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Fukuda A, Vij JK, Takanishi Y. Variety of subphase emerging sequences, the frustration of three main phases, SmC_{A}^{*}, SmC^{*}, and SmA, and the long-range interlayer interactions. Phys Rev E 2021; 104:014705. [PMID: 34412262 DOI: 10.1103/physreve.104.014705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/01/2021] [Indexed: 11/07/2022]
Abstract
Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)2470-004510.1103/PhysRevE.96.012701], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of SmC_{A}^{*}, SmC^{*}, and SmA with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of SmC_{α}^{*} which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is SmC_{A}^{*}(SmC_{α}^{*})-1/4-1/3-2/5-3/7-1/2-SmC^{*}(SmC_{α}^{*}), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between SmC_{A}^{*}(SmC_{α}^{*}) and (SmC^{*})SmC_{α}^{*}. Moreover, the experimentally confirmed extraordinary subphase emerging sequence SmC^{*}-1/2-SmC_{α}^{*} appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from SmC_{A}^{*} and SmC^{*} to SmC_{α}^{*} is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence SmC_{A}^{*}-1/3-SmC^{*} does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.
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Affiliation(s)
- Atsuo Fukuda
- Department of Electronic and Electrical Engineering, Trinity College Dublin, The University of Dublin, Dublin 2, Ireland
| | - Jagdish K Vij
- Department of Electronic and Electrical Engineering, Trinity College Dublin, The University of Dublin, Dublin 2, Ireland
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Lewandowski W, Vaupotič N, Pociecha D, Górecka E, Liz-Marzán LM. Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X-Ray Scattering. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1905591. [PMID: 32529663 DOI: 10.1002/adma.201905591] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Revised: 03/14/2020] [Accepted: 03/16/2020] [Indexed: 05/21/2023]
Abstract
Intensive research on chiral liquid crystals (LCs) has been fueled by their actively tunable physicochemical properties and structural complexity, comparable to those of sophisticated natural materials. Herein, recent progress in the discovery of new classes of chiral LCs, enabled by a combination of nano- and macroscale investigations is reviewed. First, an overview is provided of liquid crystalline phases, made of chiral and achiral low-weight molecules, that exhibit chiral structure and/or chiral morphology. Then, recent progress in the discovery of new classes of chiral LCs, particularly enabled by the application of resonant X-ray scattering is described. It is shown that the method is sensitive to modulations of molecular orientation and therefore provides information hardly accessible by means of other techniques, such as the sense of helical structures or chirality transfer across length scales. Finally, a perspective is presented on the future scope, opportunities, and challenges in the field of chiral LCs, in particular related to nanocomposites.
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Affiliation(s)
- Wiktor Lewandowski
- Faculty of Chemistry, University of Warsaw, Pasteura 1 St., Warsaw, 02-093, Poland
| | - Nataša Vaupotič
- Department of Physics, University of Maribor, Koroška 160, Maribor, 2000, Slovenia
- Jozef Stefan Institute, Jamova 39, Ljubljana, 1000, Slovenia
| | - Damian Pociecha
- Faculty of Chemistry, University of Warsaw, Pasteura 1 St., Warsaw, 02-093, Poland
| | - Ewa Górecka
- Faculty of Chemistry, University of Warsaw, Pasteura 1 St., Warsaw, 02-093, Poland
| | - Luis M Liz-Marzán
- CIC biomaGUNE and CIBER-BBN, Paseo de Miramón 182, Donostia-San Sebastián, 20014, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, 48013, Spain
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Pan L, Pindak R, Huang CC. Resonant x-ray diffraction spectrum for possible structures of the smectic liquid crystal phase with a six-layer periodicity. Phys Rev E 2014; 89:022501. [PMID: 25353483 DOI: 10.1103/physreve.89.022501] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2013] [Indexed: 11/07/2022]
Abstract
With the discovery of the smectic-C(d6)(*) (SmC(d6)(*)) phase showing six-layer periodicity [S. Wang et al., Phys. Rev. Lett. 104, 027801 (2010)] and a recent report of the observation of a possible alternative structure, the need for a reliable and accurate method for distinguishing different possible structures is more urgent than ever. Through simulations using the tensorial structure factor method, we present the resonant x-ray diffraction (RXRD) spectra for different possible structures as proposed in several theoretical studies. Subtle distinctions between models are shown. The ability and limitations of RXRD as a technique for determining the structure of this particular phase is discussed.
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Affiliation(s)
- LiDong Pan
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - R Pindak
- Photon Sciences Directorate, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - C C Huang
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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Sandhya KL, Chandani ADL, Fukuda A, Kumar S, Vij JK. Superlattice structures observed in the extraordinary phase sequence and analyzed by the phenomenological Landau model and the partially molecular model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062506. [PMID: 23848704 DOI: 10.1103/physreve.87.062506] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2013] [Indexed: 06/02/2023]
Abstract
We draw several electric-field-temperature (E-T) phase diagrams with electric-field-induced birefringence contours in the nOHFBBB1M7 (n=10) and nOTBBB1M7 (n=11) (C11) mixture system by changing the C11 concentration carefully; some of the mixtures show the unusual extraordinary phase sequence where subphases with the four-, five-, and six-layer superlattice structures emerge above the smectic-C(*) main phase. We try to understand the results in terms of two complementary models that have so far been proposed: the phenomenological Landau model of phase transitions by Dolganov et al. [P. V. Dolganov et al., Phys. Rev. E 86, 020701(R) (2012)] and the partially molecular Emelyanenko-Osipov model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)]. The observed E-T phase diagram can be well reproduced by the phenomenological model. An emergence of the subphase with the four-layer superlattice structure above smectic-C(*) is also understandable in terms of the partially molecular model. We discuss the pros and cons of the two models as well.
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Affiliation(s)
- K L Sandhya
- Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
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Dolganov PV, Zhilin VM, Dolganov VK, Kats EI. Commensurate polar smectic structures with a two-component order parameter. Phys Rev E 2011; 82:040701. [PMID: 21230230 DOI: 10.1103/physreve.82.040701] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2010] [Indexed: 11/07/2022]
Abstract
Recently Wang [Phys. Rev. Lett. 104, 027801 (2010)] discovered a novel smectic-C* liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow district, Russia
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Susman K, Zeks B, Cepic M. Theoretical analysis of continuous pitch evolution and reversed phase sequence in antiferroelectric liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031701. [PMID: 20365745 DOI: 10.1103/physreve.81.031701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2009] [Indexed: 05/29/2023]
Abstract
Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted Sm C(alpha)* phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted Sm C* phase appeared below the four-layer Sm CFI2* phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.
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Affiliation(s)
- Katarina Susman
- Faculty of Education, University of Ljubljana, Ljubljana, Slovenia
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Wang S, Pan L, Pindak R, Liu ZQ, Nguyen HT, Huang CC. Discovery of a novel smectic-C{*} liquid-crystal phase with six-layer periodicity. PHYSICAL REVIEW LETTERS 2010; 104:027801. [PMID: 20366625 DOI: 10.1103/physrevlett.104.027801] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2009] [Indexed: 05/29/2023]
Abstract
We report the discovery of a new smectic-C{*} liquid-crystal phase with six-layer periodicity by resonant x-ray diffraction. Upon cooling, the new phase appears between the SmC{alpha}{*} phase having a helical structure and the SmC{d4}{*} phase with four-layer periodicity. This SmC{d6}{*} phase was identified in two mixtures which have an unusual reversed SmC{d4}{*}-SmC{*} phase sequence. The SmC{d6}{*} phase shows a distorted clock structure. Three theoretical models have predicted the existence of a six-layer phase. However, our experimental findings are not consistent with the theories.
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Affiliation(s)
- Shun Wang
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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