Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.     

Chiral molecular glass: synthesis and characterization of enantiomerically pure thiophene-based [7]helicene

Synthesis of thiophene-based [7]helicenes, which are functionalized for both design of organic chiral glasses with strong chiroptical properties and for further homologation to higher [n]helicenes, is reported. The key synthetic transformations are kinetic resolution of the intermediate diketone and the annelation step forming the center benzene ring by means of an intramolecular McMurry reaction. Based upon X-ray crystallographic determinations of the absolute configurations for (+)-enantiomers of the diketone and the [7]helicene, stereochemical correlation between the (R) axial chirality of the diketone and the (M) helical chirality of the [7]helicene is established. One such enantiopure trimethylsilyl-substituted [7]helicene possesses enchanced chiroptical properties and forms a chiral molecular glass.     

Solvent Effects on the Absorption Spectrum of the Product and the Equilibrium Constant for the Proton Transfer Reaction from 1-Phenacylquinolinium Bromide to Amines

The equilibrium constants, K ₂, have been determined for the proton-transfer reactions of 1-phenacylquinolinium ion, PHQ⁺, with several amines {triethylamine (TEA), N,N,N′,N′-tetramethylethylenediamine (ED), N,N,N′, N′-tetramethylpropanediamine (PD), N,N,N′,N′-tetramethylbutanediamine (BD), and 1,8-bis(dimethylamino-naphthalene (DMAN)} in acetonitrile (AN), AN-tetrahydrofuran (THF) and AN-ethanol (EtOH) mixtures. The reaction was followed spectrophotometrically using a stopped-flow technique. The K ₂ value decreased for DMAN and increased for TEA with increasing vol-% of THF in AN-THF mixtures. The changes in the K ₂ value for ED, PD and BD changed in the order: ED, PD and BD from a pattern similar to TEA to a pattern similar to DMAN. The change in the K ₂ value for DMAN with increasing vol-% of THF in AN-THF mixtures was explained by the effect of polarity on the stability of P⁻Q⁺ (the deprotonated product of PHQ⁺). The effect of THF on the K ₂ value is consistent with that of the peak wavelength of the absorption spectrum of P⁻Q⁺. The change in the K ₂ value for TEA, ED, PD and BD depended on the structures of the protonated bases, one of the products for this reaction. The effect of EtOH on the K ₂ value for DMAN was examined in ternary EtOH-THF-AN mixtures that contain different amounts of EtOH and whose relative permittivities were adjusted to that of EtOH. The K ₂ value increased with increasing vol-% of EtOH because of the stabilization of P⁻Q⁺ upon the formation of the hydrogen-bonded complex with EtOH. The absorption spectrum of P⁻Q⁺ demonstrated a blue shift as the vol-% of EtOH increased.     

Application of water as a solvent in microwave-assisted extraction for analysis of PCBs and CBzs in fly ash

Polychlorinated biphenyls (PCBs) and chlorobenzenes (CBzs) are two classes of dioxin precursors formed in municipal solid waste incinerators (MSWIs); they produce negative health effects similar to those of dioxins. Reducing the analytical time required for determining the concentrations of these compounds in MSWIs is important for quickly evaluating their importance and assessing associated health risks. In the present study, water is used as a safe and environmentally friendly solvent in microwave-assisted extraction (MAE) for PCB and CBz analyses. MAE is compared with traditional Soxhlet extraction (SE) to determine the extraction efficiencies. The evaluation of extraction efficiencies shows that MAE has a high extraction efficiency compared with that of SE when water content is lower than 60%. Furthermore, the extraction time and organic solvent consumption are reduced with MAE compared with SE.     

Electrical conducting and magnetic properties of (ethylenedithiotetrathiafulvalenothioquinone-1,3-diselenolemethide)2.FeBr4 (GaBr4) crystals with two different interlayer arrangements of donor molecules

Two donor molecules newly synthesized, dimethylthio- and ethylenedithio-tetrathiafulvalenothioquinone-1,3-diselenolemethides (1 and 2), were used to prepare their charge-transfer (CT) salts with a magnetic FeBr(4)(-) counteranion. For 1, a low electrical conducting 1:1 salt (1.FeBr(4)) was obtained, in which molecules of 1 are tightly dimerized in a one-dimensional (1D) stacking column. On the other hand, 2 gave a 2:1 salt (2(2).FeBr(4)) as two different kinds of plate crystals (I and II). Both I and II possess similar stacking structures of molecules of 2 in each 1D column with a half-cut pipelike structure along the c axis. However, for I, the stacking columns are aligned in the same direction along the a and b axes, while for II they are in the same direction along the a axis, but in the reverse direction along the b axis, resulting in the difference in the relative arrangement of molecules of 2 and FeBr(4)(-) ions between the two crystals. The room-temperature electrical conductivities of the single crystals of I and II were 13.6 and 12.7 S cm(-)(1), respectively. The electrical conducting behavior in I was metallic above 170 K but changed to be semiconducting with a very small activation energy of 7.0 meV in the temperature range 4-170 K. In contrast, II showed the semiconducting behavior in the whole temperature range 77-285 K. The corresponding nonmagnetic GaBr(4)(-) salts with almost the same crystal structure as I and II showed definitively different electrical conducting properties in the metal to semiconductor transition temperature in I as well as in the magnitude of activation energy in the semiconducting region of I and II. The interaction between the d spins of FeBr(4)(-) ions was weak and antiferromagnetic in both I and II, but the magnitude of the spin interaction was unexpectedly larger compared with that in the FeBr(4)(-) salt of the corresponding sulfur derivative of 2 with closer contact between the neighboring FeBr(4)(-) ions. These electrical conducting and magnetic results suggest a significant interaction between the conducting pi electrons and the d spins of FeBr(4)(-) ions located near the columns or layers.     

A multi-mode-driven molecular shuttle: photochemically and thermally reactive azobenzene rotaxanes

The shuttling process of alpha-CyD in three rotaxanes (1-3) containing alpha-cyclodextrin (alpha-CyD) as a ring, azobenzene as a photoactive group, viologen as an energy barrier for slipping of the ring, and 2,4-dinitrobenzene as a stopper was investigated. The trans-cis photoisomerization of 1 by UV light irradiation occurred in both DMSO and water due to the movement of alpha-CyD toward the ethylene group, while the photoisomerization of 2 occurred in DMSO, but not in water. No photoisomerization was observed for 3 in both water and DMSO. The activation parameters of 1 and 1-ref in DMSO are subject to a compensation relation between deltaS(double dagger) and deltaH(double dagger); however, in water, the deltaS(double dagger) terms are not compensated by the deltaH(double dagger) terms. Alternating irradiation of the UV and visible lights resulted in a reversible change in the induced circular dichroism (ICD) bands of trans-1 and cis-1. In contrast, after the UV light irradiation, the ICD band of trans-2 decreased without the appearance of any bands of cis-2. The NMR spectra of 2 in DMSO showed coalescence of the split signals for the methylene and for the viologen protons due to the shuttling of alpha-CyD. Both the NOE differential spectra for cis-1 in water after UV light irradiation and 2 in DMSO after heating to 120 degrees C showed the negative NOE peaks assigned to interior protons of alpha-CyD, suggesting that alpha-CyD in cis-1 exists at the one ethylene moiety, and alpha-CyDs in cis-2 and 2 heated in DMSO exist at the propylene moieties.     

Improved preparation of racemic 2-amino-3-(heteroaryl)propanoic acids and related compounds containing a furan or thiophene nucleus

Racemic 2-amino-3-(heteroaryl)propanoic acids (1), mostly with a furan or thiophene nucleus as a heteroaryl group, were synthesized in 48-94% yield by the reduction of 3-(heteroaryl)-2-(hydroxyimino)propanoic acids (5) with zinc dust and formic acid in the presence of a catalytic amount of iron dust at 60 degrees C for 2 h. Under these conditions, unfavorable hydrogenolysis of bromine on the thiophene nucleus does not occur. Traditional N-formylation of the prepared 3-(heteroaryl)alanine (1) with a mixture of formic acid and acetic anhydride afforded 2-(formylamino)-3-(heteroaryl)propanoic acids (6) in 51-95% yield.     

Effect of equimolar salt to decyltrimethylammonium decyl sulfate on vesicle formation and surface adsorption

The aqueous solution of mixture of sodium decyl sulfate (SDeS) and decyltrimethylammonium bromide (DeTAB) has been found to form equilibrium multilamellar vesicles (MLV) spontaneously. We measured the surface tension of the aqueous solution of 1:1 mixture of SDeS and DeTAB as a function of temperature T at various molalities m under atmospheric pressure. The surface density, the entropy of adsorption and the entropy of vesicle formation are evaluated and compared with those of the decyltrimethylammonium decyl sulfate (DeTADeS) aqueous solution system to investigate the role of small counterions in the mechanism of equilibrium vesicle formation. The saturated surface density Gamma (H,C ) vs T curve of the SDeS/DeTAB system sits below that of the DeTADeS system. Therefore, sodium and bromide ions are negatively adsorbed and nevertheless, they neutralize the electric charge of the decyl sulfate ion DeS(-) and the decyltrimethylammonium ion DeTA(+) to some extent to weaken the electrostatic attraction between the polar head groups in the adsorbed film. The net surfactant concentration required for vesicle formation was larger in the SDeS/DeTAB system. Hence, the electrostatic attraction between the polar head groups of the surfactant ions which is one of the major driving forces for vesicle formation is weakened by the presence of the counterions Na(+) and Br(-). Small but distinct changes in the surface density and the entropies of MLV formation of the SDeS/DeTAB system from those of the DeTADeS system were also found.     

Pinacol coupling reaction of beta-halo-alpha,beta-unsaturated aldehydes promoted by TiI4

The pinacol reaction of beta-halogenated alpha,beta-unsaturated aldehydes was promoted by titanium tetraiodide to give coupling products in good yields with high dl-selectivity. Subsequent reduction with H(2)/Pd-C gave saturated vic-diols in good yields. Heck coupling reaction enabled the displacement of halogens with vinyl groups without the loss of stereochemical integrities. [reaction: see text]