Quasi-Continuous Videodensitometric Recording of Chromatograms in Circular TLC

JPC – Journal of Planar Chromatography – Modern TLC - A new method of quasi-continuous videodensitometric recording of circular thin-layer chromatography (TLC) is proposed. It is based...     

Salting out in organic solvents: a new route to carbon nanotube bundle engineering

In this study we investigate salt effects on bundle formation of carbon nanotubes (CNTs) dispersed in an organic solvent, N-methyl-2-pyrrolidone (NMP). Addition of NaI salt leads to self-assembly of CNTs into well-recognizable bundles. It is possible to control the size of the CNT bundles by varying the salt concentration.     

Single molecule charge transport: from a quantum mechanical to a classical description

This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.     

Vinylidene carbonylation at a manganese-iron complex: A density functional study of mechanism

Treating the phenylvinyldene manganese complex Cp(CO)₂MnC¹C²HPh, 1, with [Fe(CO)₄] yields the binuclear μ-vinylidene complex Cp(CO)₂MnFe(μ-C¹C²HPh)(CO)₄, 2, that further isomerizes to the carbonylated product η⁴-[Cp(CO)₂MnC¹(CO)C²HPh]Fe(CO)₃, 3. In a computational study of the mechanism using a hybrid density functional method, we considered two stereoisomers for species 2 and 3 where the phenyl group at center C² is oriented in cis (E form) or trans (Z form) fashion to the Cp(CO)₂Mn unit. Isomers 2E and 2Z were calculated to be degenerate whereas the experimentally detected species 3E is 8 kcal/mol more stable than its isomer 3Z. The two-step pathway 1 → 2Z → 3E was calculated to be the lowest-energy route with the highest activation barrier at 12 kcal/mol. The activation energy of the alternative single-step pathway 1 → 3E is 19 kcal/mol. We rationalized the stabilization of the ground state of 3E and the transition states leading to or starting from isomer 2Z as conjugation effect between the Mn-CC metallaallene fragment and the co-planar phenyl ring.     

A comparison theorem for Gromov–Witten invariants in the symplectic category

We exploit the geometric approach to the virtual fundamental class, due to Fukaya–Ono and Li–Tian, to compare Gromov–Witten invariants of a symplectic manifold and a symplectic submanifold whenever all constrained stable maps to the former are contained in the latter to first order. Various special cases of the comparison theorem in this paper have long been used in the algebraic category; some of them have also appeared in the symplectic setting. Combined with the inherent flexibility of the symplectic category, the main theorem leads to a confirmation of Pandharipande?s Gopakumar–Vafa prediction for GW-invariants of Fano classes in 6-dimensional symplectic manifolds. The proof of the main theorem uses deformations of the Cauchy–Riemann equation that respect the submanifold and Carleman Similarity Principle for solutions of perturbed Cauchy–Riemann equations. In a forthcoming paper, we apply a similar approach to relative Gromov–Witten invariants and the absolute/relative correspondence in genus 0.     

Reaction of tris(hydroxymethyl)phosphine and cinnamaldehyde in methanol

Reaction of tris(hydroxymethyl)phosphine with excess cinnamaldehyde in CH₃OH or CD₃OD, followed using NMR, proceeds via several phosphorus-containing intermediates, multiple transformations of organic parts, and with the solvent H/D isotope effect on products. In both solvents, one CH₂OH group of tris(hydroxymethyl)phosphine is readily replaced by the cinnamaldehyde moiety to give the primary product, a 1,3-oxaphosphorinane derivative. Slower replacement of the second CH₂OH group leads to a mixture of aliphatic and heterocyclic phosphine intermediates in a ratio of ~4:1 in CH₃OH and ~1:1 in CD₃OD; both intermediates contain alcohol and aldehyde groups and convert rapidly into intra- and intermolecular hemiacetals. The hemiacetals of the aliphatic phosphine rearrange further into an unsymmetrical trialkylphosphine oxide, whereas the hemiacetals of the heterocyclic phosphine react with the third mole of cinnamaldehyde to replace the third CH₂OH group of tris(hydroxymethyl)phosphine. All intermediates and products are formed as mixtures of stereoisomers.     

Multipolar resonant particle modes as elementary excitations in chain waveguides: Theory, dispersion relations and mathematical modeling

In the framework of linear electrodynamics, the theory of the resonant interaction of multipolar modes in the many body system and associated numerical techniques are proposed in the present paper. The theory rests upon certain integral field equations derived on the basis of the Stratton-Chu integral transforms, the Atkinson-Wilcox and multipole expansions. For the case of spherical geometry of the bodies, the half part of these field equations is reduced to a set of closed form dispersion relations which describe the excitation of nonradiating modes in the particle cluster of arbitrary complexity. For clusters with developed translation symmetry, we propose the method for solving the field equations which is characterized by an effective numerical scaling. For perfectly periodic one dimensional systems (chains), this scaling has a linear character. On the basis of the proposed theory and numerical technique the method of synthesis of chain plasmonic waveguides with low radiation losses is considered. Different checks targeted on the verification of the approaches are fulfilled.     

Algebras of Singular Integral Operators with Piecewise Continuous Coefficients on Reflexive Orlicz Spaces

We consider singular integral operators with piecewise continuous coefficients on reflexive Orlicz spaces L_m(σ) which are generalizations of the Lebesgue spaces L_P(σ), 1 < p < ∞. We suppose that σ belongs to a large class of Carleson curves, including curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. For the singular integral operator associated with the Riemann boundary value problem with a piecewise continuous coefficient G, we establish a Fredholm criterion and an index formula in terms of the essential range of G complemented by spiralic horns depending on the Boyd indices of L_M(σ) and contour properties. Our main result is a symbol calculus for the closed algebra of singular integral operators with piecewise continuous matrix - valued coefficients on L_Mⁿ(σ).