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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Soft Matter</journal-id>
<journal-title>Frontiers in Soft Matter</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Soft Matter</abbrev-journal-title>
<issn pub-type="epub">2813-0499</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1382925</article-id>
<article-id pub-id-type="doi">10.3389/frsfm.2024.1382925</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Soft Matter</subject>
<subj-group>
<subject>Mini Review</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Q&#x26;A of liquid crystal alignment: theory and practice</article-title>
<alt-title alt-title-type="left-running-head">Muravsky and Murauski</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/frsfm.2024.1382925">10.3389/frsfm.2024.1382925</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Muravsky</surname>
<given-names>Alexander</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2248048/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/project-administration/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Murauski</surname>
<given-names>Anatoli</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>MTLCD Lab</institution>, <institution>Private Research Unitary Enterprise &#x201c;MTLCD&#x201d;</institution>, <addr-line>Minsk</addr-line>, <country>Belarus</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Soil Analysis Laboratory</institution>, <institution>Ecole Paysanne de Lignerolles</institution>, <addr-line>Le Thieulin</addr-line>, <country>France</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Materials and Technologies of LC Devices Laboratory</institution>, <institution>Institute of Chemistry of New Materials</institution>, <institution>National Academy of Science of Belarus</institution>, <addr-line>Minsk</addr-line>, <country>Belarus</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/863902/overview">Qi-Huo Wei</ext-link>, Southern University of Science and Technology, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1798982/overview">Yubing Guo</ext-link>, Beijing Institute of Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Alexander Muravsky, <email>alexander.muravsky@gmail.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>03</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>4</volume>
<elocation-id>1382925</elocation-id>
<history>
<date date-type="received">
<day>06</day>
<month>02</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>01</day>
<month>03</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Muravsky and Murauski.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Muravsky and Murauski</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>We selected and summarized the most important aspects of liquid crystal alignment. Alignment by the surface profile and flat surface alignment are discussed as the main factors leading to the high-quality orientation of liquid crystals. The advanced level of understanding and formulation allows linking the alignment layer properties to the molecular structure of the alignment material. The paper reviews and combines the latest knowledge about liquid crystal alignment, dwells upon the relationship between the polar and azimuthal anchoring energy, explains the major particularities regarding anchoring measurements in the case of birefringent alignment materials with truly high azimuthal anchoring energy, and observes the current trends of water-friendly alignment materials and their application in geometrical phase device fabrication.</p>
</abstract>
<kwd-group>
<kwd>liquid crystal alignment</kwd>
<kwd>photoalignment</kwd>
<kwd>anchoring energy</kwd>
<kwd>liquid crystals</kwd>
<kwd>liquid crystal device technology</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Liquid Crystals</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Liquid crystal (LC) alignment is the degree of freedom essential for structural design engineering of liquid crystal devices (LCDs). To some extent, due to its complexity, common knowledge about LC alignment matter is typically reduced to a &#x201c;planar (PL) or vertical alignment (VA) layer achieved through certain standard treatments of commercial alignment material.&#x201d; The comprehension of the knowledge about contemporary levels of LC alignment requires an advanced level of understanding of anisotropic optics, holography, liquid crystals, organic chemistry, physical chemistry, material science, theoretical physics, and electro&#x2013;optical engineering. In this content, we extract and share our best practices gained through over a decade of LC alignment research. In addition, extensive data on LC alignment materials and technologies broaden the scope of theoretical possibilities and technical solutions available to scientists and engineers from the alignment material side. Thus, this paper reviews and summarizes the main aspects of LC alignment and observes its contemporary state, as well as illustrates the practical cases that introduce a wide range of possibilities given by alignment materials via this unexplored degree of freedom to liquid crystal science researchers and LC device technology developers.</p>
</sec>
<sec id="s2">
<title>2 Basics of LC alignment</title>
<sec id="s2-1">
<title>2.1 Orientation interaction</title>
<p>First, the main aspects of liquid crystal materials are discussed. The shape of the molecular structure determines whether the material has an LC phase. The LC phase material structures with dipole moments form an electromagnetic field in the volume of the LC mixture and interact with it. In the nematic LC phase, the dipole moment, <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mi mathvariant="bold-italic">C</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, is directed along the molecule. In the smectic ferroelectric LC phase, the dipole moment is transverse to the molecule and is oriented within the smectic layer.</p>
<p>In nematic LC order parameters, <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>1</italic>
</bold>
</sub> &#x3d; 0 and <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>2</italic>
</bold>
</sub> &#x3d; 0.4&#x2013;0.8, while in ferroelectric LC order parameters, <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>1</italic>
</bold>
</sub> &#x2260; 0 and <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>2</italic>
</bold>
</sub> &#x2260; 0. Further on, we only consider nematic liquid crystals.</p>
<p>LCs also exhibit elastic orientation properties. When trying to locally change the direction of orientation of molecules, there are forces that return the molecules to their average orientation state. These properties are described by the elastic theory of liquid crystals (<xref ref-type="bibr" rid="B11">Frank, 1958</xref>).</p>
<p>In free space, LC molecules are oriented randomly. The external impact (such as the electric or magnetic field) can orient LC molecules in one direction. In the case of the external field, the influence occurs on each of the molecules, and they are all oriented in the same direction given by the field.</p>
</sec>
<sec id="s2-2">
<title>2.2 Surface alignment interaction</title>
<p>Surface LC alignment is the interaction of the liquid crystal continuum with the bounding surface, leading to the orientation of the LC director at the interface in the direction <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3c6;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. It has the meaning of the boundary condition for minimizing the total energy of liquid crystal elastic deformations. This interaction is quantified in terms of the LC deformation energy at the surface that stabilizes the specified alignment direction, <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mover accent="true">
<mml:mi>n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3c6;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, which is also called anchoring energy, <italic>A</italic>, having the unit of joule per meter square. The stabilization occurs due to the increase in the anchoring energy part of the system total energy when the LC director deviates from the alignment direction, i.e., <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mo>&#x2260;</mml:mo>
<mml:msub>
<mml:mover accent="true">
<mml:mi>n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which means deviation angles <italic>&#x394;&#x3b8;</italic> and <italic>&#x394;&#x3c6;</italic> in polar coordinates (<xref ref-type="fig" rid="F1">Figure 1</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Polar coordinates of alignment direction on the surface of the alignment film.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g001.tif"/>
</fig>
<p>The anchoring energy causes the force applied to the liquid crystal media at the surface from the alignment layer, which tends to minimize the total energy of the system:<disp-formula id="equ1">
<mml:math id="m5">
<mml:mrow>
<mml:mover accent="true">
<mml:mi mathvariant="bold-italic">F</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mover accent="true">
<mml:mo>&#x2207;</mml:mo>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Needless to mention, the same force is applied to the alignment layer surface in the liquid crystal medium. In some rare cases, it may even cause inelastic deformation of the surface of the alignment layer, which is the failure of the alignment material. The nabla operator &#x2207; indicates the mathematical operation of a gradient in direction. Thus, the change in the anchoring energy makes a contribution, while the constant does not contribute to the LC alignment. The standard formulation of the anchoring energy is the Rapini&#x2013;Popoular form (<xref ref-type="bibr" rid="B1">Barbero and Durand, 1986</xref>):<disp-formula id="equ2">
<mml:math id="m6">
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mover accent="true">
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mo>&#x2219;</mml:mo>
<mml:msub>
<mml:mover accent="true">
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>which, in polar coordinates, is the sum of polar, <italic>A</italic>
<sub>
<italic>p</italic>
</sub>, and azimuthal, <italic>A</italic>
<sub>
<italic>a</italic>
</sub>, surface anchoring energies:<disp-formula id="equ3">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">p</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">p</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:msup>
<mml:mi mathvariant="bold-italic">cos</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b8;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b8;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">p</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:msup>
<mml:mi mathvariant="bold-italic">sin</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b8;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b8;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">p</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ4">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:msup>
<mml:mi mathvariant="bold-italic">cos</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:msup>
<mml:mi mathvariant="bold-italic">sin</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>where <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>p</italic>
</bold>
</sub> and <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub> are the constants of polar and azimuthal anchoring energies, respectively.</p>
<p>The actual surface LC direction is due to the anisotropy of its properties on the surface. Thus, if the surface of the substrate is treated to provide it with anisotropic properties, then the liquid crystal on such a surface will be oriented in one direction.</p>
<sec id="s2-2-1">
<title>2.2.1 Alignment by the profiled surface</title>
<p>A simple way to add anisotropy to a surface is to create a wave-like profile. This alignment technique is widely utilized in oblique vacuum deposition, embossing, and rubbing. All these methods are based on the modification of the surface profile. The alignment effect is the result of minimizing the energy of LC elastic deformation. The liquid crystal is oriented in such a way as to reduce the size of the bulk deformations caused by the surface (<xref ref-type="fig" rid="F2">Figure 2</xref>). <xref ref-type="fig" rid="F2">Figure 2A</xref> shows the orientation of the LC director along the surface profile without the elastic deformation of the liquid crystal, which minimizes the LC deformation energy. <xref ref-type="fig" rid="F2">Figure 2B</xref> shows the orientation of the LC director along the surface but perpendicular to the profile, which maximizes the LC deformation energy. The difference in the LC deformation energies at the profiled surface is subject to the parameters of the surface profile and is the cause of LC alignment.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Liquid crystal orientation on the surface profile: <bold>(A)</bold> without and <bold>(B)</bold> with elastic deformations of the liquid crystal medium.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g002.tif"/>
</fig>
<p>According to method of <xref ref-type="bibr" rid="B2">Berreman (1972)</xref>, the LC alignment impact of the surface profile on the azimuthal anchoring energy coefficient is as follows:<disp-formula id="equ5">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:msup>
<mml:mi mathvariant="bold-italic">&#x3c0;</mml:mi>
<mml:mn mathvariant="bold">3</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mi mathvariant="bold-italic">K</mml:mi>
</mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mn mathvariant="bold">3</mml:mn>
</mml:msup>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <bold>
<italic>A</italic>
</bold> is the profile height, <bold>
<italic>&#x3bb;</italic>
</bold> is the profile pitch, and <bold>
<italic>K</italic>
</bold> is the elastic constant of the liquid crystal.</p>
<p>The Berreman method admits the infinite polar anchoring energy coefficient. However, in the case of finite polar anchoring, the formula for the azimuthal anchoring coefficient is modified (<xref ref-type="bibr" rid="B10">Faetti, 1987</xref>) as follows:<disp-formula id="equ6">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:msup>
<mml:mi mathvariant="bold-italic">&#x3c0;</mml:mi>
<mml:mn mathvariant="bold">3</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mi mathvariant="bold-italic">K</mml:mi>
</mml:mrow>
<mml:msup>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mn mathvariant="bold">3</mml:mn>
</mml:msup>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mn mathvariant="bold">1</mml:mn>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c0;</mml:mi>
<mml:mi mathvariant="bold-italic">K</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Considering the equation above, it is easy to conclude that azimuthal anchoring is a part of polar anchoring or <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>p</italic>
</bold>
</sub> <bold>&#x3e; <italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub>. Thus, in the case of weak polar LC&#x2013;surface interaction, the azimuthal anchoring of the profiled surface is weak. In such a case, the coating of the surface profile with a thin layer of the polar material increases the azimuthal anchoring (<xref ref-type="bibr" rid="B12">Hileuskaya et al., 2023</xref>).</p>
<p>At the same time, for strong-anchoring (<bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub> &#x3e; 10<sup>&#x2212;5</sup>&#xa0;J/m<sup>2</sup>) cases, one can measure <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub> as the lower anchoring limit and vice versa, i.e., for low-anchoring cases (<bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub> &#x2264; 10<sup>&#x2212;7</sup>&#x2013;10<sup>&#x2013;6</sup>&#xa0;J/m<sup>2</sup>), one should consider <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>p</italic>
</bold>
</sub> as the upper anchoring limit.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Alignment by the flat surface</title>
<p>The influence of the surface on the orientation of the liquid crystal is not limited to the surface profile only. There are stronger interactions that have nothing to do with surface profiling. Photoalignment is the most striking evidence of this statement. The surface profile does not change during photoalignment, while the LC alignment direction is set by the orientation of the light polarization plane when the photoalignment material surface is exposed to polarized light.</p>
<p>The same forces and interactions that cause the orientation of LC molecules in one direction in the volume are also strong when interacting with the alignment surface. These are the dipole&#x2013;dipole interactions. If there is a layer on the surface of which the dipole moments of the molecules are oriented in one direction, then, when interacting with such a surface, the LC will be oriented in the direction specified on the surface of the alignment layer. The energy of the LC interaction with such a layer is given as follows (<xref ref-type="bibr" rid="B22">Murauski, 2009</xref>):<disp-formula id="equ7">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3c6;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>b</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:msup>
<mml:mi>z</mml:mi>
<mml:mn>6</mml:mn>
</mml:msup>
<mml:mi>k</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ8">
<mml:math id="m12">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msup>
<mml:mi>cos</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x3c6;</mml:mi>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <bold>
<italic>&#x3c6;</italic>
</bold> is the angle between the mean directions of the dipole moments of layers <italic>a</italic> and <italic>b</italic>; <bold>
<italic>&#x3bc;</italic>
</bold> is the dipole moment; <italic>z</italic> is the distance between layers <italic>a</italic> and <italic>b</italic>; <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>1</italic>
</bold>
</sub> and <bold>
<italic>P</italic>
</bold>
<sub>
<bold>
<italic>2</italic>
</bold>
</sub> are the orientation order parameters; and <bold>
<italic>&#x421;</italic>
</bold>
<sub>
<bold>
<italic>0</italic>
</bold>
</sub> is the normalizing constant.</p>
<p>In the case of smectic LC, orientational order parameter <italic>P</italic>
<sub>
<italic>1</italic>
</sub> &#x2260; 0 should be taken into account. However, in the case of nematic LC, <italic>P</italic>
<sub>
<italic>1</italic>
</sub> &#x3d; 0, and the formula is reduced, which allows us to derive the azimuthal anchoring energy coefficient as the factor of the squared cosine term (<xref ref-type="bibr" rid="B26">Muravsky et al., 2020</xref>):<disp-formula id="equ9">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">C</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mi mathvariant="bold-italic">C</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mi mathvariant="bold-italic">C</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <inline-formula id="inf5">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mi mathvariant="bold-italic">C</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the average dipole moment of the nematic liquid crystal molecule; <inline-formula id="inf6">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the dipole moment of the alignment layer molecule; <inline-formula id="inf7">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mi mathvariant="bold-italic">C</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf8">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the orientation order parameters <italic>P</italic>
<sub>
<italic>2</italic>
</sub> of the liquid crystal and the alignment layer, respectively; and <bold>
<italic>C</italic>
</bold> is the constant.</p>
</sec>
</sec>
</sec>
<sec id="s3">
<title>3 Q&#x26;A of liquid crystal alignment</title>
<sec id="s3-1">
<title>3.1 Classical rubbing alignment</title>
<p>Polyimide film is the standard LC alignment layer widely applied in LCD fabrication. After coating with the imide solution, the film undergoes high-temperature baking at typically T &#x2265; 180&#xb0;C for &#x3e;1&#xa0;h for the thermal imidization process that forms linear polyimide chains. The rubbing step that follows causes inelastic shear deformation of the polyimide film, ordering the chains at the surface along the rubbing direction (<xref ref-type="bibr" rid="B30">Stohr and Samant, 1999</xref>). In the ideal case, it is the flat surface alignment. Since the rubbing alignment effect comes not from surface scratching but due to the surface ordering of polyimide chains formed at the hard-baking step (<xref ref-type="fig" rid="F3">Figure 3</xref>), the prior high temperature is essential, while the rubbing conditions and the rubbing cloth are critical (<xref ref-type="bibr" rid="B32">Yamahara et al., 2007</xref>). High-temperature imidization is already a standard but a rather slow and limiting step. Can it be changed to an alternative?</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Process flow of the rubbed polyimide alignment layer.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g003.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Low-temperature alignment material</title>
<p>Rethinking a standard concept is always challenging. The MTLCD laboratory rethought and developed a low-temperature alignment material (LTAM) that replaced imidization with photo-crosslinking under UV light (<xref ref-type="bibr" rid="B14">Mahilny et al., 2009</xref>) (<xref ref-type="fig" rid="F4">Figure 4</xref>).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Process flow of the low-temperature alignment material (LTAM) alignment layer.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g004.tif"/>
</fig>
<p>The 1%&#x2013;2% solution of methacrylate polymer with photosensitive benzaldehyde groups in butyl acetate is applied for coating a thin film 20&#x2013;80&#xa0;nm on the substrate. Soft baking at 60&#xb0;C&#x2013;90&#xb0;C for 5&#xa0;min is performed to dry the solvent. The polymer film undergoes inelastic shear deformation of the film surface upon the standard rubbing step with cotton clothes, ordering the polymer chains along the rubbing direction. Finally, non-polarized UV-C/UV-B light exposure at wavelengths of 250&#x2013;330&#xa0;nm for &#x223c;1&#xa0;min is applied to induce photo-crosslinking of the side benzaldehyde groups, which fixes the spatial orientation of the polymer chains, making the polymer solvent insoluble and insensitive to rubbing. Such an alignment material does not possess absorption in the UV-A and blue-VIS spectral ranges for excellent photostability of the LC device.</p>
<p>Needless to mention, LTAM, originally intended for plastic substrates, has excellent chemical compatibility with a wide range of standard substrates, i.e., polyethylene terephthalate (PET), triacetyl cellulose (TAC), polycarbonate (PC), and others. The critical aspect is that common organic solvents applied for alignment layer coating, such as dimethylformamide (DMF), N-methyl-2-pyrrolidone (NMP) or even acetone, work well on glass but often fail on plastic substrates. The LTAM alignment layer was successfully applied on top of the TAC film of the internal polarizer inside 42&#x201d; IPS 3D LCD (<xref ref-type="bibr" rid="B29">Park et al., 2014</xref>).</p>
</sec>
<sec id="s3-3">
<title>3.3 Planar, vertical, and pretilt gradient LTAM for liquid crystal lenses</title>
<p>Photo-crosslinking involves modification of the polymer properties. Can light exposure change the liquid crystal pretilt angle at the surface of the photosensitive alignment layer? In fact, the LC pretilt angle is dose-dependent in the case of the alignment layer. Polar anchoring changes upon light exposure (<xref ref-type="bibr" rid="B3">Bezruchenko et al., 2018</xref>). Such LTAMs, achieved through the careful designing of polymer chemistry (<xref ref-type="bibr" rid="B4">Bezruchenko et al., 2016</xref>), can provide gradient alignment conditions tuning from VA to PL through light exposure control. The main application of pretilt angle gradient alignment materials is the fabrication of polarization-independent liquid crystal lenses (<xref ref-type="bibr" rid="B5">Bezruchenko et al., 2021</xref>) and LC lens arrays (<xref ref-type="fig" rid="F5">Figure 5</xref>) (<xref ref-type="bibr" rid="B24">Muravsky et al., 2022</xref>).</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Microscopic photograph of liquid crystal (LC) lens array with the pretilt angle gradient oriented at 45&#xb0; to light polarization observed in between crossed polarizers.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g005.tif"/>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Holographic embossing alignment for the roll-to-roll process</title>
<p>High polar interaction causes planar liquid crystal alignment with a low pretilt angle, but how do we create and control the azimuthal angle distribution? Classical rubbing causes uniform alignment on the solid substrate, but it is not suitable for the azimuthal pattern on plastic substrates. Can the formation of a profiled surface cause a patterned azimuthal angle at the surface of the LTAM alignment layer?</p>
<p>The holographic embossing process, used in relief-phase hologram manufacturing, was applied for the formation of a patterned profiled surface of a special polymer layer via embossing of a holographic matrix with predetermined directions of diffraction gratings (<xref ref-type="bibr" rid="B15">Mikulich et al., 2019</xref>). Such holographic embossing alignment allows roll-to-roll fabrication of patterned quarter- and half-wave retarders from polymerizable liquid crystals on TAC, PET, and PC substrates (<xref ref-type="bibr" rid="B21">Moiseenko et al., 2019</xref>) at a roll speed of 20&#xa0;m/min. The holographic embossing alignment has the highest process temperature of 70&#xb0;C, which achieves strong azimuthal anchoring over 10<sup>&#x2212;5</sup>&#xa0;J/m<sup>2</sup> and is suitable for q-plates and vortex retarder array fabrication (<xref ref-type="fig" rid="F6">Figure 6</xref>).</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>
<bold>(A)</bold> Scheme of roll with the holographic alignment pattern, <bold>(B)</bold> structure of the polymerizable LC device on the triacetyl cellulose (TAC) substrate, and <bold>(C)</bold> photograph of the LC photonic device array with azimuthal patterns for different topological charges observed on the aluminum reflector through the linear polarizer.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g006.tif"/>
</fig>
</sec>
<sec id="s3-5">
<title>3.5 High-anchoring photoalignment materials for LC photonics</title>
<p>Flat surface alignment is the opposite of profiled surface alignment. Can the flat surface provide a patterned azimuthal alignment of liquid crystal? Photoalignment provides a direct positive answer verified in the experiment. The photoalignment process (<xref ref-type="fig" rid="F7">Figure 7</xref>) comprises film coating, baking, and polarized light exposure. The latter induces anisotropic changes in the film that form the azimuthal LC alignment direction on the flat surface of the photoalignment material (<xref ref-type="bibr" rid="B9">Chigrinov et al., 2008</xref>).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Process flow of the photoalignment layer.</p>
</caption>
<graphic xlink:href="frsfm-04-1382925-g007.tif"/>
</fig>
<p>Flat optics and LC photonics based on the liquid crystal-mediated geometrical phase are one of the most advanced and promising applications of contemporary photoalignment technology (<xref ref-type="bibr" rid="B6">Chen et al., 2020</xref>). Successful LC device fabrication requires photoalignment materials with azimuthal anchoring energy constant <bold>
<italic>W</italic>
</bold>
<sub>
<bold>
<italic>a</italic>
</bold>
</sub> &#x3e;10<sup>&#x2212;4</sup>&#xa0;J/cm<sup>2</sup>, which is equivalent to PI rubbing used in LC displays. High azimuthal anchoring is needed to minimize deviations in the azimuthal plane of the LC optical axis from the LC alignment direction given by the alignment layer. For the flat surface case, it requires alignment materials with high dipole moments, like AtA-0042 with <inline-formula id="inf9">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x223c;</mml:mo>
<mml:mn mathvariant="bold">27.7</mml:mn>
<mml:mi mathvariant="bold">D</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B27">Muravsky et al., 2021</xref>).</p>
</sec>
<sec id="s3-6">
<title>3.6 Azimuthal anchoring energy measurement</title>
<p>The largest deviation in the azimuthal plane of achiral nematic LC is obtained in a 90-twist nematic (TN) cell, when the azimuthal orientations given by the alignment layer on top and bottom substrates are orthogonal, giving cell twist angle <inline-formula id="inf10">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mn mathvariant="bold">90</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. Such conditions induce the twist deformation of LC inside the cell, causing LC twist angle <inline-formula id="inf11">
<mml:math id="m20">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>What is the principle of azimuthal anchoring energy measurement? Torque balance is the basic principle, and it is achieved when the energies of LC twist deformation and azimuthal anchoring at both substrates are equal:<disp-formula id="equ10">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="bold-italic">K</mml:mi>
<mml:mn mathvariant="bold">22</mml:mn>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="bold">sin</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <inline-formula id="inf12">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">K</mml:mi>
<mml:mn mathvariant="bold">22</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the LC twist elastic constant, <inline-formula id="inf13">
<mml:math id="m23">
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <italic>d</italic> is the LC cell gap. Next, the standard optical method (<xref ref-type="bibr" rid="B13">Konovalov et al., 2000</xref>) is used to determine <inline-formula id="inf14">
<mml:math id="m24">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and compute <inline-formula id="inf15">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. What assumption is used by the method? It is assumed that the linearly polarized light transmitted through the twist nematic LC cell in a wave-guiding mode rotates its polarization plane to the angle, <inline-formula id="inf16">
<mml:math id="m26">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, that is equivalent to the twist angle of the LC structure, <inline-formula id="inf17">
<mml:math id="m27">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Thus, the model assumption is formulated as follows:<disp-formula id="equ11">
<mml:math id="m28">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b3;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>This assumption is not valid for an optically anisotropic alignment layer with retardation <inline-formula id="inf18">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2260;</mml:mo>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. What is the effect of alignment material birefringence on azimuthal anchoring energy measurement? In the case of birefringent alignment material, the formula is less trivial and has to be modified as follows (<xref ref-type="bibr" rid="B25">Muravsky and Murauski, 2021</xref>):<disp-formula id="equ12">
<mml:math id="m30">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b3;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mtext mathvariant="bold">acrtan</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c6;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="bold">tan</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <inline-formula id="inf19">
<mml:math id="m31">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c0;</mml:mi>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the retardation of the liquid crystal layer; <inline-formula id="inf20">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c0;</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the retardation of the alignment layer; <inline-formula id="inf21">
<mml:math id="m33">
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x26;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="bold-italic">d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf22">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2206;</mml:mo>
<mml:mi mathvariant="bold-italic">n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x26;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the birefringence and thickness of LC and alignment layers, respectively; and <inline-formula id="inf23">
<mml:math id="m35">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the wavelength of light.</p>
<p>Thus, the alignment layer birefringence, <inline-formula id="inf24">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b4;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, contributes to the increase in the light polarization plane rotation angle, <inline-formula id="inf25">
<mml:math id="m37">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, leading to overestimated <inline-formula id="inf26">
<mml:math id="m38">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values measured by the standard optical method. However, in the case of really high azimuthal anchoring, an unexpected actual result of <inline-formula id="inf27">
<mml:math id="m39">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b3;</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:mrow>
<mml:mn mathvariant="bold">90</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> may be obtained.</p>
</sec>
<sec id="s3-7">
<title>3.7 Photoinduced hole-dipole photoalignment mechanism</title>
<p>Azo dyes are one of the most efficient LC photoalignment materials (<xref ref-type="bibr" rid="B7">Chigrinov et al., 2005</xref>) that have already been researched for over 2&#xa0;decades. What experimental facts ground contemporary knowledge about the high-anchoring azo-dye photoalignment? A large set of chemical and physical experiments have been performed to clarify the role of different groups of the structure of azo-dye molecules, optimizing LC photoalignment properties and revealing the physics behind it.</p>
<p>Thus, it is established that when the intermolecular hydrogen bond blocks the cis&#x2013;trans isomerization of the azo group, the photoalignment properties vanish (<xref ref-type="bibr" rid="B19">Mikulich V. S. et al., 2015</xref>). Temperature is an alternative way to block the cis&#x2013;trans isomerization. It is established that the azo-dye photoalignment layer photosensitivity completely disappears at 103&#xb0;C and reappears at room temperature (<xref ref-type="bibr" rid="B17">Mikulich et al., 2016a</xref>). At the same time, the temperature neither affects the ability of the dye layer to orient liquid crystals nor changes the alignment direction as photoalignment azo-dye molecules are the salts of alkali metals that form intermolecular coordination bonds (<xref ref-type="bibr" rid="B23">Muravsky, 2009</xref>). The bonding energy of the coordination bonds, <inline-formula id="inf28">
<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">b</mml:mi>
<mml:mi mathvariant="bold-italic">o</mml:mi>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mi mathvariant="bold-italic">s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, is higher than the thermal energy, <inline-formula id="inf29">
<mml:math id="m41">
<mml:mrow>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, but is lower than the energy of the absorbed light photon, <inline-formula id="inf30">
<mml:math id="m42">
<mml:mrow>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mi mathvariant="bold-italic">&#x3bd;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>:<disp-formula id="equ13">
<mml:math id="m43">
<mml:mrow>
<mml:mi mathvariant="bold-italic">k</mml:mi>
<mml:mi mathvariant="bold-italic">T</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">b</mml:mi>
<mml:mi mathvariant="bold-italic">o</mml:mi>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mi mathvariant="bold-italic">s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mi mathvariant="bold-italic">&#x3bd;</mml:mi>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>where <inline-formula id="inf31">
<mml:math id="m44">
<mml:mrow>
<mml:mi mathvariant="bold-italic">k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the Boltzmann constant; <inline-formula id="inf32">
<mml:math id="m45">
<mml:mrow>
<mml:mi mathvariant="bold-italic">h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the Plank constant; <inline-formula id="inf33">
<mml:math id="m46">
<mml:mrow>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the temperature; and <inline-formula id="inf34">
<mml:math id="m47">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3bd;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the absorbed photon frequency.</p>
<p>Since the azo-dye molecules of the photoalignment layer are bonded by coordination bonds, the photoalignment properties depend on the kind of alkali metals (lithium [Li], sodium [Na], potassium [K], rubidium [Rb], or cesium [Cs]), and as verified in the experiment, the K-salts are preferable (<xref ref-type="bibr" rid="B20">Mikulich et al., 2014</xref>). According to the diffusion model of photoaligning in azo-dye layers (<xref ref-type="bibr" rid="B8">Chigrinov et al., 2004</xref>), the dye molecules became oriented perpendicular to the polarization of light exposure, increasing the dye-order parameter, <inline-formula id="inf35">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Two directions are perpendicular to the linear polarization of normal exposure: in the plane and normal to the plane of the photoalignment layer. The preferable direction of molecule orientation during light exposure depends on the dye structure and is subjected to methyl radical position (<xref ref-type="bibr" rid="B18">Mikulich et al., 2016b</xref>).</p>
<p>However, investigating the dependences of photoinduced <inline-formula id="inf36">
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<mml:mi mathvariant="bold-italic">L</mml:mi>
</mml:mrow>
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</mml:math>
</inline-formula> and <inline-formula id="inf37">
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<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:mi mathvariant="bold-italic">a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of the AtA-2 azo-dye layer on the linearly polarized light exposure dose showed that the azimuthal anchoring energy is already high at very low exposure doses, while alignment layer birefringence is close to zero (<xref ref-type="bibr" rid="B25">Muravsky and Murauski, 2021</xref>), as well as the dye molecular order parameter, <inline-formula id="inf38">
<mml:math id="m51">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
<mml:mi mathvariant="bold-italic">d</mml:mi>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">e</mml:mi>
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<mml:mo>&#x2248;</mml:mo>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. The analysis of experimental data showed that the orientation order parameter of the photoalignment layer determines not the ordering of dye molecules <inline-formula id="inf39">
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<mml:mi mathvariant="bold-italic">P</mml:mi>
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> but the order of hole dipoles photoinduced inside the photoalignment layer <inline-formula id="inf40">
<mml:math id="m53">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
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<mml:mn mathvariant="bold">2</mml:mn>
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<mml:mi mathvariant="bold-italic">o</mml:mi>
<mml:mi mathvariant="bold-italic">l</mml:mi>
<mml:mi mathvariant="bold-italic">e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B26">Muravsky et al., 2020</xref>), possibly due to the fixation of molecular orientation by coordination bonds inside the layer. In brief, the hole dipole is the part of the field of the self-consistent dipoles of all dye molecules that remain, when the molecule, having absorbed a photon, is removed.</p>
</sec>
<sec id="s3-8">
<title>3.8 Water-friendly photoalignment materials</title>
<p>The popular photoalignment azo-dye Brilliant Yellow (BY) is air humidity-dependent (<xref ref-type="bibr" rid="B31">Wang et al., 2017</xref>). Why does the water sensitivity of azo-dye happen? The dye layer is coated with the solution of the dry dimethylformamide (DMF) solvent. However, BY photoalignment properties fail if the layer comes into contacts with water or is exposed to humid air. The major troublemaker is sodium sulfonate groups of the dye structure, i.e., <italic>RSO</italic>
<sub>
<italic>3</italic>
</sub>
<italic>Na</italic>. Due to this group, the dye layer absorbs water from the air, forming crystal hydrates and losing its photosensitivity. In fact, crystal hydrate formation is a common problem of azo dyes with the sulfonate group. However, are there water-friendly photoalignment azo-dyes that are not afraid of water? FbF dye is the first type of water-friendly photoalignment material (<xref ref-type="bibr" rid="B16">Mikulich V. et al., 2015</xref>), which yields film that is completely inert to direct water contact and can be rinsed with H<sub>2</sub>O.</p>
<p>The recent trends in LC photoalignment follow sustainable development for &#x201c;GreenLab&#x201d; with the main idea of applying processes that require harmless solvents and generate less pollution. DMF is the standard solvent for azo-dye photoalignment materials. Can the DMF solvent be changed to water? Rethinking the dye structure, it is possible to refuse using DMF solvent and coat films with water. AtA-2522/AbA-2522 dyes are the second type of water-friendly photoalignment materials that can be coated in a fully functional photoalignment layer from H<sub>2</sub>O solution, which provides excellent chemical compatibility. Thus, the AtA-2522 photoalignment layer can be directly coated on top of the polymerizable LC layer for multilayer structure fabrication with advanced properties, i.e., achromatic polymerizable liquid crystal retarder (<xref ref-type="bibr" rid="B28">Muravsky et al., 2023</xref>).</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>The theory of liquid crystal alignment by flat and profiled surfaces is reviewed, focusing on the material treatment of different LC alignment techniques. The examples of rubbing, embossing, and photoalignment practices are considered and analyzed. The importance of alignment layer birefringence is revealed, and its role in the optical method for azimuthal anchoring energy measurement is underlined. The recent LC alignment trend of water-friendly photoalignment materials following sustainability for &#x201c;GreenLab&#x201d; is revealed.</p>
<p>This mini-review examines, in the most complete way, the materials and methods of their processing for the high-anchoring orientation of liquid crystals. Methods of sputtering, etching, ion etching, and other methods of surface profile alignment do not yield high anchoring and were not considered.</p>
</sec>
</body>
<back>
<sec id="s5">
<title>Author contributions</title>
<p>AlM: conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, supervision, validation, visualization, writing&#x2013;original draft, and writing&#x2013;review and editing. AnM: conceptualization, investigation, methodology, software, validation, and writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s6">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The authors acknowledge support from the European Union grant contract ENI/2021/423-841-0035.</p>
</sec>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of interest</title>
<p>Author AlM was employed by Private Research Unitary Enterprise &#x201c;MTLCD.&#x201d;</p>
<p>The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.</p>
</sec>
<sec sec-type="disclaimer" id="s8">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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