Reactions of cyclopropanone acetals with alkyl azides: carbonyl addition versus ring-opening pathways

The Lewis acid-mediated reactions of substituted cyclopropanone acetals with alkyl azides were found to strongly depend on the structure of the ketone component. When cyclopropanone acetal was treated with alkyl azides, N-substituted 2-azetidinones and ethyl carbamate products were obtained, arising from azide addition to the carbonyl, followed by ring expansion or rearrangement, respectively. When 2,2-dimethylcyclopropanone acetals were reacted with azides in the presence of BF3.OEt2, the products obtained were alpha-amino-alpha'-diazomethyl ketones, which arose from C2-C3 bond cleavage of the corresponding cyclopropanone, giving oxyallyl cations that were captured by azides. Aryl-substituted cyclopropanone acetals, when subjected to these conditions, afforded [1,2,3]oxaborazoles exclusively, which were also the result of C2-C3 bond rupture, azide capture, and then loss of nitrogen. In the reactions of n-hexyl-substituted cyclopropanone acetals with alkyl azides, a mixture of 2-azetidinones and regioisomeric [1,2,3]oxaborazoles was obtained. The reasons for the different behavior of the various systems are discussed.     

Measurements and modeling of DO2 formation in the reactions of C2D5 and C3D7 radicals with O2

Time-resolved production of HO2 and DO2 from the reactions of nondeuterated and deuterated ethyl and propyl radicals with O2 are measured as a function of temperature and pressure in the "transition region" between 623 and 748 K using the technique of laser photolysis/long path frequency modulation spectroscopy. Experimental measurements, using both pulsed-photolytic Cl-atom-initiated oxidation of ethane and propane and direct photolysis of ethyl, n-propyl, and isopropyl iodides, are compared to kinetic models based on the results of time-dependent master equation calculations with ab initio characterization of stationary points. The formation of DO2 and HO2 from the subsequent reaction of the alkyl radicals with O2 is followed by infrared frequency modulation spectroscopy. The concentration of I atoms is simultaneously monitored by direct absorption of a second laser probe on the spin-orbit transition. The kinetic models accurately describe the time scale and amplitude of the DO2 and HO2 formation resulting from C2D5 + O2, n-C3D7 + O2, i-C3D7 + O2, and i-C3H7 + O2. Overall, a very good level of agreement is found between theory and experiments over a wide range of temperatures, pressures, and O2 concentrations. Good agreement is also found between previous literature studies and the theory presented in this work except in the case of the high-temperature rate coefficients for the reaction of i-C3H7 + O2 to form propene. A reinvestigation of the high-temperature kinetics of the i-C3H7 + O2 reaction appears warranted. The results from the present work suggest that the theory for formation of HO2 from the reactions of ethyl and both isomeric forms of propyl radicals with O2 are very well established at this time. It is hoped that these reactions can now form the groundwork for the study and interpretation of larger and more complex R + O2 systems.     

Pressure and temperature dependence of the reaction of vinyl radical with ethylene

This work reports measurements of absolute rate coefficients and Rice-Ramsperger-Kassel-Marcus (RRKM) master equation simulations of the C2H3+C2H4 reaction. Direct kinetic studies were performed over a temperature range of 300-700 K and pressures of 20 and 133 mbar. Vinyl radicals (H2C=CH) were generated by laser photolysis of vinyl iodide (C2H3I) at 266 nm, and time-resolved absorption spectroscopy was used to probe vinyl radicals through absorption at 423.2 nm. Measurements at 20 mbar are in good agreement with previous determinations at higher temperature. A weighted three-parameter Arrhenius fit to the experimental rate constant at 133 mbar, with the temperature exponent fixed, gives k=(7+/-1)x10(-14) cm3 molecule(-1) s(-1) (T/298 K)2 exp[-(1430+/-70) K/T]. RRKM master equation simulations, based on G3 calculations of stationary points on the C4H7 potential energy surface, were carried out to predict rate coefficients and product branching fractions. The predicted branching to 1-methylallyl product is relatively small under the conditions of the present experiments but increases as the pressure is lowered. Analysis of end products of 248 nm photolysis of vinyl iodide/ethylene mixtures at total pressures between 27 and 933 mbar provides no direct evidence for participation of 1-methylallyl.     

High-temperature shock tube measurements of methyl radical decomposition

We have studied the two-channel thermal decomposition of methyl radicals in argon, involving the reactions CH3 + Ar --> CH + H2 + Ar (1a) and CH3 + Ar --> CH2 + H + Ar (1b), in shock tube experiments over the 2253-3527 K temperature range, at pressures between 0.7 and 4.2 atm. CH was monitored by continuous-wave, narrow-line-width laser absorption at 431.1311 nm. The collision-broadening coefficient for CH in argon, 2gamma(CH-Ar), was measured via repeated single-frequency experiments in the ethane pyrolysis system behind reflected shock waves. The measured 2gamma(CH-Ar) value and updated spectroscopic and molecular parameters were used to calculate the CH absorption coefficient at 431.1311 nm (23194.80 cm(-1)), which was then used to convert raw traces of fractional transmission to quantitative CH concentration time histories in the methyl decomposition experiments. The rate coefficient of reaction 1a was measured by monitoring CH radicals generated upon shock-heating highly dilute mixtures of ethane, C2H6, or methyl iodide, CH3I, in an argon bath. A detailed chemical kinetic mechanism was used to model the measured CH time histories. Within experimental uncertainty and scatter, no pressure dependence could be discerned in the rate coefficient of reaction 1a in the 0.7-4.2 atm pressure range. A least-squares, two-parameter fit of the current measurements, applicable between 2706 and 3527 K, gives k(1a) (cm(3) mol(-1) s(-1)) = 3.09 x 1015 exp[-40700/T (K)]. The rate coefficient of reaction 1b was determined by shock-heating dilute mixtures of C2H6 or CH3I and excess O2 in argon. During the course of reaction, OH radicals were monitored using the well-characterized R(1)(5) line of the OH A-X (0,0) band at 306.6871 nm (32606.52 cm(-1)). H atoms generated via reaction 1b rapidly react with O2, which is present in excess, forming OH. The OH traces are primarily sensitive to reaction 1b, reaction 9 (H + O2 --> OH + O) and reaction 10 (CH3 + O2 --> products), where the rate coefficients of reactions 9 and 10 are relatively well-established. No pressure dependence could be discerned for reaction 1b between 1.1 and 3.9 atm. A two-parameter, least-squares fit of the current data, valid over the 2253-2975 K temperature range, yields the rate expression k(1b) (cm(3) mol(-1) s(-1)) = 2.24 x 10(15) exp[-41600/T (K)]. Theoretical calculations carried out using a master equation/RRKM analysis fit the measurements reasonably well.     

Vibrational spectroscopy of 1,1-difluorocyclopropane-d0, -d2, and -d4: the equilibrium structure of difluorocyclopropane

IR and Raman spectra are reported for 1,1-difluorocyclopropane-d0, -d2, and -d4, and complete assignments of vibrational fundamentals are given for these species. These assignments are consistent with predictions of frequencies, intensities, and Raman depolarization ratios computed with the B3LYP/cc-pVTZ quantum chemical (QC) model. Ground state rotational constants for five 13C and deuterium isotopomers, obtained from published microwave spectra, were "corrected" into equilibrium rotational constants. The needed vibration-rotation interaction constants were computed with QC models after scaling the force constants. A semi-experimental equilibrium structure, fitted to the equilibrium moments of inertia, is rC1C = 1.470(1) A, rCC = 1.546(1) A, rCF = 1.343(1) A, rCH = 1.078(1) A, alphaFCF = 109.5(1), alphaFCC = 119.4(1) degrees, alphaHCH = 116.7(1) degrees, alphaC1CH = 117.4(1) degrees, and alphaCCH = 117.1(1) degrees. This structure agrees within the indicated uncertainties with the ab initio structure obtained from an extrapolated set of CCSD(T)/aug-cc-pVnZ calculations except for rCC = 1.548 A. The F2C-CH2 bonds are significantly shortened and strengthened; the H2C-CH2 bond is significantly lengthened and weakened.     

Effect of the linking unit on the twist-bend nematic phase in liquid crystal dimers: a comparative study of two homologous series of methylene- and ether-linked dimers

ABSTRACT

Two series of bimesogens with phenyl benzoate mesogenic units were prepared: one series having a heptamethylene spacer and the other a pentamethylene spacer with two ether-linking groups. These materials were prepared to provide experimental backing to the widely held hypothesis that methylene-linked bimesogens are more likely to exhibit the twist-bend nematic mesophase than their ether-linked counterparts. Several of the methylene-linked materials exhibited nematic and N_TB mesophases, whereas the analogous ether-linked materials gave only nematic phases albeit with significantly higher clearing points. Virtual N–N_TB transition temperatures for both methylene- and ether-linked bimesogens were extrapolated by constructing binary phase diagrams with the well-studied twist-bend material CB9CB. Contrary to our expectations these virtual transition temperatures were in most cases higher for the ether-linked bimesogens than in the analogous methylene compounds, this runs counter to reported theories and hypotheses that the incorporation of ether-linking groups should serve to destabilise the N_TB phase.     

Challenging assumptions of notational transparency: the case of vectors in engineering mathematics

ABSTRACT

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing the components of a vector are discussed in historical and current context. Popular mathematical texts use the two notations as if they are transparent and interchangeable. In this research project, engineering students’ proficiency at vector analysis was assessed and the data were analyzed using the Rasch measurement method. Results indicate that the students found items expressed in unit vector notation more difficult than those expressed in parenthesis notation. The expert experience of notation as transparent and unproblematically symbolic of underlying processes independent of notation is shown to contrast with the student experience where the less familiar notation is experienced as harder to work with.     

Parents’ Attitudes Toward Mathematics and the Influence on Their Students’ Attitudes toward Mathematics: A Quantitative Study

The purpose of this study was to investigate parents’ attitudes toward mathematics, their students' attitude toward mathematics, and the influence of the parents’ attitude on the students' attitude toward mathematics. Data analyses revealed statistically significant positive correlations between parents’ and students’ attitudes toward mathematics. Additionally, parents’ mathematics attitude significantly predicted students’ attitudes toward mathematics (n=146). By understanding the influence of parents’ attitudes on students’ attitudes toward mathematics, school efforts can be geared toward fostering favorable attitudes toward mathematics among parents.     

Development and kilogram-scale synthesis of mGlu5 negative allosteric modulator VU0424238 (auglurant)

This communication details the kilogram-scale synthesis of N-(5-fluoropyridin-2-yl)-6-methyl-4-(pyrimidin-5-yloxy)picolinamide (VU0424238, auglurant), a novel mGlu₅ negative allosteric modulator (NAM) developed as an alternative treatment for depression. The process highlights a challenging pyridine N-oxidation sequence, an S_NAr reaction, and the elimination of all chromatography steps (required in the medicinal chemistry route) with replacement by highly efficient recrystallizations (save one silica plug). The improved process was utilized for the preparation of a 1.2 kg toxicology batch, as well as a 2.82 kg GMP batch to support the Phase I trial, in very high purity (99.8%).