Path integrals over the group manifolds

Particle motion in the SU(2) manifold is quantized by path integrals. It is shown that the Poschl-Teller, Wood-Saxon, and Rosen-Morse potentials are solved by relating their propagators to the path integrations over the SU(2) manifold. Examples with some other groups are mentioned.     

Microcrystals formed in proton bombarded poly(vinyl chloride) films

Thin films of PVC were bombarded with 700 keV protons, and studied with RGA during bombardment, and later with TEM. A great mass loss was observed, and the remaining material was found to contain many micro-crystals with interplanar spacings of 0.25 and 0.28 nm within an amorphous matrix.     

Particle production in a class of anisotropic cosmologies

Scalar particle production is studied in a class of anisotropic spacetimes which are the exact solutions of Einstein equations with a perfect stiff fluid. Massless field creations are also discussed.     

Anomalous NMR behavior of meso compounds with remote stereogenic centers on addition of chiral shift reagent or chiral solvating agent

A problem has arisen in using chiral shift reagents (CSR) and chiral solvating agents (CSA) to determine meso and racemic forms of diastereoisomers in which the stereogenic centers of the molecules are separated by achiral spacers. It is found that NMR signals of both meso and racemic forms of diastereoisomers may exhibit doubling on addition of CSR/CSA, which means that unequivocal assignments cannot be made without characterizing the effects for separate meso and racemic forms; this is particularly important for additions of CSR/CSA at relatively low concentrations, which always result in the splitting of some NMR signals of diastereoisomers. The phenomenon is demonstrated in the (31)P NMR spectra of meso and racemic forms of three spermine-bridged gem-disubstituted cyclotriphosphazatrienes, 1a-c, and compared with analogous achiral molecules, the per-substituted spermine-bridged cyclotriphosphazatrienes 2a-d. As expected, only one set of (31)P NMR signals was observed for the achiral compounds 2a-d, even on addition of CSA. Two sets of (31)P NMR ABX multiplets corresponding to meso and racemic diastereoisomers were observed for compounds 1a-c; on addition of CSA, the signals of at least one of the multiplets for each compound separated into more than the expected groups of three lines with an intensity distribution of 2:1:1. To understand this phenomenon, the meso and racemic forms of 1a and 1b and the meso form of 1c have been separated and characterized by X-ray crystallography. On addition of CSA to the racemic forms of 1a and 1b, the (31)P NMR spectrum shows the expected doubling of signals, but, unexpectedly, the same is observed for each of the meso forms of 1a-c. Analogous results using both CSA and CSR have been obtained for the meso and racemic forms of the diastereoisomeric piperazine-bridged macrocyclic-phosphazene compound, 3, whereas no effect was observed for the two meso forms of the doubly bridged macrocyclic-phosphazene compound 4. The phenomenon of doubling of the (31)P NMR signals of the meso form of singly bridged cyclotriphosphazatrienes, 1a-c and 3, is explained by consideration of the equilibrium in solution of independent complexation of a chiral ligand with molecules that have two chiral cyclophosphazene moieties separated by an achiral spacer group. The results show that the stereogenicity of such diastereoisomeric molecules in solution cannot be characterized unequivocally by NMR measurements on addition of either CSR or CSA.     

Poly(2-(dimethylamino)ethyl methacrylate) brushes fabricated by surface-mediated RAFT polymerization and their response to pH

In this study, well-defined, high density poly(2-(dimethylamino)ethyl methacrylate) [poly(DMAEMA)] brushes were fabricated by the combination of the self-assembly of a monolayer of RAFT agent and surface-mediated RAFT polymerization. The whole fabrication process of the poly(DMAEMA) was followed by water contact angles, grazing angle-Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and atomic force microscopy. Kinetic studies revealed a linear increase in poly(DMAEMA) film thickness with polymerization time, indicating that the chain growth from the surface was a controlled process. Characterization of the poly(DMAEMA) brushes, such as molecular weight and thickness determination, were measured by gel permeation chromatography, and ellipsometry, and the grafting density was estimated. The pH response of the poly(DMAEMA) brushes was further investigated and the results verified the “brush-like” to “mushroom-like” transition of the poly(DMAEMA) chains due to the reversible protonation/deprotonation upon changing the solution pH.     

Hybrid phospholipid bilayer coatings for separations of cationic proteins in capillary zone electrophoresis

Protein separations in CZE suffer from nonspecific adsorption of analytes to the capillary surface. Semipermanent phospholipid bilayers have been used to minimize adsorption, but must be regenerated regularly to ensure reproducibility. We investigated the formation, characterization, and use of hybrid phospholipid bilayers (HPBs) as more stable biosurfactant capillary coatings for CZE protein separations. HPBs are formed by covalently modifying a support with a hydrophobic monolayer onto which a self‐assembled lipid monolayer is deposited. Monolayers prepared in capillaries using 3‐cyanopropyldimethylchlorosilane (CPDCS) or n‐octyldimethylchlorosilane (ODCS) yielded hydrophobic surfaces with lowered surface free energies of 6.0 ± 0.3 or 0.2 ± 0.1 mJ m^?2, respectively, compared to 17 ± 1 mJ m^?2 for bare silica capillaries. HPBs were formed by subsequently fusing vesicles comprised of 1,2‐dilauroyl‐sn‐glycero‐3‐phosphocholine or 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine to CPDCS‐ or ODCS‐modified capillaries. The resultant HPB coatings shielded the capillary surface and yielded reduced electroosmotic mobility (1.3–1.9 × 10^?4 cm² V^?1s^?1) compared to CPDCS‐ and ODCS‐modified or bare capillaries (3.6 ± 0.2 × 10^?4 cm² V^?1s^?1, 4.8 ± 0.4 × 10^?4 cm² V^?1s^?1, and 6.0 ± 0.2 × 10^?4 cm² V^?1s^?1, respectively), with increased stability compared to phospholipid bilayer coatings. HPB‐coated capillaries yielded reproducible protein migration times (RSD ≤ 3.6%, n ≥ 6) with separation efficiencies as high as 200 000 plates/m.     

Unusual products in the reactions of hexachlorocyclotriphosphazatriene with sodium aryloxides

Reactions of hexachlorocyclotriphosphazatriene, N₃P₃Cl₆ 1 , with sodium aryloxides have been studied. Compound 1 was found to react by the nucleophilic substitution pathway to yield monocyclophosphazenes [N₃P₃Cl₆(OC₆H₂Bu¹₃-2,4,6) 5 and N₃P₃Cl₄(OC₆H₂Me-4-Bu¹₂-2,6)₂ 6 ] and bi(cyclophosphazenes) ([Cl₅N₃P₃-P₃N₃Cl₄(OC₆H₃Bu¹₂-2,6)] 7 and [N₃P₃(OC₆H₃Bu¹₂-2,6)₅]₂ 8 ). The unusual bi(cyclophosphazenes) 7 and 8 are the first examples of two cyclotriphosphazene rings linked by a P(SINGLE BOND)P bond [2.193 (2) Å], which have been obtained by reacting 1 with ArONa. The structures of compounds 5–8 are ascertained by elemental analyses, ¹H-, ³¹P-¹³C-NMR, IR, and MS spectra. The molecular structure of monocyclic-phosphazene 5 was determined by X-ray diffraction techniques for further structural assignment. It crystallizes in the monoclinic space group P2₁/m with a = 6.144(2), b = 17.079(9), c = 13.181(9) Å, β = 92.79(7), and Z = 2, R = 0.074. Compound 5 is on a crystallographic mirror plane, and there is only a half molecule in the asymmetric unit. © 1996 John Wiley & Sons, Inc.     

Some novel photosensitive diacetylene diurethanes and their mixtures in common polymers

Some new octa-3,5-diynylene diurethanes were prepared using 3-butyn-1-ol, and all were found to be highly light-sensitive and to undergo topochemical polymerization on exposure to irradiation. The di-n-octyldiurethane was mixed with vinyl polymers such as poly(vinyl acetate) and poly(N,N-dimethylamino-ethyl methacrylate) and the mixtures were made into thin films by spin coating. The films were then irradiated by an electron beam to polymerize the diacetylene. The purple films thus obtained showed third-order nonlinear susceptibility, χ⁽³⁾, of the order of 10⁻¹⁰–10⁻¹¹ e.s.u.     

奇异摄动初值问题的一致收敛有限差分法

通过一阶和二阶导数讨论了带小参数的线性二阶常微分方程的初值问题.在均匀网格上得出了带常数拟合因子的指数型拟合差分格式,给出了离散最大模意义上的一阶一致收敛性.文中给出了数值结果.