Molecular chirality and chiral parameters

Harris, Amanda; Kamien, Randall D.; Lubensky, T. C.

doi:10.1103/revmodphys.71.1745

Cited by 319 publications

(327 citation statements)

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“…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…”

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confidence: 99%

Density functional theory for chiral nematic liquid crystals

et al. 2014

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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...

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Density functional theory for chiral nematic liquid crystals

et al. 2014

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“…Predicting, only on the basis of the molecular structure, the most basic parity of chiral LC ordering, the rightvs. left-handedness, is still a challenge (2)(3)(4). One would expect the problem to become easier when restricted to molecular structures with a clean cylindrical shape decorated with regular helical structures and charges, such as DNA, G-quartets, and filamentous viruses.…”

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Right-handed double-helix ultrashort DNA yields chiral nematic phases with both right- and left-handed director twist

Zanchetta

Giavazzi

Nakata

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Concentrated solutions of duplex-forming DNA oligomers organize into various mesophases among which is the nematic (N Ã ), which exhibits a macroscopic chiral helical precession of molecular orientation because of the chirality of the DNA molecule. Using a quantitative analysis of the transmission spectra in polarized optical microscopy, we have determined the handedness and pitch of this chiral nematic helix for a large number of sequences ranging from 8 to 20 bases. The B-DNA molecule exhibits a right-handed molecular double-helix structure that, for long molecules, always yields N Ã phases with left-handed pitch in the μm range. We report here that ultrashort oligomeric duplexes show an extremely diverse behavior, with both left-and right-handed N Ã helices and pitches ranging from macroscopic down to 0.3 μm. The behavior depends on the length and the sequence of the oligomers, and on the nature of the end-to-end interactions between helices. In particular, the N Ã handedness strongly correlates with the oligomer length and concentration. Right-handed phases are found only for oligomers shorter than 14 base pairs, and for the sequences having the transition to the N Ã phase at concentration larger than 620 mg∕mL. Our findings indicate that in short DNA, the intermolecular doublehelical interactions switch the preferred liquid crystal handedness when the columns of stacked duplexes are forced at high concentrations to separations comparable to the DNA double-helix pitch, a regime still to be theoretically described.cholesteric | RNA U nderstanding how the physicochemical details of macromolecules affect their interactions and their self-ordering properties represents one of the major challenges in the physics of soft and biological matter. In particular, because most of the biologically relevant molecules are chiral-i.e., they lack mirror symmetry-the relevant biointeractions are typically highly sensitive to the molecular handedness. One important effect of chiral interactions is the propagation of chirality from the molecular structure to the supramolecular assemblies such as aggregates or ordered phases. Often, in this phenomenon, minor molecular modifications are amplified to produce remarkable changes in the macroscopic ordering, as for DNA supercoiling and its biological role (1). The propagation of chirality has been studied in various systems, including thermotropic liquid crystals (LCs) and lyotropic assemblies of viruses, DNA, polymers, and dye aggregates. Despite the generality of the phenomenon, its understanding is still poor. Predicting, only on the basis of the molecular structure, the most basic parity of chiral LC ordering, the rightvs. left-handedness, is still a challenge (2-4). One would expect the problem to become easier when restricted to molecular structures with a clean cylindrical shape decorated with regular helical structures and charges, such as DNA, G-quartets, and filamentous viruses. However, even in this limited frame, experimental and theoretical results appear difficult to fi...

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“…DOI: 10.1103/PhysRevLett.96.018305 PACS numbers: 82.70.ÿy, 61.30.Vx Molecules with chiral symmetry cannot be superimposed on their mirror image. Such molecules can assemble into a variety of complex chiral structures of importance to both physics and biology [1]. Chirality has a special prominence in the field of liquid crystals, and the presence of a chiral center can dramatically alter the liquid-crystalline phase behavior and its material properties [2].…”

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Entropy-Driven Formation of a Chiral Liquid-Crystalline Phase of Helical Filaments

et al. 2006

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We study the liquid-crystalline phase behavior of a concentrated suspension of helical flagella isolated from Salmonella typhimurium. Flagella are prepared with different polymorphic states, some of which have a pronounced helical character while others assume a rodlike shape. We show that the static phase behavior and dynamics of chiral helices are very different when compared to simpler achiral hard rods. With increasing concentration, helical flagella undergo an entropy-driven first order phase transition to a liquid-crystalline state having a novel chiral symmetry. DOI: 10.1103/PhysRevLett.96.018305 PACS numbers: 82.70.ÿy, 61.30.Vx Molecules with chiral symmetry cannot be superimposed on their mirror image. Such molecules can assemble into a variety of complex chiral structures of importance to both physics and biology [1]. Chirality has a special prominence in the field of liquid crystals, and the presence of a chiral center can dramatically alter the liquid-crystalline phase behavior and its material properties [2]. For example, achiral rods form a nematic phase with long-range orientational order. However, rearranging a few atoms to create a microscopically chiral molecule can transform a nematic into a cholesteric phase. Locally, a cholesteric phase has a structure in which molecules are organized in layers. Within a layer, the molecules are parallel to each other, while the molecular orientation is slightly rotated between two adjacent layers. This order at least partially satisfies the pair interaction between neighboring chiral molecules which tends to twist their mutual orientation. Even for the fairly simple example of a cholesteric phase, it is difficult to establish a rigorous relation between the microscopic chirality of the constituent molecules and the macroscopic chirality characterized by the cholesteric pitch [3,4].In stark contrast to our poor understanding of the cholesteric phase, microscopic theories of nematic liquid crystals have been very fruitful [5]. Onsager realized that a simple fluid of concentrated hard rods will form a stable nematic phase. Using his theory, it is possible to predict the macroscopic phase behavior of a nematic suspension of hard rods from microscopic parameters such as rod concentration and rod aspect ratio. Because of the dominance of repulsive interactions, phase transitions within the Onsager model belong to a class of entropy-driven phase transitions. Inspired by the success of the Onsager theory, Straley made the first attempt at formulating a microscopic theory of the cholesteric phase [4]. In this work, hard-rod interactions are extended to threaded rods, which have an appearance similar to screws. The excluded volume between two threaded rods is at a minimum not when they are parallel to each other but when they approach each other at an angle at which their chiral grooves can interpenetrate. This results in the formation of a cholesteric phase that is, as in the Onsager model, entirely driven by entropic excluded volume interactions.Biopolymers suc...

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Molecular chirality and chiral parameters

Cited by 319 publications

References 20 publications

Density functional theory for chiral nematic liquid crystals

Density functional theory for chiral nematic liquid crystals

Right-handed double-helix ultrashort DNA yields chiral nematic phases with both right- and left-handed director twist

Entropy-Driven Formation of a Chiral Liquid-Crystalline Phase of Helical Filaments

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