Density functional theory for chiral nematic liquid crystals

Abstract

Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Letter we address the problem by means of a novel density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropydriven cholesteric phase, which can be either right-or left-handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an interplay between local nematic alignment and excluded-volume differences between left-and right-handed particle pairs.PACS numbers: 64.70.mf, 64.70.pv, 61.30.Cz, 61.30.St Cholesteric phases, also known as chiral nematics, are fascinating examples of liquid crystals. Liquid crystals are phases of matter characterized by a degree of spontaneous breaking of the rotational and translational symmetries that is higher than in the liquid and lower than in the crystal phase. In the nematic phase, for example, the particles self-organize by all aligning along a common direction (the nematic director), while keeping their centers of mass homogeneously distributed in space. Chiral nematic liquid crystals are peculiar as their nematic director rotates like a helix around a chiral director, thus giving rise to a chiral distribution of the orientations of the particles [1]. A cholesteric phase can be either righthanded (as in Fig. 1(a)) or left-handed, depending on the handedness of the helix drawn by the nematic directorn. The wavelength associated to a full rotation of the nematic director around the chiral directorχ is known as the cholesteric pitch P . Cholesteric phases are commonly found in both thermotropic molecular compounds (e.g., derivatives of cholesterol [2][3][4][5]) and in lyotropic colloidal suspensions of, e.g., DNA [6,7] and filamentous viruses [8][9][10][11][12]. Their widespread occurrence explains why cholesterics were the first liquid-crystal phase experimentally observed [2]. The pitch is experimentally known to take values several orders of magnitude higher than the size of the constituent particles, reaching the visible-light wavelength in molecular compounds. For this reason, and for their liquid-like rheological properties, cholesterics have long found wide technological application in the opto-electronic industry [13].Despite their long history and widespread technological applications, surprisingly little is understood about this chiral state of matter. A fundamental open question regards the relationship between macroscopic and microscopic chirality, i.e., between the handedness of the phase and that of the constituent particles [14][15][16][17]. Moreover, it is still to be unambiguously proved that hard chiral interactions alone can give rise to an entropy-stabilized chiral-nematic phase [17,18]. The problem in interpreting experimental data is largely due to the limitations of theory and simulation method...

Nanocellulose Fragmentation Mechanisms and Inversion of Chirality from the Single Particle to the Cholesteric Phase

“…Although the formation of the cholesteric liquid crystal phase is well known for nanocellulose 9 , the general underlying mechanism behind the formation of the cholesteric phase is still not completely resolved 25 . Chirality on the single particle level is a necessary but not sufficient condition to develop a cholesteric phase since also the thermodynamic state of the system 34 35 . Furthermore, a single point mutation of the major coat protein was found to change the chirality of the cholesteric phase from left-handed (for fd wt virus) to right-handed (for fd Y21M) 36 .…”

Twisting with a twist: supramolecular helix fluctuations in chiral nematics

“…4). This suggests that the crossover from one handedness to the other upon changing the thermodynamic state (particle concentration or temperature) as reported in a number of recent studies [19,[22][23][24]37] constitutes some higherorder phase transition where director fluctuations diverge critically at the compensation point.…”

OCT imaging with temporal dispersion induced intense and short coherence laser source

“…1(a)) of periodicity P , which is related with the optical wavelength λ by the following relationship [18]: $$\lambda ={\mathrm{normaln}}_{\text{avg}}\text{.P}$$ $$\mathrm{\Delta }\lambda =\mathrm{\Delta }\text{n.}\mathrm{P}$$ where n avg is the average refractive index and Δn is the birefringence of the liquid crystal molecule. Because of this unique optical property of the CLC, incoming light of wavelength λ senses the helical periodicity parallel to the helix axis inside the CLC medium.…”

“…1b). Well inside the bandgap, optical modes, spontaneous emission, and vacuum fluctuation are all absent [18–20], but more and more away from the central wavelength ( λ 0 ) of the bandgap, the medium offers an inappropriate periodicity very regularly (because of high packing density of supramolecular arrangement) onto the available longitudinal modes and behaves as a temporally dispersive medium [20]. Single handed CLC-helix provides the dispersion only to the same handed circularly polarized light, but opposite handed circularly polarized light remains un-dispersed.…”