An Elastic Quartic Twist Theory for Chromonic Liquid Crystals
Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so lar...
Saved in:
| Published in | Journal of elasticity Vol. 155; no. 1-5; pp. 469 - 489 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.07.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0374-3535 1573-2681 |
| DOI | 10.1007/s10659-022-09983-4 |
Cover
Loading…
| Abstract | Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703,
2022
). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length
in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate
. |
|---|---|
| AbstractList | Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length "Equation missing"
in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate "Equation missing"
. Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022 ). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate . Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length [inline-graphic not available: see fulltext] in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate [inline-graphic not available: see fulltext]. |
| Author | Paparini, Silvia Virga, Epifanio G. |
| Author_xml | – sequence: 1 givenname: Silvia orcidid: 0000-0003-3970-0875 surname: Paparini fullname: Paparini, Silvia organization: Dipartimento di Matematica, Università di Pavia – sequence: 2 givenname: Epifanio G. orcidid: 0000-0002-2295-8055 surname: Virga fullname: Virga, Epifanio G. email: eg.virga@unipv.it organization: Dipartimento di Matematica, Università di Pavia |
| BookMark | eNp9kD1rwzAQhkVJoUnaP9DJ0FntSWdZ8tAhmPQDAqWQzsKR5cYhsRJJpuTf16kLhQ6Z3uHuufd4JmTUutYScsvgngHIh8AgEzkFzinkuUKaXpAxExIpzxQbkTGgTCkKFFdkEsIGAHKVwpg8ztpkvi1DbEzy3pX-lMuvJsRkubbOH5Pa-aRYe7dzbT9aNIeuqZLCH0Mst-GaXNZ92JvfnJKPp_myeKGLt-fXYragBjOMtIIqx5VUORpTcl5zqDOUOTLGKoFSCV4ZqDhwWFmR1aVVAislDUjkLIMap-RuuLv37tDZEPXGdb7tKzWC4lxlqRT9Fh-2jHcheFvrvW92pT9qBvqkSQ-adK9J_2jSaQ-pf5BpYhkb10ZfNtvzKA5o6HvaT-v_vjpDfQPJ5Hx6 |
| CitedBy_id | crossref_primary_10_1063_5_0153831 crossref_primary_10_1103_PhysRevE_108_064701 crossref_primary_10_1080_02678292_2024_2324465 crossref_primary_10_1016_j_molliq_2024_124035 crossref_primary_10_1080_02678292_2024_2313023 crossref_primary_10_1080_02678292_2023_2190626 crossref_primary_10_1016_j_wavemoti_2024_103486 |
| Cites_doi | 10.1007/BF00251555 10.1016/0375-9601(85)90126-4 10.1103/RevModPhys.71.1745 10.1063/1.1674612 10.1039/C5SM01632K 10.1080/21680396.2019.1581103 10.1080/02678292.2015.1078917 10.1039/TF9332900883 10.1103/PhysRevLett.70.194 10.1007/978-1-4899-2867-2 10.1051/jphyscol:1969413 10.1126/sciadv.aaw8331 10.1007/978-3-319-52806-9 10.1002/cpa.22050 10.1039/C8SM01829D 10.1103/PhysRevX.6.011033 10.1080/02678298708086335 10.1080/02678292.2018.1512167 10.1103/PhysRevE.92.019905 10.1021/acsomega.8b03335 10.1103/PhysRevE.100.012702 10.3390/cryst10070604 10.1038/ncomms9067 10.1103/PhysRevLett.78.1476 10.1002/9783527619276.ch15c 10.1038/am.2017.84 10.1134/1.558425 10.1016/j.molliq.2018.11.029 10.1039/B926374H 10.1103/PhysRevE.84.031704 10.1080/14786437308227417 10.1103/PhysRevE.101.012703 10.1039/C0SM00065E 10.1051/jphys:01972003305-6059100 10.1073/pnas.1614620114 10.1007/s10659-022-09899-z 10.1103/PhysRevE.91.050501 10.1016/S1359-0294(98)80019-8 10.1017/S095679252000008X 10.1039/DF9582500019 10.1140/epje/i200101159 10.1103/PhysRevE.106.044703 10.1209/epl/i2001-00513-x 10.1103/PhysRevLett.109.037801 10.1007/s00205-021-01733-5 10.1007/978-3-642-75975-8_11 10.1039/D2SM01420C 10.1080/02678292.2011.614720 10.1529/biophysj.105.064550 10.1073/pnas.1100087108 10.1063/1.1761821 10.1039/TF9332900945 10.1103/PhysRevE.100.052701 10.1090/S0002-9904-1978-14553-4 10.1146/annurev-conmatphys-031620-105712 10.1103/PhysRevLett.90.198302 10.1007/s00332-022-09833-6 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2023 The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2023 – notice: The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION 7SR 7TB 8BQ 8FD FR3 JG9 KR7 |
| DOI | 10.1007/s10659-022-09983-4 |
| DatabaseName | Springer Nature OA Free Journals CrossRef Engineered Materials Abstracts Mechanical & Transportation Engineering Abstracts METADEX Technology Research Database Engineering Research Database Materials Research Database Civil Engineering Abstracts |
| DatabaseTitle | CrossRef Materials Research Database Civil Engineering Abstracts Engineered Materials Abstracts Technology Research Database Mechanical & Transportation Engineering Abstracts Engineering Research Database METADEX |
| DatabaseTitleList | CrossRef Materials Research Database |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Nature OA Free Journals url: http://www.springeropen.com/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering |
| EISSN | 1573-2681 |
| EndPage | 489 |
| ExternalDocumentID | 10_1007_s10659_022_09983_4 |
| GrantInformation_xml | – fundername: Università degli Studi di Pavia |
| GroupedDBID | -54 -5F -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 28- 29K 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 6TJ 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABEFU ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GPTSA GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9P PF0 PT4 PT5 Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SCV SDH SDM SGB SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 W4F WH7 WJK WK8 YLTOR Z45 Z5O Z7S Z7Y Z7Z Z86 Z8N Z8S Z8T ZMTXR ZY4 ~02 ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION 7SR 7TB 8BQ 8FD ABRTQ FR3 JG9 KR7 |
| ID | FETCH-LOGICAL-c363t-d0d93b7893cca22f20f63793111d537852dc0d2020be56fae853d87c0732160f3 |
| IEDL.DBID | U2A |
| ISSN | 0374-3535 |
| IngestDate | Fri Jul 25 12:26:23 EDT 2025 Thu Apr 24 23:00:07 EDT 2025 Tue Jul 01 00:20:28 EDT 2025 Fri Feb 21 02:39:02 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1-5 |
| Keywords | Chromonic liquid crystals Curvature elasticity Nematic liquid crystals Quartic free energy 76A15 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c363t-d0d93b7893cca22f20f63793111d537852dc0d2020be56fae853d87c0732160f3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-2295-8055 0000-0003-3970-0875 |
| OpenAccessLink | https://link.springer.com/10.1007/s10659-022-09983-4 |
| PQID | 3082286475 |
| PQPubID | 326256 |
| PageCount | 21 |
| ParticipantIDs | proquest_journals_3082286475 crossref_primary_10_1007_s10659_022_09983_4 crossref_citationtrail_10_1007_s10659_022_09983_4 springer_journals_10_1007_s10659_022_09983_4 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-07-01 |
| PublicationDateYYYYMMDD | 2024-07-01 |
| PublicationDate_xml | – month: 07 year: 2024 text: 2024-07-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Dordrecht |
| PublicationPlace_xml | – name: Dordrecht – name: Groningen |
| PublicationSubtitle | The Physical and Mathematical Science of Solids |
| PublicationTitle | Journal of elasticity |
| PublicationTitleAbbrev | J Elast |
| PublicationYear | 2024 |
| Publisher | Springer Netherlands Springer Nature B.V |
| Publisher_xml | – name: Springer Netherlands – name: Springer Nature B.V |
| References | Dozov (CR25) 2001; 56 Javadi, Eun, Jeong (CR9) 2018; 14 Lydon (CR4) 2011; 38 Dierking, Martins Figueiredo Neto (CR5) 2020; 10 Rapini, Papoular (CR42) 1969; 30 Lydon (CR3) 2010; 20 Nayani, Chang, Fu, Ellis, Fernandez-Nieves, Park, Srinivasarao (CR6) 2015; 6 Lydon (CR1) 1998; 3 Grelet, Fraden (CR49) 2003; 90 Lelidis, Barbero (CR28) 2016; 43 Lin, Wang (CR53) 2022 Meyer, Balian, Weill (CR26) 1976 Zhou (CR43) 2017 Peng, Lavrentovich (CR20) 2015; 11 Machon, Alexander (CR38) 2016; 6 Burylov (CR55) 1997; 85 Shadpour, Vanegas, Nemati, Hegmann (CR22) 2019; 4 Selinger (CR37) 2018; 6 Paparini, Virga (CR15) 2022; 32 Lydon (CR2) 1998 Selinger (CR39) 2022; 13 Virga (CR13) 2019; 100 Nayani, Fu, Chang, Park, Srinivasarao (CR21) 2017; 114 Tortora, Mishra, Prešern, Doye (CR45) 2020; 6 Tortora, Park, Kang, Savaryn, Hong, Kaznatcheev, Finotello, Sprunt, Kumar, Lavrentovich (CR18) 2010; 6 Virga (CR50) 1989; 107 Eun, Kim, Jeong (CR57) 2019; 100 Lelidis, Barbero (CR30) 2019; 275 Virga (CR36) 1994 Stanley, Hong, Strey (CR44) 2005; 89 Ericksen (CR14) 1966; 9 Barbero, Lelidis (CR29) 2019; 46 Oseen (CR33) 1933; 29 Harris, Kamien, Lubensky (CR46) 1997; 78 Paparini, Virga (CR17) 2022; 106 Zocher (CR35) 1933; 29 Davidson, Kang, Jeong, Still, Collings, Lubensky, Yodh (CR58) 2015; 92 Nehring, Saupe (CR23) 1971; 54 Meyer (CR12) 1973; 27 Lin, Poon, Chow, Gulliver, Levy, Sullivan (CR51) 1996 Kornyshev, Leikin, Malinin (CR48) 2002; 7 Davidson, Kang, Jeong, Still, Collings, Lubensky, Yodh (CR7) 2015; 91 Tortora, Lavrentovich (CR19) 2011; 108 Zhou, Nastishin, Omelchenko, Tortora, Nazarenko, Boiko, Ostapenko, Hu, Almasan, Sprunt, Gleeson, Lavrentovich (CR56) 2012; 109 Long, Selinger (CR16) 2022 Longa, Monselesan, Trebin (CR31) 1987; 2 Frank (CR34) 1958; 25 Cladis, Kléman (CR11) 1972; 33 Geng, Lin (CR52) 2022; 243 Ondris-Crawford, Crawford, Zumer, Doane (CR10) 1993; 70 Fu, Nayani, Park, Srinivasarao (CR8) 2017; 9 Long, Selinger (CR41) 2023 Harris, Kamien, Lubensky (CR47) 1999; 71 Cestari, Diez-Berart, Dunmur, Ferrarini, de la Fuente, Jackson, Lopez, Luckhurst, Perez-Jubindo, Richardson, Salud, Timimi, Zimmermann (CR27) 2011; 84 Oldano, Barbero (CR24) 1985; 110 Osserman (CR54) 1978; 84 Golovaty, Novack, Stenberg (CR32) 2021; 32 Pedrini, Virga (CR40) 2020; 101 Virga, Markovitz, Mizel, Owen (CR59) 1991 C. Long (9983_CR16) 2022 F.H. Lin (9983_CR51) 1996 L. Tortora (9983_CR19) 2011; 108 Z. Geng (9983_CR52) 2022; 243 A. Pedrini (9983_CR40) 2020; 101 F. Lin (9983_CR53) 2022 E.G. Virga (9983_CR13) 2019; 100 I. Lelidis (9983_CR30) 2019; 275 S. Zhou (9983_CR43) 2017 C.B. Stanley (9983_CR44) 2005; 89 Z.S. Davidson (9983_CR58) 2015; 92 S.V. Burylov (9983_CR55) 1997; 85 S. Shadpour (9983_CR22) 2019; 4 M. Cestari (9983_CR27) 2011; 84 A. Rapini (9983_CR42) 1969; 30 J. Fu (9983_CR8) 2017; 9 C.W. Oseen (9983_CR33) 1933; 29 E.G. Virga (9983_CR50) 1989; 107 J. Eun (9983_CR57) 2019; 100 I. Dierking (9983_CR5) 2020; 10 R.B. Meyer (9983_CR26) 1976 R. Osserman (9983_CR54) 1978; 84 A. Kornyshev (9983_CR48) 2002; 7 S. Zhou (9983_CR56) 2012; 109 A.B. Harris (9983_CR46) 1997; 78 J. Lydon (9983_CR3) 2010; 20 I. Lelidis (9983_CR28) 2016; 43 E. Grelet (9983_CR49) 2003; 90 Z.S. Davidson (9983_CR7) 2015; 91 J. Lydon (9983_CR1) 1998; 3 J. Lydon (9983_CR2) 1998 M.M.C. Tortora (9983_CR45) 2020; 6 E.G. Virga (9983_CR59) 1991 D. Golovaty (9983_CR32) 2021; 32 J. Lydon (9983_CR4) 2011; 38 K. Nayani (9983_CR21) 2017; 114 T. Machon (9983_CR38) 2016; 6 I. Dozov (9983_CR25) 2001; 56 J.L. Ericksen (9983_CR14) 1966; 9 F.C. Frank (9983_CR34) 1958; 25 P.E. Cladis (9983_CR11) 1972; 33 C. Long (9983_CR41) 2023 H. Zocher (9983_CR35) 1933; 29 J.V. Selinger (9983_CR37) 2018; 6 S. Paparini (9983_CR15) 2022; 32 J. Nehring (9983_CR23) 1971; 54 A. Javadi (9983_CR9) 2018; 14 L. Tortora (9983_CR18) 2010; 6 J.V. Selinger (9983_CR39) 2022; 13 S. Paparini (9983_CR17) 2022; 106 C. Peng (9983_CR20) 2015; 11 L. Longa (9983_CR31) 1987; 2 K. Nayani (9983_CR6) 2015; 6 G. Barbero (9983_CR29) 2019; 46 C. Oldano (9983_CR24) 1985; 110 R.B. Meyer (9983_CR12) 1973; 27 R.J. Ondris-Crawford (9983_CR10) 1993; 70 E.G. Virga (9983_CR36) 1994 A.B. Harris (9983_CR47) 1999; 71 |
| References_xml | – volume: 107 start-page: 371 year: 1989 end-page: 390 ident: CR50 article-title: Drops of nematic liquid crystals publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00251555 – volume: 110 start-page: 213 issue: 4 year: 1985 end-page: 216 ident: CR24 article-title: An ab initio analysis of the second-order elasticity effect on nematic configurations publication-title: Phys. Lett. A doi: 10.1016/0375-9601(85)90126-4 – volume: 71 start-page: 1745 year: 1999 end-page: 1757 ident: CR47 article-title: Molecular chirality and chiral parameters publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.71.1745 – volume: 54 start-page: 337 issue: 1 year: 1971 end-page: 343 ident: CR23 article-title: On the elastic theory of uniaxial liquid crystals publication-title: J. Chem. Phys. doi: 10.1063/1.1674612 – volume: 11 start-page: 7221 year: 2015 end-page: 7446 ident: CR20 article-title: Chirality amplification and detection by tactoids of lyotropic chromonic liquid crystals publication-title: Soft Matter doi: 10.1039/C5SM01632K – volume: 6 start-page: 129 year: 2018 end-page: 142 ident: CR37 article-title: Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals publication-title: Liq. Crystallogr. Rev. doi: 10.1080/21680396.2019.1581103 – start-page: 273 year: 1976 end-page: 373 ident: CR26 article-title: Structural problems in liquid crystal physics publication-title: Molecular Fluids. Les Houches Summer School in Theoretical Physics – volume: 43 start-page: 208 issue: 2 year: 2016 end-page: 215 ident: CR28 article-title: Nematic phases with spontaneous splay–bend deformation: standard elastic description publication-title: Liq. Cryst. doi: 10.1080/02678292.2015.1078917 – volume: 29 start-page: 883 issue: 4 year: 1933 end-page: 899 ident: CR33 article-title: The theory of liquid crystals publication-title: Trans. Faraday Soc. doi: 10.1039/TF9332900883 – volume: 70 start-page: 194 year: 1993 end-page: 197 ident: CR10 article-title: Curvature-induced configuration transition in confined nematic liquid crystals publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.70.194 – year: 1994 ident: CR36 publication-title: Variational Theories for Liquid Crystals doi: 10.1007/978-1-4899-2867-2 – volume: 30 start-page: 4 issue: C4 year: 1969 end-page: 54456 ident: CR42 article-title: Distorsion d’une lamelle mématique sous champ magnétique conditions d’ancrage aux parois publication-title: J. Phys., Colloq. doi: 10.1051/jphyscol:1969413 – volume: 6 start-page: 5163 issue: 31 year: 2020 end-page: 5168 ident: CR45 article-title: Chiral shape fluctuations and the origin of chirality in cholesteric phases of DNA origamis publication-title: Sci. Adv. doi: 10.1126/sciadv.aaw8331 – year: 2017 ident: CR43 publication-title: Lyotropic Chromonic Liquid Crystals. Springer Theses doi: 10.1007/978-3-319-52806-9 – year: 2022 ident: CR53 article-title: Isotropic-nematic phase transition and liquid crystal droplets publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.22050 – volume: 14 start-page: 9005 year: 2018 end-page: 9011 ident: CR9 article-title: Cylindrical nematic liquid crystal shell: effect of saddle-splay elasticity publication-title: Soft Matter doi: 10.1039/C8SM01829D – volume: 6 year: 2016 ident: CR38 article-title: Umbilic lines in orientational order publication-title: Phys. Rev. X doi: 10.1103/PhysRevX.6.011033 – volume: 2 start-page: 769 issue: 6 year: 1987 end-page: 796 ident: CR31 article-title: An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals publication-title: Liq. Cryst. doi: 10.1080/02678298708086335 – volume: 46 start-page: 535 issue: 4 year: 2019 end-page: 542 ident: CR29 article-title: Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach publication-title: Liq. Cryst. doi: 10.1080/02678292.2018.1512167 – volume: 92 year: 2015 ident: CR58 article-title: Erratum: Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity [Phys. Rev. E 91, 050501(R) (2015)] publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.019905 – volume: 4 start-page: 1662 year: 2019 end-page: 1668 ident: CR22 article-title: Amplification of chirality by adenosine monophosphate-capped luminescent gold nanoclusters in nematic lyotropic chromonic liquid crystal tactoids publication-title: ACS Omega doi: 10.1021/acsomega.8b03335 – start-page: 91 year: 1996 end-page: 121 ident: CR51 article-title: On nematic liquid crystal droplets publication-title: Elliptic and Parabolic Methods in Geometry – volume: 100 year: 2019 ident: CR57 article-title: Effects of chiral dopants on double-twist configurations of lyotropic chromonic liquid crystals in a cylindrical cavity publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.100.012702 – volume: 10 start-page: 604 issue: 7 year: 2020 ident: CR5 article-title: Novel trends in lyotropic liquid crystals publication-title: Crystals doi: 10.3390/cryst10070604 – volume: 6 start-page: 8067 year: 2015 ident: CR6 article-title: Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders publication-title: Nat. Commun. doi: 10.1038/ncomms9067 – volume: 78 start-page: 1476 year: 1997 end-page: 1479 ident: CR46 article-title: Microscopic origin of cholesteric pitch publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.78.1476 – start-page: 981 year: 1998 end-page: 1007 ident: CR2 article-title: XVIII publication-title: Chromonics doi: 10.1002/9783527619276.ch15c – volume: 9 start-page: 393 year: 2017 ident: CR8 article-title: Spontaneous emergence of twist and formation of monodomain in lyotropic chromonic liquid crystals confined to capillaries publication-title: NPG Asia Mater. doi: 10.1038/am.2017.84 – volume: 85 start-page: 873 issue: 1 year: 1997 end-page: 886 ident: CR55 article-title: Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity publication-title: J. Exp. Theor. Phys. doi: 10.1134/1.558425 – volume: 275 start-page: 116 year: 2019 end-page: 121 ident: CR30 article-title: Nonlinear nematic elasticity publication-title: J. Mol. Liq. doi: 10.1016/j.molliq.2018.11.029 – volume: 20 start-page: 10071 year: 2010 end-page: 10099 ident: CR3 article-title: Chromonic review publication-title: J. Mater. Chem. doi: 10.1039/B926374H – volume: 84 year: 2011 ident: CR27 article-title: Phase behavior and properties of the liquid-crystal dimer 1′′,7′′-bis(4-cyanobiphenyl-4′-yl) heptane: a twist-bend nematic liquid crystal publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.84.031704 – volume: 27 start-page: 405 issue: 2 year: 1973 end-page: 424 ident: CR12 article-title: On the existence of even indexed disclinations in nematic liquid crystals publication-title: Philos. Mag. doi: 10.1080/14786437308227417 – volume: 101 year: 2020 ident: CR40 article-title: Liquid crystal distortions revealed by an octupolar tensor publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.101.012703 – volume: 6 start-page: 4157 year: 2010 end-page: 4167 ident: CR18 article-title: Self-assembly, condensation, and order in aqueous lyotropic chromonic liquid crystals crowded with additives publication-title: Soft Matter doi: 10.1039/C0SM00065E – volume: 33 start-page: 591 issue: 5–6 year: 1972 end-page: 598 ident: CR11 article-title: Non-singular disclinations of strength in nematics publication-title: J. Phys. France doi: 10.1051/jphys:01972003305-6059100 – volume: 114 start-page: 3826 issue: 15 year: 2017 end-page: 3831 ident: CR21 article-title: Using chiral tactoids as optical probes to study the aggregation behavior of chromonics publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1614620114 – year: 2022 ident: CR16 article-title: Violation of Ericksen inequalities in lyotropic chromonic liquid crystals publication-title: J. Elast. doi: 10.1007/s10659-022-09899-z – volume: 91 year: 2015 ident: CR7 article-title: Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.91.050501 – volume: 3 start-page: 458 issue: 5 year: 1998 end-page: 466 ident: CR1 article-title: Chromonic liquid crystal phases publication-title: Curr. Opin. Colloid Interface Sci. doi: 10.1016/S1359-0294(98)80019-8 – volume: 32 start-page: 177 issue: 1 year: 2021 end-page: 198 ident: CR32 article-title: A novel Landau-de gennes model with quartic elastic terms publication-title: Eur. J. Appl. Math. doi: 10.1017/S095679252000008X – volume: 25 start-page: 19 year: 1958 end-page: 28 ident: CR34 article-title: On the theory of liquid crystals publication-title: Discuss. Faraday Soc. doi: 10.1039/DF9582500019 – volume: 7 start-page: 83 year: 2002 end-page: 93 ident: CR48 article-title: Chiral electrostatic interaction and cholesteric liquid crystals of DNA publication-title: Eur. Phys. J. E doi: 10.1140/epje/i200101159 – volume: 106 year: 2022 ident: CR17 article-title: Paradoxes for chromonic liquid crystal droplets publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.106.044703 – volume: 56 start-page: 247 issue: 2 year: 2001 ident: CR25 article-title: On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules publication-title: Europhys. Lett. doi: 10.1209/epl/i2001-00513-x – volume: 109 year: 2012 ident: CR56 article-title: Elasticity of lyotropic chromonic liquid crystals probed by director reorientation in a magnetic field publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.037801 – volume: 243 start-page: 1181 year: 2022 end-page: 1221 ident: CR52 article-title: The two-dimensional liquid crystal droplet problem with a tangential boundary condition publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-021-01733-5 – start-page: 211 year: 1991 end-page: 230 ident: CR59 article-title: Drops of nematic liquid crystals publication-title: Mechanics and Thermodynamics of Continua doi: 10.1007/978-3-642-75975-8_11 – year: 2023 ident: CR41 article-title: Explicit demonstration of geometric frustration in chiral liquid crystals publication-title: Soft Matter doi: 10.1039/D2SM01420C – volume: 38 start-page: 1663 issue: 11–12 year: 2011 end-page: 1681 ident: CR4 article-title: Chromonic liquid crystalline phases publication-title: Liq. Cryst. doi: 10.1080/02678292.2011.614720 – volume: 89 start-page: 2552 issue: 4 year: 2005 end-page: 2557 ident: CR44 article-title: DNA cholesteric pitch as a function of density and ionic strength publication-title: Biophys. J. doi: 10.1529/biophysj.105.064550 – volume: 108 start-page: 5163 issue: 13 year: 2011 end-page: 5168 ident: CR19 article-title: Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.1100087108 – volume: 9 start-page: 1205 issue: 6 year: 1966 end-page: 1207 ident: CR14 article-title: Inequalities in liquid crystal theory publication-title: Phys. Fluids doi: 10.1063/1.1761821 – volume: 29 start-page: 945 year: 1933 end-page: 957 ident: CR35 article-title: The effect of a magnetic field on the nematic state publication-title: Trans. Faraday Soc. doi: 10.1039/TF9332900945 – volume: 100 year: 2019 ident: CR13 article-title: Uniform distortions and generalized elasticity of liquid crystals publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.100.052701 – volume: 84 start-page: 1182 year: 1978 end-page: 1238 ident: CR54 article-title: The isoperimetric inequality publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1978-14553-4 – volume: 13 start-page: 49 year: 2022 end-page: 71 ident: CR39 article-title: Director deformations, geometric frustration, and modulated phases in liquid crystals publication-title: Annu. Rev. Condens. Matter Phys. doi: 10.1146/annurev-conmatphys-031620-105712 – volume: 90 year: 2003 ident: CR49 article-title: What is the origin of chirality in the cholesteric phase of virus suspensions? publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.90.198302 – volume: 32 start-page: 74 year: 2022 ident: CR15 article-title: Stability against the odds: the case of chromonic liquid crystals publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-022-09833-6 – volume: 29 start-page: 883 issue: 4 year: 1933 ident: 9983_CR33 publication-title: Trans. Faraday Soc. doi: 10.1039/TF9332900883 – volume: 29 start-page: 945 year: 1933 ident: 9983_CR35 publication-title: Trans. Faraday Soc. doi: 10.1039/TF9332900945 – volume: 78 start-page: 1476 year: 1997 ident: 9983_CR46 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.78.1476 – start-page: 211 volume-title: Mechanics and Thermodynamics of Continua year: 1991 ident: 9983_CR59 doi: 10.1007/978-3-642-75975-8_11 – volume: 109 year: 2012 ident: 9983_CR56 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.037801 – volume: 101 year: 2020 ident: 9983_CR40 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.101.012703 – volume: 14 start-page: 9005 year: 2018 ident: 9983_CR9 publication-title: Soft Matter doi: 10.1039/C8SM01829D – volume: 100 year: 2019 ident: 9983_CR57 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.100.012702 – volume: 243 start-page: 1181 year: 2022 ident: 9983_CR52 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-021-01733-5 – volume: 33 start-page: 591 issue: 5–6 year: 1972 ident: 9983_CR11 publication-title: J. Phys. France doi: 10.1051/jphys:01972003305-6059100 – volume: 27 start-page: 405 issue: 2 year: 1973 ident: 9983_CR12 publication-title: Philos. Mag. doi: 10.1080/14786437308227417 – volume: 25 start-page: 19 year: 1958 ident: 9983_CR34 publication-title: Discuss. Faraday Soc. doi: 10.1039/DF9582500019 – start-page: 91 volume-title: Elliptic and Parabolic Methods in Geometry year: 1996 ident: 9983_CR51 – volume-title: Lyotropic Chromonic Liquid Crystals. Springer Theses year: 2017 ident: 9983_CR43 doi: 10.1007/978-3-319-52806-9 – volume: 107 start-page: 371 year: 1989 ident: 9983_CR50 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00251555 – start-page: 273 volume-title: Molecular Fluids. Les Houches Summer School in Theoretical Physics year: 1976 ident: 9983_CR26 – volume: 10 start-page: 604 issue: 7 year: 2020 ident: 9983_CR5 publication-title: Crystals doi: 10.3390/cryst10070604 – volume: 92 year: 2015 ident: 9983_CR58 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.019905 – volume: 6 start-page: 5163 issue: 31 year: 2020 ident: 9983_CR45 publication-title: Sci. Adv. doi: 10.1126/sciadv.aaw8331 – year: 2022 ident: 9983_CR53 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.22050 – volume: 43 start-page: 208 issue: 2 year: 2016 ident: 9983_CR28 publication-title: Liq. Cryst. doi: 10.1080/02678292.2015.1078917 – volume: 46 start-page: 535 issue: 4 year: 2019 ident: 9983_CR29 publication-title: Liq. Cryst. doi: 10.1080/02678292.2018.1512167 – volume: 114 start-page: 3826 issue: 15 year: 2017 ident: 9983_CR21 publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1614620114 – volume: 32 start-page: 177 issue: 1 year: 2021 ident: 9983_CR32 publication-title: Eur. J. Appl. Math. doi: 10.1017/S095679252000008X – volume: 56 start-page: 247 issue: 2 year: 2001 ident: 9983_CR25 publication-title: Europhys. Lett. doi: 10.1209/epl/i2001-00513-x – volume: 4 start-page: 1662 year: 2019 ident: 9983_CR22 publication-title: ACS Omega doi: 10.1021/acsomega.8b03335 – volume: 38 start-page: 1663 issue: 11–12 year: 2011 ident: 9983_CR4 publication-title: Liq. Cryst. doi: 10.1080/02678292.2011.614720 – year: 2023 ident: 9983_CR41 publication-title: Soft Matter doi: 10.1039/D2SM01420C – volume: 106 year: 2022 ident: 9983_CR17 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.106.044703 – volume: 2 start-page: 769 issue: 6 year: 1987 ident: 9983_CR31 publication-title: Liq. Cryst. doi: 10.1080/02678298708086335 – volume: 70 start-page: 194 year: 1993 ident: 9983_CR10 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.70.194 – volume: 6 year: 2016 ident: 9983_CR38 publication-title: Phys. Rev. X doi: 10.1103/PhysRevX.6.011033 – volume: 54 start-page: 337 issue: 1 year: 1971 ident: 9983_CR23 publication-title: J. Chem. Phys. doi: 10.1063/1.1674612 – volume: 90 year: 2003 ident: 9983_CR49 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.90.198302 – volume-title: Variational Theories for Liquid Crystals year: 1994 ident: 9983_CR36 doi: 10.1007/978-1-4899-2867-2 – volume: 6 start-page: 4157 year: 2010 ident: 9983_CR18 publication-title: Soft Matter doi: 10.1039/C0SM00065E – volume: 275 start-page: 116 year: 2019 ident: 9983_CR30 publication-title: J. Mol. Liq. doi: 10.1016/j.molliq.2018.11.029 – volume: 84 start-page: 1182 year: 1978 ident: 9983_CR54 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1978-14553-4 – volume: 110 start-page: 213 issue: 4 year: 1985 ident: 9983_CR24 publication-title: Phys. Lett. A doi: 10.1016/0375-9601(85)90126-4 – volume: 13 start-page: 49 year: 2022 ident: 9983_CR39 publication-title: Annu. Rev. Condens. Matter Phys. doi: 10.1146/annurev-conmatphys-031620-105712 – year: 2022 ident: 9983_CR16 publication-title: J. Elast. doi: 10.1007/s10659-022-09899-z – volume: 30 start-page: 4 issue: C4 year: 1969 ident: 9983_CR42 publication-title: J. Phys., Colloq. doi: 10.1051/jphyscol:1969413 – volume: 32 start-page: 74 year: 2022 ident: 9983_CR15 publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-022-09833-6 – volume: 108 start-page: 5163 issue: 13 year: 2011 ident: 9983_CR19 publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.1100087108 – volume: 7 start-page: 83 year: 2002 ident: 9983_CR48 publication-title: Eur. Phys. J. E doi: 10.1140/epje/i200101159 – volume: 6 start-page: 129 year: 2018 ident: 9983_CR37 publication-title: Liq. Crystallogr. Rev. doi: 10.1080/21680396.2019.1581103 – volume: 85 start-page: 873 issue: 1 year: 1997 ident: 9983_CR55 publication-title: J. Exp. Theor. Phys. doi: 10.1134/1.558425 – volume: 9 start-page: 393 year: 2017 ident: 9983_CR8 publication-title: NPG Asia Mater. doi: 10.1038/am.2017.84 – volume: 20 start-page: 10071 year: 2010 ident: 9983_CR3 publication-title: J. Mater. Chem. doi: 10.1039/B926374H – volume: 6 start-page: 8067 year: 2015 ident: 9983_CR6 publication-title: Nat. Commun. doi: 10.1038/ncomms9067 – volume: 3 start-page: 458 issue: 5 year: 1998 ident: 9983_CR1 publication-title: Curr. Opin. Colloid Interface Sci. doi: 10.1016/S1359-0294(98)80019-8 – volume: 11 start-page: 7221 year: 2015 ident: 9983_CR20 publication-title: Soft Matter doi: 10.1039/C5SM01632K – volume: 71 start-page: 1745 year: 1999 ident: 9983_CR47 publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.71.1745 – volume: 91 year: 2015 ident: 9983_CR7 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.91.050501 – volume: 100 year: 2019 ident: 9983_CR13 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.100.052701 – volume: 84 year: 2011 ident: 9983_CR27 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.84.031704 – volume: 89 start-page: 2552 issue: 4 year: 2005 ident: 9983_CR44 publication-title: Biophys. J. doi: 10.1529/biophysj.105.064550 – start-page: 981 volume-title: Chromonics year: 1998 ident: 9983_CR2 doi: 10.1002/9783527619276.ch15c – volume: 9 start-page: 1205 issue: 6 year: 1966 ident: 9983_CR14 publication-title: Phys. Fluids doi: 10.1063/1.1761821 |
| SSID | ssj0009840 |
| Score | 2.416698 |
| Snippet | Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 469 |
| SubjectTerms | Biomechanics Capillary tubes Classical and Continuum Physics Classical Mechanics Crystal growth Droplets Elastic properties Engineering Internal energy Liquid crystals Materials Science Mathematical Applications in the Physical Sciences Paradoxes Sequences Theoretical and Applied Mechanics |
| Title | An Elastic Quartic Twist Theory for Chromonic Liquid Crystals |
| URI | https://link.springer.com/article/10.1007/s10659-022-09983-4 https://www.proquest.com/docview/3082286475 |
| Volume | 155 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED7RdoGBRwFRKJUHNrCUxI8kYxW1VLymVipTlMSxVKkUaFoh_j2XxCEFARJThvg8fOfzfZbvPgNcREzIVMUplcilKRe2or6OFJXS07biylWFpND9gxxN-M1UTE1TWFZVu1dXksVOvdHsJoVP8-pzZDUeo7wBLYFn93xdT5x-LbXrFW2QubAKZYIJ0yrz8xxf01HNMb9dixbZZrgPu4Ymkn7p1wPYShdt2DOUkZiAzNqws6EneAh4mCcDpMNoRIpqTfyO39CRpGzBJ8hQSS6H-5QL4pK72et6pkiwfEeKOM-OYDIcjIMRNe8j0IRJtqLKUj6LXWQc6AbH0Y6lJcN4w-1LCeZ6wlGJpRAhK06F1FGKqVl5boJR7djS0uwYmovnRXoChAtfJ7EQypcxR4aBtk7sR0ImccK4lh2wK5jCxIiH529YzMNa9jiHNkRowwLakHfg8tPmpZTO-HN0t0I_NGGUhbmWjuNJ7ooOXFUeqX__Ptvp_4afwTbCxMsy3C40V8t1eo5kYxX3oNW_frwd9KARyKBXrLQP9e3J8Q |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8JAEJ4oHNSDKGpEUffgTddA99H24IEQEOVxggRPDdttEyKi8ojRX--03QoSNeHUw-5s2pmdma_ZmW8BLgdMyECrgErE0pSLsqZuONBUSicsa65tHVMKtTuy0eMPfdE3TWHTtNo9PZKMI_VSs5sULo2qzxHVOIzyTchy_AcXGchW7h6btQXZrhM3QkbUKpQJJkyzzO-r_ExIC5S5cjAa55t6DnrpmyZlJk8385m68T9XSBzX_ZQ92DUAlFSSHbMPG8E4DzkDRolx9WkedpaYCg_gtjImNQTaKETiOlB8dt9xi5CkuZ8g9iUR0e5zRLVLWsO3-VCT6uQDwedoegi9eq1bbVBz8wL1mWQzqkvaZcpGLIMGtqzQKoWSoSdjYNSC2Y6wtF_SFkJNFQgZDgJM-tqxfYwXVlmWQnYEmfHLODgGwoUb-koI7UrFEbugrKXcgZC-8hkPZQHKqfo939CSR7djjLwFoXKkLQ-15cXa8ngBrr5lXhNSjn9nF1OresZBp17E0mM5ktuiANepkRbDf692st70C9hqdNstr3XfaZ7CNqqMJ8W-RcjMJvPgDCHNTJ2bHfwFM0nndQ |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60gujBR1WsVt2DN11s9pXkWGpL1Vo8tNBbaLJZKNRa-0D8987mYaqo4CmH7Ozhm8zuF3a-bwEuh1yqWIcxVcilqZCOpr4ZaqqUZxwttKsTS6HHrmr3xf1ADlZU_Em3e34kmWoarEvTZHEz1eZmRfimpE9tJzoyHI9TsQ4buBw7tqmrz-qF7a6XSCKtyQrlkstMNvPzHF-3poJvfjsiTXae1h7sZJSR1NMc78NaPCnDbkYfSVac8zJsr3gLHgD-2JMmUmMMIknnJj57b5hUksrxCbJVYq1xn605LumMXpcjTRqzd6SL4_kh9FvNXqNNs7sSaMQVX1Bd0z4PXWQfmBLGDKsZxbH2cCnTkrueZDqqaYbkMIylMsMYt2ntuRFWOHNUzfAjKE1eJvExECF9E4VSal-FAtkGxrLQH0oVhREXRlXAyWEKosxI3N5nMQ4KC2QLbYDQBgm0gajA1WfMNLXR-HN0NUc_yEpqHlhfHeYp4coKXOcZKV7_PtvJ_4ZfwObTbSvo3HUfTmELERNpd24VSovZMj5DDrIIz5PP7AOvMs6v |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Elastic+Quartic+Twist+Theory+for+Chromonic+Liquid+Crystals&rft.jtitle=Journal+of+elasticity&rft.au=Paparini%2C+Silvia&rft.au=Virga%2C+Epifanio+G.&rft.date=2024-07-01&rft.pub=Springer+Netherlands&rft.issn=0374-3535&rft.eissn=1573-2681&rft.volume=155&rft.issue=1-5&rft.spage=469&rft.epage=489&rft_id=info:doi/10.1007%2Fs10659-022-09983-4&rft.externalDocID=10_1007_s10659_022_09983_4 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0374-3535&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0374-3535&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0374-3535&client=summon |