Elasticity of lyotropic nematic liquid crystals: a review of experiments, theory and simulation

Abstract

ABSTRACT The elastic response of liquid crystals (LCs) to external perturbations is of eminent importance for both their theoretical understanding and practical application. While the elasticity of thermotropic nematic LCs has been widely studied, far less is known about the elastic properties of lyotropic nematic LCs. In recent years however, several observations of spontaneous mirror symmetry breaking in lyotropic LCs (LLCs) confined in curved geometries stimulated increasing scientific interest in the elastic behaviour of lyotropic nematics. In this review article, we have now compiled the known experimental data on the elastic constants of different classes of nematic LLCs, ranging from micellar via chromonic and polymeric to particle-based LLCs. The experimental findings are compared with simulation results on various model systems and discussed in the light of current theoretical concepts. As a result of these considerations, it is shown that the elastic properties of nematic LLCs can indeed be very different and strongly depending on the nature of their particular nanoscopic building blocks (such as micelles, molecular stacks, semiflexible polymer chains, solid nanoparticles, biofilaments), namely their size, aspect ratio and flexibility, as well as their specific interactions. Nevertheless, in all cases the twist constant K 22 is by far the smallest of the three elastic constants of a certain system and an order of magnitude smaller than typical values found in thermotropic nematics. It also appears that the splay constant K 11 is mainly determined by the aspect ratio of the particular LLC building blocks and the bend constant K 33 by their flexibility. The one-constant approximation, often used for thermotropic nematics, clearly fails in the case of LLCs. Finally, our observations also make obvious that the current knowledge about the elastic properties of LLCs is still incomplete and thus improvements are necessary, both in terms of experimental investigations and theoretical studies. Abbreviations: 5CB: 4-Cyano-4'-pentylBiphenyl; BLG: β-LactoGlobulin; CCNC: Carboxylated Cellulose NanoCrystal; CDEAB: N; N-Dimethyl-N-Ethylhexadecyl-Ammonium Bromide; CNC: Cellulose NanoCrystal; COM: Centre Of Mass; CsPFO: Caesium PerFluoroOctanoate; DACl: DecylAmmonium Chloride; DCF: Direct Correlation Function; DFT: Density Functional Theory; DLS: Dynamic Light Scattering; DOH: 1-Decanol; DSCG: DiSodium CromoGlycate; GB: Gay–Berne; HSC: Hard SpheroCylinder; LLC: Lyotropic Liquid Crystal; LCLC: Lyotropic Chromonic Liquid Crystal; MC: Monte Carlo; MD: Molecular Dynamics; NC: Nematic phase of rod-like (Calamitic) building blocks; ND: Nematic phase of Disc-like building blocks; ODF: Orientational Distribution Function; PBG: Poly-γ-Benzyl-Glutamate; SDS: Sodium Dodecyl Sulfate; SCNC: Sulfated Cellulose NanoCrystal; SSY: SunSet Yellow; TMV: Tobacco Mosaic Virus