Molecular diffusion in liquid crystals and chiral discrimination. I. Theory

The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper.     

Molecular theory of dielectric relaxation in nematic dimers

This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of alpha,omega-bis[(4-cyanobiphenyl-4'-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density p(eq)(beta(A),beta(B)) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simultaneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer alpha-[(4-cyanobiphenyl)-4'-yloxy]-omega-(4-decylanilinebenzylidene-4'-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases.     

Highly stereoselective one-pot procedure to prepare bis- and tris-chalcogenide alkenes via addition of disulfides and diselenides to terminal alkynes

We present here the reaction of diorganoyl dichalcogenides with terminal alkynes under catalyst-free conditions, by a one-pot procedure, to prepare bis- and tris-chalcogenide alkenes selectively, avoiding the previous preparation of chalcogen alkynes. The reaction proceeded cleanly under mild reaction conditions, and the addition of dichalcogenides to alkynes occurred stereoselectively to give exclusively the corresponding Z isomers. We observed that the selectivity control was governed by the effective participation of the hydroxyl group from propargyl alcohols. In addition, the bis-chalcogenide alkenes were exclusively obtained with propargyl alcohol having the acidic hydroxyl group proton. Conversely, the alkynes with no potentially acidic hydroxyl group proton, at propargyl positions, gave exclusively the tris-chalcogenide alkenes.     

Unprecedented copper-catalyzed asymmetric conjugate addition of organometallic reagents to alpha,beta-unsaturated lactams

For the first time, an excellent enantioselectivity has been obtained in the conjugate addition of hard organometallic reagents to alpha,beta-unsaturated lactams bearing appropriate protecting-activating groups on the nitrogen.     

The Effects of Temperature of Condensation on the Thermal Stability and Morphology of 1,4-Phenylenediamine-1-Propylsilica Xerogels

1,4-phenylenediamine-1-propylsilica hybrid xerogels were obtained for two composition at different temperatures of gelation, from 5 up to 70C. The morphological effects produced by the different gelation temperatures were investigated by using N₂ adsorption-desorption isotherms and scanning electron microscopy. The thermal stability of the organic groups and their distribution on the xerogel matrix, i.e. the fraction of the organic groups that were trapped in closed pores, formed during the xerogel synthesis, and the fraction of organic groups present on the surface, were obtained by using infrared thermal analysis. The higher porosity of the xerogels and the higher thermal stability of the organic groups were achieved for samples gelled at 25C.     

Asymmetric aminolysis of aromatic epoxides: a facile catalytic enantioselective synthesis of anti-beta-amino alcohols

[reaction: see text] The first asymmetric aminolysis of trans-aromatic epoxides with anilines is described. The process affords enantioenriched anti-beta-amino alcohols in up to 99% ee. The complete regio- and diastereoselectivity observed uses commercially available [Cr(Salen)Cl] as a Lewis acid catalyst and in combination with a very simple experimental procedure renders the present reaction a facile and practical tool for the synthesis of chiral nonracemic anti-beta-amino alcohols.     

Rhodium-catalyzed addition of aryldifluoromethylsilanes to N-sulfonylaldimines

The addition of aryldifluoromethylsilanes to N-sulfonylaldimines was found to be catalyzed by a rhodium complex, [Rh(cod)(MeCN)₂]BF₄, in the presence of potassium fluoride to give the corresponding arylated N-sulfonylamines in good yield. The reaction mechanism would involve the generation of a fluoride-coordinated arylsilicate and the transmetalation between the arylsilicate and the rhodium complex to give the arylrhodium species as a key intermediate.     

Self-Diffusion in Uniaxial Liquid Crystals

Expressions are given for the translational diffusion parameters of non-spherical solutes in nematic and smectic-A phases, as measured by magnetic field gradient spin-echo NMR.     

Symmetry constraints for real dispersionless Veselov-Novikov equation

Symmetry constraints for dispersionless integrable equations are discussed. It is shown that under symmetry constraints, the dispersionless Veselov-Novikov equation is reduced to the (1+1)-dimensional hydrodynamic-type systems. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.