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Brand HR, Pleiner H. Macroscopic dynamics of the ferroelectric smectic [Formula: see text] phase with [Formula: see text] symmetry. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:10. [PMID: 38305841 PMCID: PMC11226535 DOI: 10.1140/epje/s10189-024-00406-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 01/05/2024] [Indexed: 02/03/2024]
Abstract
We present the macroscopic dynamics of ferroelectric smectic A, smectic [Formula: see text], liquid crystals reported recently experimentally by three groups. In this fluid and orthogonal smectic phase, the macroscopic polarization, [Formula: see text], is parallel to the layer normal thus giving rise to [Formula: see text] overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to non-polar smectic A phases, we find a static cross-coupling between compression of the layering and bending of the layers, which does not lead to elastic forces, but to elastic stresses. In addition, it turns out that a reversible cross-coupling between flow and the magnitude of the polarization modifies the velocities of both, first and second sound. At the same time, the relaxation of the polarization gives rise to dissipative effects for second sound at the same order of the wavevector as for the sound velocity. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Apparently this type of terms has never been considered before for smectic phases. The question how the linear [Formula: see text] coupling in the energy alters the macroscopic response behavior when compared to usual non-polar smectic A phases is also addressed.
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Affiliation(s)
- Helmut R Brand
- Department of Physics, University of Bayreuth, 95440, Bayreuth, Germany
| | - Harald Pleiner
- Max Planck Institute for Polymer Research, 55021, Mainz, Germany.
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2
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Thoen J, Cordoyiannis G, Jiang W, Mehl GH, Glorieux C. Phase transitions study of the liquid crystal DIO with a ferroelectric nematic, a nematic, and an intermediate phase and of mixtures with the ferroelectric nematic compound RM734 by adiabatic scanning calorimetry. Phys Rev E 2023; 107:014701. [PMID: 36797863 DOI: 10.1103/physreve.107.014701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
High-resolution calorimetry has played a significant role in providing detailed information on phase transitions in liquid crystals. In particular, adiabatic scanning calorimetry (ASC), capable of providing simultaneous information on the temperature dependence of the specific enthalpy h(T) and on the specific heat capacity c_{p}(T), has proven to be an important tool to determine the order of transitions and render high-resolution information on pretransitional thermal behavior. Here we report on ASC results on the compound 2,3',4',5'-tetrafluoro[1,1'-biphenyl]-4-yl 2,6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate (DIO) and on mixtures with 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). Both compounds exhibit a low-temperature ferroelectric nematic phase (N_{F}) and a high-temperature paraelectric nematic phase (N). However, in DIO these two phases are separated by an intermediate phase (N_{x}). From the detailed data of h(T) and c_{p}(T), we found that the intermediate phase was present in all the mixtures over the complete composition range, albeit with strongly decreasing temperature width for that phase with decreasing mole fraction of DIO (x_{DIO}). The x_{DIO} dependence on the transition temperatures for both transitions could be well described by a quadratic function. Both these transitions were weakly first order. The true latent heat of the N_{x}-N transition of DIO was as low as L=0.0075±0.0005J/g and L=0.23±0.03J/g for the N_{F}-N_{x} transition, which is about twice the previously reported value of 0.115 J/g for the N_{F}-N transition in RM734. In the mixtures both transition latent heats decrease gradually with decreasing x_{DIO}. At all the N_{x}-N transitions pretransition fluctuation effects are absent and these transitions are purely but very weakly first order. As in RM734 the transition from the N_{F} to the higher-temperature phase exhibits substantial pretransitional behavior, in particular, in the high-temperature phase. Power-law analysis of c_{p}(T) resulted in an effective critical exponent α=0.88±0.1 for DIO and this value decreased in the mixtures with decreasing x_{DIO} toward α=0.50±0.05 reported for RM734. Ideal mixture analysis of the phase diagram was consistent with ideal mixture behavior provided the total transition enthalpy change was used in the analysis.
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Affiliation(s)
- J Thoen
- Laboratory for Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
| | - G Cordoyiannis
- Condensed Matter Physics Department, Jožef Stefan Institute, 1000 Ljubljana, Slovenia
| | - W Jiang
- Department of Chemistry, University of Hull, Hull HU6 7RX, United Kingdom
| | - G H Mehl
- Department of Chemistry, University of Hull, Hull HU6 7RX, United Kingdom
| | - C Glorieux
- Laboratory for Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
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Yang J, Zou Y, Tang W, Li J, Huang M, Aya S. Spontaneous electric-polarization topology in confined ferroelectric nematics. Nat Commun 2022; 13:7806. [PMID: 36528675 PMCID: PMC9759571 DOI: 10.1038/s41467-022-35443-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 12/02/2022] [Indexed: 12/23/2022] Open
Abstract
Topological textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially-distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures, which appear during the emergence and growth of quasi-2D ferroelectric nematic domains. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Both experimental and an extended mean-field modelling reveal that the polarization strength plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.
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Affiliation(s)
- Jidan Yang
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China
| | - Yu Zou
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China
| | - Wentao Tang
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China
| | - Jinxing Li
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China
| | - Mingjun Huang
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China ,grid.79703.3a0000 0004 1764 3838Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou, 510640 China
| | - Satoshi Aya
- grid.79703.3a0000 0004 1764 3838South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou, 510640 China ,grid.79703.3a0000 0004 1764 3838Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou, 510640 China
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4
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Kocot A, Loska B, Arakawa Y, Mehl GH, Merkel K. Study of the Experimental and Simulated Vibrational Spectra Together with Conformational Analysis of Thioether Cyanobiphenyl-Based Liquid Crystal Dimers. Int J Mol Sci 2022; 23:ijms23148005. [PMID: 35887352 PMCID: PMC9316788 DOI: 10.3390/ijms23148005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Revised: 07/15/2022] [Accepted: 07/18/2022] [Indexed: 11/16/2022] Open
Abstract
Infrared spectroscopy (IR) and quantum chemistry calculations that are based on the density functional theory (DFT) have been used to study the structure and molecular interactions of the nematic and twist-bend phases of thioether-linked dimers. Infrared absorbance measurements were conducted in a polarized beam for a homogeneously aligned sample in order to obtain more details about the orientation of the vibrational transition dipole moments. The distributions to investigate the structure and conformation of the molecule dihedral angle were calculated. The calculated spectrum was compared with the experimental infrared spectra and as a result, detailed vibrational assignments are reported.
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Affiliation(s)
- Antoni Kocot
- Institute of Materials Engineering, Faculty of Science and Technology, University of Silesia, ul. 75. Pułku Piechoty, 41-500 Chorzów, Poland; (A.K.); (B.L.)
| | - Barbara Loska
- Institute of Materials Engineering, Faculty of Science and Technology, University of Silesia, ul. 75. Pułku Piechoty, 41-500 Chorzów, Poland; (A.K.); (B.L.)
| | - Yuki Arakawa
- Department of Applied Chemistry and Life Science, Graduate School of Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan;
| | - Georg H. Mehl
- Department of Chemistry, University of Hull, Hull HU6 7RX, UK;
| | - Katarzyna Merkel
- Institute of Materials Engineering, Faculty of Science and Technology, University of Silesia, ul. 75. Pułku Piechoty, 41-500 Chorzów, Poland; (A.K.); (B.L.)
- Correspondence: ; Tel.: +48-32-349-7630
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Anzivino C, van Roij R, Dijkstra M. Coupling between splay deformations and density modulations in splay-bend phases of bent colloidal rods. Phys Rev E 2022; 105:L022701. [PMID: 35291166 DOI: 10.1103/physreve.105.l022701] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.
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Affiliation(s)
- Carmine Anzivino
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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6
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Rosseto MP, Selinger JV. Modulated phases of nematic liquid crystals induced by tetrahedral order. Phys Rev E 2022; 105:024708. [PMID: 35291139 DOI: 10.1103/physreve.105.024708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Accepted: 02/15/2022] [Indexed: 06/14/2023]
Abstract
Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay, and a fourth mode Δ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the Δ mode of director deformation. Because of geometric frustration, the Δ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.
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Affiliation(s)
- Michely P Rosseto
- Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná 5790-87020-900, Brazil
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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Mandle RJ, Sebastián N, Martinez-Perdiguero J, Mertelj A. On the molecular origins of the ferroelectric splay nematic phase. Nat Commun 2021; 12:4962. [PMID: 34400645 PMCID: PMC8367997 DOI: 10.1038/s41467-021-25231-0] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 07/13/2021] [Indexed: 11/25/2022] Open
Abstract
Nematic liquid crystals have been known for more than a century, but it was not until the 60s–70s that, with the development of room temperature nematics, they became widely used in applications. Polar nematic phases have been long-time predicted, but have only been experimentally realized recently. Synthesis of materials with nematic polar ordering at room temperature is certainly challenging and requires a deep understanding of its formation mechanisms, presently lacking. Here, we compare two materials of similar chemical structure and demonstrate that just a subtle change in the molecular structure enables denser packing of the molecules when they exhibit polar order, which shows that reduction of excluded volume is in the origin of the polar nematic phase. Additionally, we propose that molecular dynamics simulations are potent tools for molecular design in order to predict, identify and design materials showing the polar nematic phase and its precursor nematic phases. Nematic liquid crystals with polar order bear great potential for many applications but their rational design is difficult. Mandle et al. outline a set of design principles for this new phase of matter, guided by experiments and simulation, showing polar order to be driven by steric interactions.
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Affiliation(s)
- Richard J Mandle
- School of Physics and Astronomy, University of Leeds, Leeds, UK. .,Department of Chemistry, University of York, York, UK.
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8
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Kats EI. Stability of the uniform ferroelectric nematic phase. Phys Rev E 2021; 103:012704. [PMID: 33601555 DOI: 10.1103/physreve.103.012704] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 01/05/2021] [Indexed: 11/07/2022]
Abstract
The recent discovery of the ferroelectric nematic phase N_{F} resurrects a question about the stability of the uniform N_{F} state with respect to the formation of either a standard for the solid ferroelectric domain structure or for the often occurring liquid crystal space modulation of the polarization vector P (and naturally coupled to P nematic director n). In this work, within Landau mean-field theory, we investigate the linear stability of the minimal model admitting the conventional paraelectric nematic N and N_{F} phases. Our minimal model (in addition to the standard terms of the expansion over the P and director gradients) includes the standard for liquid crystals, the director flexoelectric coupling term (f), and, often overlooked in the literature (although similar by its symmetry to the director flexoelectric coupling), the flexodipolar coupling (β). We find that in the easy-plane anisotropy case (when the configuration with P orthogonal to n is energetically favorable), the uniform N_{F} state loses its stability with respect to one-dimensional (1D) or two-dimensional (2D) modulation. If f≠0, the 2D modulation threshold (β_{c2} value) is always higher than its 1D counterpart value β_{c1}. There is no instability at all if one neglects the flexodipolar coupling (β=0). In the easy-axis case (when n prefers to align along P), both instability (1D and 2D) thresholds are the same, and the instability can occur even at β=0. We speculate that the phases with 1D or 2D modulations can be identified as discussed in the literature [see M. P. Rosseto and J. V. Selinger, Phys. Rev. E 101, 052707 (2020)2470-004510.1103/PhysRevE.101.052707] for single-splay or double-splay nematics.
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Affiliation(s)
- E I Kats
- Landau Institute for Theoretical Physics, RAS, 142432 Chernogolovka, Moscow Region, Russia
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9
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First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics. Proc Natl Acad Sci U S A 2020; 117:14021-14031. [PMID: 32522878 PMCID: PMC7322023 DOI: 10.1073/pnas.2002290117] [Citation(s) in RCA: 87] [Impact Index Per Article: 21.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm2, the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.
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Rosseto MP, Selinger JV. Theory of the splay nematic phase: Single versus double splay. Phys Rev E 2020; 101:052707. [PMID: 32575186 DOI: 10.1103/physreve.101.052707] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
Recent experiments have reported a novel splay nematic phase, which has alternating domains of positive and negative splay. To model this phase, previous studies have considered a one-dimensional (1D) splay modulation of the director field, accompanied by a 1D modulation of polar order. When the flexoelectric coupling between splay and polar order becomes sufficiently strong, the uniform nematic state becomes unstable to the formation of a modulated phase. Here we reexamine this theory in terms of a recent approach to liquid crystal elasticity, which shows that pure splay deformation is double splay rather than planar single splay. Following that reasoning, we propose a structure with a two-dimensional (2D) splay modulation of the director field, accompanied by a 2D modulation of polar order, and show that the 2D structure generally has a lower free energy than the 1D structure.
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Affiliation(s)
- Michely P Rosseto
- Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná 5790-87020-900, Brazil
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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Sebastián N, Cmok L, Mandle RJ, de la Fuente MR, Drevenšek Olenik I, Čopič M, Mertelj A. Ferroelectric-Ferroelastic Phase Transition in a Nematic Liquid Crystal. PHYSICAL REVIEW LETTERS 2020; 124:037801. [PMID: 32031856 DOI: 10.1103/physrevlett.124.037801] [Citation(s) in RCA: 67] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Indexed: 05/15/2023]
Abstract
Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes the formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5-10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory.
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Affiliation(s)
| | - Luka Cmok
- Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Richard J Mandle
- Department of Chemistry, University of York, York YO10 5DD, United Kingdom
| | - María Rosario de la Fuente
- Department of Applied Physics II, University of the Basque Country (UPV/EHU), Apdo.644-48080 Bilbao, Spain
| | - Irena Drevenšek Olenik
- Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000, Ljubljana, Slovenia
| | - Martin Čopič
- Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000, Ljubljana, Slovenia
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