Chiral Motion Research Articles

SELF-AVOIDING CHIRAL WALKS

We describe a simple, discrete model of deterministic chiral motion on a square lattice. The model is based on rotating walkers with trailing tails spanning L lattice bonds. These tail segments cannot overlap and their leading A segments cannot be crossed. As prescribed by their chirality, walkers must turn if possible, or go straight, or else correct earlier steps recursively. The resulting motion traces unbound trajectories and complex periodic orbits with various symmetries. Periods tend to decrease with increasing L and vary between L and L2. Interacting walkers can form intricate pair states. Some orbits match pinned spiral tip trajectories observed experimentally in excitable systems.

Chiral sedimentation of extended objects in viscous media

We study theoretically the chirality of a generic rigid object's sedimentation in a fluid under gravity in the low Reynolds number regime. We represent the object as a collection of small Stokes spheres or stokeslets and the gravitational force as a constant point force applied at an arbitrary point of the object. For a generic configuration of stokeslets and forcing point, the motion takes a simple form in the nearly free draining limit where the stokeslet radius is arbitrarily small. In this case, the internal hydrodynamic interactions between stokeslets are weak, and the object follows a helical path while rotating at a constant angular velocity omega about a fixed axis. This omega is independent of initial orientation and thus constitutes a chiral response for the object. Even though there can be no such chiral response in the absence of hydrodynamic interactions between the stokeslets, the angular velocity obtains a fixed nonzero limit as the stokeslet radius approaches zero. We characterize empirically how omega depends on the placement of the stokeslets, concentrating on three-stokeslet objects with the external force applied far from the stokeslets. Objects with the largest omega are aligned along the forcing direction. In this case, the limiting omega varies as the inverse square of the minimum distance between stokeslets. We illustrate the prevalence of this robust chiral motion with experiments on small macroscopic objects of arbitrary shape.

Discussions about whether radioactive half life can be changed by mechanic motion

In this essay, some discussions and comments about the paper entitled “Can the decay rate of 32P be changed by mechanic motion?” (Ding et al., Science in China Series B: Chemistry (Chinese version), 2008, 38(11):1035–1037) are given. It was strongly suggested that its experimental methods, data calculations and conclusion should be reconsidered. After the data were recalculated, the new results supported that the chiral mechanic motion could induce the changes of radioactive half life.

A Self-Assembled Homooxacalix[3]arene-based Dimeric Capsule Constructed by a PdII−Pyridine Interaction Which Shows a Novel Chiral Twisting Motion in Response to Guest Inclusion

A capsule-like molecule was constructed by dimerization of pyridine-containing homooxacalix[3]aryl esters utilizing a Pd(II)-pyridine interaction when Li(+) ions were bound to the ionophoric lower rims. (1)H NMR spectral studies showed that the self-assembled molecular capsule 3b.(Li(+))(2) has a highly symmetrical D(3)(h)-structure. It was also found that this self-assembled molecular system can form capsular structures in the presence of Na(+) or ammonium (RNH(3)(+)) ions. Very interestingly, these molecular capsules are twisted into triply bridged helical structures, and chiral RNH(3)(+) guests included in the cavity induce a change in the (P) versus (M) ratio, resulting in high chiral induction ( approximately 70%). These results indicate that the self-assembled molecular capsule 3b has a novel chiral factor in which the (P) versus (M) equilibrium is readily controllable by the inclusion of chiral guest molecules.

Effect of Earth’s orbital chirality on elementary particles and unification of chiral asymmetries in life on different levels

Life is chirally asymmetric at all scales from microscopic elementary particles to molecular and macroscopic levels. How these chiral asymmetries in life on different levels are unified remains unanswered. It has been demonstrated that both the biomolecular homochirality and biological rhythms can be caused by the right-handed helical force-field of the Earth’s orbital chirality (EOC). Similar to the helical biomolecules (1), it is here suggested that the right-handed EOC force-field could make the right-handed elementary particles more stable than their left-handed enantiomers to result in the symmetry violation of elementary particles, and the EOC could also cause the macroscopic predominant selection of right-handed asymmetries of living objects (e.g. the helical seashells and plants). Our studies indicated that the weak force in weak interaction may only be a form of the EOC force-field at the microscopic particle level, and the chiral asymmetries in life on various levels could be unified by the natural right-handed EOC force-field. Moreover, the chiral and quantum effects, time, mass, rhythms and relativity could also be unified by the interaction of the EOC force-field with chiral motions and structures under certain conditions.

Chiral metal as a ferromagnetic super spin chain

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low-energy spin states. The result is of a universal form and coincides with that for a hermitian random matrix.

Differential scattering of spin ± (1/2) polarized neutrons by chiral systems. I. Theory

A theoretical model is developed for treating the scattering of longitudinally polarized neutrons by a chiral array of nuclei. The model is restricted to consideration of nonmagnetic scattering systems comprised of ’’spinless’’ nuclei, and only forward scattering is considered. The differential scattering of spin ± (1/2) polarized neutrons is presumed to arise via a ’’spin–orbit’’ coupling mechanism in which the spin of the neutron is coupled to the orbital (vibrational) motions of the nuclei in the neutron–nuclei interaction region. Only low-energy neutron scattering by vibrational excitations (or deexcitations) is considered. Neutron–nuclei interactions are described in terms of (1) neutron absorption–emission processes; (2) neutron reflection processes; and (3) neutrons moving through the (long-range) Coulombic field of the nuclei. General expressions are developed for the differential scattering amplitudes of spin ± (1/2) polarized neutrons interacting with nuclei undergoing chiral vibrational motion.

Theory of Natural Optical Activity in Crystalline NiSO4· 6H2O

The optical activity of crystalline NiSO4· 6H2O is exclusively a property of the solid state, arising from a dissymmetric crystal environment. The rotatory strengths and dipole strengths associated with electronic transitions within the Ni2+ 3d manifold of states are calculated to second order in perturbation theory. It is assumed that optical activity is induced in the ligand-field bands of the octahedral NiO6 clusters by the perturbing influence of the neighboring crystal environment which has C2 symmetry. A crystal-field representation is adopted so that the crystal perturber sites (the H atoms of the water ligands, and O and S atoms of the SO42− anions) are treated as point charges ``seen'' by the NiO6 chromophoric sites. The signs and relative magnitudes of the rotatory strengths calculated for the 3A2g→3T2g, 3A2g→3T1g(F), and 3A2g→3T1g(P) cubic transitions of Ni2+ are in substantial agreement with experiment. It is concluded that the CD spectrum of crystalline NiSO4· 6H2O in the near infrared, visible, and near ultraviolet regions can be understood in terms of a model on which the optical activity is assumed to arise from dissymmetric perturbations of individual Ni2+ sites rather than from chiral exciton motion over the helically arranged Ni(H2O)62+ clusters.