The gas-phase pyrolysis of alkyl nitrites. III. Isopropyl nitrite

The rate of decomposition of isopropyl nitrite (IPN) has been studied in a static system over the temperature range of 130–160°C. For low concentrations of IPN (1–5 × 10^?5M), but with a high total pressure of CF₄ (～0.9 atm) and small extents of reaction (～1%), the first-order rates of acetaldehyde (AcH) formation are a direct measure of reaction (1), since k₃ » k₂(NO): \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {\rm IPN}\begin{array}{rcl} 1 \\ {\rightleftarrows} \\ 2 \\ \end{array}i - \Pr \mathop {\rm O}\limits^. + {\rm NO},i - \Pr \mathop {\rm O}\limits^. \stackrel{3}{\longrightarrow} {\rm AcH} + {\rm Me}. $\end{document} Addition of large amounts of NO (～0.9 atm) in place of CF₄ almost completely suppressed AcH formation. Addition of large amounts of isobutane – t-BuH – (～0.9 atm) in place of CF₄ at 160°C resulted in decreasing the AcH by 25%. Thus 25% of \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^{\rm .} $\end{document} were trapped by the t-BuH (4): \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + t - {\rm BuH} \stackrel{4}{\longrightarrow} i - \Pr {\rm OH} + (t - {\rm Bu}). $\end{document} The result of adding either NO or t-BuH shows that reaction (1) is the only route for the production of AcH. The rate constant for reaction (1) is given by k₁ = 10^{16.2±0.4–41.0±0.8}/θ sec^?1. Since (E₁ + RT) and ΔH°₁ are identical, within experimental error, both may be equated with D(i-PrO-NO) = 41.6 ± 0.8 kcal/mol and E₂ = 0 ± 0.8 kcal/mol. The thermochemistry leads to the result that \documentclass{article}\pagestyle{empty}\begin{document}$ \Delta H_f^\circ (i - {\rm Pr}\mathop {\rm O}\limits^{\rm .} ) = - 11.9 \pm 0.8{\rm kcal}/{\rm mol}. $\end{document} From ΔS°₁ and A₁, k₂ is calculated to be 10^10.5±0.4M^?1·sec^?1. From an independent observation that k₆/k₂ = 0.19 ± 0.03 independent of temperature we find E₆ = 0 ± 1 kcal/mol and k₆ = 10^9.8+0.4M^?;1·sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + {\rm NO} \stackrel{6}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} In addition to AcH, acetone (M₂K) and isopropyl alcohol (IPA) are produced in approximately equal amounts. The rate of M₂K formation is markedly affected by the ratio S/V of different reaction vessels. It is concluded that the M₂K arises as the result of a heterogeneous elimination of HNO from IPN. In a spherical reaction vessel the first-order rate of M₂K formation is given by k₅ = 10^9.4–27.0/θ sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm IPN} \stackrel{5}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} IPA is thought to arise via the hydrolysis of IPN, the water being formed from HNO. This elimination process explains previous erroneous results for IPN.     

Collectively compact sets of nonlinear operators in locally convex spaces

Collectively compact sets of (linear) operators in Banach spaces have been studied and used by P. M. Anselone [2] and others in connection with integral operators. In this paper we show that a relevant part of the theory extends to bounded (in general nonlinear) operators in locally convex spaces.     

Interference effects between modes in open resonators

Interference effects between modes in open-resonators may seriously modify the resonance characteristics. Constructive and destructive interference may take place. For multimode conditions many path lengths exhibit resonance modification.Work supported by the U. K. Science Research Council.     

The gas phase pyrolysis of alkyl nitrites. I. t-butyl nitrite

The rate of decomposition of t-butyl nitrite (TBN) has been studied in a static system over the temperature range of 120–160°C. For low concentrations of TBN (10^?5- 10^?4M), but with a high total pressure of CF₄ (～0.9 atm) and small extents of reaction (～1%), the first-order homogeneous rates of acetone (M₂K) formation are a direct measure of reaction (1), since k₃» k₂ (NO): TBN . Addition of large amounts of NO in place of CF₄ almost completely suppresses M₂K formation. This shows that reaction (1) is the only route for this product. The rate of reaction (1) is given by k₁ = 10^16.3–40.3/θ s^?1. Since (E₁ + RT) and ΔH are identical, both may be equated with D(RO-NO) = 40.9 ± 0.8 kcal/mole and E₂ = O ± 1 kcal/mole. From ΔS and A₁, k₂ is calculated to be 10^10.4M^?1 ·s^?1, implying that combination of t? BuO and NO occurs once every ten collisions. From an independent observation that k₂/k₂′ = 1.7 ± 0.25 independent of temperature, it is concluded that k₂′ = 10^10.2M^?1 · s^?1 and k₁′ = 10^15.9?40.2/θ s^?1; . This study shows that MeNO arises solely as a result of the combination of Me and NO. Since NO is such an excellent radical trap for t-Bu\documentclass{article}\pagestyle{empty}\begin{document}${\rm Me\dot O}$\end{document}, reaction (2) may be used in a competitive study of the decomposition of t? Bu\documentclass{article}\pagestyle{empty}\begin{document}${\rm Me\dot O}$\end{document} in order to obtain the first absolute value for k₃. Preliminary results show that k₃ (∞) = 10^15.7–17.0/θ s^?1. The pressure dependence of k₃ is demonstrated over the range of 10^?2?1 atm (160°C). The thermochemistry for reaction (3) implies that the Hg 6(³P₁) sensitised decomposition of t-BuOH occurs via reaction (m): In addition to the products accounted for by the TBN radical split, isobutene is formed as a result of the 6-centre elimination of HONO: TBN \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \to \limits^7 $\end{document} isobutene + HONO. The rate of formation of isobutene is given by k₇ = 10^12.9–33.6/θ s^?1. t-BuOH, formed at a rate comparable to that of isobutene–at least in the initial stages–is thought to arise as a result of secondary reactions between TBN and HONO. The apparent discrepancy between this and previous studies is reconciled in terms of the above parallel reactions (1) and (7), such that k + 2k₇ = 10^14.7–36.2/θ s^?1.     

The gas-phase decomposition of alkoxy radicals

It is shown that it is possible to obtain good data for the rate constant for the decomposition of alkoxy radicals [RO] by using nitric oxide as a radical trap. Two experimental systems have been used. The first system involves the use of dialkyl peroxides [(RO)₂] as thermal sources of alkoxy radicals. The peroxide concentration was ～10^?4M, nitric oxide ～2 × 10^?4M, and the extent of reaction was ～10%. The total pressure was altered using carbon tetrafluoride as an inert gas. The mechanism is Hence R₂/R₃ = k₂[N O]/k₃. Our previous studies show that k₂ lies in the range 10^10.3±0.2M^?1·sec^?1. The second system employs alkyl nitrites [RONO] as a thermal source of alkoxy radicals. The experimental conditions are very similar, except that we chose to use an atmosphere of nitric oxide for initial experiments. If anything nitric oxide appears to be superior to carbon tetrafluoride as an energy transfer agent. The mechanism is Hence R₃ = k₁'k₃[RO NO]/(k₃ + k₂ + k₆ [N O]). Results are given for R = t-Am, s-Bu, t-Bu, i-Pr, Et, and Me. In addition the first unequivocal evidence is given for the pressure dependence of k₃ when R = t-Bu. The implications for atmospheric chemistry and combustion are also discussed.     

Convergence of a lattice model of the boltzmann equation

It is shown that the solutions of a (spatially) discrete model of the Boltzmann equation converge in a weak sense as the lattice spacing approaches zero. The method follows a compactness argument of Arkeryd.     

Some Tentative Findings on Corporate Financial Simulation Models<Superscript>†</Superscript>

A framework for classifying corporate models is presented. Criteria for selecting the approach most appropriate for strategic planning are suggested. Experience of developing corporate financial simulation models in three separate companies is analysed. This is related to findings from an analysis of thirty-four models reported in the literature and of two surveys in the United States.     

Real-time analysis of enzymatic surface-initiated polymerization using surface plasmon resonance (SPR)

The kinetics of enzymatic surface-initiated polymerization of PHB on gold surface has been examined by SPR and the resultant polymer layers characterized by AFM and FT-IR spectrometry. The immobilized enzyme catalyzed surface-initiated polymerization of 3HB-CoA, resulting in the formation of a polymer brush on the surface. The rate of polymer growth from the surface was monitored by SPR in real-time. Polymer growth as measured by the increase in the resonance angle showed no apparent lag phase during the polymerization reaction. SPR analysis also revealed that the thickness of the polymer film could be controlled by varying the initial enzyme density on the surface. The average thicknesses of the PHB film after polymerization reaction were 95, 45 and 15 nm for the surfaces that were treated with 0.5, 0.3 and 0.1*10(-6) M of enzyme, respectively. The binding of PHA synthase at different concentration to the mixed SAMs and subsequent polymerization.     

Competition between lipases and monoglycerides at interfaces

Tensiometry (the pendant drop technique), interfacial shear rheology, and ellipsometry have been used to study the effect of polar lipids that are generated during fat digestion on the behavior of lipases at the oil-water interface. Both Sn-1,3 regiospecific and nonregiospecific lipases have been used, and a noncatalytically active protein, beta-lacloglobulin, has been used as reference in the interfacial shear rheology experiments. The results from the pendant drop measurements and the interfacial rheology studies were in agreement with each other and demonstrated that the Sn-2 monoglyceride, which is one of the lipolysis products generated when a Sn-1,3 regiospecific lipase catalyzes triglyceride hydrolysis, is very interfacially active and efficiently expels the enzyme from the interface. Ellipsometry conducted at the liquid-liquid interface showed that the lipase forms a sublayer in the aqueous phase, just beneath the monoglyceride-covered interface. Sn-1/3 monoglycerides do not behave this way because they are rapidly degraded to fatty acid and glycerol and the fatty acid (or the fatty acid salt) does not have enough interfacial activity to expel the lipase from the interface. Since the lipases present in the gastrointestinal tract are highly Sn-1,3 regiospecific, we believe that the results obtained can be transferred to the in vivo situation. The formation of stable and amphiphilic Sn-2 monoglycerides can be seen as a self-regulatory process for fat digestion.