202] One or more materials, the one or more materials including one or more surfaces in contact with the volume,

[0203] wherein the one or more surfaces are configured to impart a favorable surface polarity to the SmA F liquid crystal forming molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0204] 81. An apparatus comprising:

[0205] A volume, the volume including ferroelectric smectic A (SmA F ) Liquid crystal forming molecules, the volume comprising SmA F Liquid crystal phase, the SmA F The liquid crystal phase includes a dipole SmA throughout the volume F A vector orientation field of liquid crystal forming molecules, the dipole molecules having a finite first hyperpolarizability β;

[0206] One or more electrical connections for applying an electric field to the SmA F liquid crystal forming molecules; and

[0207] One or more materials, the one or more materials including one or more surfaces in contact with the volume,

[0208] wherein the one or more surfaces are configured to impart a favorable surface polarity to the SmA F liquid crystal forming molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0209] 82. The apparatus according to any one of Examples 79 - 81, wherein the apparatus is for electro - optic phase, amplitude, or polarization modulation of an electromagnetic field.

[0210] 83. The apparatus according to any one of Examples 79 - 81, wherein the apparatus is for non - linear optical mixing of an electromagnetic field, including second - harmonic generation and sum - and difference - frequency generation.

[0211] 84. The apparatus according to any one of Examples 79 - 81, wherein the apparatus is for non - linear optical terahertz (THz) electromagnetic field generation and / or sensing.

[0212] 85. The device according to any one of Examples 79 - 81, wherein the device is for non - linear optical frequency conversion.

[0213] 86. The device according to any one of Examples 79 - 81, wherein the device is a component of a photonic integrated circuit.

[0214] 87. A material comprising a fiber of SmA F liquid crystal.

[0215] 88. A material comprising a thin film of SmA F liquid crystal.

[0216] 89. The material according to any one of Examples 87 or 88, the material incorporated into a composite material comprising a polymer, an amphiphilic, and / or a solid component.

[0217] 90. The material according to any one of Examples 87 - 89, the material comprising a functional textile or fabric.

[0218] 91. A device based on the material according to any one of Examples 87 - 90, wherein the device is a sensor, an actuator, and / or an energy conversion device.

[0219] 92. A device based on the material according to any one of Examples 87 - 89, wherein the device is an electro - optical device.

[0220] 93. A material comprising SmA F liquid crystal includes bipolar molecules having a large first hyperpolarizability β, wherein the bipolar molecules have a polar orientation order that controls the second - order non - linear optical properties of the material.

[0221] The exemplary embodiments of the present disclosure described above do not limit the scope of the present invention, because these embodiments are merely examples of the embodiments of the present invention. Any equivalent embodiments are intended to fall within the scope of the present invention. In fact, various modifications of the present disclosure (such as alternative useful combinations of the described elements) may become apparent to those skilled in the art from the description. Such modifications and embodiments are also intended to fall within the scope of the appended claims.

Claims

1. A device, the device comprising a volume containing a ferroelectric smectic A (SmA F ) liquid crystal forming fluid and means for containing the fluid, the fluid comprising molecules which are organized into layers, the molecules having one or more electric dipoles, the molecules having spontaneously formed a ferroelectric polarization density, the polarization density comprising a non-zero local unidirectional average orientation of the dipoles, and the polarization density comprising a magnitude and a vector direction in the volume, the vector direction being locally normal to the layers.

2. The device according to claim 1, for the electrical control of an electromagnetic field, wherein the device comprises one or more electrodes for applying an electric field to the volume, and the electromagnetic field propagates in the volume, and the electric field causes the polarization density to change in magnitude, thereby generating a change in the electromagnetic field.

3. The device according to claim 1, for the electrical control of an electromagnetic field, wherein the device comprises one or more electrodes for applying an electric field to the volume, and the electromagnetic field to be controlled propagates in the volume, and the electric field causes the polarization density to change in vector direction, thereby generating a change in the electromagnetic field.

4. The device according to claim 1, for generating an electrically driven motion, wherein the device comprises one or more electrodes for applying an electric field to the volume, and the electric field causes the polarization density to change in the vector direction and / or in magnitude, thereby generating a change in the shape of the volume or a physical motion.

5. The device according to claim 1, for performing mechanical sensing, wherein the device comprises one or more electrodes for measuring the electric potential or current within the volume, the electric potential and / or current being generated by a change in the polarization density, the change being caused by a change in stress within the volume or a change in the shape of at least a part of the volume.

6. The device according to claim 1, for thermally generating a charge density, wherein the device comprises one or more electrodes for measuring the electric potential within the volume or obtaining the current within the volume, the electric potential and / or current being generated by a change in the polarization density, the change in the polarization density being produced by a change in the temperature of the volume.

7. The device according to any one of claims 1 - 6, wherein the volume is contained between parallel surfaces.

8. The device according to claim 7, wherein the electric field / the electric field is applied parallel to the surfaces.

9. The device according to claim 7, wherein the polarization density is parallel to the surfaces.

10. The device according to any one of claims 7 or 8, wherein the electromagnetic field has a polarization parallel to the surfaces.

11. The device according to claim 2 or claim 3, wherein the polarization components of the electric field, the polarization density, and the electromagnetic field are along the same straight line.

12. The device according to any one of claims 2, 3 or 7, wherein the electromagnetic field comprises one or more of microwaves, infrared rays, visible light, ultraviolet rays, and X - rays that propagate within the device or are reflected from the device.

13. The device according to claim 1, for performing molecular dipole scavenging, wherein the polarization density generates local molecular - scale cavities that bind the molecules having dipoles in the volume.

14. The device according to any one of claims 1 - 13, wherein the ferroelectric smectic A liquid - crystal - forming fluid comprises a dimer, oligomer, or polymer material.

15. The device according to any one of claims 1 - 13, wherein the ferroelectric smectic A liquid - crystal - forming fluid comprises an elastomeric material.

16. The device according to any one of claims 1-13, wherein the ferroelectric smectic A liquid crystal forming fluid comprises glass.

17. The device according to any one of claims 1-16, wherein the molecules comprise stabilizing features suitable for the ferroelectric smectic A phase, including one or more of the following: (1) a rod-like shape with a molecular major axis suitable for smectic A liquid crystal alignment; (2) a substantial molecular net dipole parallel to the molecular major axis, which stabilizes the head-to-tail chains of the rod-like molecules; (3) local charges of alternating signals distributed along the molecular major axis giving molecular sub-components along the molecular length; (4) a minimum flexible tail for enabling the dipole charges to interact, but providing sufficient flexibility to inhibit crystallization; and (5) lateral groups for controlling the relative positions of the side-by-side molecules along the director to promote their polar order.

18. A method of using the device according to any one of claims 1-17. B: Claims related to the polar alignment of the substrate:

19. A device comprising: Volume, said volume comprising ferroelectric smectic A (SmA F ) liquid crystal forming molecules, said volume containing SmA F liquid crystal phase, said SmA F liquid crystal phase comprising a vector orientation field of the electrode polarization density throughout said volume; and One or more materials, the one or more materials comprising one or more surfaces in contact with the volume, wherein the one or more surfaces are configured to impart a favorable surface polarity to the molecules, the favorable surface polarity controlling the vector orientation at the interface with the one or more surfaces.

20. The device according to claim 19, wherein the one or more materials comprise a first material and a second material, the first material comprising a first surface in contact with the volume, and the second material comprising a second surface in contact with the volume.

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