Devices containing ferroelectric nematic liquid crystal forming molecules, and methods for forming and using the same.

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 of related applications This application claims the benefit of U.S. Provisional Patent Application No. 63 / 132,194, filed on December 30, 2020, 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. Research funded by the federal government This invention was made with government support under authorization numbers DMR1420736, DMR2005170, and DMR1710711 granted by the U.S. Science Foundation. The government has specific rights to this invention. [Background technology]

[0002] Nematic liquid crystals (LCs) are useful because their collective response to applied fields and surface forces is readily apparent. In liquid crystals, the bulk response is the long-range deformation of the fluid-elastic field of molecular orientation, and the confinement plane establishes geometric and topological structural constraints. In the field of electro-optics, these two fundamental elements of LC phenomenology are combined to give rise to LC display technology, which enabled the transformation of portable computing in the 20th century. In this development, until very recently, nematic electro-optics was based on the alignment of bulk dielectrics, where quadrupole coupling to an applied electric field induces polarization within nonpolar LCs, generating torque and molecular reorientation. Surface interactions used to realize desired device structures are also quadrupole, and common treatments such as buffing or photo-orientation are explained by the Rapini-Popoular (RP) model and its variations.

[0003] Nematic liquid crystals are fluids with an internal long-range orientation order. In statistical terms, the phase transition from the isotropic phase to the nematic phase breaks the orientation symmetry, resulting in Goldstone modes in the nematic phase, which represent spatial variations in the director n(r), which is the local average molecular orientation. Due to the perfect orientation symmetry of the isotropic phase, the nematic director does not have a generally favorable orientation, and therefore the harmonic (elastic) energy cost of the orientation variation of the wave vector q decreases to zero at long wavelengths according to Kq², where K is the orientation (Frank) elastic constant. Three-dimensional bulk nematic samples can be oriented by providing arbitrarily small forces, such as arbitrarily small applied electric or magnetic fields, that couple to the nematic orientation via a quadrupole anisotropic dielectric or diamagnetic material. Nematic order also responds infinitely to boundary conditions, i.e., to surfaces where orientation anisotropy exists. Since nematics are fluid, these conditions allow for placing the nematics in a selected container, allowing them to spontaneously temper to form a selected three-dimensional (3D) space-filling director-oriented structure, and enabling this structure to respond to an applied field in a predictable manner. In practice, the surface and field must be strong enough to eliminate defects and cause reorientation at a speed that is useful.

[0004] In recent years, novel nematic liquid crystal phases have been shown to be ferroelectric nematics (NF), offering various opportunities to utilize LC fields and surface phenomena in exciting and powerful new ways. NF LC is a 3D liquid with macroscopic electric polarization P(r). At the nanoscale, each molecular dipole is macroscopically transformed into a strong oriented coupling that makes P(r) locally parallel to ±n(r). The molecular long axis, local average molecular long axis orientation, and uniaxial optical axis of this phase are suppressed to be nearly parallel. Thus, the polarization gives the coupling between n(r) and the applied electric field E a linear NF that prevails over dielectric coupling at low E. The NF phase exhibits almost complete self-stable spontaneous polar ordering, with a polar ordering parameter p=<cos(βi)> The value is ≥0.9, where βi is the angle between a typical molecular dipole and the local average polarization density P. The resulting large spontaneous polarization P ≈ 6 μC / cm²2 This enables the reorientation of electric field-induced nematic directors, and consequently, the electro-optic (EO) response to an electric field applied to a typical cell of about 1 V / cm in size, which is several thousand times smaller than the equivalent reorientation of dielectric nematics.

[0005] Any discussions, including the discussions of problems and solutions described in this chapter, are included in this disclosure solely for the purpose of providing context for this disclosure and should not be construed as acknowledging that any or all of these discussions were known at the time the invention was made, or otherwise constitute prior art. [Overview of the Initiative]

[0006] This summary is provided to introduce a set of concepts. This summary is not intended to identify any major 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 this disclosure relate to devices and methods for using and forming such devices. According to exemplary embodiments of the present disclosure, the device comprises a volume containing ferroelectric nematic liquid crystal forming molecules, wherein the volume contains a ferroelectric nematic liquid crystal phase, the ferroelectric nematic liquid crystal phase containing a vector 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 may be configured to give a preferred surface polarity of the molecules, the preferred surface polarity controlling the vector orientation at the interface with the one or more surfaces.

[0008] Further examples of the present disclosure provide a method for controlling a preferred vector orientation in three dimensions of the polarization field of a ferroelectric liquid crystal at an interface with one or more materials. The method may include the steps of 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 to the molecules, the preferred surface polarity controlling the preferred vector orientation of the molecules in the volume.

[0009] Further exemplary embodiments of the present disclosure provide a method for forming a ferroelectric nematic liquid crystal device. The method comprises 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 giving the molecules a preferred surface polarity, the preferred surface polarity controlling the vector orientation at the interface with the first surface.

[0010] According to further examples of the present disclosure, the device comprises a volume containing ferroelectric liquid crystal forming molecules and a first material including a first surface in contact with the volume, the first surface being configured to control the vector orientation of molecules in the volume at the interface with the first surface by providing a preferred surface polarity for the molecules.

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

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

[0013] A more complete understanding of the exemplary embodiments of this disclosure can be derived by referring to the detailed description and claims, and considering them together with the following exemplary figures. [Brief explanation of the drawing]

[0014] [Figure 1] This figure shows the cell structures 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 but no pretilt (director parallel to the surface). This surface is nonpolar, allowing for the formation of domains with opposite ferroelectric polarization (d=11 μm, T=120°C). (B, D, E) Antipolarar cells with unidirectional surface buffing that provide planar alignment with a few degrees of pretilt (d=4.6 μm). Pretilt couples the NF polarization to the intrinsic surface normal polarity (polymer on one side, LC on the other), giving in-planar polarity anchoring of bulk NF. Therefore, cooling by N-NF transition with a temperature difference between plates allows polarly oriented monodomains to grow from the cooled plate. (E) When the cell is cooled to the NF phase by antiparallel buffing of the two plates, the orientation closer to the warmer plate undergoes a surface reorientation transition to a lower-energy polar state, generating a π twist in the nP field. This twist can be either left-handed (LH) or right-handed (RH), and a 2π twist wall separates these two states. The LH and RH states are optically degenerate between the intersecting polarizer and analyzer. (F) Schematic diagram of the U state and the πT states of LH and RH. 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]This figure shows the orientation state of an antipolarar cell. A stable π-twist (πT) state in the NF phase, induced by surface polarity anchoring generated using antiparallel unidirectional buffing at T=125°C and imaged using a DTLM. The iridescent arrows from red to blue represent a series of increasing x-level ferroelectric polarization orientations within the cell (x=0, d / 4, d / 2, 3d / 4, d, where d=3.5μm). The pink arrows show the azimuthal trajectory of φ(x) from bottom to top of the cell, which is also the direction of light propagation. (A, B) Left-handed (LH) πT state (orange) growing into a uniform (U) state. The U state is dark between the intersecting polarizer and analyzer when n is parallel or normal to the analyzer, but shows birefringence when rotated (B). The color of the πT state does not strongly depend on the cell orientation. (C) Schematic diagram of the U state as well as the LH and RH πT states. In the absence of a gradient T, a uniform director state grows from each surface, forming a PPR wall near the cell center. The twist deformation in the PPR wall, shown for the yellow vector, initially requires the flank energy of the local twist, but eventually reduces the energy, resulting in a topological transition that transforms the PPR wall into a uniform director twist between the cell plates. (D, E) Resolving the crossover of the analyzers releases 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 electric field polarization in an antipolar cell. (A to 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 gap center, E=(0.66v) V / mm, where v is the voltage applied across the electrode gap. The buffing direction is along the z-axis, oriented 3° away from parallel to the electrode edges, and thus 93° away from E. This 3° offset breaks the mirror symmetry in E, causing the n-P coupling to preferentially rotate counterclockwise in response to the P×E torque (B, white arrow). With the applied voltage increasing in the range of 0V<v<0.3V, the image progresses from (A) to (H). The iridescent arrows from red to blue represent the ferroelectric polarization orientation at a series of increasing x levels in 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 to K) This is a graph of the director profile φ(x) for the LH and RH states, calculated from static simulations of the electric field / elastic torque balance equations described herein. All profiles have fixed surface alignment with φ(0)=-87° and φ(3.5 μm)=93°. Note that the LH profile is graphed such that φ increases downward. The πT state of RH is shown similarly to Figures 1 and 2, and is graphed in (J) and (K). Since P in the RH state has a component induced opposite to E, the electric field is strongly deformed by pushing 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 most have P induced along E, making this a favorable state for the electric field. (E, I) The electric field tends to expel the LH twist to the surfaces to fill the cell center with the preferred orientation. (D) The πT states of LT and RN are separated by a 2π twist wall. (E to H) Since the electric field hardly increases when the domain wall moves, the internal structures of the LH and RH states barely change over this range.(I~K) The insets show the hue of white light transmission between the intersecting polarizer and analyzer. [Figure 4]This figure shows the NF electro-optics and dynamics of RM734 at T=110℃. (A) Overview of electric field-induced polarization reversal (ERV) and viscosity-limited (ERT) reorientation data and modeling. ERV method: Black dots are electric field reversal data, colored circles are from (C), and white circles and white solid lines are from (B). ERT method: Cyan colored squares are from (E), and white circles and white dotted lines are from (D). The ERV time is longer because electric field reversal generates some soliton response, similar to (B), during which part of the cell waits for the soliton to pass through and be reoriented. (B) The ERV solution of the torque balance equation shows the response of a square wave to electric field reversal, where P before is in the πT state of RH, and P after is in a low-torque, unstable equilibrium state until the soliton passes off the surface. The final state (red line) has a 2π twisted wall at the center of the cell, which disappears due to restructuring of order (cyan arrow), leaving the πT state of LH (dashed line). When the soliton reaches the center of the cell, director reorientation occurs (white circle), giving the optical transmission peak in (C) (white circle). (C) Optical transmission peak between crossing polarizer and analyzer following electric field reversal. The time of arrival of the soliton at the center of the cell is graphed in (A) and color-coded as in (C). The same set of peaks appear from - to + as a - to + transition, indicating that each transition completely switches the palmability of the πT state. (D) Simulated ERT response of the πT state of uniformly twisted RH for an E field favoring the central cell orientation of φ=0. The final E-induced state (black) indicates that the electric field penetration length ξE=√K / PE of the surface orientation to the cell is small in 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), and this can be used to analyze the uniform φ(t) data at (E). At (E), four gold electrode cells (NSEW) have random planar alignments, a pulsed voltage is applied to W, and NS and E are grounded. A small DC bias sets the initial orientation φo to approximately 45°, and the transmission I(t) between the intersecting P and A is measured. Response times from 10% to 90% with respect to the electric field amplitude are shown as cyan squares at (A).For smaller applied fields, the response time decreases according to 1 / E, and this is used to determine γ. The deviation from the 1 / E dependence at larger E values ​​is due to the effect of the depolarization voltage at these electrodes and appears only for a short time. [Figure 5] This figure shows a device according to an example of the present disclosure. [Modes for carrying out the invention]

[0015] It should be understood that the elements in the figures are shown for simplicity and clarity and are not necessarily drawn to actual size. For example, some dimensions of the elements in the figures may be emphasized relative to others in order to aid in understanding the embodiments shown in this disclosure.

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

[0017] Exemplary embodiments of this disclosure provide an improved device. The exemplary device comprises a volume containing ferroelectric nematic liquid crystal forming molecules and one or more materials including one or more surfaces in contact with the volume.

[0018] According to an example of the present disclosure, the volume comprises a ferroelectric nematic liquid crystal phase, the ferroelectric nematic liquid crystal phase comprising a vector orientation field of electric polarization density throughout the volume, and one or more surfaces configured to provide a preferred surface polarity of molecules, the preferred surface polarity controlling the vector orientation at the interface with one or more surfaces. One or more materials may include a first material comprising a first surface in contact with the volume, and a second material comprising a second surface in contact with the volume. The second surface may be configured to provide a preferred surface polarity of molecules, thereby controlling the vector orientation of molecules in the volume at the interface with the second surface. The preferred surface polarity of molecules may include a component that is locally normal to and directed away from at least one of the one or more surfaces. The preferred surface polarity of a molecule may include a component that is locally tangential to at least one of the one or more surfaces, and the component may include a preferred orientation inherent around the surface normal to at least one of the one or more surfaces. According to an example of this disclosure, the preferred surface polarity of a molecule includes a component brought about by unidirectional buffing of one of the one or more surfaces. According to an additional example, the preferred surface polarity of a molecule is brought about by oblique illumination of one of the one or more surfaces with electromagnetic waves (e.g., having wavelengths in the range of about 0.1 μm to about 10 μm). According to an additional example, the surface polarity of a molecule may include a component brought about via photopolymerization induced by illumination of one of the one or more surfaces. According to a further example, the preferred surface polarity of a molecule includes a component brought about via photopolymerization induced by illumination of one of the one or more surfaces, where the illumination is oblique. In some cases, the preferred surface polarity of a molecule includes a component brought about via photodegradation induced by illumination of one of the one or more surfaces.According to an example of this disclosure, the preferred surface polarity of a molecule includes a component obtained by photopolymerization induced by illumination of one of one or more surfaces. According to a further example, the preferred surface polarity of a molecule includes a component obtained by deposition of a material on one of one or more surfaces. The deposition may be oblique. According to a further example of this disclosure, the preferred surface polarity of a molecule includes a component obtained by etching of a material from one or more materials. The etching may be oblique. According to a further example of this disclosure, the device includes one or more electrical connections for applying an electric field to a volume, and / or a device for applying an electromagnetic field to a volume.

[0019] Further examples of this disclosure provide a method for controlling a preferred vector orientation of a ferroelectric liquid crystal polarization field in three dimensions at an interface with one or more materials. 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 to the molecules, the preferred surface polarity controlling the preferred 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 preferred surface polarity of the molecules may include a component that is locally normal to the surface and directed toward the surface. In some cases, the preferred surface polarity of the molecules may include a component that is locally normal to the surface and directed toward away from the surface. The preferred surface polarity of the molecules may include a component that is locally tangential to the first surface. The component may include an inherent preferred orientation around the surface normal. In some cases, the preferred surface polarity of the molecules may include a component brought about by unidirectional buffing of the first surface. The preferred surface polarity of a molecule may include a component brought about by oblique illumination of a first surface with electromagnetic waves (e.g., having wavelengths in the range of about 0.10 μm to about 10 μm). In some cases, the preferred surface polarity of a molecule may include a component brought about by photopolymerization induced by oblique illumination of the first surface. In some cases, the preferred surface polarity of a molecule may include a component brought about by photodegradation induced by oblique illumination of the first surface. The preferred surface polarity of a molecule may include a component brought about by oblique deposition of a material onto the first surface and / or oblique etching of a material from the first surface. According to various examples of this disclosure, contact between the first surface and the volume occurs in a first temperature phase, and the volume is cooled to a ferroelectric nematic phase at a second temperature. The volume may contain a nematic phase at the first temperature. In some cases, the volume may contain an isotropic material at the first temperature. The volume may contain a ferroelectric nematic phase. In a further example of this disclosure, interface control is used to establish polar vector orientation in three dimensions of the spontaneous polarization field within the volume of a ferroelectric nematic liquid crystal.

[0020] Further examples of the present disclosure provide a method for forming a ferroelectric nematic liquid crystal device. The method comprises 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 giving the molecules a preferred surface polarity, which controls the vector orientation at the interface with the first surface. Interface control establishing polar vector orientation in three dimensions of the spontaneous polarization field within the volume of ferroelectric nematic liquid crystal can be achieved by cooling the liquid crystal volume from a higher temperature phase to a ferroelectric nematic liquid crystal phase, where the higher temperature phase is a non-ferroelectric nematic phase, and the cooling is configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase. The cooling may be configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase, where the gradient allows the ferroelectric nematic phase to be formed first on a selected surface. The method may further include the step of applying an electric field to the ferroelectric nematic phase. As an addition or alternative, this method may include providing dopant molecules dissolved in a ferroelectric nematic phase. The dopant molecules have a dipole moment, which is preferentially aligned to be adjacent to or near it by the vector orientation field of the FNLC. In a further example, 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 as the temperature decreases (e.g., 10 times the viscosity of the material in the isotropic phase). 8 (This results in a higher viscosity.)

[0021] Further additional examples of this disclosure provide another device. The device comprises a volume containing ferroelectric liquid crystal forming molecules and a first material comprising a first surface in contact with the volume, the first surface being configured to control the vector orientation of molecules in the volume at the interface with the first surface by providing a preferred surface polarity for the molecules. The volume contains a ferroelectric nematic phase. The device may include any of the features described above in relation to other devices and / or methods for forming the device.

[0022] The inventors demonstrate that the polar ordering of NF in the devices described herein brings about novel changes to nematic interactions with boundary surfaces, key aspects of nematic LC science, and its future potential for the technology. The inventors demonstrate that by controlling the polarity of the 2D boundary surface of polar molecules, it is possible to construct a vector orientation distribution of its 3D volume. In the simplest example, if the preferred polarization orientation is vectorially unidirectional over most of the surface, the NF volume polarization can be likewise oriented without the need for an applied field, and is polarized to a vectorially uniform orientation by the surface.

[0023] Samples of materials with spontaneous vector order, such as ferromagnets and ferroelectrics, are divided 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, and these fields are made locally parallel to the surface to minimize the internal energy. The deliberate disruption of this scheme by application of an external field (field poling), for example placing an iron rod in a magnetic field to produce a bar magnet, or the external reversal of the polarization of ferroelectric nanocrystals acting as bit storage units in non-volatile solid-state memories, is an important process in their use. Field poling of soft materials, such as corona poling of chromophores including polymers to produce polarized monodomains for nonlinear optical and electronic electro-optic applications, has not been successful because high fields are required. In contrast, the present inventors have found that by surface poling of ferroelectric nematics, nearly complete polar order monodomain ordering can be achieved even in the absence of a poling field.

[0024] In ferroelectric nematics, the reduction in symmetry associated with the emergence of the bulk polarization density P(r) results in a macroscopic coupling of P and the applied field E via the bulk energy density U PE =-P·E. For molecules in which the net molecular dipole is approximately parallel to the long steric axis of the molecule, P(r) is macroscopically coupled to be parallel to ±n(r) by the orientation energy preference U Pn =-u Pn |(n·P) / P|. The energy density coefficient u Pn can be estimated as u Pn ≒k B T / vol, where vol is the volume of the molecule. When a gradual change in the orientation of P(r) is applied at x=0, n(r) has a distance |x|=ξ≒√(K / u Pn) follows. Therefore, P(r) and ±n(r) are essentially locked in orientation together on a macroscopic scale, and thus, 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 a polarization inversion wall that reverses P by 180° in a uniform n field.

[0025] The descriptions of exemplary embodiments provided herein are illustrative and intended for illustrative purposes only, and are not intended to limit the scope of this disclosure or the claims. Furthermore, the descriptions of some embodiments having the described features are not intended to exclude other embodiments having additional features or incorporating different combinations of the described features.

[0026] In this disclosure, any two numbers of a variable can constitute an effective range of that variable, and any range shown may include or exclude the endpoints. In addition, any value of a variable shown (whether shown with “approximately” or not) refers to an exact value or an approximate value, may include equals, and may refer to the mean, median, representative, majority, etc. Furthermore, in this disclosure, the terms “includes,” “composed of,” and “have” may independently refer to “typically or broadly include,” “includes,” “essentially consists of,” or “consists of.” In this disclosure, any defined meaning is not necessarily excluded from the usual customary meaning.

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

[0028] The following examples illustrate various devices and methods for forming and using them. These examples are illustrative and are not intended to limit the scope of the present invention.

[0029] Polar surface anchoring - At the intersection of P(r) and the boundary surface, a polarization charge / region is located on the surface, along with external ions and electron charges, as well as N F Long-range interactions induced by the electric field with the director occur. However, since the boundary surface itself is always inherently polar, the local surface interaction, characterized by the energy / region of the LC surface interaction W(θ,φ) and the orientation of the director n(r) on the surface relative to its normal (θ,φ), must include a polarity contribution in addition to the nonpolar RP term. Surface manifold r s and a vector field S(r) defined at all points in the direction normal to the interface of the plane locally. s ) can be chosen to represent an unavoidable element of polarity associated with the surface. S(r s ) generally gives the location and value of the maximum value of the structural gradient, such as the interfacial electric polarization density, the density of some molecular component of the LC or boundary phase, or the polarization density of the molecular component of the interface material.

[0030] N F The appearance of polarization in the phase is due to term W P (r s )∝P(r s )·S(r s ) is added to W, which prioritizes the 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 polishing buffing, the nematic director orientation on the surface is subject to RP-type interactions, which in itself gives a preferred in-plane (y,z) alignment of n(r), which is the surface energy density W Q Stabilized by (φ), where φ gives the in-plane orientation between n and the buffing direction z. 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, the inventors of the present invention W Q (φ) = wQ W is sin(2φ) Q (φ) is a quadrupole, and here w Q is a phenomenological coefficient. In the case of bidirectional buffing or normal incident light orientation in the (x,z) plane, the preferred director orientation also has n parallel to the surface (the example of PLANAR, shown by the white double arrows 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 polarity symmetry, bending along n.

[0031] On the other hand, if in-plane anisotropy is introduced by unidirectional buffing along z, or by oblique optical orientation in the (x,z) plane or some other oblique treatment, the preferred surface orientation of n for this treatment is not parallel to the surface but forms some angle 0 < ψ < π / 2 with respect to the surface plane (the PRETILTED example). In such a pretilted geometry, in equilibrium there exists a component of P along S, and the intrinsic polarity of the surface normal (gray arrow in Figure 1B) is coupled to both the in-plane and normal components of P, so W P is non-zero. That is, the pretilt quadrupole interaction provides equivalent surface energies for n and -n by pretilt, while the surface energies for P and -P are different. In Figure 1B, gray / white arrows are used to represent this polarity feature in the surface interaction. If φ is the in-plane azimuthal angle between c, which is the in-plane component of n, and the rubbing direction z, then W s (φ) is mirror symmetric with respect to the rubbing direction [W s (φ) = W s (-φ)] is given by equation W s (φ) = W Q (φ)+W P (φ) = w Q sin(2φ)+w P We can choose such that sin(ψ)cos(φ) exists, where w P w is a phenomenological coefficient. LC surface energy density w Q The quadrupole anisotropy of w has been widely studied experimentally. In contrast, w PThis is required by symmetry, but its magnitude or sign is unknown. In this specification, the inventors of N F We demonstrate in-plane polar surface alignment of the phase, and using this, obtain an estimate of the polar component of the anchoring energy, showing that such interaction allows for complete polarity control of the geometry of the nematic director of a cell aligned in plane. We induce a twisted state of the nematic director and apply an in-plane electric field to produce voltage-controlled optical activity, achieving a faster response using a much smaller field.

[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 The material was packed into a glass cell, with a gap of thickness d separating the plates, one of which was patterned with ITO or gold electrodes spaced L apart for the application of an in-plane electric field. The cells were optically investigated using depolarized transmission light microscopy imaging (DTLM) with incident white light and single-wavelength transmission measurements with a 632 nm HeNe laser beam focused to a 30 μm diameter spot. Both random planar glass surfaces giving a Schlierene texture in the N phase and plates coated with a buffed polymer alignment layer that gives planar monodomains of the N phase when cooled from an isotropic phase were used.

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

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

[0035] NN FThe transition cools a nonpolar, aligned cell with a spatially uniform temperature at -1°C / min, which is first patterned by a texture of irregular domains extending locally parallel to n(r) appearing on a submicron scale, then tempered to millimeters in length into a pattern of lines with low optical contrast at approximately 2°C intervals, which are also generally oriented along n(r). These lines become coarse or developed to form closed loops of about 10-200 microns in some places, which have a distinctive, elongated, characteristic lens shape along n(r), as shown in Figures 1A and 1C. These lines form the boundaries of pure polarization reversals (PPRs) between ferroelectric domains of P with opposite signs, and these domains occupy nearly equal areas of the cell, i.e., showing little preference for any particular sign of P. Applying a small probe field allows visualization of distinct orientations of P, providing important evidence for the ferroelectric nematic phase of RM734. Therefore, nonpolar alignment results in uniform quality alignment of n, providing good extinction between the intersecting polarizer and analyzer, with hectomicron to millimeter-scale domains of opposite sign to P aligned.

[0036] NN F In a spatially uniform temperature-aligned cell of a SYNPOLAR cooled by the transition at -1°C / min, a uniform N-phase nematic monodomain is formed. F It grows as polar monodomains in the phase. This texture is given defects by the appearance of a crystalline phase at T≈90°C, but by tempering from T=120°C to room temperature, glassy, ​​uniform birefringent monodomains are obtained.

[0037] The inventors also investigated the effects of in-planar polarity ordering and alignment of a single surface within a cell using the Aryasova and Reznick temperature gradient method. Aryasova and Reznick studied the phase behavior of nematic LC structures and LCs between glass plates while maintaining a constant temperature difference ΔT across the cell thickness. Aryasova and Reznick found that when cooled by a phase transition from isotropic (I) to nematic (N) under these conditions, the acquired dominant nematic alignment was that of the colder cell surface. Therefore, when a temperature gradient is applied, the I / N interface first appears at the colder surface and moves from that surface to the other as a quasi-planar sheet. In a cell where one plate is coated with a rubbed polymer film and the other with an untreated polymer film to provide random planar alignment, it was found that this type of cooling resulted in a cell with uniform planar alignment when nematics were grown from the rubbed surface, or a defective Schlieren texture when nematics were grown from the other randomly planar alignment surface within the same cell.

[0038] RM734 maintains a temperature difference of approximately 2°C between the outside of the top and bottom cell plates, with the top plate being colder, while NN in the ANTIPOLAR cell. F The transition caused cooling at -1°C / min. The temperature difference in the intercellular gap containing LC can be estimated to be ΔT ≈ 0.1°C. In these cells, N to N F The transfer to N F In phase, a sharp boundary with significant birefringence is observed. This boundary moves across the cell towards the lower plate, and as shown in Figures 1B and 1C, polarity N F The monodomain is preserved. This cooling process is schematically shown in Figure 1B, where Figure 1B is N FThis indicates that the phase nucleates and emerges nematically from the colder surface, growing and filling the entire gap between the plates, as evidenced by the remaining uniformly orange birefringent color, thus realizing a uniformly birefringent oriented structure. This state has a birefringent color that disappears between the crossing polarizer and analyzer, indicating a planar or nearly planar alignment, i.e., n and P are uniform across the cells and parallel to the plates. Such a planarly aligned N with a large P F A key feature of the cell is its block polarization structure, the extent of Pn bonds at the interface, and P x The termination of the process is suppressed by the high electrostatic energy cost of the polarization charge. Therefore, the surface P = 6 μC / cm 2 For this, the polarization self-electric field penetration length ξ P =√K εo / P 2 Within a range of approximately 0.1 nm, the pretilt applied to the surface disappears, the P(r)-n(r) bond becomes locally parallel to the cell plate, and the orientation becomes E x = 0. When P rotates and develops the x component, E is due to the polarization charge on the surface. x However, this acts to return P to a parallel position to the plate. The in-plane orientation of P can be investigated by applying an in-plane electric field of several V / cm. The uniform orientation of nP in this grown monodomain showed that colder surfaces nucleate and grow P in its preferred polar orientation, while warmer surfaces are forced to adopt an unfavorable polar orientation. In the SYNPOLAR cell, both surfaces eventually reach a favorable state.

[0039] Cooling NN FIf the transition is stopped at approximately 7°C or below, this situation persists, and polar monodomains expand and fill the cell region. 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 the purple region in Figure 1D. This purple region has its own set of internal domain walls (Figure 1D). In particular, as shown in Figures 2A and 2B, the optical attenuation between polarizers intersecting with n aligned with optical polarization is no longer obtained in this new domain, indicating a heterogeneous director field, with only the possibility of a twisted state in the absence of an applied electric field, where n is parallel to the plate and reorients spirally with a constant ∂φ / ∂x. Within this twisted domain, the internal domain wall separates a region that exhibits identical brightness and color between the intersecting polarizer and analyzer (Figure 1D), which becomes darker or brighter depending on the sign of the non-intersecting angle when the polarizer and analyzer are uncrossed (Figures 2E, 2F). This is the optical signature of pairs of identical twisted states with opposite palmarity [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 and a first material having a first surface 202 and a second material having a second surface 204.

[0040] NN F Because the uniform orientation field of n(x) growing in the transition has its preferred orientation at colder plates (x=d) and less energetically favorable conditions at warmer surfaces (x=0), the inventors have found that a lower T transition to the twisted state results in a twist elastic energy density U of the bulk director field. T = 1 / 2K(∂φ(x) / ∂x) 2We propose that this results in the inversion of nP to its energetically favorable orientation at a warmer surface, at the expense of [something]. A convenient parameterization of the anchoring strength of such anisotropic surface interaction 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 the distance l to the surface. For typical rubbing polyimide alignment, K = 5pN and w Q ≒10 -4 J / m 2 By using l Q Approximately 50 nm is obtained, and thus deformation occurs in the LC film with a thickness of several microns used here, and n(r) on the surface is essentially fixed along one of the preferred quadrupole orientations. A portion of the π twist in LC is d / (d+2l Q Since ) ≈ 1, the torque transmitted by bulk flank elasticity and applied to the surface does not move the orientation at each surface away from the preferred energy minimum φ ≈ 0 or π for quadrupole surface rubbing. In current antipolar surfaces, W on the warmer surface Q These minimum values ​​are φ=0 and φ=π, and W P For this reason alone, the minimum value at φ=0 is at a higher energy, and the minimum value at φ=π is at a lower energy. Therefore, the minimum value at φ=0 is metastable, and as the magnitude of P increases, T decreases, w P As the size of increases, a transition from φ=0 to φ=π becomes possible on warmer surfaces. In the case of a linear π twist φ(z)=πx / d, the U required for this transition to occur is T The conditions from are, w P >Kπ 2 / 4d ≈ 5x10 -6 J / m 2 This minimum requirement is w Qis considerably smaller. The properties of the surface normal polar order of LC vary widely, ranging from full polar ordering of 5CB on semiconductor surfaces to disorder in the case of mirror-symmetric molecules. Ferroelectric chiral smectics exhibit polar surface interactions, including preferred normal polarization reversal at the surface and induction of polarization at the surface. In the latter experiment, the chiral smectic A that exhibits electroclinic effects has an effective surface field E normal to the surface s ≒2 V / μm, and has a normal component of polarization at the surface. If the polar force is electrostatic, the corresponding energy per area U P depends on l, which is the thickness of the interaction volume, and U P ≒PE s l. In the case of the N F 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 should be obtained. Surface polarity can also induce LC polarization, thereby inducing a flexoelectric ordered electric gradient near the surface.

[0041] As shown in Figure 1B, when considering in more detail the surface phenomenon that becomes warmer as the N-N F growth surface approaches, the N F phase is replaced by the N phase that contacts the warmer buffed surface, and its director is located at one of the quadrupolar director alignment surface energy minima. The N F director has the same alignment, but the polar alignment induced in the N phase by this surface does not match the alignment of the incoming N F surface, and a PPR wall is formed in the uniform director field. This geometry is at least metastable at temperatures close to the N-N F transition. At lower temperatures, the orientation of n near the surface changes by π and transitions to another quadrupolar minimum, leaving P at the anchored surface. When the temperature gradient along x is reduced, N FAs the PPR wall grows from both surfaces, a PPR wall is formed within the bulk. This case is schematically shown in Figure 2C, which also illustrates a simple topological transition that can occur, where a suitable twist deformation of Pn in the PPR wall reduces the magnitude of the reversal of the P component, leading to the disappearance of the PPR wall and the appearance of a twisted wall, which then spreads and fills the cells, giving rise to a πT state. This is a barrier-restricted transition, as the initial twist must substantially exceed the width of the PPR wall. The process of disappearing the PPR wall near the warmer surface is essentially the same when a gradient of T is present. As a result of such a barrier-restricted topological transition, heterogeneous nucleation and growth are seen in Figure 2. The sharp boundaries between the uniform π-twist states are evidence of metastability for the φ=0° surface state in the warmer plate. Therefore, the surface orientation transition between the quadrupole surface energy minimums at φ=0 and φ=-π is solitonic, and the structure is very similar to that of a stabilized π-reorientation wall in chiral smectic ferroelectric LC (SSFLC), which is similarly described by the double-sine Gordon equation.

[0042] The walls separating the πT states are topological and are 2π twist walls (2πTW). These states are shown in Figure 1 and Figure 2, which show that in this cell geometry, with the rubbing direction substantially parallel to the electrode edge, the polarization P(x=d / 2) at the mid-height in the cell is normal to the electrodes, in the y direction for the πTL state and in the -y direction for πTR, and thus parallel or antiparallel to the applied field E. The 2πTW consists of 2π twist disclination lines in the bulk n and P fields (Figure 2, Figure 3). The topological transition that gives the electric field-induced nucleation of the twist wall loop in Figure 3 is also barrier-limited, resulting in heterogeneous nucleation of the LH domain seen in Figure 3. In combination with chiral doping for controlling the relative stability of different twist states that are otherwise degenerate used in twisted nematic devices, by using selected bidirectionally rubbed or unidirectionally rubbed alignment surfaces with appropriate pretilt, it should be clear from this discussion that virtually any geometry of the twist plane reorientation of the n-P coupling of ferroelectric nematics can be stabilized between the plates.

[0043] In-plane ferroelectric optics and dynamics - Considering the geometry of the planar alignment cell described above, the dynamic response of electric field-induced alignment can be classified into two main types: those brought about mainly by electric field rotation (ERT) and those brought about mainly by electric field reversal (ERV). This division is shown in the dynamically simulated 1D electric field-induced alignment profiles φ(x,t) of Figure 4A and Figure 4B, which show the applied in-plane field E switched on at time t=0 y these distinct dynamic limits of the response of the initially LH πT state to. Figure 4D is the ERT case, modeling the effect of this kind of change in E that would be generated by stepwise electric field rotation y . Here E y favors the alignment P=P y , which is also the starting P at the cell center [P(x=d / 2)=P shown in Figure 2 y]. After this event is completed, the final electric field-induced configuration (black curve in Figure 4D) is subjected to electric field reversal (ERV). In the case of cells with nonpolar surfaces, the polar orientation on these surfaces can be independently reversed, resulting in a uniform mixture of πTL and πTR states, and the resulting surface walls can be moved by the applied field. In contrast, in an ANTIPOLAR cell with a thickness of 3.5 μm, we observed electric field-induced reorientation of the polar surface, and the surface remained at a preferred minimum polarity in the E-field experiment, and simulations of the ANTIPOLAR cell presented herein in Figures 4B and 4D have a fixed surface orientation. However, generally, a finite W s Surface orientation transitions induced by electric field-induced torque may also exist with respect to (φ). The inventors consider the cases of ERT, domain walls, and ERV in the following three chapters. In each case, the electric field variable E is applied to the measurement area, i.e., the probe laser spot in the ERT and ERV cases, and to the electrode gap center relative to the domain dynamic image. At the gap center E ≈ 0.66v / (1mm), v is the voltage applied to the electrode gap, and the reduction is due to the spread of the electric field in the x-direction from the narrow electrode edge.

[0044] ERT Dynamics - In the ERT response Δφ, the electric field-induced reorientation of P to be parallel to the applied E is |Δφ| ≤ 90°. Electric field 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 applied field E y = DeGennes field penetration length ξ for 40V / mm E=√K / PE≒50nm, this condition is continuously achieved everywhere in the cell with a fixed topology, except for the surface regions at x=0 and x=d where the twist is confined to a thickness equivalent thereto. At an electric field E>1V / mm where the twist is confined to surface regions with a thickness less than the wavelength, the optical transmission of this cell approximates that of a uniform birefringent slab, and near-extinction is obtained with the crossed polarizer and analyzer positioned along y and z. In this simulation, E y =40V / 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 alignment response to the applied field is governed by the dynamic torque balance equation T, which is simulated in Figures 4B and 4D E =γφ(x,t) t =-PE y sinφ(x,t)+Kφ(x,t) xx , where γ is the nematic rotational viscosity. As generally applicable herein, when ξ E <<d, the ferroelectric and viscous torques dominate, and the ferroelectric / viscous torque balance independently controls the response of each ξ E ×ξ E ×ξ E volume element of the sample. When φ(t) is chosen to be uniform within the volume, the present inventors obtain -PE y sinφ(t)=γφ(t) t , which yields φ E (t)=2tan -1 [tan(φ o (x) / 2)exp(-tPE y / γ)], where φ o (x) is the initial angle between P and E y in the relevant volume, and further yields E y =V IN / L, where L is the effective electrode gap. For small φ E (t), this gives exponential kinetics with a characteristic relaxation time τ E =γ / PE y . These approximate φ E (t)t ≒φ E (t) / τ E As can be seen in Figure 4D, during reorientation, φ E The linearity of (x) should be maintained. ERT reorientation response time τ E This is the intrinsic viscosity limit response time, scaled by 1 / E to the fastest possible response time for a given γ and P, and is graphed as the lower white line in Figure 4A from the simulation in Figure 4D. In the geometry including the four electrodes in Figure 4E, the shortest E is at the West electrode. y The electro-optic response of the ERT geometry was measured in RM734 by reorienting a 5 μm thick random planar cell using pulses at T=110°C. A small DC bias was initially applied to the West electrode to φ o Giving an angle of approximately 45°, the initial transmission intensity I between the intersecting polarizer and analyzer o This was maximized. Assuming uniform orientation, the transmission strength is I(φ(t))=I o sin[2φ(t)] 2 It is given by φ(t)=φ E The typical measurement response (solid cyan curve) fitted by (t) (blue line) is E y = For an electric field step of 40V / mm τ E This results in γ / PE = 71 μs. 0.66 V / mm <E y The optical response was measured in the range of <36V / mm, and I(φ E (t)) is adapted and graphed as a cyan square in Figure 4A. E vs E y The data was obtained. In the lower half of this range, the inventors determined that φ E As expected for (t), τ E ∝ 1 / E y However, in the case of a higher electric field, τ E is E y We found that it decreased much more slowly than [the other factor]. P = 6 μC / cm 2 By using and fitting lower electric field data, γ = 0.15 Pa·s is given, which is used in the simulation τ EProvide the values, and a dotted line representing the white model is shown in Figure 4A.

[0046] To understand the behavior at high electric fields, the inventors consider that a large P value provides a strong coupling of orientation to the applied field and also brings about ubiquitous space charge effects, which can significantly slow down the motion. In all of the planar infield cells investigated here, N has electrodes. F A thin, effective insulating barrier exists at the phase interface, and the barrier is either non-polarized or has a fixed polarization orientation. Such a layer is N F A portion of the applied voltage is used to maintain the physical separation distance of free charge carriers from the polarization charge pressed against the insulating interface. For example, a polymer film used for alignment creates such a layer, but the interface is N F Even in the gold cell shown in Figure 4E, such an insulating layer exists. Capacitance C farads / cm 2 If it has φ E E of the above equation for (t) y =V IN / L is E y =V IN / L→[V IN -(P / C)cosφ E It should be corrected according to (t)] / L, thereby reducing the depolarization voltage (P / C) cosφ E (t) y This reduces the leakage. Generally, these capacitors are prone to leakage, and free charge passes through the polarization charge, and this process is connected to the resistor RΩ / cm in parallel with C. 2 It can be modeled as E. The inventors then proceed to E y =V IN / L → (V IN / L){1-(P / C)cosφ E Get (t)·exp[-t / RC]}. Slow E y Therefore, the response is slow enough for the P / C voltage to relax, and the entire V is over the LC layer. IN Leaving the / L field, τ E =γ / PE y This gives it the behavior.

[0047] Domain-mediated dynamics – Generally, for small applied in-plane E, the πT states of LH and RH have different net energies of interaction with the electric field. As a result, if both are present in the cell, the 2πTW boundary between them moves in the y,z plane, expanding the region of these states at lower energies in the electric field, or nucleating new lower-energy ones. Such 2πTW formation or motion is essentially hysteresis and, in some cases, allows for bistable electro-optic effects. An example of 2πTW formation using an ANTIPOLAR cell with in-plane d=3.5μm and ITO electrodes spaced 1mm apart is shown in Figure 3. The electric field is fluctuating very slowly (about 0.1Hz) and weak at E<0.3V / mm, and the significant continuous strain of the πT state of RH with increasing field is amplified by the nucleation and growth of the less strained πT domain of LH, eventually occupying the entire cell region (Figure 3), and remaining even when E returns to zero. The electric field direction is shifted by 3° from the bisector of the antiparallel buffing direction, prioritizing the counterclockwise reorientation of P. As a result, the 2π twisted 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 starts from the electric field-restricted LH state, which is the final configuration of the ERT process (black solid curves in Figures 4D and 4B), and E y This is simulated by reversing the sign of E. Here, the entire cell center is E y P is oriented in the opposite direction, and in this orientation, P receives zero torque from the electric field and therefore does not respond. However, near the surface where P is reoriented preferentially, torque exists, and therefore a response begins here, with velocity v=ξ E / τ E This then develops into a soliton that propagates toward the center of the cell, and the electric field reversal time τ R =d / 2v≒τ E (d / 2ξ EThe center is reached within ). This aligns the sheet to the center at x=d / 2, and P results in a reorientation of δφ=2π between equivalent orientations of P. This sheet disappears via a topological process of order reconstruction or the spontaneous emergence of twisted rotational loops, in either case the palmarity changes, leaving a πT configuration of RH restricted by the electric field. Simulate time τ R This is graphed as the white line at the top in Figure 4A, and together with E, τ R ∝E -1 / 2 While it fluctuates as, τ E ∝E -1 Therefore, in this electric field range, τ is the elapsed time at P at φ=0 waiting for the soliton to arrive. R is τ E It is larger in comparison.

[0049] The ERV dynamics were experimentally investigated in the response of the twisted state in Figure 2 to a square wave drive, as simulated in Figure 4B. The optical response allows for the identification of the soliton propagation (bright pink) and topological transition (bright blue) regions. Figure 4C shows the optical transmission (parallel to E) through the intersecting polarizer / analyzer over time following the voltage reversal of the square wave at t=0. This response is identical for + / - and - / + reversals, indicating that a complete transition between the limited T states of LH and RH is obtained with each reversal. After the soliton has propagated and reorientation is complete, the baseline optical transmission is very slow, rotating only 90° and with a thickness of ξ E The surface region depolarizes the light. As E increases, the soliton becomes thinner, resulting in a smaller overall light transmission by the moving soliton (bright pink region). The arrival of the soliton at the cell center is indicated by a separate light peak (white circle in Figures 4B and 4C) and is brought about by a transient, extended linear variation of φ(x) with respect to φ(x)=0 (white circle in Figures 4B and 4C). Immediately after this peak, order reconstruction occurs, completing the transition to the inverse palmar limiting state (bright blue region). The overall transition time τ for this process R This is graphed against E in Figure 4A (the color of the points corresponds to the color in Figure 4C), τ EMuch longer. The simulation in Figure 4B shows a similar τ with no tunable parameters. R We provide values, i.e., only the γ / PE values ​​from the ERT data are used. Optical and polarization field reversal response times are also graphed from Figure 3C, obtained for square wave driving, although with different cell geometries (black dots) (X. Chen, E. Korblova, D. Dong, X. Wei, R. Shao, L. Radzihovsky, M. Glaser, J. Maclennan, D. Bedrov, D. Walba, NA 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 equivalent to those in Figures 4B and 4C, showing a similar response delay effect of electric field reversal. Interestingly, all of these individual datasets are equivalent to the τ expected in the soliton model. R ∝E -1 / 2 Rather, almost τ R ∝E -1This exhibits a dependence. This difference may be due to assumptions in soliton models and simulations that initially, a perfect polar order exists away from the surface and the P field is stable at φ=0. When the electric field switches, this condition causes each soliton to advance by half the cell thickness, d / 2, and switch the cell. However, in reality, due to defects, surface imperfections, and thermal variations, P rarely becomes φ=0 inside the cell, and after the electric field switches, it is subjected to torque and begins to reorient heterogeneously. This process proceeds more rapidly as the electric field increases, leading to local nucleation and soliton-mediated growth of substantially reoriented domains, depending on the size and orientation deviations of the seeding. The net time for a complete inversion decreases because the distance that solitons must advance becomes smaller to the extent that such domains appear and expand. τ R ∝E -1 The behavior of E -1 / 2 As E increases according to this, it should be suggested that the average soliton displacement decreases. The ERV data in Figure 4A should suggest that this may be a universal behavior.

[0050] Nematic and ferroelectric nematic textures—LCs—possess a remarkable combination of fluidity and order, manifesting as an inherently easy macroscopic response to surfaces. Within thin cells between flat plates, the bulk LC configuration is strongly influenced by surface interactions, leading to the formation of unique textures that are micron- to millimeter-scale bulk structural themes reflecting the balance of surface, electric field, and elastic energy. Analysis of these textures, typically using depolarized transmission light microscopy, allows for the investigation of both surface alignment properties and key bulk LC properties such as phase behavior, elasticity, and symmetry. Friedel's discovery of smectics is a prime example of this. If two surface preferences differ within a cell, then generally, each preference should appear in the bulk in some form, either within any given cell or as a statistical average of LC structures across many cells. For example, in the case of a composite aligned cell (one side n normal to the surface and the other side n parallel to the surface), a broadly curved nematic texture exhibits both preferences. If two surfaces are structurally equivalent but have different preferred orientations, for example, if they are rubbed in orthogonal directions, then the different surface preferences must be represented equally in some way within the bulk LC, and in practice, a nematic texture with a 90° twist is formed. On the other hand, a smectic aligned to a plane can correspond to the surfaces within such 90° cells by forming domains that locally fill the cells, some following the 0° surface and others following the 90° surface, and on average the area will be equal across many cells.

[0051] This brings a new N for LC alignment physics. FA cell of the phase is obtained, and similar conditions appear for the polar order of the surface. If the 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 represented. The first clear example of such behavior of nematics is the πT state of a cell with opposite unidirectional buffing on two surfaces, shown in Figures 1 and 2. These states have a symmetrical orientation distribution at φ=π / 2 and therefore equally include incompatible polar surface orientations. This scenario involves 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 gives a uniform director field, the PPR wall is parallel to the cell plate and causes a transition between the two surfaces. The transition to the twisted state in Figure 2C is limited by the barrier, and therefore the PPR wall is stable or metastable depending on its energy cost for twisting. When cooling without a gradient, N / N F The interface can enter the cell from both sides and interact with each other. For example, if thermal interactions exist, the approach of one interface, which releases heat, slows the progress of the other, thus creating the possibility of instability in the coupled Mullins-Sekerkra.

[0052] Polar medium - The LC (e.g., volume as described herein) of bulk FN can be considered as a 3D polar medium filled with a continuous unit vector field v(r) = P(r) / P, and its 3D structure is determined by its electrostatic and Frank elasticity, as well as the 2D positional and vector properties of its interaction with its surface. Such a 3D polar medium can act as a vector solvent that locally orients polar solute molecules along v(r). If we consider a single RM734 molecule in bulk FN as an ideal test solute molecule in a ferroelectric nematic solvent, then P = 6 μC / cm 2In contrast, the inventors have found from atomic simulations that, when the molecular dipole is parallel to v(r) relative to the antiparallel orientation, such a solute molecule can be reversed from its preferred orientation by approximately 10k B The electrostatic energy cost of T can be estimated. Thus, v(r) is an electric field that substantially strongly aligns a molecule with a suitable stereochemical and bipolar structure (e.g., a rod-shaped molecule with a longitudinal mean dipole moment) and is ultimately controlled by the surface.

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

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

[0055] Figure 5 shows a device 500 according to various embodiments and examples of the present disclosure. The device 500 includes a volume 502 and one or more materials 504, 506 including one or more surfaces 508, 510 that are in contact with the volume 502. The device 500 also includes one or more electrical connections 512, 514 for applying an electric field to the volume and a device 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 invention, as these embodiments are merely examples of embodiments of the invention. Any equivalent embodiments are intended to fall within the scope of the invention. In practice, various modifications of the present disclosure, including useful alternative combinations of the elements described, in addition to those illustrated and described herein, will be apparent to those skilled in the art from this description. Such modifications and embodiments are also intended to fall within the scope of the appended claims. The present invention includes the following embodiments. [1] A volume containing ferroelectric nematic liquid crystal forming molecules, wherein the volume contains a ferroelectric nematic liquid crystal phase, and the ferroelectric nematic liquid crystal phase contains a vector orientation field of electric polarization density throughout the entire volume, The material comprises one or more materials including one or more surfaces that come into contact with the volume, The one or more surfaces are configured to give the molecule a preferred surface polarity, and the preferred surface polarity controls the vector orientation at the interface with the one or more surfaces. device. [2] The device according to claim 1, wherein the one or more materials include a first material having a first surface in contact with the volume and a second material having a second surface in contact with the volume. [3] The device according to claim 2, wherein the second surface is configured to provide a preferred surface polarity for the molecules and to control the vector orientation of the molecules in the volume at the interface with the second surface. [4] The device according to any one of 1 to 3, wherein the preferred surface polarity of the molecule includes a component that is locally normal to and away from at least one of the one or more surfaces. [5] The device according to any one of 1 to 3, wherein the preferred surface polarity of the molecule includes a component that is locally normal to and directed toward at least one of the one or more surfaces. [6] The device according to any one of 1 to 3, wherein the preferred surface polarity of the molecule includes a component that is locally tangential to at least one of the one or more surfaces. [7] The device according to claim 6, wherein the component includes a preferred orientation inherent to the surface normal for at least one of the one or more surfaces. [8] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by unidirectional buffing of one of the one or more surfaces. [9] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by oblique illumination of one of the one or more surfaces with electromagnetic waves.

[10] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by photopolymerization induced by illumination of one of the one or more surfaces.

[11] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by photopolymerization induced by illumination of one of the one or more surfaces, and the illumination is oblique.

[12] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by photodegradation induced by illumination of one of the one or more surfaces.

[13] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by photopolymerization induced by illumination of one of the one or more surfaces.

[14] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by the deposition of the material on one of the one or more surfaces.

[15] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is brought about by the deposition of a material on one of the one or more surfaces, and the deposition is oblique.

[16] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is obtained by etching the material from one or more of the materials.

[17] The device according to any one of 1 to 7, wherein the preferred surface polarity of the molecule is obtained by etching the material from one or more materials, and the etching is oblique.

[18] One or more electrical connections for applying an electric field to the aforementioned volume The devices described in any one of 1 to 17, further including the devices described in 1 to 17.

[19] Apparatus for applying an electromagnetic field or electric field to the aforementioned volume The devices described in any one of 1 to 14, further including the devices described in 1 to 14.

[20] A method for controlling the preferred vector orientation of the polarization field of a ferroelectric liquid crystal at an interface with one or more materials in three dimensions, The steps include providing a volume containing ferroelectric liquid crystal forming molecules, The steps include providing a first material having a first surface that contacts the aforementioned volume, A method comprising the steps of using the first surface to give the molecule a preferred surface polarity, wherein the preferred surface polarity controls the preferred vector orientation of the molecule within the volume.

[21] The method according to 20, further comprising the step of providing a second material having a second surface that contacts the aforementioned volume.

[22] The method according to 20 or 21, wherein the preferred surface polarity of the molecule includes a component that is locally normal to the surface and directed toward the surface.

[23] The method according to 20 or 21, wherein the preferred surface polarity of the molecule is induced to be locally normal to the surface and away from the surface.

[24] The method according to any one of 20 to 23, wherein the preferred surface polarity of the molecule is locally tangential to the first surface.

[25] The method according to 24, wherein the component includes a specific preferred orientation around the surface normal.

[26] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is provided by a component obtained by unidirectional buffing of the first surface.

[27] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is brought about by using oblique illumination of the first surface with electromagnetic waves.

[28] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is brought about by photopolymerization induced by oblique illumination of the first surface.

[29] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is brought about by photodegradation induced by oblique illumination of the first surface.

[30] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is brought about by the oblique deposition of the material onto the first surface.

[31] The method according to any one of 20 to 25, wherein the preferred surface polarity of the molecule is brought about by oblique etching of the material from the first surface.

[32] The method according to any one of 20 to 31, wherein the contact between the first surface and the volume occurs in a first temperature phase, and the volume is cooled to become the ferroelectric nematic phase at a second temperature.

[33] The method according to 32, wherein the volume contains a nematic phase at the first temperature.

[34] The method according to 32 or 33, wherein the volume comprises an isotropic material at the first temperature.

[35] The method according to any one of 20 to 34, wherein the volume includes a ferroelectric nematic phase.

[36] The method according to any one of 20 to 35, wherein interface control is used to establish polar vector orientation in three dimensions of the spontaneous polarization field within the volume of a ferroelectric nematic liquid crystal.

[37] A method for forming a ferroelectric nematic liquid crystal device, The steps include providing a volume containing nematic ferroelectric liquid crystal forming molecules, The steps include providing a first material including a first surface that contacts the aforementioned volume, A method comprising the step of giving the molecule a preferred surface polarity, wherein the preferred surface polarity controls the vector orientation at the interface with the first surface.

[38] The method according to any one of 20 to 37, wherein interface control for establishing polar vector orientation in three dimensions of the spontaneous polarization field within the volume of the 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.

[39] The method according to 38, wherein the higher temperature phase is a non-ferroelectric nematic phase.

[40] The method according to 38 or 39, wherein the cooling is configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase.

[41] The method according to 38 or 39, wherein the cooling is configured to maintain a temperature gradient within the liquid crystal during cooling to the ferroelectric nematic phase, and the gradient allows the ferroelectric nematic phase to be formed first on a selected surface.

[42] The method according to 16 to 35, further comprising the step of applying an electric field to the ferroelectric nematic phase.

[43] The device and method according to 1 to 42, further comprising dopant molecules dissolved in the ferroelectric nematic phase.

[44] The device and method according to 43, wherein the dopant molecule has a dipole moment, and the dipole moment is preferentially aligned to be adjacent to or near it by the vector orientation field of the FNLC.

[45] The device and method according to claims 1 to 44, wherein the ferroelectric nematic phase is a mixture of two or more distinct molecular species.

[46] The device and method according to 45, wherein the ferroelectric nematic phase is a eutectic mixture.

[47] The device and method according to claims 1 to 46, wherein the volume vector orientation of the FNLC forms an oriented glass when the temperature decreases.

[48] The volume containing ferroelectric liquid crystal forming molecules, A first material including a first surface that contacts the aforementioned volume, The first surface is configured to provide the molecules with a preferred surface polarity and to control the vector orientation of the molecules within the volume at the interface with the first surface. device.

[49] The device according to 48, wherein the volume includes a ferroelectric nematic phase.

[50] A device as described in 48 or 49, including any of the restrictions in 2 to 19 and 43 to 47.

Claims

1. A volume containing ferroelectric nematic liquid crystal forming molecules, wherein the volume contains a ferroelectric nematic liquid crystal phase, and the ferroelectric nematic liquid crystal phase contains an electric polarization density throughout the entire volume, The material comprises one or more materials including one or more surfaces that come into contact with the volume, The one or more surfaces are configured to provide the polarity of the molecules that control the vector orientation of the electric polarization density at the interface with the one or more surfaces. device.

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

3. The device according to claim 2, wherein the second surface is configured to provide the polarity of the molecule that controls the vector orientation of the electric polarization density at the interface with the second surface.

4. The device according to claim 1, wherein the polarity of the molecule includes a component that is perpendicular to at least one of the one or more surfaces and is guided toward away from at least one of the one or more surfaces.

5. The device according to claim 1, wherein the polarity of the molecule includes a component whose polarity is perpendicular to at least one of the one or more surfaces and is guided toward at least one of the one or more surfaces.

6. The device according to claim 1, wherein the polarity of the molecule is a component that is tangential to at least one of the one or more surfaces.

7. The device according to claim 6, wherein the component includes an orientation about an axis perpendicular to at least one of the one or more surfaces.

8. The device according to claim 1, wherein the polarity of the molecule is provided by a component obtained by unidirectional buffing of one of the one or more surfaces.

9. A method for controlling the vector orientation of electric polarization density in three dimensions of a ferroelectric liquid crystal at an interface with one or more materials, The steps include providing a volume containing ferroelectric liquid crystal forming molecules, The steps include providing a first material having a first surface that contacts the aforementioned volume, A method comprising the step of using the first surface to give polarity to the molecules that control the vector orientation of the electric polarization density in the volume.

10. The method according to claim 9, further comprising the step of providing a second material having a second surface that contacts the aforementioned volume.

11. The method according to claim 9, wherein the polarity of the molecule is perpendicular to the surface and includes a component that is directed toward the surface.

12. The method according to claim 9, wherein the polarity of the molecule is perpendicular to the surface and is guided toward away from the surface.

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

14. The method according to claim 13, wherein the component includes orientation about an axis perpendicular to the first surface.

15. A method for forming a ferroelectric nematic liquid crystal device, The steps include providing a volume containing nematic ferroelectric liquid crystal forming molecules and having electric polarization density, The steps include providing a first material including a first surface that contacts the aforementioned volume, A method comprising the step of giving polarity to the molecule to control the vector orientation of the electric polarization density at the interface with the first surface.

16. The method according to claim 9, wherein interface control for establishing polar vector orientation in three dimensions of the spontaneous polarization field within the volume of the 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. The method according to claim 16, wherein the higher temperature phase is a non-ferroelectric nematic liquid crystal phase.

18. The method according to claim 16, wherein the cooling is configured to maintain a temperature gradient in a direction perpendicular to the first surface in the liquid crystal during cooling to the ferroelectric nematic liquid crystal phase.

19. The method according to claim 16, wherein the cooling is configured to maintain a temperature gradient in a direction perpendicular to the first surface in the liquid crystal during cooling to the ferroelectric nematic liquid crystal phase, the temperature gradient enabling the ferroelectric nematic liquid crystal phase to be initially formed on the selected surface.

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

21. The device according to claim 20, wherein the ferroelectric nematic liquid crystal phase is a eutectic mixture.

22. The device according to any one of claims 1 to 8, wherein the volume vector orientation of the molecule forms an oriented glass when the temperature of the molecule decreases.

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