Equilibrium Twist Research Articles

Heliconical-fluctuation-induced compensation point in the diluted cholesteric phase of mixtures containing the flexible dimer CB7CB.

We show experimentally and theoretically that the heliconical fluctuations that develop in a cholesteric phase (Ch) close to a transition to a chiral twist-bend nematic phase (N_{TB}) may lead to the appearance of a compensation point. At this point, the equilibrium twist of the cholesteric phase vanishes and changes sign. Mixtures of the flexible dimer CB7CB and the rodlike molecules 8CB or 5CB, doped with a small amount of the chiral molecules R811, S2011, CC, or CB15, are used in experiments to determine the conditions for the appearance of a compensation point.

Chiral and achiral mechanisms of self-limiting assembly of twisted bundles.

A generalized theory of the self-limiting assembly of twisted bundles of filaments and columns is presented. Bundles and fibers form in a broad variety of supramolecular systems, from biological to synthetic materials. A widely-invoked mechanism to explain their finite diameter relies on chirality transfer from the molecular constituents to collective twist of the assembly, the effect of which frustrates the lateral assembly and can select equilibrium, finite diameters of bundles. In this article, the thermodynamics of twisted-bundle assembly is analyzed to understand if chirality transfer is necessary for self-limitation, or instead, if spontaneously-twisting, achiral bundles also exhibit self-limited assembly. A generalized description is invoked for the elastic costs imposed by twist for bundles of various states of intra-bundle order from nematic to crystalline, as well as a generic mechanism for generating twist, classified both by chirality but also the twist susceptibility of inter-filament alignment. The theory provides a comprehensive set of predictions for the equilibrium twist and size of bundles as a function of surface energy as well as chirality, twist susceptibility, and elasticity of bundles. Moreover, it shows that while spontaneous twist can lead to self-limitation, assembly of twisted achiral bundles can be distinguished qualitatively in terms of their range of equilibrium sizes and thermodynamic stability relative to bulk (untwisted) states.

Properties of Nonlinear Torsional Waves Effective on Solar Swirling Plasma Motions

Abstract We model the evolution of solar helical structures: swirling motions, tornadoes, and spirals in the context of nonlinear magnetohydrodynamic waves. By considering vorticity and magnetic twist, the nonlinear forces that confine and shape helical or swirling plasma motions are incorporated in nonlinear partial differential equations. The solution to the governing equations provides insight on the significance of the equilibrium conditions. The key in providing explicit expressions for the compressive perturbations in the presence of equilibrium twist and vorticity is the second-order thin flux tube approximation. Nonlinear differential equations for the perturbations of the density, tube cross sectional area, and longitudinal speed are obtained in terms of the characteristics of the torsional wave, which itself is determined by the magnetic twist and vorticity. The analytic nonlinear solutions enable measurement of the efficiency of the equilibrium magnetic twist and vorticity, which confine and shape swirling motions differently as they evolve up the solar atmosphere. For chromospheric and coronal conditions, the nonlinear induced density perturbations increase with vorticity and decrease with magnetic twist. Regarding confinement, the nonlinear forces prove that the vorticity is predominant compared to the twist. The vorticity acts similarly to the shear flow in confining plasma swirling motions. It features in the compressive perturbations due to the ponderomotive force. We conclude that weak vorticities and twists are easily dominated by the plasma-β. For observing swirling plasma motions and tornadoes, focus must be on regions with high vorticity.

Role of impurities in the Lehmann effect of cholesteric liquid crystals: Towards an alternative model

The Lehmann effect is the rotation of cholesteric droplets when they are submitted to a temperature gradient. So far, this effect was only observed in the coexistence region between the cholesteric phase and its isotropic liquid. This zone of coexistence is due to the presence in the LC of impurities. In this paper, we show that the rotation velocity of the droplets does not depend on the choice of the impurity and on its concentration, providing that the variations of the equilibrium twist and the rotational viscosity are taken into account. These results were obtained by doping the cholesteric LC (a diluted mixture of 7CB and R811) with nonmesogenic and mesogenic impurities. The nonmesogenic impurities used are the biphenyl, the hexachloroethane, and a fluorinated polyether polymer. The mesogenic impurity is the LC I52. From these experiments we conclude that the Lehmann effect is certainly not due to a chemical torque of the type described by Leslie, Akopyan, and Zel'dovich. Finally, we propose alternative avenues that might be explored to understand the Lehmann effect.

Short DNA persistence length in a mesoscopic helical model

The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available to base pair fluctuations and derive the partition function. The apparent persistence lengths of a set of short chains have been computed as a function of the twist conformation both in the over-twisted and the untwisted regimes, whereby the equilibrium twist is selected by free energy minimization. The obtained values are significantly lower than those generally attributed to kilo-base long DNA. This points to an intrinsic helix flexibility at short length scales, arising from large fluctuational effects and local bending, in line with recent experimental indications. The interplay between helical untwisting and persistence length has been discussed for a heterogeneous fragment by weighing the effects of the sequence specificities through the non-linear stacking potential.

End-to-end distance and contour length distribution functions of DNA helices.

I present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible configurations for each dimer in the sequence, selects the global equilibrium twist conformation for the molecule, and determines the average base pair distances along the molecule backbone. Integrating over the base pair radial and angular fluctuations, I derive the room temperature distribution functions as a function of the sequence length. The obtained values for the most probable end-to-end distance and contour length distance, providing a measure of the global molecule size, are used to examine the DNA flexibility at short length scales. It is found that, also in molecules with less than ∼60 base pairs, coiled configurations maintain a large statistical weight and, consistently, the persistence lengths may be much smaller than in kilo-base DNA.

Torsional wave propagation in solar tornadoes

Aims. We investigate the propagation of torsional waves in coronal structures together with their collimation effects in the context of magnetohydrodynamic (MHD) theory. The interplay of the equilibrium twist and rotation of the structure, e.g. jet or tornado, together with the density contrast of its internal and external media is studied to shed light on the nature of torsional waves.Methods. We consider a rotating magnetic cylinder embedded in a plasma with a straight magnetic field. This resembles a solar tornado. In order to express the dispersion relations and phase speeds of the axisymmetric magnetohydrodynamic waves, the second-order thin flux tube approximation is implemented for the internal medium and the ideal MHD equations are implemented for the external medium.Results. The explicit expressions for the phase speed of the torsional wave show the modification of the torsional wave speed due to the equilibrium twist, rotation, and density contrast of the tornado. The speeds could be either sub-Alfvenic or ultra-Alfvenic depending on whether the equilibrium twist or rotation is dominant. The equilibrium twist increases the phase speed while the equilibrium rotation decreases it. The good agreement between the explicit versions for the phase speed and that obtained numerically proves adequate for the robustness of the model and method. The density ratio of the internal and external media also play a significant role in the speed and dispersion. Conclusions. The dispersion of the torsional wave is an indication of the compressibility of the oscillations. When the cylinder is rotating or twisted, in contrast to when it only possesses a straight magnetic field, the torsional wave is a collective mode. In this case its phase speed is determined by the Alfven waves inside and outside the tornado.

Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules.

We study the role of the sample thickness d and of the concentration C of chiral molecules during the Lehmann rotation of cholesteric droplets of radius R subjected to a temperature gradient G→. Two configurations are studied depending on how the helix is oriented with respect to G→. The first result is that, at fixed C and R, the rotation velocity ω increases with d when the helix is parallel to G→, whereas it is independent of d when the helix is perpendicular to G→. The second result is that, for a given C,ω0=limR→0ω(R) is the same for the two types of droplets independently of d. This suggests that the, as yet unknown, physical mechanism responsible for the droplet rotation is the same in the two types of droplets. The third result is that the Lehmann coefficient ν[over ¯] defined from the Leslie-like relation ω0= G¯G/γ1 (with γ_1 the rotational viscosity) is proportional to the equilibrium twist q. Last, but not least, the ratio R¯=ν ¯/q depends on the liquid crystal chosen but is independent of the chiral molecule used to dope the liquid crystal.

Leslie thermomechanical power in diluted cholesteric liquid crystals

I measure the Leslie thermomechnical coefficient ν in diluted cholesteric liquid crystals. The chiral molecules are R811 and cholesteryl chloride (CC) and the host nematic liquid crystals are 7CB and MBBA. I show that ν is proportional to the concentration of chiral molecules C when . This allows me to define the Leslie thermomechanical power as by analogy with the helical twisting power, where q denotes the equilibrium twist. I show that the LTP (dynamic in nature) and the HTP (static in nature) are independent in sign and magnitude. In addition, the same chiral molecule can rotate clockwise or counterclockwise depending on the host nematic liquid crystal used.

Thermodynamics of twisted DNA with solvent interaction

The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over ~10(7)-10(8) base pair paths, a large number of double helix configurations is taken into account consistently with the physical requirements of the model potential. The partition function is computed as a function of the twist. It is found that the equilibrium twist angle, peculiar of B-DNA at room temperature, yields the stablest helicoidal geometry against thermal disruption of the base pair hydrogen bonds. This result is corroborated by the computation of thermodynamical properties such as fractions of open base pairs and specific heat.

Long-wavelength torsional modes of solar coronal plasma structures

Aims. We consider the effects of the magnetic twist and plasma rotation on the propagation of torsional m = 0 perturbations of cylindrical plasma structures (straight magnetic flux tubes) in the case when the wavelength is much longer than the cylinder diameter. Methods. The second order thin flux tube approximation is used to derive dispersion relations and phase relations in linear longwavelength axisymmetric magnetohydrodynamic waves in uniformly twisted and rotating plasma structures. Results. Asymptotic dispersion relations linking phase speeds with the plasma parameters are derived. When twist and rotation are both present, the phase speed of torsional waves depends upon the direction of the wave propagation, and also the waves are compressible. The phase relations show that in a torsional wave the density and azimuthal magnetic field perturbations are in phase with the axial magnetic field perturbations and anti-phase with tube cross-section perturbations. In a zero-β non-rotating plasma cylinder confined by the equilibrium twist, the density perturbation is found to be about 66 percent of the amplitude of the twist perturbation in torsional waves.

Thermomechanically driven spirals in a cholesteric liquid crystal

We show that the continuous cholesteric fingers, which form in homeotropic samples at the unwinding temperature of the cholesteric phase, drift and spiral when they are subjected to a temperature gradient. This phenomenon is attributed to the appearance of a Lehmann thermomechanical torque. Measurements of the finger drift velocity on both sides of the compensation temperature of a cholesteric mixture show that the Lehmann coefficient does not change sign (and so does not vanish) at this temperature contrary to the equilibrium twist. There is thus no direct relationship between the thermomechanical Lehmann coefficient and the equilibrium twist. The nonvanishing of the Lehmann coefficient at the compensation temperature is due to the absence of inversion symmetry in a compensated cholesteric in spite of its nematiclike structure. This comes from the chirality of the molecules. The ratio of the Lehmann coefficient over the rotational viscosity is also measured as a function of temperature.

Weak Anchoring Effects in Nematic Liquid Crystals

We consider a twisted nematic liquid crystal confined by two parallel boundary plates. The nematic is subject to an in-plane magnetic field applied in a direction parallel to the plates. At the lower plate the director is strongly anchored so that the director twist is fixed. On the upper surface we introduce an easy direction for the director. Although the director prefers to align with the easy direction, the actual twist exhibited at the upper surface may differ from the easy direction twist. This is due to the competition between elastic, magnetic and anchoring effects. We examine and compare two surface energies that model the weak anchoring at the upper plate. For both energies, equilibrium twist profiles for the director within the sample have been obtained by minimizing the total free energy for the system.

Director Orientation of a Twisted Nematic Under the Influence of an In-Plane Magnetic Field

ABSTRACT We consider an incompressible nematic liquid crystal that exhibits an equilibrium twist profile across the cell due to in-plane but opposing anchoring directions at the plates. We examine the director orientation under the influence of a magnetic field applied in a direction parallel to the plates. Characteristic switching times are determined as the angle of twist on the plates and the direction of the applied field are varied. Furthermore, extending classical analyses we discuss Freedericksz transitions and critical field strengths.

Fibril stability in solutions of twisted -sheet peptides: a new kind of micellization in chiral systems

The problem of fibril (fibre) formation in chiral systems is explored theoretically being supported by experiments on synthetic de novo 11-mer peptide forming self-assembled -sheet tapes. Experimental data unambiguously indicate that the tapes form fibrils of nearly monodisperse thickness ca . 8-10 nm. Fibril formation and stabilisation are attributed to inter-tape face-to-face attraction and their intrinsic twist, correspondingly. The proposed theory is capable of predicting the fibril aggregation number and its equilibrium twist in terms of molecular parameters of the primary tapes. The suggested novel mechanism of twist stabilisation of finite aggregates (fibrils) is different to the well-known stabilisation of micelles in amphiphilic systems, and it is likely to explain the formation and stability of fibrils in a wide variety of systems including proteinaceous amyloid fibres, sickle-cell hemoglobin fibres responsible for HbS anemia, corkscrew threads found in chromonics in the presence of chiral additives and native cellulose microfibrillar crystallites. The theory also makes it possible to extract the basic molecular parameters of primary tapes (inter-tape attraction energy, helical twist step, elastic moduli) from the experimental data.

P–T diagrams of the system of CH3(CH2)n−1 self-assembled on the Au(111) crystal surface

Equilibrium states of the system of self-assembled monolayers (SAM’s) of n-alkanethiol molecules CH3(CH2)n−1 chemiabsorbed on the Au(111) crystal surface are considered in relation to temperature and external pressure applied normally to the surface. Couplings between the atoms (C, H) of the n-alkanethiols are approximated both by the Morse potential and by the Lennard-Jones one. Couplings between the n-alkanethiols and the crystal surface are approximated by the 12-3 potential. Because of the symmetry Z2 of the n-alkanethiols in the tilted state the system is reduced to the Ising model on the triangular lattice with two competing exchange parameters. Calculated p–T diagrams of the tilted system include the following phases: para, ferro, incommensurate, and structure 2×1. The incommensurate phase results from competition between the exchange parameters. It is shown that for some specific choices of the coupling constants the p–T diagram has tricritical points. The temperatures of phase transitions and equilibrium tilt, twist, and azimuthal angles depending on the coupling constants are found. All phase transitions are of the first order. Temperature behavior of heat capacity is calculated.

Influence of Fluctuations on DNA Curvature: A Comparison of Flexible and Static Wedge Models of Intrinsically Bent DNA

Matrix-generator and Monte Carlo methods have been employed to study the influence of thermal fluctuations on the overall sizes and shapes of curved pieces of DNA. The DNA model involves the independent angular parameters relating successive base-pair steps: the sequence-dependent equilibrium values and fluctuations of the twist, tilt, and roll angles. The curved sequence under study is the (A 5X 5) n repeating polymer, the AA and XX steps having different equilibrium roll and twist values. Both planar circles and superhelices are analysed. Detailed comparison is made between the rigorous statistical mechanical representation of the DNA and simplified static models currently used in the literature. That is, a more realistic "flexible wedge" model is contrasted with the existing "static wedge" model of DNA curvature, which is demonstrated to be inadequate. The size of the coils is described by the unperturbed root-mean-square end-to-end distance and the shape by a ratio of the principal moments of the radius of gyration. The moment ratios indicate that when DNA is relatively short (e.g. its length is shorter than half a turn of the static superhelix), the flexible chains are more "short and thick" than the static structure. The end-to-end distances, however, are practically the same in the two models. For longer DNA fragments, the flexible chain is more extended in terms of the end-to-end distance and more globular in terms of the moment ratio. Thus, fluctuations "blur" the curvature of longer DNA fragments compared with static models. Furthermore, the overall average shape of slightly curved DNA subject to natural bending and twisting fluctuations is essentially indistinguishable from that of the corresponding "straight" DNA. Such configurational similarities are apparently responsible for the relative insensitivity of the polyacrylamide gel matrix to small degrees of DNA curvature. These findings raise serious questions regarding the quantitative estimation of wedge angles in DNA from electrophoretic experiments, based on static models. Comparison between planar circles and superhelices shows that when fluctuations are considered, the flexible circles are more spherical than the superhelices. The results imply that when DNA bending is exactly "in phase" with the helical repeat (i.e. when the DNA loop is exactly planar at 0 K), the DNA coil is packed more tightly than when bending and twisting are "out of phase" (and a superhelix is formed at 0 K). This finding is consistent with polyacrylamide gel electrophoresis data testifying to an increase in DNA retardation when twisting is more precisely "tuned". Finally, it is found that asymmetry of bending in the roll co-ordinate can produce significant macroscopic curvature of DNA. "Skewed" bending of AA steps in the A 5X 5 polymer is indistinguishable from symmetric bending with the same mean value and fluctuation of roll. Asymmetric rolling in the AA dimer thus can introduce substantial curvature in DNAs containing A n · T n blocks, even if the lowest energy stacked arrangement of AA base-pair steps is nearly flat, thereby resolving apparent contradictions between the crystallographic and solution structures of chains containing A n · T n tracts.

Resonance effects of diabatic surface crossing within the torsional spectrum of 9-(N-carbazolyl) anthracene observed by supersonic jet fluorescence spectroscopy

Using the supersonic jet technique and laser-induced fluorescence spectroscopy, the ground and excited state surface of isolated 9-(N-carbazolyl) anthracene (C9A) is investigated. Ground and excited state torsional potentials of high accuracy are deduced from excitation and fluorescence spectra, considering characteristic patterns of Franck–Condon factors within the dispersed fluorescence. S0 exhibits a very flat double minimum potential (equilibrium twist angle 77.5°, barrier 17 cm−1); the barrier for perpendicularity in S1 is approximately 1050 cm−1 and the equilibrium angle is shifted towards coplanarity (64°). An unusual intensity profile of the long progression found in the fluorescence excitation spectrum is ascribed to a resonant nonradiative decay channel within the excited state surface. State selective fluorescence decay rates vs excess vibrational energy confirm this resonant relaxation process. This uncommon observation leads to a model of diabatic surface crossing along the torsional coordinate where the crossing ‘‘dark’’ state is discussed as a predicted charge transfer state or a higher lying triplet state, mediating further electronic relaxation. Although extended intermolecular vibrational redistribution (IVR) is present in the fluorescence spectra from high vibrational levels, this process is of secondary importance for the resonant nonradiative relaxation.

Conformational Behaviour of Phenylpyrroles — a Semiempirical Molecular Orbital Study

Equilibrium twist angles and rotational barriers for the three isomeric phenylpyrroles were calculated by means of MNDO and AM1. In each case MNDO incorrectly predicts the perpendicular conformation as the most stable one. In agreement with experimental evidence AM1 predicts only slight deviations from planarity and very low 0°-barriers (1-phenylpyrrole: 0 = 28°, E = 1.6 kJ mol-1; 2-phenylpyrrole: θ = 27°, E = 0.8 kJ mol-1; 3-phenylpyrrole: θ = 19°, E = 0.2 kJ mol-1). The reasons for the complete failure of MNDO are analyzed by partitioning the total energy into one- and two-center terms. The most significant improvement of AM1 over MNDO is found to be the much better description of repulsive interactions between nonbonded atoms. Possible further improvements of AM1 are briefly discussed.

Microwave spectrum and ab initio computations for ethylene carbonate. Part 1.—Conformation and ring inversion

The conformation and ring inversion in ethylene carbonate have been investigated using microwave spectroscopy and ab initio computations. The vibrational satellite spectra of the normal isotopic species of ethylene carbonate and the rotational constants of Backvall et al.(Tetrahedron Lett. 1980, 21, 4985) for cis- and trans-[1,2-2H2]ethylene carbonate show the molecule to have a twisted C2 equilibrium conformation. The vibrational satellite spectra have been analysed in terms of independent ring-bending and twisting vibration. A potential function for the twisting vibration derived from the variation of the rotational constants with vibrational state, and vibrational energy separations obtained from relative intensities and Coriolis perturbations give an equilibrium twist angle of 19° and a barrier to ring inversion of 2.8 kJ mol–1. The twist angle has also been obtained from inertial data, and a value of 15° is obtained using two methods of calculation. Ab initio computations of the ring-puckering potential-energy surface have been made using STO-3G and STO-3-21 G orbitals and complete geometry optimization. The STO-3G computations predict a planar C2ν equilibrium geometry, but with the twisting vibration being lower in frequency and more anharmonic than the bending vibration. The STO-3-21G computations predict a C2 conformation with an equilibrium twist angle of 14° and barrier to inversion through the planar ring conformation of 1.1 kJ mol–1. The computed barrier to ring inversion by pseudorotation is 14.3 kJ mol–1.