Facile synthesis of polystyrene bearing highly branched perfluorinated groups

A novel styrene monomer with a highly branched perfluoroalkenyl group was readily prepared in good yield from hexafluoropropene trimer and hydroxystyrene. The fluorinated monomer radically polymerized yielded a white powdery polymer which was soluble in fluorinated solvents and had good water repellency. The polymer had a unique high glass transition temperature despite the introduction of perfluorinated groups. The monomer was copolymerized with styrene, and their monomer reactivity ratios were determined.     

A density functional theory study applied for carbon and oxygen isotope effects in the system Ni(CO)4/CO

DFT calculations were carried out on the carbon and oxygen isotopomers of CO and Ni(CO)₄ and results compared with (Spindel's) experimental results on the carbon and oxygen isotope exchange equilibria between CO and Ni(CO)₄. The isotopic equilibrium constants, K_B, of carbon and oxygen exchange reactions between CO and Ni(CO)₄ complexes were theoretically calculated as the ratio of the reduced partition function ratios (RPFRs) of the ¹³C/¹²C and ¹⁸O/¹⁶O isotopic pairs for CO and Ni(CO)₄ on the assumption of the internal harmonic vibrations. The agreement between calculated separation factor and Spindel's experimental data are surprisingly good, including the temperature dependence.     

DFT-GIAO calculations of 19F NMR chemical shifts for perfluoro compounds

The (19)F NMR shieldings for 53 kinds of perfluoro compounds were calculated by the B3LYP-GIAO method using the 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311++G(d,p), 6-311G(2d,2p), 6-311++G(2d,2p), 6-311++G(2df,2p), 6-311++G(3d,2p), and 6-311++G(3df,2p) basis sets. The diffuse functions markedly reduce the difference between the calculated and experimental chemical shifts. The calculations using the 6-31++G(d,p) basis set give the chemical shifts within 10 ppm deviations from experimental values except for the fluorine nuclei attached to an oxygen atom, a four- and a six-coordinated sulfur atom, and FC(CF(3))(2) attached to a sulfur atom.     

Intramolecular reaction of a phenonium ion. Novel lactonization of 4-aryl-5-tosyloxypentanoates and 4-aryl-5-tosyloxyhexanoates concomitant with a phenyl rearrangement

The novel lactonizations of methyl 4-aryl-5-tosyloxypentanoate 1 and 4-aryl-5-tosyloxyhexanoate 3 concomitant with a phenyl rearrangement are reported. The lactonizations were promoted by silica gel or heating in various solvents. By examining the effects of substituents of the aromatic ring on the reactivity, it was found that the reaction proceeded via a phenonium ion. This finding was supported by the stereochemical results for the lactonization of optical active 1. Silica gel-promoted lactonization of 1 gave only gamma-lactone 2, whereas that of 3 afforded gamma-lactone 4 and delta-lactone 5. These lactonizations proved to be kinetically controlled. On the other hand, when 3c was heated in CH(3)NO(2) at 70 degrees C, the highly selective formation of 4c was observed. Further detailed experiments confirmed that the thermal lactonization in CH(3)NO(2) was thermodynamically controlled.     

Multiple Pentafluorophenylation of 2,2,3,3,5,6,6‐Heptafluoro‐3,6‐dihydro‐2H‐1,4‐oxazine with an Organosilicon Reagent: NMR and DFT Structural Analysis of Oligo(perfluoroaryl) Compounds

The reagent Me₃Si(C₆F₅) was used for the preparation of a series of perfluorinated, pentafluorophenyl‐substituted 3,6‐dihydro‐2H‐1,4‐oxazines ( 2 – 8 ), which, otherwise, would be very difficult to synthesize. Multiple pentafluorophenylation occurred not only on the heterocyclic ring of the starting compound 1 (Scheme), but also in para position of the introduced C₆F₅ substituent(s) leading to compounds with one to three nonafluorobiphenyl (C₁₂F₉) substituents. While the tris(pentafluorophenyl)‐substituted compound 3 could be isolated as the sole product by stoichiometric control of the reagent, the higher‐substituted compounds 5 – 8 could only be obtained as mixtures. The structures of the oligo(perfluoroaryl) compounds were confirmed by ¹⁹F‐ and ¹³C‐NMR, MS, and/or X‐ray crystallography. DFT simulations of the ¹⁹F‐ and ¹³C‐NMR chemical shifts were performed at the B3LYP‐GIAO/6‐31++G(d,p) level for geometries optimized by the B3LYP/6‐31G(d) level, a technique that proved to be very useful to accomplish full NMR assignment of these complex products.     

Difference spatial distribution function analysis of aqueous solutions. IV. Hydration structure changes of ethylene glycol solutions throughout conformational change process from gGg' to tGg' conformers

Monte Carlo (MC) simulations were carried out for an infinitely dilute aqueous solution of two stable conformers (gGg' and tGg') and of three conformations between gGg' and tGg' conformers of ethylene glycol (EG) at 298K. Based on the spatial distribution function (SDF) goo(x,y,z), obtained from the MC simulation in the above conformations in liquid water, the high distribution of hydration water molecules could be divided into hydrogen acceptor (HA), hydrogen donor (HD), MIX (overlapped distribution of HA and HD), and hydrophobic hydration (HH) regions. The spatial orientations of hydrogen-bonded water molecules were found to be of a linear type with a triple-layer structure in the HA region and HA part (in the MIX region), and double-layer structures in the HD region and HD part (in the MIX region). In addition, it was apparent that the spatial orientations of these water molecules were of the linear type throughout the conformational change process from gGg' to tGg' conformers in liquid water. From the difference SDF (DSDF), deltagoo(x,y, z), between the SDFs of two conformations, we concluded that the distribution of hydration water molecules in the HA and HD parts of the MIX region are governed by the competition of internal hydrogen bonds between the hydrogen atom and two lone-pair electrons on the oxygen atom of an EG molecule.     

Orientational photorefractive effects observed in polymer-dispersed liquid crystals

We present a novel type of photorefractive polymer-dispersed liquid crystal (PDLC) that contains a polymer, low-molecular liquid crystals (LC's), and a photoconductive sensitizer. Photorefractivity is demonstrated by two-beam-coupling experiments with an external dc field. This material shows highly sensitive photorefractivity, and a purely refractive-index grating (Dn >/= 3.0 x 10(-3)) is generated by irradiation of interference light (lambda=632.8 nm) . The grating in the photorefractive PDLC's shows strong anisotropy, and the dynamics depends strongly on the composition. In the case of a 40:60 weight ratio of polymer:LC's, the photorefractive PDLC's present a stable memory effect.     

A note on a question of J. Nekovár and the Birch and Swinnerton-Dyer conjecture

If is a square-free integer, then let denote the elliptic curve over given by the equation

Let denote the Hasse-Weil -function of , and let denote the `algebraic part' of the central critical value . Using a theorem of Sturm, we verify a congruence conjectured by J. Neková\v{r}. By his work, if denotes the 3-Selmer group of and is a square-free integer with , then we find that

     

Values of Gaussian hypergeometric series

Let be prime and let be the finite field with elements. In this note we investigate the arithmetic properties of the Gaussian hypergeometric functions

where and respectively are the quadratic and trivial characters of For all but finitely many rational numbers there exist two elliptic curves and for which these values are expressed in terms of the trace of the Frobenius endomorphism. We obtain bounds and congruence properties for these values. We also show, using a theorem of Elkies, that there are infinitely many primes for which is zero; however if or , then the set of such primes has density zero. In contrast, if or , then there are only finitely many primes for which Greene and Stanton proved a conjecture of Evans on the value of a certain character sum which from this point of view follows from the fact that is an elliptic curve with complex multiplication. We completely classify all such CM curves and give their corresponding character sums in the sense of Evans using special Jacobsthal sums. As a consequence of this classification, we obtain new proofs of congruences for generalized Apéry numbers, as well as a few new ones, and we answer a question of Koike by evaluating over every