Phase diagram of a model melt of bent--core molecules

References

• Takezoe H, Eremin A. Bent-shaped liquid crystals: structures and physical properties. Boca Raton: CRC Press; 2017.
   Google Scholar
• Jákli A, Lavrentovich OD, Selinger JV. Physics of liquid crystals of bent-shaped molecules. Rev Mod Phys. 2018 Nov;90:045004.
   Web of Science ®Google Scholar
• Sepelj M, Lesac A, Baumeister U, et al. Intercalated liquid-crystalline phases formed by symmetric dimers with an [small alpha],[small omega]-diiminoalkylene spacer. J Mater Chem. 2007;17(12):1154–1165. .
   Web of Science ®Google Scholar
• Imrie CT, Henderson PA. Liquid crystal dimers and higher oligomers: between monomers and polymers. Chem Soc Rev. 2007;36(12):2096–2124.
   PubMed Web of Science ®Google Scholar
• Panov VP, Nagaraj M, Vij JK, et al. Spontaneous periodic deformations in nonchiral planar-aligned bimesogens with a nematic-nematic transition and a negative elastic constant. Phys Rev Lett. 2010 Oct;105(16):167801. .
   PubMed Web of Science ®Google Scholar
• Panov VP, Balachandran R, Nagaraj M, et al. Microsecond linear optical response in the unusual nematic phase of achiral bimesogens. Appl Phys Lett. 2011;99(26):261903. .
   Web of Science ®Google Scholar
• Henderson PA, Imrie CT. Methylene-linked liquid crystal dimers and the twist-bend nematic phase. Liq Cryst. 2011;38(11–12):1407–1414.
   Web of Science ®Google Scholar
• Cestari M, Diez-Berart S, Dunmur DA, et al. Phase behavior and properties of the liquid-crystal dimer 1″,7 ″ -bis(4-cyanobiphenyl-4 ′-yl) heptane: A twist-bend nematic liquid crystal. Phys Rev E. 2011 Sep;84(3):031704. .
   Web of Science ®Google Scholar
• Chen D, Porada JH, Hooper JB, et al. Chiral heliconical ground state of nanoscale pitch in a nematic liquid crystal of achiral molecular dimers. Proc Nat Acad Sci. 2013;110(40):15931–15936. .
   PubMed Web of Science ®Google Scholar
• Borshch V, Kim YK, Xiang J, et al. Nematic twist-bend phase with nanoscale modulation of molecular orientation. Nat Commun. 2013;4(1):2635. .
   PubMed Web of Science ®Google Scholar
• Chen D, Nakata M, Shao R, et al. Twist-bend heliconical chiral nematic liquid crystal phase of an achiral rigid bent-core mesogen. Phys Rev E. 2014 Feb;89(2):022506. .
   PubMed Web of Science ®Google Scholar
• Wang Y, Singh G, Agra-Kooijman DM, et al. Room temperature heliconical twist-bend nematic liquid crystal. CrystEngComm. 2015;17(14):2778–2782. .
   Web of Science ®Google Scholar
• Al-Janabi A, Mandle RJ, Goodby JW. Isomeric trimesogens exhibiting modulated nematic mesophases. RSC Adv. 2017;7(75):47235–47242.
   Web of Science ®Google Scholar
• Tuchband MR, Paterson DA, Salamończyk M, et al. Distinct differences in the nanoscale behaviors of the twist–bend liquid crystal phase of a flexible linear trimer and homologous dimer. Proc Nat Acad Sci. 2019;116(22):10698–10704. .
   PubMed Web of Science ®Google Scholar
• Stevenson WD, An J, Zeng X, et al. Twist-bend nematic phase in biphenylethane-based copolyethers. Soft Matter. 2018;14(16):3003–3011. .
   PubMed Web of Science ®Google Scholar
• Walker R, Pociecha D, Abberley JP, et al. Spontaneous chirality through mixing achiral components: a twist-bend nematic phase driven by hydrogen-bonding between unlike components. Chem Commun. 2018;54(27):3383–3386. .
   PubMed Web of Science ®Google Scholar
• Mandle RJ, Davis EJ, Archbold CT, et al. Apolar bimesogens and the incidence of the twist–bend nematic phase. Chem Eur J. 2015;21(22):8158–8167. .
   PubMed Web of Science ®Google Scholar
• Paterson DA, Abberley JP, Harrison WT, et al. Cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase. Liq Cryst. 2017;44(1):127–146.
   Web of Science ®Google Scholar
• Dawood AA, Grossel MC, Luckhurst GR, et al. On the twist-bend nematic phase formed directly from the isotropic phase. Liq Cryst. 2016;43(1):2–12. .
   Web of Science ®Google Scholar
• Archbold CT, Davis EJ, Mandle RJ, et al. Chiral dopants and the twist-bend nematic phase - induction of novel mesomorphic behaviour in an apolar bimesogen. Soft Matter. 2015;11(38):7547–7557. .
   PubMed Web of Science ®Google Scholar
• Hoffmann A, Vanakaras AG, Kohlmeier A, et al. On the structure of the Nx phase of symmetric dimers: inferences from nmr. Soft Matter. 2015;11(5):850–855. .
   PubMed Web of Science ®Google Scholar
• Gorecka E, Salamonczyk M, Zep A, et al. Do the short helices exist in the nematic tb phase? Liq Cryst. 2015;42(1):1–7. .
   Web of Science ®Google Scholar
• Samulski ET, Vanakaras AG, Photinos DJ. The twist bend nematic: a case of mistaken identity. Liq Cryst. 2020;47:1–6.
   Web of Science ®Google Scholar
• Heist LM, Samulski ET, Welch C, et al. Probing molecular ordering in the nematic phases of para-linked bimesogen dimers through NMR studies of flexible prochiral solutes. Liq Cryst. 2020;47:1–16.
   Web of Science ®Google Scholar
• Dozov I, Luckhurst GR. Setting things straight in ‘the twist-bend nematic: a case of mistaken identity’. Liq Cryst. 2020;47:1–18.
   Web of Science ®Google Scholar
• Dozov I. On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules. EPL (Europhysics Letters). 2001;56(2):247.
   Google Scholar
• Emsley JW, Lesot P, Luckhurst GR, et al. Chiral solutes can seed the formation of enantiomorphic domains in a twist-bend nematic liquid crystal. Phys Rev E. 2013 Apr;87(4):040501. .
   Web of Science ®Google Scholar
• Panov VP, Vij JK, Mehl GH. Twist-bend nematic phase in cyanobiphenyls and difluoroterphenyls bimesogens. Liq Cryst. 2017;44(1):147–159.
   Web of Science ®Google Scholar
• Mandle RJ. The dependency of twist-bend nematic liquid crystals on molecular structure: a progression from dimers to trimers, oligomers and polymers. Soft Matter. 2016;12(38):7883–7901.
   PubMed Web of Science ®Google Scholar
• Gorecka E, Vaupotič N, Zep A, et al. A twist-bend nematic (ntb) phase of chiral materials. Angew Chem. 2015;54(35):10155–10159. .
   Google Scholar
• Walker R, Pociecha D, Storey JMD, et al. The chiral twist-bend nematic phase (N*TB). Chem Eur J. 2019;25(58):13329–13335. .
   PubMed Web of Science ®Google Scholar
• Abberley JP, Killah R, Walker R, et al. Heliconical smectic phases formed by achiral molecules. Nat Commun. 2018;9:228.
   PubMed Web of Science ®Google Scholar
• Salamończyk M, Vaupotič N, Pociecha D, et al. Multi-level chirality in liquid crystals formed by achiral molecules. Nat Commun. 2019;10(1):1922. .
   PubMed Web of Science ®Google Scholar
• Meyer R. Structural problems in liquid crystal physics. In: Balian R, Weill G, editors. Molecular fluids (les houches summer school on theoretical physics 1973). New York: Gordon and Breach; 1976. p. 271–343.
   Google Scholar
• Lorman VL, Mettout B. Unconventional mesophases formed by condensed vector waves in a medium of achiral molecules. Phys Rev Lett. 1999 Feb;82(5):940–943.
   Web of Science ®Google Scholar
• Lorman VL, Mettout B. Theory of chiral periodic mesophases formed from an achiral liquid of bent-core molecules. Phys Rev E. 2004 Jun;69(6):061710.
   Web of Science ®Google Scholar
• Shamid SM, Dhakal S, Selinger JV. Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals. Phys Rev E. 2013 May;87(5):052503.
   Web of Science ®Google Scholar
• Memmer R. Liquid crystal phases of achiral banana-shaped molecules: a computer simulation study. Liq Cryst. 2002;29(4):483–496.
   Web of Science ®Google Scholar
• Lubensky TC, Radzihovsky L. Theory of bent-core liquid-crystal phases and phase transitions. Phys Rev E. 2002 Sep;66(3):031704.
   Web of Science ®Google Scholar
• Kats EI, Lebedev VV. Landau theory for helical nematic phases. JETP Lett. 2014;100(2):110–113.
   Web of Science ®Google Scholar
• Longa L, Pajak G. Modulated nematic structures induced by chirality and steric polarization. Phys Rev E. 2016 Apr;93(4):040701.
   PubMed Web of Science ®Google Scholar
• Longa L, Tomczyk W. Twist-bend nematic phase in the presence of molecular chirality. Liq Cryst. 2018;45(13–15):2074–2085.
   Web of Science ®Google Scholar
• Longa L, Tomczyk W. Twist-bend nematic phase from Landau-de Gennes perspective. J Phys Chem C. 2020. DOI:https://doi.org/10.1021/acs.jpcc.0c05711
   Google Scholar
• Aliev MA, Ugolkova EA, Kuzminyh NY. The helicoidal modulated nematic phases in a model system of V–shaped molecules. Int J Modern Phys B. 2019;33(10):1950079.
   Web of Science ®Google Scholar
• Virga EG. Double-well elastic theory for twist-bend nematic phases. Phys Rev E. 2014 May;89(5):052502.
   Web of Science ®Google Scholar
• Barbero G, Evangelista LR, Rosseto MP, et al. Elastic continuum theory: towards understanding of the twist-bend nematic phases. Phys Rev E. 2015 Sep;92(3):030501. .
   Web of Science ®Google Scholar
• Lelidis I, Barbero G. Nematic phases with spontaneous splay–bend deformation: standard elastic description. Liq Cryst. 2016;43(2):208–215.
   Web of Science ®Google Scholar
• Barbero G, Lelidis I. Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach. Liq Cryst. 2019;46(4):535–542.
   Web of Science ®Google Scholar
• Greco C, Luckhurst GR, Ferrarini A. Molecular geometry, twist-bend nematic phase and unconventional elasticity: a generalised Maier-Saupe theory. Soft Matter. 2014;10(46):9318–9323.
   PubMed Web of Science ®Google Scholar
• Greco C, Ferrarini A. Entropy-driven chiral order in a system of achiral bent particles. Phys Rev Lett. 2015 Sep;115(14):147801.
   PubMed Web of Science ®Google Scholar
• Tomczyk W, Pajak G, Longa L. Twist-bend nematic phases of bent-shaped biaxial molecules. Soft Matter. 2016;12:7445–7452.
   PubMed Web of Science ®Google Scholar
• Osipov MA, Pajak G. Effect of polar intermolecular interactions on the elastic constants of bent-core nematics and the origin of the twist-bend phase. Eur Phys J E. 2016;39(4):45.
   PubMed Web of Science ®Google Scholar
• Vanakaras AG, Photinos DJ. A molecular theory of nematic-nematic phase transitions in mesogenic dimers. Soft Matter. 2016;12(7):2208–2220.
   PubMed Web of Science ®Google Scholar
• Matsuyama A. Director-pitch coupling-induced twist-bend nematic phase. J Phys Soc Jpn. 2016;85(11):114606.
   Google Scholar
• Matsuyama A. Twist-bend nematic phases of banana-shaped molecules with an axial chirality. Liq Cryst. 2019;46(15):2301–2321.
   Web of Science ®Google Scholar
• To TBT, Sluckin TJ, Luckhurst GR. Molecular field theory for biaxial nematics formed from liquid crystal dimers and inhibited by the twist-bend nematic. Phys Chem Chem Phys. 2017;19(43):29321–29332.
   PubMed Web of Science ®Google Scholar
• Aliev MA, Ugolkova EA, Kuzminyh NY. The Landau–de Gennes free energy expansion of a melt of V-shaped polymer molecules. J Chem Phys. 2016;145(8):084908.
   PubMed Web of Science ®Google Scholar
• Hołyst R, Schick M. Correlations in a rigid-flexible diblock copolymer system. J Chem Phys. 1992;96(1):730–739.
   Web of Science ®Google Scholar
• Hołyst R, Oswald P. Liquid-crystalline order in polymer systems: basic models. Macromol Theory Simul. 2001;10(1):1–16.
   Web of Science ®Google Scholar
• Landau L, Lifshitz E. Statistical physics. Part 1. Pergamon Press, Oxford;1980.
   Google Scholar
• de Gennes PG. Short range order effects in the isotropic phase of nematics and cholesterics. Mol Cryst Liq Cryst. 1971;12(3):193–214.
   Web of Science ®Google Scholar
• Pokrovsky VL, Patashinskii AZ. Fluctuation theory of phase transitions. London: Pergamon Press; 1979.
   Google Scholar
• Allender D, Longa L. Landau–de Gennes theory of biaxial nematics reexamined. Phys Rev E. 2008 Jul;78(1):011704.
   Web of Science ®Google Scholar
• Zhu C, Tuchband MR, Young A, et al. Resonant carbon K-edge soft X-ray scattering from lattice-free heliconical molecular ordering: soft dilative elasticity of the twist-bend liquid crystal phase. Phys Rev Lett. 2016 Apr;116(14):147803. .
   PubMed Web of Science ®Google Scholar
• Mandle RJ, Archbold CT, Sarju JP, et al. The dependency of nematic and twist-bend mesophase formation on bend angle. Sci Rep. 2016;6(1):36682. .
   PubMed Web of Science ®Google Scholar
• Meyer C, Luckhurst GR, Dozov I. The temperature dependence of the heliconical tilt angle in the twist-bend nematic phase of the odd dimer CB7CB. J Mater Chem C. 2015;3(2):318–328.
   Web of Science ®Google Scholar
• Bloomfield JK, Face SH, Moss Z. Indefinite integrals of spherical bessel functions. arXiv preprint arXiv:170306428. 2017;0;1–12
   Google Scholar