Devices containing ferroelectric nematic liquid crystal forming molecules and methods of making and using same - Patents.com

Abstract

The surface polarity of a ferroelectric nematic can be configured to generate vector control of the orientation of its bulk polarization field. Contact between a surface with in-plane polarity and a ferroelectric nematic liquid crystal can generate a preferred in-plane orientation of the ferroelectric polarization field at its interface, thereby forming highly polarized fluid or glassy monodomains without electric field poling. Using the material surface as a pathway, planar aligned cells with various orientation director / polarization configurations, including twisted states, can be formed. In a π-twisted cell obtained by double-sided antiparallel unidirectional buffing, we demonstrate three separate modes of ferroelectric nematic electro-optic response: intrinsic viscosity-limited electric field-induced molecular reorientation, electric field-induced motion of domain walls separating twisted states of opposite chirality, and propagation of polarization reorientation solitons from the cell plates to the cell center upon electric field reversal.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Patent Application No. 63 / 132,194, filed December 30, 2020, and entitled "DEVICE INCLUDING FERROELECTRIC NEMATIC LIQUID CRYSTAL-FORMING MOLECULES AND METHODS OF FORMING AND USING SAME," the contents of which are incorporated herein by reference. Federally funded research This invention was made with government support under grant numbers DMR1420736, DMR2005170, and DMR1710711 awarded by the National Science Foundation. The government has certain rights in this invention. [Background technology]

[0002] Nematic liquid crystals (LCs) are useful because of their facile collective response to applied fields and surface forces. In liquid crystals, the bulk response is a long-range deformation of the molecular orientation due to the fluid-elastic field, while confining surfaces establish geometric and topological structural constraints. In the realm of electro-optics, these two fundamental elements of LC phenomenology combined to produce LC display technology, which enabled the revolution in portable computing in the 20th century. Until very recently, this evolution relied on bulk dielectric alignment, where quadrupolar coupling to an applied electric field induces polarization in nonpolar LCs, generating torque and molecular reorientation. Surface interactions used to achieve desirable device structures are similarly quadrupolar, and common processes such as buffing or photoalignment are described by the Rapini-Popoular (RP) model and its variants.

[0003] Nematic liquid crystals are fluids with internal long-range orientational order. In statistical terms, the phase transition from the isotropic phase to the nematic phase breaks orientational symmetry, resulting in Goldstone modes in the nematic phase, which describe spatial variations in the director n(r), the local average molecular orientation. Due to the perfect orientational symmetry of the isotropic phase, the nematic director has no globally preferred orientation, and therefore the harmonic (elastic) energy cost of orientational fluctuations of the wave vector q decreases to zero at long wavelengths according to Kq2, where K is the orientational (Frank) elastic constant. Three-dimensional bulk nematic samples can be oriented by providing arbitrarily small forces, such as an applied electric or magnetic field, that couple the nematic orientation through quadrupolar anisotropic dielectrics or diamagnetic materials, respectively. The nematic order is similarly infinitely responsive to boundary conditions, i.e., surfaces where orientational anisotropy exists. Because nematics are fluids, these conditions allow us to place them in a selected container, spontaneously temper them into a selected three-dimensional (3D) space-filling director alignment structure, and have this structure respond in a predictable way to an applied field. In practice, the surface and field must be strong enough to eliminate defects and cause reorientation fast enough to be useful.

[0004] Recently, a novel nematic liquid crystal phase, the ferroelectric nematic (NF), has been demonstrated, offering a variety of opportunities for employing LC fields and surface phenomena in exciting and powerful new ways. NF LCs are 3D liquids with a macroscopic electric polarization P(r). At the nanoscale, each molecular dipole is macroscopically transformed into a strong orientational coupling that makes P(r) locally parallel to ±n(r), the steric long axis of its molecule, the local average molecular long axis orientation, and the phase is constrained to be nearly parallel to the uniaxial optic axis. Thus, polarization imparts a linear NF to the coupling between n(r) and the applied electric field E, which dominates over the dielectric coupling at low E. The NF phase exhibits nearly complete self-stabilizing spontaneous polar ordering, with a polar order parameter p =<cos(βi)> ≥ 0.9, where βi is the angle between the typical molecular dipole and the local average polarization density P. The resulting large spontaneous polarization P≈6 μC / cm2 enables electric-field-induced nematic director reorientation and concomitant electro-optic (EO) response to electric fields applied to a typical cell on the order of 1 V / cm, which is several thousand times smaller than the equivalent reorientation of a dielectric nematic.

[0005] Any discussion, including the discussion of problems and solutions set forth in this section, is included in this disclosure solely for the purpose of providing a context for the present disclosure, and should not be construed as an admission that any or all of this discussion was known at the time the invention was made or otherwise constitutes prior art. Summary of the Invention

[0006] This summary is provided to introduce a selection of concepts. It 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.

[0007] Various embodiments of the present disclosure relate to devices and methods of using and forming the devices. According to an exemplary embodiment of the present disclosure, a device includes a volume containing ferroelectric nematic liquid crystal forming molecules, the volume including a ferroelectric nematic liquid crystal phase, the ferroelectric nematic liquid crystal phase including a vectorial orientation field of electric polarization density throughout the volume, and one or more materials including one or more surfaces in contact with the volume, the one or more surfaces being configurable to impart a preferred surface polarity of the molecules, the preferred surface polarity controlling the vectorial orientation at interfaces with the one or more surfaces.

[0008] According to a further example of the present disclosure, there is provided a method for controlling preferred vector orientation in three dimensions of a polarization field of a ferroelectric liquid crystal at an interface with one or more materials, which may include providing a volume containing ferroelectric 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 preferred surface polarity of the molecules, wherein the preferred surface polarity controls the preferred vector orientation of the molecules within the volume.

[0009] According to yet a further exemplary embodiment of the present disclosure, there is provided a method of forming a ferroelectric nematic liquid crystal device, the method comprising the steps of providing a volume containing ferroelectric liquid crystal forming molecules in a nematic state, providing a first material including a first surface in contact with the volume, and imparting a preferred surface polarity of the molecules, the preferred surface polarity controlling vector orientation at an interface with the first surface.

[0010] According to yet a further example of the present disclosure, a device includes a volume including ferroelectric liquid crystal forming molecules and a first material including a first surface in contact with the volume, the first surface configured to impart a preferred surface polarity to the molecules to control the vector orientation of the molecules within the volume at an interface with the first surface.

[0011] Further examples are set forth in the claims, including the dependent claims. Unless stated otherwise, dependent claims may be combined with independent claims or other dependent claims in any combination.

[0012] These and other embodiments will become readily apparent to those skilled in the art from the following detailed description of specific embodiments, which proceeds with reference to the drawings, and the present disclosure is not limited to any particular embodiment disclosed.

[0013] A more complete understanding of the exemplary embodiments of the present disclosure can be derived by reference to the detailed description and claims, and by consideration in conjunction with the following exemplary figures. [Brief explanation of the drawings]

[0014] [Figure 1] Cell structure of the NF phase of RM734 under different planar alignment conditions, imaged using depolarized transmission light microscopy (DTLM). (A, C) Cells with bidirectional surface buffing provide planar alignment and no pretilt (director parallel to the surface). This surface is nonpolar, allowing the formation of domains of opposite ferroelectric polarization (d = 11 μm, T = 120 °C). (B, D, E) Antipolar cells with unidirectional surface buffing (d = 4.6 μm) provide planar alignment with a few degrees of pretilt. The pretilt couples the NF polarization to the intrinsic surface-normal polarity (polymer on one side, LC on the other), providing in-plane polar anchoring of the bulk NF. Therefore, cooling through the N-NF transition with a temperature difference between the plates results in the growth of a polar-oriented monodomain from the cooling plate. (E) As the cell cools to the NF phase by buffing the two plates antiparallel, the orientation closer to the warmer plate undergoes a surface reorientation transition to a lower-energy polar state, resulting in a π-twist in the nP field. This twist can be either left-handed (LH) or right-handed (RH), and a π-twist wall separates these two states. The LH and RH states are optically degenerate between crossed polarizers and analyzers. (F) Schematic of the U state and the LH and RH π-T states. In the absence of a T gradient, a uniform director state grows from each surface, forming a PPR wall near the cell center. Scale bars: (A) 20 μm, (B) 200 μm. [Figure 2]Figure 1. Illustrates the orientation states of an ANTIPOLAR cell. A stable π-twist (πT) state in the NF phase, induced by surface polar anchoring created using antiparallel unidirectional buffing at T = 125 °C and imaged using DTLM. The red-to-blue rainbow arrows represent the ferroelectric polarization orientation at a series of increasing x levels in the cell (x = 0, d / 4, d / 2, 3d / 4, d, where d = 3.5 μm). The pink arrow indicates the azimuthal trajectory of φ(x) from bottom to top of the cell, which is also the direction of light propagation. (A, B) A left-handed (LH) πT state (orange) growing into a uniform (U) state. The U state is dark between crossed polarizers and the analyzer when n is parallel or normal to the analyzer, but exhibits birefringence when rotated (B). The color of the πT state does not strongly depend on the cell orientation. (C) Schematic of the U state and the LH and RH πT states. In the absence of a T gradient, a uniform director state grows from each surface, forming a PPR wall near the cell center. The twist deformation in the PPR wall, shown relative to the yellow vector, initially requires the flank energy of the local twist, but eventually lowers the energy, leading to a topological transition that converts the PPR wall into a uniform director twist between the cell plates. (D, E) Uncrossing the analyzer lifts the optical degeneracy of the LH and RH states, revealing chirality and optical symmetry under simultaneous specular reflection (LH to RH) and inversion at non-crossing angles. (E) The LH and RH states are separated by a 2π twist wall. Scale bar: 200 μm. [Figure 3]This is a diagram showing the reversal of low-field polarization in an ANTIPOLAR cell. (A - H) The right-handed (RH) πT state in a cell of RM734 with a thickness d = 3.5 μm at T = 110°C. This cell has ITO electrodes with a 1 mm gap, generating an electric field E in the normal direction at the electrode edges. At the center of the gap, E = (0.66v) V / mm, where v is the voltage applied across the electrode gap. The buffering direction is along the z-axis, oriented 3° away from parallel to the electrode edge and thus 93° away from E. This 3° deviation breaks the mirror symmetry in E and preferentially rotates the n - P junction counterclockwise in response to the P×E torque (B, white arrow). As the applied voltage increases in the range 0V < v < 0.3V, the images progress from (A) to (H). The red-to-blue rainbow arrows represent the ferroelectric polarization orientations at a series of increasing x levels within the cell (x = 0, d / 4, d / 2, 3d / 4, d). The pink arrow indicates the azimuthal trajectory from the bottom to the top of the cell, which is also the light propagation direction. (I - K) Graphs of the director profile φ(x) for the LH and RH states calculated from the static simulation of the electric field / elastic torque balance equation described herein. All profiles have a surface orientation fixed at φ(0) = -87° and φ(3.5 μm) = 93°. Note that the LH profile is graphed such that φ increases downward. The RH πT state is shown as in FIGS. 1 and 2 and graphed in (J) and (K). Since P in the RH state has a component induced opposite to E, it is strongly deformed as the electric field pushes P counterclockwise from the right side to the left side of the circle. (B, C) At V ≈ 40 mV (E ≈ 26 mV / mm at the gap center), the LH πT state appears at several locations via heterogeneous nucleation and mostly has P induced along E, which is a favorable state for the electric field. (E, I) The electric field tends to drive the LH twist out of the surface and fill the cell center with a favorable orientation. (D) The πT states of LT and RN are separated by a 2π twist wall. (E - H) Since the electric field increases little when the domain wall moves, the LH and RH states have little internal structure change over this range.(I-K) Insets show the hue of white light transmission between crossed polarizers and analyzer. [Figure 4]NF electro-optics and dynamics of RM734 at T = 110 °C. (A) Overview of electric-field-induced polarization reversal (ERV) and viscosity-restricted (ERT) reorientation data and modeling. ERV scheme: black dots are electric-field reversal data; colored circles are from (C); white circles and solid white lines are from (B). ERT scheme: cyan squares are from (E); white circles and dotted white lines are from (D). Because the electric-field reversal generates some soliton response, similar to (B), the ERV time is longer, during which part of the cell waits for the soliton to pass and reorient. (B) The ERV solution of the torque balance equation shows the response to a square-wave electric field reversal. Before this, P is in the πT state of RH, and after this, P is in an unstable equilibrium state at low torque until the soliton leaves the surface and passes through. The final state (red line) has a 2π twist wall at the cell center, which disappears due to reorganization of order (cyan arrow), leaving behind the LH πT state (dashed line). When the soliton reaches the cell center, a director reorientation (white circle) occurs, giving rise to the optical transmission peak in (C). (C) Optical transmission peaks between crossed polarizers and analyzers following electric field reversal. The soliton's arrival time at the cell center is plotted in (A) and color-coded as in (C). The same set of peaks appears as the - to + transition, indicating that each transition completely switches the handedness of the πT state. (D) Simulated ERT response of the uniformly twisted RH πT state to an E field favoring the central cell orientation at φ=0. The final E-induced state (black) indicates that the electric field penetration length ξE = √K / PE of the surface orientation into the cell is small at this electric field. In this case, each element dx = ξE of the director profile φ(x) responds independently to the electric field as φE(t) (see herein), which can be used to analyze the uniform φ(t) data in (E). (E) A four-gold electrode cell (NSEW) has random planar alignment, and a pulsed voltage is applied to W, while NS and E are grounded. A small DC bias sets the starting orientation φo at approximately 45°, and the transmission I(t) between the crossing P and A is measured. The 10%–90% response times versus electric field amplitude are shown as cyan squares in (A).For smaller applied fields, the response time decreases as 1 / E and is used to determine γ. The deviation from the 1 / E dependence at large E is due to the effect of the depolarizing voltage at these electrodes and is only apparent for a short time. [Figure 5] FIG. 1 illustrates a device according to an example of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0015] It will be understood that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale, for example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to aid in understanding the illustrated embodiments of the present disclosure.

[0016] Although specific embodiments and examples are disclosed below, those skilled in the art will understand that the present disclosure extends beyond the specifically disclosed embodiments and / or applications of the present disclosure, as well as obvious modifications and equivalents thereof. Therefore, it is intended that the scope of the present disclosure should not be limited by the specific embodiments described herein. The figures presented herein are not intended to be the actual appearance of any particular material, apparatus, structure, or device, but are merely representations used to describe embodiments of the present disclosure.

[0017] Exemplary embodiments of the present disclosure provide improved devices, including a volume containing ferroelectric nematic liquid crystal forming molecules and one or more materials including one or more surfaces contacting the volume.

[0018] According to examples of the present disclosure, the volume includes a ferroelectric nematic liquid crystal phase, the ferroelectric nematic liquid crystal phase comprising a vector-orienting field of electric polarization density throughout the volume, and the one or more surfaces configured to impart a preferred surface polarity of molecules, the preferred surface polarity controlling the vector orientation at an interface with the one or more surfaces. The one or more materials can include a first material including a first surface contacting the volume and a second material including a second surface contacting the volume. The second surface can be configured to impart a preferred surface polarity of molecules to control the vector orientation of molecules within the volume at an interface with the second surface. The preferred surface polarity of the molecules can include a component locally normal to and oriented away from at least one of the one or more surfaces. The preferred surface polarity of the molecules can include a component locally normal to and oriented toward at least one of the one or more surfaces. The preferred surface polarity of the molecules can include a component that is locally tangential to at least one of the one or more surfaces, the component having a unique preferred azimuthal orientation about a surface normal to at least one of the one or more surfaces. According to examples of the present disclosure, the preferred surface polarity of the molecules can include a component that is induced by unidirectional buffing of one of the one or more surfaces. According to additional examples, the preferred surface polarity of the molecules can be induced using oblique illumination of one of the one or more surfaces with electromagnetic waves (e.g., having a wavelength in the range of about 0.1 μm to about 10 μm). According to additional examples, the preferred surface polarity of the molecules can include a component that is induced via photopolymerization induced by illumination of one of the one or more surfaces. According to further examples, the preferred surface polarity of the molecules can include a component that is induced via photopolymerization induced by illumination of one of the one or more surfaces, the illumination being oblique. In some cases, the preferred surface polarity of the molecules can include a component that is induced via photodegradation induced by illumination of one of the one or more surfaces.According to examples of the present disclosure, the preferred surface polarity of the molecule includes a component that is brought about through photopolymerization induced by illumination of one of the one or more surfaces. According to further examples, the preferred surface polarity of the molecule includes a component that is brought about by deposition of material onto one of the one or more surfaces. The deposition can be oblique. According to further examples, the preferred surface polarity of the molecule includes a component that is brought about by etching of material from one or more materials. The etching can be oblique. According to further examples of the present disclosure, the device includes one or more electrical connections for applying an electric field to the volume and / or an apparatus for applying an electromagnetic field to the volume.

[0019] According to a further example of the present disclosure, a method for controlling the preferred vector orientation in three dimensions of a polarization field of a ferroelectric liquid crystal at an interface with one or more materials is provided. An exemplary method includes providing a volume containing ferroelectric 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 preferred surface polarity of the molecules, the preferred surface polarity controlling the preferred vector orientation of the molecules in the volume. The method can further include providing a second material having a second surface in contact with the volume. The preferred surface polarity of the molecules can include a component locally normal to the surface and induced toward the surface. In some cases, the preferred surface polarity of the molecules can include a component locally normal to the surface and induced away from the surface. The preferred surface polarity of the molecules can include a component locally tangential to the first surface. The component can include an intrinsic preferred azimuthal orientation about the surface normal. In some cases, the preferred surface polarity of the molecules can include a component resulting from unidirectional buffing of the first surface. The preferred surface polarity of the molecules can include a component that is induced using oblique illumination of the first surface with electromagnetic waves (e.g., having a wavelength in the range of about 0.10 μm to about 10 μm). In some cases, the preferred surface polarity of the molecules can include a component that is induced via photopolymerization induced by oblique illumination of the first surface. In some cases, the preferred surface polarity of the molecules can include a component that is induced via photodegradation induced by oblique illumination of the first surface. The preferred surface polarity of the molecules can include a component that is induced by oblique deposition of material onto the first surface and / or oblique etching of material from the first surface. According to various examples of the present disclosure, contact of the first surface with the volume occurs at a first temperature phase, and the volume cools to a ferroelectric nematic phase at a second temperature. The volume can include a nematic phase at the first temperature. In some cases, the volume includes an isotropic material at the first temperature. The volume can include a ferroelectric nematic phase. According to a further example of the present disclosure, interfacial control is used to establish polar vector alignment in three dimensions of the spontaneous polarization field within the volume of a ferroelectric nematic liquid crystal.

[0020] According to a further example of the present disclosure, a method for forming a ferroelectric nematic liquid crystal device is provided. The method includes providing a volume containing ferroelectric liquid crystal-forming molecules in a nematic state, providing a first material including a first surface in contact with the volume, and imparting a preferred surface polarity to the molecules, the preferred surface polarity controlling vector orientation at the interface with the first surface. The interfacial control of establishing polar vector orientation in three dimensions of the spontaneous polarization field within the ferroelectric nematic liquid crystal volume can be achieved by cooling the liquid crystal volume from a higher temperature phase to a ferroelectric nematic liquid crystal phase, the higher temperature phase being a non-ferroelectric nematic phase, and the cooling configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase. The cooling can be configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase, the gradient allowing the ferroelectric nematic phase to form initially on a selected surface. The method can further include applying an electric field to the ferroelectric nematic phase. Additionally or alternatively, the method can include providing dopant molecules dissolved in a ferroelectric nematic phase. The dopant molecules have a dipole moment that is preferentially aligned adjacent or proximate thereto by the vectorial orientation field of the FNLC. According to further examples, the ferroelectric nematic phase is a mixture of two or more distinct molecular species. In some cases, the ferroelectric nematic phase is a eutectic mixture. According to any of the above examples, the volume vector orientation of the FNLC forms an oriented glass upon cooling (e.g., 10 times the viscosity of the material in the isotropic phase). 8 (resulting in a higher viscosity).

[0021] According to yet a further example of the present disclosure, another device is provided. The device includes a first material having a volume containing ferroelectric liquid crystal-forming molecules and a first surface in contact with the volume, the first surface configured to impart a preferred 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 includes a ferroelectric nematic phase. The device can include any of the features described above in connection with other devices and / or methods for forming the device.

[0022] We show that the polar ordering of NFs in the devices described herein results in a novel change in nematic-to-surface interaction, a key aspect of nematic LC science and its promise for technology. We demonstrate that controlling the polarity of a polar molecule's 2D boundary surface can lead to the construction of a vectorial orientation distribution in its 3D volume. In the simplest example, if the preferred polarization orientation is vectorially unidirectional across most of the surface, the NF volume polarization can be similarly oriented, becoming vectorially polarized by the surface in a uniform orientation, without the need for an applied field.

[0023] Samples of materials with spontaneous vector order, such as ferromagnets and ferroelectrics, divide into domains of different orientations of magnetization M(r) or polarization P(r), respectively, so as to minimize the energy of the internal and external magnetic or electric fields they generate. By orienting these fields locally parallel to the surface, their internal energy is minimized. Intentionally disrupting this picture through the application of external fields (field poling), such as placing an iron rod in a magnetic field to create a bar magnet, or externally reversing the polarization of ferroelectric nanocrystals that serve as bit storage in nonvolatile solid-state memory, is a key process in their use. Field poling of soft materials, such as corona poling of chromophore-containing polymers to generate polarization monodomains for nonlinear optical and electronic electro-optical applications, has been unsuccessful due to the high fields required. In contrast, we have found that surface poling of ferroelectric nematics can achieve nearly perfect polar monodomain ordering even in the absence of a poling field.

[0024] In ferroelectric nematics, the symmetry reduction associated with the appearance of the bulk polarization density P(r) leads to the bulk energy density U PE This gives rise to the macroscopic coupling of P to the applied field E by = -P·E. For molecules whose net molecular dipole is nearly parallel to the molecular long steric axis, P(r) is the orientation energy preferential U Pn =-u Pn Macroscopically coupled to be parallel to ±n(r) by |(n·P) / P|. Energy density coefficient u Pn u Pn ≒k B It can be estimated as T / vol, where vol is the volume of the molecule. If we apply a step change in orientation of P(r) at x=0, n(r) is the distance |x|=ξ≒√(K / u Pn) Therefore, P(r) and ±n(r) are essentially locked together in orientation on a macroscopic scale, and therefore when a field is applied, the response is generally to reorient n(r) by reorienting P(r). The exception to this is the motion of the poled walls, which flips P by 180° in a uniform n field.

[0025] The descriptions of exemplary embodiments provided herein are exemplary and intended for purposes of explanation only, and the following descriptions are not intended to limit the scope of the disclosure or the claims. Moreover, the description of multiple embodiments having stated features is not intended to exclude other embodiments having additional features or other embodiments incorporating different combinations of the stated features.

[0026] In this disclosure, any two numbers of a variable can constitute a valid range for that variable, and any range stated can include or exclude endpoints. In addition, any value of a stated variable (whether stated with "about" or not) can refer to an exact or approximate value, can include equivalents, and can refer to an average, median, representative, majority, etc. Furthermore, in this disclosure, the terms "comprise," "comprised of," and "having" can, in some embodiments, independently refer to "typically or broadly including," "comprises," "consisting essentially of," or "consisting of." In this disclosure, any defined meaning does not necessarily exclude the ordinary and accustomed meaning.

[0027] The surface can include any suitable surface, including those described herein. The surface can include an interface. [Example]

[0028] The following examples illustrate various devices and methods of making and using the devices. These examples are illustrative and are not meant to limit the scope of the invention.

[0029] Polar Surface Anchoring - At the intersection of P(r) and the boundary surface, polarized charges / areas are located on the surface, which are connected to the external ionic and electronic charges, as well as N F A long-range, electric-field-induced interaction with the director occurs. However, since the boundary surface itself is always polar in nature, the local surface interaction, characterized by the energy / area of ​​LC-surface interaction, W(θ,φ), and the orientation of the director n(r) at the surface relative to its normal, (θ,φ), must contain a polar contribution in addition to the nonpolar RP term. The surface manifold r s and a vector field S(r s ) can be chosen to represent the unavoidable element of polarity associated with the surface. S(r s ) generally gives the location and value of the maximum of a structural gradient, such as the interfacial electric polarization density, the density of some molecular component of the LC or interfacial phase, or the polarization density of a molecular component of the interface material.

[0030] N F The appearance of polarization in the phase is due to the term W P (r s )∝P(r s )·S(r s ) to W, which prioritizes a preferred sign for the component of P along the surface normal direction, chosen to be x. In addition, if the surface structure has in-plane anisotropy, for example as a result of bidirectional abrasive buffing, the nematic director orientation at the surface undergoes RP-type interactions, which themselves impart a preferential in-plane (y,z) alignment of n(r), which in turn imparts a surface energy density W Q It is stabilized by (φ), where φ gives the in-plane azimuthal orientation between n and the buffing direction z. W Q (φ) must be anisotropic but nonpolar, and therefore mirror-symmetric with respect to the buffing and its in-plane normal [W Q (φ)=W Q (-φ)=W Q (π-φ)=W Q (π+φ)]. Following RP, we Q (φ)=wQ sin(2φ) = W Q (φ) is the quadrupole, where w Q is a phenomenological coefficient. In the case of bidirectional buffing or normal-incidence light orientation in the (x,z) plane, the preferred director orientation also has n parallel to the surface (the PLANAR case depicted by the white double-headed arrow in Figure 1A). The intrinsic surface polarity (gray arrow in Figure 1A) is normal to this preferred orientation and therefore does not induce in-plane polar symmetry and is folded along n.

[0031] On the other hand, if in-plane anisotropy is introduced by unidirectional buffing along z, or by oblique photoalignment in the (x,z) plane, or by some other oblique treatment, the surface orientation of n preferred for this treatment is not parallel to the surface, but forms some angle 0<ψ<π / 2 with the surface plane (the pretilted case). In such pretilted geometries, there exists a component of P along S at equilibrium, coupling the intrinsic polarity of the surface normal (gray arrow in Figure 1B) to both the in-plane and normal components of P, thus W P is non-zero. That is, the pretilt quadrupolar interaction provides equivalent surface energies for n and -n due to the pretilt, whereas the surface energies for P and -P are different. In Figure 1B, gray / white arrows are used to represent this polar feature in the surface interaction. If φ is the in-plane azimuthal angle between c, the in-plane component of n, and the rubbing direction z, then W s (φ) is a mirror image of the rubbing direction [W s (φ)=W s (-φ)], which is the formula W s (φ)=W Q (φ)+W P (φ)=w Q sin(2φ)+w P sin(ψ)cos(φ), where w P is a phenomenological coefficient. LC surface energy density w Q The quadrupole anisotropy of has been widely studied experimentally. Pis required by symmetry, but its magnitude or sign is unknown. Herein, we consider N F We demonstrate in-plane polar surface alignment of the phases and use this to obtain an estimate of the polar component of the anchoring energy, showing that such interactions enable full polar control of the nematic director geometry in in-plane aligned cells. We induce a twisted state in the nematic director and apply an in-plane electric field to produce voltage-controlled optical activity, achieving faster response using much smaller fields.

[0032] RM734 (RJ Mandle, SJ Cowling, JW Goodby, A nematic to nematic transformation exhibited by a rod-like liquid crystal. Phys. Chem. Chem. Phys. 19, 11429-11435 (2017). DOI: 10.1039 / c7cp00456g) {Isotropic (I) → 182°C → Nematic (N) → 133°C → Ferroelectric nematic (N) F )} was filled into a glass cell, with a gap of thickness d separating the plates, and one of the plates was patterned with an ITO or gold electrode spaced by L for application of an in-plane electric field. The cell was optically investigated using depolarized transmission light microscopy (DTLM) with incident white light and single-wavelength transmission measurements with 632 nm HeNe laser light focused to a 30 μm diameter spot. Both random planar glass surfaces, which give a schlieren texture in the N phase, and plates coated with a buffed polymer alignment layer, which gives a planar monodomain of the N phase upon cooling from the isotropic phase, were used.

[0033] The polymer alignment cell comprises a cell with d = 11 μm in weak bidirectionally buffed alignment layers 102, 104 around volume 106, providing a preferred alignment of n parallel to the buffing direction and the surface. This alignment ensures that the director (yellow in Figure 1A) is aligned normal to the intrinsic surface polarity and does not break the polar symmetry along n (white line in Figure 1A). These are NONPOLAR in-plane surfaces, forming a NONPOLAR cell.

[0034] We also used cells with thicknesses d = 3.5 μm and 4.6 μm with buffed polyimide alignment layers 108, 110 and volume 112, providing a preferred alignment of n at surfaces parallel to the buffing direction and tilted from the surface plane by a small pretilt angle ψ ≈ 3° (Figure 1B). In this case, according to the discussion above, the intrinsic surface polarity (gray arrows in Figure 1B) now has a component along the preferred director orientation. This breaks the polar symmetry along n (gray / white arrows in Figure 1B), and the surface thus exhibits a preferred in-plane orientation of P at the surface, which we simply call POLAR. When buffing is unidirectional and parallel on the two flat surfaces of the cell, we call these surfaces SYNPOLAR; when unidirectional buffing is antiparallel, we call it ANTIPOLAR.

[0035] NN FA nonpolar, aligned cell with a spatially uniform temperature through the transition was cooled at -1 °C / min. This was first patterned by a texture of irregular domains extending locally parallel to n(r), appearing on a submicron scale. It then tempered into a pattern of low-optical-contrast lines spaced approximately 2 °C apart, up to millimeters in length, also generally oriented along n(r). These lines roughened or developed to form closed loops on the order of 10–200 microns in some places, which had a distinctive, characteristic lens shape elongated along n(r), as shown in Figures 1A and 1C. These lines formed pure polarization reversal (PPR) boundaries between ferroelectric domains of P with opposite signs of P. These domains occupy roughly equal areas of the cell, i.e., they showed little preference for a particular sign of P. Applying a small probe field allowed visualization of the distinct orientation of P, providing key evidence for the ferroelectric nematic phase of RM734. Thus, nonpolar alignment results in uniform quality alignment of n, giving good extinction between crossed polarizers and analyzers, with side-by-side hectomicron- to millimeter-scale domains of opposite signs of P.

[0036] NN F In aligned SYNPOLAR cells with spatially uniform temperature cooled at -1 °C / min through the transition, a uniform N-phase nematic monodomain was observed. F This texture is imperfectly characterized by the appearance of crystalline phases at T = 90 °C, but tempering from T = 120 °C to room temperature results in a glassy, ​​uniformly birefringent monodomain.

[0037] We also used Aryasova and Reznick's temperature gradient method to investigate the effects of in-plane polar order and alignment on a single surface within the cell. Aryasova and Reznick studied the nematic LC structure and phase behavior for LC between glass plates while maintaining a constant temperature difference, ΔT, across the cell thickness. Aryasova and Reznick found that upon cooling through the isotropic (I) to nematic (N) phase transition under these conditions, the dominant nematic alignment acquired was that of the cooler cell surface. Thus, when a temperature gradient was applied, the I / N interface first appeared at the cooler surface and moved from that surface to the other as a quasi-planar sheet. In cells where one plate is coated with a rubbed polymer film and the other with an untreated polymer film to give random planar alignment, this type of cooling was found to result in a cell with uniform planar alignment when growing nematic from the rubbed surface, or in the same cell, a defective Schlieren texture when growing nematic from the other random planar alignment surface.

[0038] The RM734 achieves the same thermal conductivity as the NN in the ANTIPOLAR cell, maintaining a temperature difference of approximately 2°C between the outside of the top and bottom cell plates, with the top plate being cooler. F The transition cooled at -1°C / min. The temperature difference in the cell gap containing the LC can be estimated to be ΔT ≈ 0.1°C. In these cells, N to N F The transition to N F The apparent birefringence of the N-polar phase appears at a sharp boundary. As this boundary moves across the cell toward the bottom plate, the polar N-polar phase appears to be larger than the N-polar phase, as shown in Figures 1B and 1C. F This cooling process is shown diagrammatically in Figure 1B, which shows the N FThe phase nucleates and emerges from the cooler surface in a nematic state, growing to fill the entire gap between the plates, as evidenced by the uniform orange birefringence color left behind, demonstrating a uniformly birefringent oriented structure. This state has a birefringence color that vanishes between crossed polarizers and analyzers, indicating planar or near-planar alignment, i.e., n and P are uniform across the cell and parallel to the plates. Such planar-aligned N with large P F The key feature of the cell is the block polarization structure, which is the broadening of the Pn bonds at the interface and the P x The termination of the polarization is inhibited by the high electrostatic energy cost of the polarization charge. Therefore, P = 6 μC / cm 2 The polarization self-field penetration length ξ P =√K εo / P 2 Within ≈0.1 nm, the pretilt imposed on the surface disappears, the P(r)-n(r) bonds become locally parallel to the cell plate, and the orientation is E x = 0. When P rotates and develops the x component, E due to the surface polarization charge x acts to return P parallel to the plates. The in-plane orientation of P can be probed by applying an in-plane electric field of a few V / cm. The uniform orientation of nP in this grown monodomain indicated that the cooler surface nucleates and grows its preferred polar orientation of P, while the warmer surface forces it to adopt an unpreferred polar orientation. In SYNPOLAR cells, both surfaces eventually become favored.

[0039] Cooling is NN FIf the transition is stopped at approximately 7°C or less, this state persists, with the polar monodomain expanding and filling the cell area. However, if the ANTIPOLAR cell is further cooled to T≈120°C, a structural transition occurs, and multiple domain boundaries nucleate and move across the cell, leaving behind the purple region in Figure 1D. This purple region has its own set of internal domain walls (Figure 1D). Notably, as shown in Figures 2A and 2B, this new domain no longer exhibits optical attenuation between crossed polarizers with n aligned with the optical polarization. This indicates a nonuniform director field, and in the absence of an applied electric field, the only possible twisted state is where n is parallel to the plates and reorients helically with a constant ∂φ / ∂x. Within this twist domain, internal domain walls separate regions that exhibit identical brightness and color between crossed polarizers and analyzers (Figure 1D), and when the polarizers and analyzers are uncrossed, these regions become darker or brighter depending on the sign of the uncrossed angle (Figures 2E, 2F). This is the optical signature of a pair of identical twist states of opposite handedness [left-handed (LH) or right-handed (RH)]. At a given location within the cell, the passage of the orange-to-purple boundary mediates a spontaneous transition to macroscopic chirality. In Figure 2, device 200 includes 206, a first material having a first surface 202, and a second material having a second surface 204.

[0040] NN F Since the uniform azimuthal orientation field of n(x) growing at the transition has its preferred orientation at the cooler plate (x = d) and less energetically favorable conditions at the warmer surface (x = 0), we hypothesize that the lower T transition to the twisted state is due to the twist elastic energy density U of the bulk director field. T =1 / 2K(∂φ(x) / ∂x) 2We propose that this results in a reversal of nP to its energetically favorable orientation at the warmer surface, at the expense of . A convenient parameterization of the anchoring strength of such anisotropic surface interactions is given by the "surface penetration length" l = K / w, where K is the twist elastic constant and w is the associated energy density coefficient. Applying a torque to the LC director induces a linear φ(x), which extrapolates to zero distance l to the surface. A typical rubbed polyimide alignment requires K = 5 pN and w Q ≒10 -4 J / m 2 By using Q ≈50 nm, thus resulting in deformation of the few microns thick LC film used here, where n(r) at the surface is essentially fixed along one of the preferred quadrupolar orientations. The fraction of the π twist in the LC is d / (d+2l Q ) ≈ 1, torque applied to the surface, transmitted by bulk flank elasticity, does not move the orientation at each surface further away than the energy minimum φ ≈ 0 or π where rubbing of the quadrupolar surface is favorable. For the present ANTIPOLAR surface, W on the warmer surface Q These minimum values ​​of are φ=0 and φ=π, and W P The minimum at φ=0 is at a higher energy and the minimum at φ=π is at a lower energy simply because the minimum at φ=0 is at a higher energy and the minimum at φ=π is at a lower energy. Therefore, the minimum at φ=0 is metastable and decreases with increasing magnitude of P as T decreases. P As the magnitude of φ increases, the transition from φ=0 to φ=π becomes possible at a warmer surface. For a linear π twist φ(z)=πx / d, the U T The condition from w P >Kπ 2 / 4d≒5x10 -6 J / m 2 This minimum requirement is QThe nature of the surface-normal polar order of LCs varies widely, from the perfect polar ordering of 5CB on the semiconductor surface to disorder in the case of mirror-symmetric molecules. Ferroelectric chiral smectics exhibit polar-surface interactions that include favorable normal polarization reversal at the surface and the induction of polarization at the surface. In the latter experiment, chiral smectic A, which exhibits electroclinical effects, exhibits an effective surface field E normal to the surface. s The normal component of polarization at the surface is subjected to ≈2V / μm. If the force is electrostatic, the corresponding energy / area U P depends on l, the thickness of the interaction volume, and U P ≒PE s l. N F For the phase, assuming an interaction volume of molecular dimensions, a similar estimation gives U P ≒10 -4 J / m 2 and w P =U P sinψ≒10 -5 J / m 2 The surface polarity can also induce LC polarization, thereby inducing an electric gradient of flexoelectric order near the surface.

[0041] As shown in Figure 1B, NN F Considering the surface phenomenon in more detail, where the growing surface becomes warmer as it approaches, N F The N phase displaces the N phase in contact with the warmer buffed surface, and its director lies in one of the quadrupole-director oriented surface energy minima. F The directors have the same orientation, but the polar orientation induced in the N phase by this surface is different from that of the approaching N F The PPR wall is formed in a uniform director field, not aligned with the orientation of the plane. This geometry is F At temperatures close to the transition, it is at least metastable. At lower temperatures, the orientation of n close to the surface changes by π, transitioning to another quadrupole minimum, but leaving P fixed at the surface. If the temperature gradient along x is reduced, N Fgrows from both surfaces, and PPR walls form in the bulk. This case is shown diagrammatically in Figure 2C, which also illustrates a simple topological transition that can occur, whereby an appropriate twist deformation of Pn at the PPR wall reduces the magnitude of the P component inversion, leading to the annihilation of the PPR wall and the emergence of twist walls, which then expand to fill the cell and give rise to a πT state. This is a barrier-limited transition because the initial twist must substantially exceed the width of the PPR wall. In the presence of a T gradient, the process of annihilation of the PPR wall near the warmer surface is essentially the same. Such a barrier-limited topological transition results in the heterogeneous nucleation and growth seen in Figure 2. The sharp boundary between uniform π-twist states is evidence of metastability for the φ = 0° surface state in the warmer plate. Thus, the surface orientation transition between the quadrupolar surface energy minima at φ = 0 and φ = -π is a soliton, very similar in structure to the surface-stabilized π-reorientation walls in chiral smectic ferroelectric LCs (SSFLCs), which are similarly described by the double sine-Gordon equation.

[0042] The walls separating the πT states are topological, 2π twist walls (2πTW). These states are illustrated in Figures 1 and 2, which show that in this cell geometry, with the rubbing direction nearly parallel to the electrode edges, the polarization P (x = d / 2) at mid-height within the cell is normal to the electrodes, in the y direction for the πTL state and in the -y direction for the πTR state, and therefore parallel or antiparallel to the applied field E. The 2πTW consists of 2π twist disclination lines in the bulk n and P fields (Figures 2 and 3). The topological transition that provides the electric-field-induced nucleation of the twist wall loops in Figure 3 is also restricted to the barrier, resulting in the heterogeneous nucleation of the LH domains seen in Figure 3. It should be clear from this discussion that virtually any geometry of twisted planar reorientation of the nP bonds in a ferroelectric nematic can be stabilized between the plates by using selected bidirectionally or unidirectionally rubbed alignment surfaces with appropriate pretilts, in combination with chiral doping to control the relative stability of different otherwise degenerate twist states used in twisted nematic devices.

[0043] In-plane ferroelectric optics and dynamics. Considering the geometry of the planar alignment cell described above, the dynamic response of the electric field-induced alignment can be divided into two main types: those driven primarily by electric field rotation (ERT) and those driven primarily by electric field reversal (ERV). This division is illustrated in the dynamically simulated 1D electric field-induced alignment profile φ(x,t) in Figures 4A and 4B, which show the dynamic response of the applied in-plane field E (x,t) switched on at time t = 0. y Figure 4D shows these distinct dynamical limits of the response of the first LH πT state to E. y We model the effect of this kind of change in E y is the orientation P=P y This is also the starting P at the cell center [P(x=d / 2)=P as shown in Figure 2]. y]. After this event is complete, the final electric-field-induced configuration (black curve in Figure 4D) is subjected to electric-field reversal (ERV). For cells with nonpolar surfaces, the polar orientation on these surfaces can be independently reversed, resulting in a mixture of uniform πTL and πTR states, and the resulting surface walls can be moved by the applied field. In contrast, in 3.5 μm-thick ANTIPOLAR cells, we observe electric-field-induced polar surface reorientation; the surface remains at the preferred polarity minimum in E-field experiments, and the simulations of ANTIPOLAR cells presented herein in Figures 4B and 4D show a fixed surface orientation. However, in general, for a finite W s There may also be surface orientation transitions induced by electric-field-induced torques on (φ). We consider the cases of ERT, domain walls, and ERV in the following three sections. In all cases, the electric field variable E is that applied to the measurement area, i.e., the probe laser spot in the ERT and ERV cases, and the electrode gap center for domain dynamic images. At the gap center, E ≈ 0.66v / (1mm), where v is the voltage applied to the electrode gap, and the reduction is due to the electric field spreading in the x-direction from the thin electrode edges.

[0044] ERT dynamics - The ERT response Δφ is the electric field induced reorientation of P to be parallel to the applied torque T. E =-PE y sinφ tends to rotate P toward φ=0. E in the πTφ(x) geometry of Figure 2D y By applying >0, P = 6 μC / cm 2 and the applied field E y = 40V / mm for the deGennes field penetration length ξ E=√K / PE ≒ 50 nm equivalent thickness, excluding the surface regions at x = 0 and x = d where the twist is squeezed, this condition is continuously obtained anywhere within the cell with a fixed topology. In the electric field E > 1 V / mm where the twist is restricted to the surface region with a thickness less than the wavelength, the light transmission of this cell approximates that of a uniform birefringent slab, and almost extinction is obtained with the intersecting polarizer and analyzer positioned along y and z. In this simulation, E y = 40 V / mm and the surface anchoring is assumed to be infinitely strong, fixed at φ(x = 0) = π / 2 and φ(x = d) = -π / 2 respectively.

[0045] The orientation response to the applied field is simulated by the dynamic torque balance equation T E = γφ(x,t) t =-PE y sinφ(x,t)+Kφ(x,t) xx where γ is the nematic rotational viscosity. Generally, as applicable here, when ξ E << d, the torques of ferroelectricity and viscosity are dominant, and the ferroelectric / viscosity torque balance controls the response of each ξ E ×ξ E ×ξ E volume element independently. When φ(t) is chosen to be uniform within the volume, the inventors obtain -PE y sinφ(t)=γφ(t) t which results in φ E (t)=2tan -1 [tan(φ o (x) / 2)exp(-tPE y / γ)], where φ o (x) is the starting angle between P and E y in the volume, and further E y =V IN / L, where L is the effective electrode gap. For small φ E (t), this gives exponential dynamics with a characteristic relaxation time τ E = γ / PE y . These approximations φ E (t)t ≒φ E (t) / τ E As can be seen in Figure 4D, E The linearity of (x) should be maintained. ERT reorientation response time τ E is the intrinsic viscosity limited response time, the fastest achievable for a given γ and P, scaled by 1 / E, and is plotted as the lower white line in Figure 4A from the simulation in Figure 4D. The short E at the West electrode in the four-electrode geometry in Figure 4E y The electro-optic response of the ERT geometry was measured in RM734 by reorienting a 5 μm thick random planar cell at T = 110 °C using a pulse. A small DC bias was first applied to the West electrode to obtain a φ o ≈45°, the starting transmission intensity I between the crossed polarizer and analyzer o Assuming uniform orientation, the transmission intensity is I(φ(t)) = I o sin[2φ(t)] 2 is given by φ(t)=φ E A typical measured response (cyan solid curve) fitted by (t) (blue line) is shown for E y = 40V / mm for an electric field step of τ E = γ / PE = 71 μsec. 0.66 V / mm <E y The optical response was measured in the range of <36 V / mm, and I(φ E (t)) and graphed as a cyan square in Figure 4A. E vs. E y In the lower half of this range, we obtained data for φ E As expected for (t), τ E ∝1 / E y However, for higher electric fields, τ E is E y It was found that the P value decreased much more slowly with increasing P = 6 μC / cm. 2 Fitting the lower electric field data using gives γ = 0.15 Pa·s, which is the τ used in the simulations. Eprovides the value of , and the dotted line for the white model is given in Figure 4A.

[0046] To understand the high-field behavior, we consider that a large value of P provides strong coupling of orientation to the applied field, as well as ubiquitous space charge effects that can significantly slow down the motional states. In all of the in-plane field cells investigated here, the N F At the interface between the phases there is an effectively thin insulating barrier, which has no polarization or the orientation of the polarization is fixed. F Part of the applied voltage is used to maintain the physical separation of free charge carriers from the polarization charges that are forced onto the insulating interface by the F Even in the cell of Figure 4E, where the capacitance is 0.1F / cm, such an insulating layer is present. 2 If φ E E in the above equation for (t) y =V IN / L is E y =V IN / L→[V IN -(P / C)cosφ E (t)] / L, which should be corrected according to the depolarization voltage (P / C)cosφ E (t) by E y Generally, these capacitors are leaky, allowing free charge to pass through the polarization charge and reduce this process through a resistance RΩ / cm in parallel with C. 2 We then modeled E y =V IN / L → (V IN / L){1-(P / C)cosφ E (t)·exp[-t / RC]}. Slow E y In this case, the response is slow enough for the P / C voltage to relax, and the full V IN / L field, and τ E =γ / PE y gives the behavior of

[0047] Domain-Mediated Dynamics - Generally, for small applied in-plane E, the LH and RH πT states have different net energies of interaction with the electric field. As a result, if both are present in the cell, the 2πT boundary between them moves in the y,z plane, expanding the area of ​​these lower-energy states in the electric field, or nucleating new lower-energy ones. Such 2πT formation or motion is hysteretic in nature, potentially enabling bistable electro-optic effects. Figure 3 shows an example of 2πT formation using an ANTIPOLAR cell with in-plane d = 3.5 μm and ITO electrodes spaced 1 mm apart. The electric field is very slowly varying (approximately 0.1 Hz) and weak, with E < 0.3 V / mm, and significant continuous distortion of the RH πT state with increasing field is reinforced by the nucleation and growth of less distorted LH πT domains, which eventually occupy the entire cell area (Figure 3) and remain even when E returns to zero. The electric field direction is offset by 3° from the bisector of the antiparallel buffing direction, favoring a counterclockwise reorientation of P. As a result, the 2π twist walls separating the domains cancel each other out when they come into contact and disappear as the LH region grows.

[0048] ERV dynamics. ERV reorientation begins from the field-limited LH state, which is the final configuration of the ERT process (Figure 4D, solid black curve in Figure 4B), and continues through E y where the entire cell center is simulated by reversing the sign of E y and in this orientation P experiences zero torque from the electric field and is therefore unresponsive. However, near the surface where P is reoriented preferentially to the surface, a torque is present and therefore a response begins here, with velocity v=ξ E / τ E The soliton propagates toward the cell center with the electric field reversal time τ R =d / 2v≒τ E (d / 2ξ E) to the center. This causes the sheet to align at the center at x=d / 2, resulting in a reorientation of P with δφ=2π between the equivalent orientations of P. The sheet then disappears via a topological process of reordering or the spontaneous appearance of twisted disclination loops, which in either case change handedness and leave a πT configuration of RH restricted by the electric field. The simulated time τ R is graphed as the upper white line in Figure 4A, and together with E, τ R ∝E -1 / 2 while τ E ∝E -1 In this electric field range, the time P elapses at φ=0 waiting for the soliton to arrive is τ R is τ E It is larger than.

[0049] ERV dynamics were experimentally investigated in the response of the twisted state of Figure 2 to square-wave driving, as simulated in Figure 4B. The optical response allows for the identification of regions of soliton propagation (light pink) and topological transition (light blue). Figure 4C shows the optical transmission (parallel to E) through crossed polarizer / analyzers versus time following a square-wave voltage reversal at t = 0. The response is identical for + / - and - / + reversals, indicating that a complete transition between the LH and RH limiting T states is obtained with each reversal. After the soliton propagates and reorientation is complete, the baseline optical transmission is very slow, rotating only 90° and decreasing in thickness ξ E The surface area of ​​the cell depolarizes the light. As E increases, the soliton becomes thinner, resulting in a smaller overall light transmission by the traveling soliton (light pink region). The arrival of the soliton at the cell center is indicated by a distinct optical peak (white circle in Figure 4B, 4C) and is brought about by a transient, extended linear variation of φ(x) about φ(x) = 0 (white circle in Figure 4B, 4C). This peak is immediately followed by a reorganization of the order, completing the transition to the limiting state of opposite handedness (light blue region). The overall transition time for this process, τ R is plotted against E in Figure 4A (point colors match those in Figure 4C), and τ EThe simulation in Figure 4B shows a similar τ R values ​​are given, i.e., only the γ / PE values ​​from the ERT data are used. The optical and polarization field reversal response times from Figure 3C obtained for different cell geometries (black dots) but for square-wave driving are also plotted (X. Chen, E. Korblova, D. Dong, X. Wei, R. Shao, L. Radzihovsky, M. Glaser, J. Maclennan, D. Bedrov, D. Walba, N.A. Clark, First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: spontaneous polar domains and striking electro-optics, Proceedings of the National Academy of Sciences of the United States of America 117, 14021-14031 (2020)). These response times are comparable to those in Figures 4B and 4C, indicating a similar response delay behavior of electric field reversal. Interestingly, all of these individual data sets exhibit a τ that is within the range expected by the soliton model. R ∝E -1 / 2 Instead, it is almost τ R ∝E -1The results show a dependence of . This difference may be due to the assumption in soliton models and simulations that perfect polar order initially exists away from the surface and that the P field stabilizes at φ = 0. When the electric field is switched, this condition causes each soliton to travel half the cell thickness, d / 2, and switch cells. In reality, however, due to defects, surface imperfections, and thermal fluctuations, P only occasionally reaches φ = 0 inside the cell, where it experiences a torque and begins to reorient inhomogeneously after the electric field is switched. This process proceeds more rapidly as the electric field is increased, resulting in the local nucleation and soliton-mediated growth of substantially reoriented domains, depending on the size and orientation deviation of the seeding. To the extent that such domains emerge and expand, the net time for complete reversal decreases because the distance the soliton must span is reduced. τ R ∝E -1 The behavior of E -1 / 2 This should suggest that the average soliton travel distance decreases with increasing E according to . The ERV data in Figure 4A should suggest that this could be universal behavior.

[0050] Nematic and Ferroelectric Nematic Textures - LCs possess a remarkable combination of fluidity and order, manifesting in an inherently facile macroscopic response to surfaces. Within thin cells between flat plates, bulk LC configurations are strongly influenced by surface interactions, resulting in the formation of distinctive textures, themes of bulk structure on the micron- to millimeter-scale that reflect the balance of surface, electric field, and elastic energies. Analysis of these textures, typically using depolarized transmission light microscopy, allows for investigation of both surface alignment characteristics and key bulk LC properties such as phase behavior, elasticity, and symmetry. Friedel's discovery of smectics is a prime example of this. When two surface preferences differ in a cell, each preference should generally manifest in some form in the bulk, either within any given cell or as a statistical average of LC structures across many cells. For example, in a hybrid aligned cell (one side normal to the surface, n-axis, and the other side parallel to the surface, n-axis), a curved nematic texture exhibits both preferences. If the two surfaces are structurally equivalent but have different preferred orientations, e.g., rubbed in orthogonal directions, the different surface preferences must somehow be equally represented in the bulk LC, effectively forming a 90° twisted nematic texture. On the other hand, planar aligned smectics can accommodate the surfaces in such a 90° cell by forming domains that locally fill the cell, some following the 0° surface and others following the 90° surface, resulting in equal areas averaged over many cells.

[0051] This allows for new N for LC alignment physics. FCells of different phases are obtained, and similar conditions for surface polar ordering emerge. If two cell surfaces have different preferred polar orientations, both must be confirmed in the cell texture. If these surfaces are structurally identical but have different polar orientations, the incompatible polar orientations must be equally expressed. The first clear example of such behavior in nematics is the πT state of a cell with opposite unidirectional buffing on the two surfaces shown in Figures 1 and 2. These states have a symmetric distribution of azimuthal orientations at φ=π / 2 and therefore equally contain incompatible polar surface orientations. This scenario is exemplified by the N from one surface leaving the PPR wall on the other surface. F This is achieved by the growth of a temperature gradient, which becomes unstable at lower temperatures and leads to the formation of a twisted state. Cooling without a gradient leads to the formation of a PPR inside the cell, as shown in Figure 2C, which provides a uniform director field and the PPR walls are parallel to the cell plates, creating a transition between the two surface preferences. The transition to the twisted state in Figure 2C is barrier-limited, and therefore the PPR walls are stable or metastable depending on the energy cost of twisting. Cooling without a gradient results in a N / N F Interfaces can enter the cell from both sides and interact with each other. For example, there may be thermal interactions, where the approach of one interface releasing heat retards the progress of the other, creating the possibility of coupled Mullins-Sekerkra instability.

[0052] Polar Medium—The LC of bulk FN (e.g., the volume described herein) can be thought of as a 3D polar medium filled with a continuous unit vector field v(r) = P(r) / P, whose 3D structure is determined by its electrostatic and Frank elastic properties, as well as the 2D positional and vectorial properties of its interactions with the surface. Such a 3D polar medium can act as a vector solvent, locally orienting polar solute molecules along v(r). If we consider a single RM734 molecule in RM734 of bulk FN as an ideal test solute molecule in a ferroelectric nematic solvent, P = 6 μC / cm. 2For , we estimate from atomistic simulations that it takes approximately 10 k to flip such a solute molecule from its preferred orientation, with its molecular dipole parallel to v(r) for an antiparallel orientation. B We can estimate the electrostatic energy cost of T. Thus, v(r) is a substantially strong aligning electric field for molecules with appropriate steric and dipolar structure (e.g., rod-like molecules with an average longitudinal dipole moment), ultimately controlled by the surface.

[0053] We have shown that in ferroelectric nematics, surface polarity plays an entirely new role in providing coupling to the macroscopic electric field variables. material and method Synthesis of RM734 - 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoic acid (RM734) is a rod-shaped mesogen first synthesized by Mandle et al., cited above. It has an isotropic (I) phase and two additional phases, a nematic (N), with transition temperatures of I - 187°C-N - 133°C-N. X It was reported that the temperature was I-188°C-N-133°C-N by the preparation by the present inventors described in the reference (M. O'Neill, S.M. Kelly, Photoinduced surface alignment for liquid crystal displays. J.Phys.D-Appl.Phys.33 R67-R84 (2000). DOI:10.1088 / 0022-3727 / 33 / 10 / 201). F The transition temperature of -X is given.

[0054] Observation of response to applied electric field—An experimental cell was formed by filling the LC sample between glass plates spaced apart by the desired gap d. For application of an in-plane electric field, the plates (e.g., 102, 104, 202, 204) were coated with lithographically patterned ITO or gold electrodes. The plates could be any material with a surface. Cells with unidirectionally buffed alignment layers were obtained from Instec, Inc. Experiments were performed in a temperature-controlled environment, and electro-optical observations were performed using depolarized transmission light microscopy, with the cell mounted on the rotating stage of a research microscope and imaged with transmitted light between polarizers.

[0055] 5 illustrates a device 500 according to various embodiments and examples of the present disclosure. Device 500 includes a volume 502 and one or more materials 504, 506 including one or more surfaces 508, 510 in contact with volume 502. Device 500 also includes one or more electrical connections 512, 514 for applying an electric field to the volume, and an apparatus 516 for applying an electromagnetic field to the volume.

[0056] The exemplary embodiments of the present disclosure described above do not limit the scope of the present invention, as these embodiments are merely examples of embodiments of the present invention. Any equivalent embodiments are intended to fall within the scope of the present invention. Indeed, various modifications of the present disclosure, in addition to those shown and described herein, will be apparent to those skilled in the art from this description, including alternative useful combinations of the elements described. Such modifications and embodiments are also intended to fall within the scope of the appended claims.

Claims

1. a volume containing ferroelectric nematic liquid crystal forming molecules, said volume comprising a ferroelectric nematic liquid crystal phase, said ferroelectric nematic liquid crystal phase comprising a vectorial orientation field of electric polarization density throughout said volume; and one or more materials comprising one or more surfaces in contact with the volume; the one or more surfaces are configured to impart a preferred surface polarity to the molecules, the preferred surface polarity controlling the vector orientation at the interface with the one or more surfaces; device.

2. The device of claim 1 , wherein the one or more materials include a first material including a first surface in contact with the volume and a second material including a second surface in contact with the volume.

3. The device of claim 2 , wherein the second surface is configured to impart a preferred surface polarity to the molecules to control vector orientation of the molecules within the volume at an interface with the second surface.

4. The device of claim 1 , wherein the preferred surface polarity of the molecules comprises a component that is locally normal to and directed away from at least one of the one or more surfaces.

5. The device of claim 1 , wherein the preferred surface polarity of the molecules comprises a moiety that is locally normal to and directed toward at least one of the one or more surfaces.

6. The device of claim 1 , wherein the preferred surface polarity of the molecules comprises a component that is locally tangential to at least one of the one or more surfaces.

7. The device of claim 6 , wherein the moiety comprises a unique preferred azimuthal orientation about a surface normal to at least one of the one or more surfaces.

8. The device of claim 1 , wherein the preferred surface polarity of the molecules comprises a moiety that is brought about by unidirectional buffing of one of the one or more surfaces.

9. 1. A method for controlling preferred vector orientation in three dimensions of a polarization field of a ferroelectric liquid crystal at an interface with one or more materials, comprising: Providing a volume containing ferroelectric liquid crystal forming molecules; providing a first material having a first surface in contact with the volume; and using said first surface to impart a preferred surface polarity of said molecules, said preferred surface polarity controlling said preferred vector orientation of said molecules within said volume.

10. The method of claim 9 further comprising providing a second material having a second surface in contact with the volume.

11. 10. The method of claim 9, wherein the preferred surface polarity of the molecules comprises a component that is locally normal to and directed towards the surface.

12. 10. The method of claim 9, wherein the preferred surface polarity of the molecule comprises a component that is locally normal to the surface and directed away from the surface.

13. The method of claim 9 , wherein the preferred surface polarity of the molecule comprises a component that is locally tangential to the first surface.

14. The method of claim 13 , wherein the components include a unique preferred azimuthal orientation about the surface normal.

15. 1. A method of forming a ferroelectric nematic liquid crystal device, comprising: providing a volume containing ferroelectric liquid crystal forming molecules in a nematic state; providing a first material including a first surface in contact with the volume; and imparting a preferred surface polarity to said molecules, said preferred surface polarity controlling vector orientation at an interface with said first surface.

16. 10. The method of claim 9, wherein interfacial control of establishing polar vector orientation in three dimensions of a spontaneous polarization field within the volume of ferroelectric nematic liquid crystal is achieved by cooling the volume of liquid crystal from a higher temperature phase to a ferroelectric nematic liquid crystal phase.

17. 17. The method of claim 16, wherein the higher temperature phase is a non-ferroelectric nematic phase.

18. The method of claim 16 , wherein the cooling is configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase.

19. 17. The method of claim 16, wherein the cooling is configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase, the gradient enabling the ferroelectric nematic phase to form initially on selected surfaces.

20. The device of claim 1 , wherein the ferroelectric nematic phase is a mixture of two or more distinct molecular species.

21. The device of claim 20 , wherein the ferroelectric nematic phase is a eutectic mixture.

22. 22. The device and method of claim 1-21, wherein the volume vector orientation of the FNLC forms an oriented glass upon decreasing the temperature.

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