Degree Of Chirality Research Articles

Desymmetrization and degree of chirality

Chiral objects, viewed as distorted derivatives of achiral ones, may be represented by points in a configuration space that is spanned by a set of symmetry coordinates derived for the symmetry group of the achiral object of highest symmetry. We propose a measure (d) that quantifies the displacement of the representative point for a chiral object away from thenearest point representing an achiral object in such a multi-dimensional configuration space. If the symmetry coordinates are chosen so as to yield a similarity invariant measure, then the valuesd; obtained for a series ofi chiral objects can serve as a basis for comparing the degrees of chirality of these objects. The chirality of triangles inE 2 is studied by this method, and it is shown that the most chiral triangle in terms of this measure corresponds to one that is infinitely flat, and that may be approached but is never attained. This result is compared to others obtained previously for the same system by the use of different measures of chirality.

The relation between molecular shape and molecular rotations in chiral halogenated alkanes

A good predictive correlation was found between the degree of shape chirality as measured by a structural parameter Id (defined in the text), and the molecular rotation in the series CH3CHR(X) where R is an alkyl and X is a halogen atom. The relation between this correlation and previously reported molecular refraction correlations is described. Example: predicted molecular rotation for 2-Cl-butane: 31; measured: 35.

On geometric measures of chirality

In this paper we discuss the concepts of “measure of chirality” and “degree of chirality” as functions of the shape of a molecular model M. The measure of chirality χ( M) is defined as a continuous, real-valued, and similarity-invariant function of M such that χ( M) = 0 when M is achiral, and χ( M')= −χ( M), where M' is the enantiomorph of M. The degree of chirality is defined as ¦χ( M) ¦. We discuss the application of one such function, based on the idea of maximal overlap (superimposition) of M and M' to tetrahedra, simplexes in E 3. An analysis of the properties of this function leads to the conclusion that, although a least chiral tetrahedron exists, the most chiral one might only be approachable as a limit. A rigorous analytical study of the corresponding function for triangles, simplexes in E 2, serves to illustrate this conclusion.

Ferrimagnetic-helimagnetic transition in an XY magnet with infinitely many phases

The authors present an anisotropic frustrated classical spin model, in which the coexistence of continuous and discrete degrees of freedom can be explicitly considered. They investigate an array of planar (XY) spins with usual bilinear exchange, on decorated lattices both in two and three dimensions, whose zero-temperature state is infinitely degenerate. The set of ground states includes a uniform ferrimagnetic arrangement, a uniform helimagnet, and any arbitrary admixture of these in the form of coexisting striped domains. Each ground state in the degeneracy manifold can be exactly mapped to a specified configuration of an anisotropic Ising model on the dual lattice. Ising spins represent the discrete chirality degrees of freedom. Low-temperature continuous excitations (spin waves) couple these Ising spins, selecting the configuration corresponding to the ferrimagnetic state (order by thermal disorder). Adding a competing next-nearest-neighbour interaction allows one to tune a transition to the helimagnet; at low temperature the transition occurs through an infinite sequence of steps, consisting of first-order phase transitions to successive ferrimagnetic phases, each made of helimagnetically ordered stripes of constant width. The width increases from phase to phase, and chirality alternates from stripe to stripe. A discussion of the relationship between decorated continuous spin models and multi-spin interaction is given.

Thin-wire scatterers in chiral media

The effect of the handedness of chiral materials on the differential scattering cross section of embedded conducting wires is examined. The bow-tie-shaped induced current distributions and the resulting forbidden zone of radiation are explained through fundamental physical principles. We find that thin-wire scatterers can be divided into subchiral, chiral, and superchiral classes according to the degree of chirality of the host material and the electromagnetic length of the wire.

Two-dimensional rotational dynamic chirality and a chirality scale

A scale for the quantitative assessment of the degree of shape chirality and for the absolute assignment of handedness is developed. The scale is based on a new definition of chirality, which, in turn, is based on the dynamic rotational properties of molecules. These concepts and their demonstration are carried out for the case of two-dimensional chirality, i.e., for chirality issues associated with adsorbate-surface interaction

A new molecular ordering in helical liquid crystals

In the pursuit of new ferroelectric liquid crystals, a novel intermediary state of matter, the helical smectic A* mesophase, was discovered. This layered phase was found between the isotropic liquid and the smectic C* phase in a variety of optically active (R)- and (S)-1-methylheptyl 4{prime}-(((4{double prime}-n-alkoxyphenyl)propioloyl)oxy)biphenyl-4-carboxylates. In these materials, the temperature at which the transition to the ferroelectric smectic C* phase occurs is relatively close to that of the clearing point. Moreover, the materials show a high degree of chirality. These two properties ensure that the A* phase possesses relatively large molecular fluctuations, which give rise to twist and bend distortions resulting in the stabilization of a helical structure. This new phase is apparently miscible with the classical smectic A phase, thereby classifying it as the chiral modification of the A phase.

Chiral order in a two-dimensional XY spin glass.

Ordering phenomena in the two-dimensional $\mathrm{XY}$ (plane-rotator) spin glass are studied by Monte Carlo simulations, with particular attention to the behavior of the chirality, which is an Ising-like multispin variable associated with a broken reflection symmetry. The chiral degrees of freedom are found to order in a markedly different manner from the $\mathrm{XY}$ spins: Indeed, the chiral susceptibility can be accurately mapped onto the spin-glass susceptibility of a pure Ising spin glass.

Monte Carlo Studies of the Two-Dimensional Random-BondXYModel–A Chiral Spin Glass

A Monte Carlo study is made on the two-dimensional plane-rotator ( X Y ) model on the square lattice with random ± J interactions particularly with interest in the chirality degrees of freedom introduced by Villain. It is suggested that the model exhibits a phase transition at a finite temperature into a “chiral spin glass” phase.

The wave equation for zero rest-mass particles

It is shown that (γ · ∂ ∂x ) + 1 2 χ (1 ± γ 5) Ψ ± = 0 may also be taken as the wave equation for zero rest mass, spin 1 2 particles. The new parameter is a measure of the degree of chirality. The investigations of the invariance properties of the equation lead to the same as those of the usual two-component neutrino theory with the exceptions of γ 5 invariance. It seems plausible that at least one of the neutrinos satisfies this kind of wave equation.