Effects of molecular structure on the stability of a thermotropic liquid crystal. Gas electron diffraction study of the molecular structure of phenyl benzoate.

As a model of the core of molecules forming liquid crystals, the molecular structure of phenyl benzoate (Ph-C(=O)-O-Ph) at 409 K was determined by gas electron diffraction, and the relationship between the gas-phase structures of model compounds and the nematic-to-liquid transition temperatures was studied. Structural constraints were obtained from RHF/6-31G ab initio calculations. Vibrational mean amplitudes and shrinkage corrections were calculated from the harmonic force constants given by normal coordinate analysis. Thermal vibrations were treated as small-amplitude motions, except for the phenyl torsion, which was treated as a large-amplitude motion. The potential function for torsion was assumed to be V(phi(1),phi(2)) = V(12)(1 - cos 2phi(1))/2 + V(14)(1 - cos 4phi(1))/2 + V(22)(1 - cos 2phi(2))/2, where phi(1) and phi(2) denote the torsional angles around the C-Ph and O-Ph bonds, respectively. The potential constants (V(ij)()/kcal mol(-)(1)) and the principal structure parameters (r(g)/A, angle(alpha)/deg) with the estimated limits of error (3sigma) are as follows: V(12) = -1.3 (assumed); V(14) = -0.5(9); V(22) = 3.5(15); r(C=O) = 1.208(4); r(C(=O)-O) = 1.362(6); r(C(=O)-O) - r(O-C) = -0.044 (assumed); r(C(=O)-C) = 1.478(10); = 1.396(1); angleOCO = 124.2(13); angleO=CC = 127.3(12); angleCOC = 121.4(22); ( angleOCC(cis) - angleOCC(trans))/2 = 3.0(15); ( angleC(=O)CC(cis) - angleC(=O)CC(trans))/2 = 4.8(17), where < > means an average value and C-C(cis) and C-C(trans) bonds are cis and trans to the C(=O)-O bond, respectively. The torsional angle around the O-Ph bond was determined to be 64(+26,-12) degrees. An apparent correlation was found between the contributions of the cores to the clearing point of liquid crystals and the gas-phase structures of model compounds of the cores of mesogens, i.e., phenyl benzoate, trans-azobenzene (t-AB), N-benzylideneaniline, N-benzylideneaniline N-oxide (NBANO), trans-azoxybenzene (t-AXB), and trans-stilbene. The structures of t-AB, NBANO, and t-AXB have been obtained by our research group.     

Higher-Order Structure of Poly(Ethylene 2,6-Naphthalene Dicarboxylate) Fibers Produced by Direct High-Speed Spin-Drawing

In order to efficiently produce poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) fibers comprising α-phase crystallites with a high melting temperature, a direct high-speed spin-drawing (HSSD) system was implemented. The higher-order structure of the HSSD PEN fibers was investigated by focusing on the radial anisotropy of the fibers. A nucleating agent was added to the PEN fibers, and its effect on the formation of the higher-order structure was also studied. Highly crystalline PEN fibers predominantly composed of α-phase crystallites were produced by operating the HSSD system at 4?km/min. The PEN fibers exhibited a melting temperature of 288.8?°C and a storage modulus of 31.4?GPa. The excellent thermal stability of the HSSD PEN fibers was presumably brought about by the formation of a shish-kebab-like structure. The generation of the shish-kebab-like structure and radial anisotropy seemed to be more dependent on the effect of tensile stress during the drawing process rather than from the nucleating additive. The nucleating agent used in this study effectively increased both the α- and β-phase crystallite sizes. Such structural modification, however, did not appear to contribute to the thermal stability enhancement of the PEN fibers.     

Random surfaces in three-dimensional simplicial gravity

A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of three-dimensional DT manifold with topology. A new scaling behavior of genus distributions of boundary surfaces is found. Furthermore, these surfaces are compared with the random surfaces generated by the two-dimensional DT method which are well known as a correct discretized method of the two-dimensional quantum gravity.     

Characterization of H(n, q) by the parameters

Distance-regular graphs which have the same parameters as the Hamming scheme H(n, q) are classified. If q ≠ 4, H(n, q) is the only such graph. If q = 4, there are precisely $\text{[}\text{n}\text{2}\text{]}$ (isomorphism classes of) such graphs other than H(n, q).     

Even edge colorings of a graph

It is shown that the minimum number of colors needed to paint the edges of a graph G so that in every cycle of G there is a nonzero even number of edges of at least one color is ?log_2χ(G)?.     

Influence of Crosslinking and Porosity on the Uranium Adsorption of Macroreticular Chelating Resin Containing Amidoxime Groups

Macroreticular chelating resins (RNH) containing amidoxime groups with various degrees of crosslinking were synthesized by using various amounts of divinylbenzene (DVB) or/and poly(ethylene glycol) dimeth-acrylate [ethylene glycol dimethacrylate (IG), diethylene glycol dimethacrylate (2G), triethylene glycol dimethacrylate (3G), tetraethylene glycol dimethacrylate (4G), and nanoethylene glycol dimethacrylate (9G)] as crosslinking reagent. The effects of crosslinking reagents on the pore structure, ion-exchange capacity, swelling ratio, and adsorption ability for uranium of RNH were investigated. The adsorption ability of RNH for uranium was tested by use of natural seawater or U-spiked seawater. RNH-1G samples prepared by using 1G were shown to have macroreticular structures by measuring the specific surface area. RNH-1G had high adsorption ability and good physical stability. Though RNH-4G samples obtained by using 4G had little macroreticular structure (macropore), these resins showed high adsorption ability for uranium on treatment with 0. 1 M NaOH at 30°C for 15 h. RNH-4G was found to have low physical and chemical stability. For the preparation of RNH with effective pore structure for the recovery of uranium, as well as chemical and physical stability, the simultaneous use of DVB and 1G or 4G as crosslinking reagent was examined (abbreviated as RNH-DVB-1G and RNH-DVB-4G). The RNH-DVB-1G showed high adsorption ability for uranium. Repeated use did not cause deterioration of either RNH-DVB-1G or RNH-DVB-4G. RNH-DVB-1G samples with various degrees of crosslinking were prepared, and the uranium recovery of the resins was also investigated by a column method. Although the RNH-DVB-1G samples with the same degree of crosslinking had almost the same content of amidoxime groups, the uranium recovery of each RNH-DVB-1G sample was considerably different and increased by treatment with alkali solution. These results indicate that the adsorption ability of RNH-DVB-1G for uranium in seawater was not only affected by the macropores but also by the micropores formed by swelling of the resins.     

Novel methodology to control the adsorption structure of cationic porphyrins on the clay surface using the "size-matching rule"

Saponite-type clays that have different cation exchange capacities were successfully synthesized by hydrothermal synthesis. The structure and properties were analyzed by X-ray diffraction, X-ray fluorescence, (27)Al NMR, FT-IR, thermogravimetric and differential thermal analysis, atomic force microscopy, and cation exchange capacity measurement. The intercharge distances on the synthetic saponite (SS) surfaces were calculated to be 0.8-1.9 nm on the basis of a hexagonal array. The complex formation behavior between SS and cationic porphyrins was examined. It turns out that the average intermolecular distance between porphyrin molecules on the SS surface can be controlled, depending on the charge density of the SS. In the case of tetrakis(1-methylpyridinium-4-yl)porphyrin (H(2)TMPyP(4+)), the average intermolecular distances on the SS surface can be controlled from 2.3 to 3.0 nm on the basis of a hexagonal array. It was also found that absorption maxima of porphyrins depend on the charge density of the SS. The adsorption behavior of porphyrin on the SS surface can be rationally understood by the previously reported "size-matching rule". This methodology using host-guest interaction can realize a unique adsorption structure control of the porphyrin molecule on the SS surface, where the gap distance between guest porphyrin molecules is rather large. These findings will be highly valuable to construct photochemical reaction systems such as energy transfer in the complexes.     

On randomlyn-cyclic digraphs

A digraphD is called randomlyn-cyclic if for each vertexv ofD, every (directed) path with initial vertexv and having length at mostn – 1 can be extended to av – v (directed) cycle of lengthn. This notion was first introduced by Chartrand, Oellermann and Ruiz [3] and they determined all randomly 3, 4 and 5-cyclic diagraphs. In this paper, we will provide the characterization of randomlyn-cyclic digraphs forn 6.     

Total Synthesis of Pectenotoxin‐2

Pectenotoxin‐2 (PTX2) is a shellfish toxin and has a non‐anomeric spiroacetal, which is not stabilized by an anomeric effect. The selective construction of the non‐anomeric spiroacetal has been a major problem in the synthesis of PTX2. Described herein is the stereoselective total synthesis of PTX2 via the isomerization of anomeric spiroacetal pectenotoxin‐2b (PTX2b). The synthesis of PTX2b was achieved by a simple process including sulfone‐mediated assembly of spirocyclic and bicyclic acetals and subsequent macrocyclization by ring‐closing olefin metathesis. Finally, the selective construction of PTX2 was accomplished by the early termination of a dynamic transition process to equilibrium in the acid‐catalyzed isomerization of anomeric PTX2b. [6,6]‐Spiroacetal pectenotoxin‐2c (PTX2c) was also synthesized from PTX2b. The cytotoxicity assay of the synthetic compounds against HepG2 and Caco2 cancer cells showed a potency of the order: PTX2?PTX2b>PTX2c.