Isomerism in some 1-oxa-3,5-dithians and the X-ray structure determination of 2,6-bis(trichloromethyl)-4-dichloromethylene-1-oxa-3,5-dithian

2,6-bis (trichloromethyl)-4-dichloromethylene-1-oxa-3,5-dithian is triclinic,P¯1,a=10.125(3),b=10.294(3),c=14.631(10) Å,=92.84(5),=96.51(5), =96.18(2)°,V=1503 ų,Z=4. The structure was solved by direct methods, from data collected at room temperature on an Enraf-Nonius CAD4 diffractometer, and refined by least squares to a finalR value of 0.035 using 3961 reflections. The conformation of the molecules is twist-boat, one molecule being almost symmetrically twisted about the O-C(Cl₂) direction. The range of endocyclic O-C-S angles is 111.8(3) to 115.1(3)° and data are given which support the possibility of there being a correlation between the endocyclic O-C(X)-S angle, the C-O-C(X)-C(Cl₃) torsion angle, and the C-S-C(X)-C(Cl₃) torsion angle. The -CCl₃ groups are in pseudoequatorial positions. Average bond lengths (Å) for the two molecules are C-O 1.405, C(sp ³)-S 1.822, C(sp ²)-S 1.759, C-C_eq 1.529 and average endocyclic angles (°) are O 117.3, C (sp ³) 113.5, S 97.4, C(sp ²) 119.3, the esds on the individual bond lengths and angles being in the ranges of 0.003–0.004 Å and 0.2–0.4° respectively.     

Structure and conformation of 6-nitro-2-trichloromethyl-1,3-benzdioxin-4-one: X-ray crystallographic determination

6-nitro-2-trichloromethyl-1,3-benzdioxin-4-one is monoclinic,P2₁/n;a=5.969(2),b=11.646(1),c=16.953(1) Å;=98.03(2)°;Z=4. The structure was solved by direct methods, from data collected at room temperature on an Enraf-Nonius CAD4 diffractometer, and refined by least squares to a finalR value of 0.030 using 1530 reflections.The heterocyclic ring is a distorted half-boat and is substituted equatorially by a trichloromethyl group. Dihedral angles are (a) 4.87(7)° between the mean plane of the aromatic ring and the plane containing the two carbon atoms common to both rings plus the two atoms bonded to these, and (b) 16.8(2)° between the carbonyl group and the aromatic ring. The conformation is discussed with reference to the two previously reported X-ray structures of 1,3-benzdioxin-4-ones and to two isocoumarins.     

Structure and conformation of 6-nitro-2,4-bis(dichloromethyl)-1,3-benzdioxin

6-Nitro-2,4-bis(dichloromethyl)-1,3-benzdioxin is monoclinic,P2₁/c, witha=8.514(1),b=22.187(3),c=7.931(1) Å,=117.96(1)°,Z=4. The structure was solved, from data collected with MoK radiation on an Enraf-Nonius CAD4 diffractometer, by direct methods and refined by full-matrix least squares using 2170 unique reflections to give a finalR factor of 0.032. The heterocyclic ring in the title compound has an envelope conformation with thecis-dichloromethyl groups in pseudoequatorial positions. The average C-C(HCl₂) distance is 1.516(4) Å. A comparison is given with the structure of the analogous compound 6-nitro-2,4-bis(trichloromethyl)-1,3-benzdioxin (Irving, A., and Irving, H. M. N. H. (1986)J. Crystallogr. Spectrosc. Res. 16, 703) which also containscis-halogenoalkyl groups but in which the –CCl₃ group at the 4-position occupies a pseudoaxial position.     

Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees

Methodology and Computing in Applied Probability - We study a portfolio optimization problem involving the loss averse policyholder of a variable annuity with a guaranteed minimum maturity benefit....     

Coordination Mode and Kinetic Behavior of the Tetracarbonatozirconate Ion

The behavior of [Zr(CO₃)₄]⁴⁻ complex in solution is studied by determining the coordination mode of the carbonato ligands and the kinetic law of the equilibrium between free and complexed carbonates. Raman polarization and dynamic ¹³C-NMR experiments show that complexed carbonates are bidentate. Magnetization-transfer experiments give the values of pseudo-first-order rate constants for the equilibrium with no net chemical transformation. The treatment of these parameters suggests a second-order rate law. As no solvent effect is noticed, an associative mechanism of ligand exchange is proposed.     

A kinetic study of the polymerization of pure meta-divinylbenzene and pure para-divinylbenzene

The kinetics of the polymerization of pure meta-divinylbenzene (DVB) and pure para-divinylbenzene at 70°C have been studied in the presence of toluene and 2-ethylhexanoic acid. The apparent rate constant ratios (k_p/k_t)^1/2 for these systems have been calculated. meta-Divinylbenzene polymerizes at a higher rate than the para-isomer in both toluene and 2-EHA, and the polymerization rates of meta-DVB and para-DVB before the gel point were both higher in the presence of 2-EHA than in toluene. The monomer conversion at the visual gel point is higher for para-DVB than for meta-DVB. The gel point has also been determined indirectly by size exclusion chromatography, and these results are consistent with the gel times observed visually. The conversion of pendant vinyl groups during the polymerization has been determined by bromination. It is found that the homopolymers of poly(para-DVB) have a substantially higher content of pendant vinyl groups than poly(meta-DVB) both during and at the end of the polymerization. The molecular weight distribution (MWD) prior to gelation has been determined by size exclusion chromatography (SEC). Weight average (M̄_w); and number average (M̄_n) molecular weight prior to gelation and of the sol fractions after gelation have also been measured by SEC. There are larger fractions of high molecular weight polymers prior to gelation, when the polymerization was run in the presence of toluene, than in 2-EHA, mainly due to the differences in solvating power of the two diluents. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3345–3359, 1999     

Solid‐state nuclear magnetic resonance relaxation times in crosslinked macroporous polymer particles of divinylbenzene homopolymers

Monodisperse porous particles of poly(divinylbenzene) prepared by the activated swelling method have been investigated by solid‐state ¹³C crosspolarization magic‐angle spinning (CPMAS) nuclear magnetic resonance (NMR) relaxation measurements. Homopolymeric combinations of two porogens (toluene and 2‐ethylhexanoic acid) and two monomers (meta‐ and para‐divinylbenzene) were studied. Residual vinyl groups were systematically reacted with increasing amounts of bromine, producing 20 different polymers samples for which we measured crosspolarization times, T_CH, proton rotating frame spin‐lattice relaxation, T, ¹³C spin‐lattice relaxation, T, and proton spin‐lattice relaxation, T. These parameters were chosen to reflect expected changes in a wide range of frequencies of motion as a function of structure. Relative differences in the molecular mobility of the major functional groups (aromatic, vinyl and aliphatic) is related to initial reactants used, vinyl concentration, relative reactivity of vinyl groups, distribution of vinyl groups, pore structure, and degree of crosslinking. Variable temperature ¹H combined rotation and multiple pulse NMR (CRAMPS) was used to derive activation energies for selected samples via measurement of the proton spin‐lattice relaxation time, T. Irreversible thermal effects were observed in ambient temperature relaxation after heating to temperatures in the range of 393–418 K. Simple univariate statistical analyses failed to reveal consistent correlations among the known variables. However, the application of more sophisticated multivariate and neural network analyses allowed excellent structure–property predictions to be made from the relaxation time data. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1307–1328, 1999     

Synthesis of thermotropic LCPs using p‐methoxycarbonyloxy aromatic acids

4‐Methoxycarbonyloxybenzoic acid (MCOBA) and 6‐methoxycarbonyloxy‐2‐naphthoic acid (MCONA) were synthesized as new monomers to replace 4‐acetoxybenzoic acid (ABA) and 6‐acetoxy‐2‐naphthoic acid (ANA) in the synthesis of liquid crystal polymers. MCOBA and MCONA (73 : 27, mol : mol) were reacted at temperatures ranging from 220 to 325°C in bulk. The copolymer (M_w = 14,200) has a T_g (90°C) and a T_m (249°C). The MCOBA/MCONA copolymer is lighter in color than the ABA/ANA copolymer. During the copolymerization, six by‐products were collected, isolated, and analyzed, and their formation was investigated. The copolymerization rate was studied by the measurement of evolved carbon dioxide. The polymerization of MCOBA and MCONA is cleaner and faster than the polymerization of ABA and ANA. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1703–1707, 1999     

Effect of lithium perchlorate on the spontaneous copolymerization of 4‐vinylpyridine with various electron‐rich vinyl monomers

The spontaneous copolymerization of 4‐vinylpyridine (4‐VP) activated with lithium perchlorate (LiClO₄) with various electron rich monomers (p‐methoxystyrene, MeOSt; p‐methylstyrene, MeSt; styrene, St) was investigated in various solvent systems at 75°C. Increasing the LiClO₄ concentration and the nucleophilicity of the electron rich monomer increased the copolymer yields. Both ¹H‐NMR and elemental analysis confirmed the almost 1:1 copolymer structure for VP/MeOSt system which possessed high molecular weight and narrow polydispersity (PDI). Compared to 4‐VP activated with zinc chloride, LiClO₄ systems showed slightly lower yields and much narrower PDI. We also investigated the spontaneous copolymerization of 4‐VP activated with various protic acids in the reaction with various electron rich comonomers. However, generally protic salt forms showed less solubility in organic solvents and showed low molecular weight polymer products with low yields. The proposed initiation mechanism exhibits the formation of a σ‐bond between the β‐carbons of the two donor‐acceptor monomers, creating the 1,4‐tetramethylene biradical intermediate initiating the copolymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1709–1716, 1999