Reactions of silylene with unreactive molecules. 2. nitrogen: gas-phase kinetic and theoretical studies

Time-resolved studies of the reaction of silylene, SiH2, with N-2 have been attempted at 296, 417, and 484 K, using laser flash photolysis to generate and monitor SiH2. No conclusive evidence for reaction could be found even with pressures of N-2 of 500 Torr. This enables us to set upper limits of ca. 3 x 10(-15) cm(3) molecule(-1) s(-1) for the second-order rate constants. A lower limit for the activation energy, E-a, of ca. 47 kJ mol(-1) is also derived. Ab initio calculations at the G3 level indicate that the only SiH2N2 species of lower energy than the separated reactants is the H2Si...N-2 donor-acceptor (ylid) species with a relative enthalpy of -26 kJ mol(-1), insufficient for observation of reaction under the experimental conditions. Ten bound species on the SiH2N2 surface were found and their energies calculated as well as those of the potential dissociation products: HSiN + NH((3)Sigma(-)) and HNSi + NH((3)Sigma(-)). Additionally two of the transition states involving cyclic-SiH2N2 (siladiazirine) were explored. It appears that siladiazirine is neither thermodynamically nor kinetically stable. The findings indicate that Si-N-d bonds (where N-d is double-bonded nitrogen) are not particularly strong. An unexpected cyclic intermediate was found in the isomerization of silaisocyanamide to silacyanamide.

Time-resolved gas-phase kinetic and quantum chemical studies of reactions of silylene with chlorine-containing species. 1. HCl

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with HCL The reaction was studied in the gas phase at 10 Torr total pressure in SF6 bath gas, at five temperatures in the range of 296-611 K. The second-order rate constants fitted the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.51 +/- 0.06) + (1.92 +/- 0.47 kJ mol(-1))/RTIn10 Experiments at other pressures showed that these rate constants were unaffected by pressure in the range of 10-100 Torr, but showed small decreases in value of no more than 20% ( +/- 10%) at I Toff, at both the highest and lowest temperatures. The data are consistent with formation of an initial weakly bound donor-acceptor complex, which reacts by two parallel pathways. The first is by chlorine-to-silicon H-shift to make vibrationally excited chlorosilane, SiH3Cl*, which yields HSiCl by H-2 elimination from silicon. In the second pathway, the complex proceeds via H-2 elimination (4-center process) to make chlorosilylene, HSiCl, directly. This interpretation is supported by ab initio quantum calculations carried out at the G3 level which reveal the direct H-2 elimination route for the first time. RRKM modeling predicts the approximate magnitude of the pressure effect but is unable to determine the proportions of each pathway. The experimental data agree with the only previous measurements at room temperature. Comparisons with other reactions of SiH2 are also drawn.

Gas phase kinetic and quantum chemical studies of the reactions of silylene with the methylsilanes. Absolute rate constants, temperature dependences, RRKM modelling and potential energy surfaces

Time resolved studies of silylene, SiH2, generated by the 193 nm laser. ash photolysis of phenylsilane, have been carried out to obtain rate coefficients for its bimolecular reactions with methyl-, dimethyl- and trimethyl-silanes in the gas phase. The reactions were studied over the pressure range 3 - 100 Torr with SF6 as bath gas and at five temperatures in the range 300 - 625 K. Only slight pressure dependences were found for SiH2 + MeSiH3 ( 485 and 602 K) and for SiH2 + Me2SiH2 ( 600 K). The high pressure rate constants gave the following Arrhenius parameters: [GRAPHICS] These are consistent with fast, near to collision-controlled, association processes. RRKM modelling calculations are consistent with the observed pressure dependences ( and also the lack of them for SiH2 + Me3SiH). Ab initio calculations at both second order perturbation theory (MP2) and coupled cluster (CCSD(T)) levels, showed the presence of weakly-bound complexes along the reaction pathways. In the case of SiH2 + MeSiH3 two complexes, with different geometries, were obtained consistent with earlier studies of SiH2 + SiH4. These complexes were stabilised by methyl substitution in the substrate silane, but all had exceedingly low barriers to rearrangement to product disilanes. Although methyl groups in the substrate silane enhance the intrinsic SiH2 insertion rates, it is doubtful whether the intermediate complexes have a significant effect on the kinetics. A further calculation on the reaction MeSiH + SiH4 shows that the methyl substitution in the silylene should have a much more significant kinetic effect ( as observed in other studies).

Direct detection of dimethylstannylene and tetramethyldistannene in solution and the gas phase by laser flash photolysis of 1,1-dimethylstannacyclopent-3-enes

The photochemistry of 1,1-dimethyl- and 1,1,3,4-tetramethylstannacyclopent-3-ene (4a and 4b,respectively) has been studied in the gas phase and in hexane solution by steady-state and 193-nm laser flash photolysis methods. Photolysis of the two compounds results in the formation of 1,3-butadiene (from 4a) and 2,3-dimethyl-1,3-butadiene (from 4b) as the major products, suggesting that cycloreversion to yield dimethylstannylene (SnMe2) is the main photodecomposition pathway of these molecules. Indeed, the stannylene has been trapped as the Sn-H insertion product upon photolysis of 4a in hexane containing trimethylstannane. Flash photolysis of 4a in the gas phase affords a transient absorbing in the 450-520nm range that is assigned to SnMe2 by comparison of its spectrum and reactivity to those previously reported from other precursors. Flash photolysis of 4b in hexane solution affords results consistent with the initial formation of SnMe2 (lambda(max) approximate to 500 nm), which decays over similar to 10 mu s to form tetramethyldistannene (5b; lambda(max) approximate to 470 nm). The distannene decays over the next ca. 50 mu s to form at least two other longer-lived species, which are assigned to higher SnMe2 oligomers. Time-dependent DFT calculations support the spectral assignments for SnMe2 and Sn2Me4, and calculations examining the variation in bond dissociation energy with substituent (H, Me, and Ph) in disilenes, digermenes, and distannenes rule out the possibility that dimerization of SnMe2 proceeds reversibly. Addition of methanol leads to reversible reaction with SnMe2 to form a transient absorbing at lambda(max) approximate to 360 nm, which is assigned to the Lewis acid-base complex between SnMe2 and the alcohol.

The kinetics of the gas-phase decomposition of the 2-methyl-2-butoxyl and 2-methyl-2-pentoxyl radicals

The kinetics of the title reactions have been studied by relative-rate methods as a function of temperature. Relative-rate coefficients for the two decomposition channels of 2-methyl-2-butoxyl have been measured at five different temperatures between 283 and 345 K and the observed temperature dependence is consistent with the results of some previous experimental studies. The kinetics of the two decomposition channels of 2-methyl-2-pentoxyl have also been investigated, as a function of temperature, relative to the estimated rate of isomerisation of this radical. Room-temperature rate coefficient data for the two decomposition channels of both 2-methyl-2-pentoxyl and 2-methyl-2-butxoyl (after combining the relative rate coefficient for this latter with a value for the rate coefficient of the major channel, extrapolated from the data presented by Batt et al., Int. J. Chem. Kinet., 1978, 10, 931) are shown to be consistent with a non-linear kinetic correlation, for alkoxyl radical decomposition rate data, previously presented by this laboratory (Johnson et al., Atmos. Environ., 2004, 38, 1755-1765).

Correlation-type structure activity relationships for the kinetics of gas-phase RO2 self-reactions and reaction with HO2

Structure activity relationships (SARs) are presented for the gas-phase reactions of RO2 with HO2, and the self- and cross-reactions of RO2. For RO2+HO2 the SAR is based upon a correlation between the logarithm of the measured rate coefficient and a calculated ionisation potential for the molecule R-CH=CH2, R being the same group in both the radical and molecular analogue. The correlation observed is strong and only for one RO2 species does the measured rate coefficient deviate by more than a factor of two from the linear least-squares regression line. For the self- and cross-reactions of RO2 radicals, the SAR is based upon a correlation between the logarithm of the measured rate coefficient and the calculated electrostatic potential (ESP) at the equivalent carbon atom in the RH molecule to which oxygen is attached in RO2, again R being the same group in the molecule and the radical. For cases where R is a simple alkyl-group, a strong linear correlation observed. For RO2 radicals which contain lone pair-bearing substituents and for which the calculated ESP<-0.05 self-reaction rate coefficients appear to be insensitive to the value of the ESP. For RO2 of this type with ESP>-0.05 a linear relationship between log k and the ESP is again observed. Using the relationships, 84 out of the 85 rate coefficients used to develop the SARs are predicted to within a factor of three of their measured values. A relationship is also presented that allows the prediction of the Arrhenius parameters for the self-reactions of simple alkyl RO2 radicals. On the basis of the correlations, predictions of room-temperature rate coefficients are made for a number of atmospherically important peroxyl-peroxyl radical reactions. (C) 2003 Elsevier Ltd. All rights reserved.

Formation of organic acids from the gas-phase ozonolysis of terpinolene

Gas-phase ozonolysis of terpinolene was studied in static chamber experiments using gas chromatography coupled to mass spectrometric and flame ionisation detection to separate and detect products. Two isomers of C-7-diacids and three isomers of C-7-aldehydic acids were identified in the condensed phase after derivatisation. Possible mechanisms of formation of these acids were investigated using different OH radical scavengers and relative humidities, and were compared to those reported earlier for the ozonolysis of beta-pinene. In addition, branching ratios for some of the individual reaction steps, e. g. the branching ratio between the two hydroperoxide channels of the C-7-CI, were deduced from the quantitative product yield data. Branching ratios for POZ decomposition and the stabilisation/decomposition of the C-7-CI were also obtained from measurements of the C-7 primary carbonyl product.

Mechanisms for the formation of organic acids in the gas-phase ozonolysis of 3-carene

This paper describes experimental studies aimed at elucidating mechanisms for the formation of low-volatility organic acids in the gas-phase ozonolysis of 3-carene. Experiments were carried out in a static chamber under 'OH-free' conditions. A range of multifunctional acids-which are analogous to those observed from alpha-pinene ozonolysis-were identified in the condensed phase using gas chromatography coupled to mass spectrometry after derivation. Product yields were determined as a function of different OH radical scavengers and relative humidities to give mechanistic information about their routes of formation. Furthermore, an enone and an enal derived from 3-carene were ozonised in order to probe the early mechanistic steps in the reaction and, in particular, which of the two initially formed Criegee intermediates gives rise to which products. Branching ratios for the formation of the two Criegee Intermediates are determined. Similarities and differences in product formation from 3-carene and alpha-pinene ozonolysis are discussed and possible mechanisms-supported by experimental evidence-are developed for all acids investigated.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Gas-phase reactions of NO3 and N2O5 with (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol

The night-time atmospheric chemistry of the biogenic volatile organic compounds (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO3) with these stress-induced plant emissions were measured using the discharge-flow technique. We employed off-axis continuous-wave cavity-enhanced absorption spectroscopy (CEAS) for the detection of NO3, which enabled us to work in excess of the hexenol compounds over NO3. The rate coefficients determined were (2.93 +/- 0.58) x 10(-13) cm(3) molecule(-1) s(-1), (2.67 +/- 0.42) x 10(-13) cm(3) molecule(-1) s(-1), (4.43 +/- 0.91) x 10(-13) cm(3) molecule(-1) s(-1), (1.56 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1), and (1.30 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1) for (Z)-hex-4-en-1-ol, (Z)-hex-3en-1-ol, (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol. The rate coefficient for the reaction of NO3 with (Z)-hex-3-en-1-ol agrees with the single published determination of the rate coefficient using a relative method. The other rate coefficients have not been measured before and are compared to estimated values. Relative-rate studies were also performed, but required modification of the standard technique because N2O5 (used as the source of NO3) itself reacts with the hexenols. We used varying excesses of NO2 to determine simultaneously rate coefficients for reactions of NO3 and N2O5 with (E)-hex-3-en-1-ol of (5.2 +/- 1.8) x 10(-13) cm(3) molecule(-1) s(-1) and (3.1 +/- 2.3) x 10(-18) cm(3) molecule(-1) s(-1). Our new determinations suggest atmospheric lifetimes with respect to NO3-initiated oxidation of roughly 1-4 h for the hexenols, comparable with lifetimes estimated for the atmospheric degradation by OH and shorter lifetimes than for attack by O-3. Recent measurements of [N2O5] suggest that the gas-phase reactions of N2O5 with unsaturated alcohols will not be of importance under usual atmospheric conditions, but they certainly can be in laboratory systems when determining rate coefficients.

Time-resolved gas-phase kinetic, quantum chemical and RRKM studies of reactions of silylene with cyclic ethers

Time-resolved kinetic studies of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reactions with oxirane, oxetane, and tetrahydrofuran (THF). The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at four or five temperatures in the range 294-605 K. All three reactions showed pressure dependences characteristic of third-body-assisted association reactions with, surprisingly, SiH2 + oxirane showing the least and SiH2 + THF showing the most pressure dependence. The second-order rate constants obtained by extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equations where the error limits are single standard deviations: log(k(oxirane)(infinity)/cm(3) molecule(-1) s(-1)) = (-11.03 +/- 0.07) + (5.70 +/- 0.51) kJ mol(-1)/RT In 10 log(k(oxetane)(infinity)/cm(3) molecule(-1) s(-1)) = (-11.17 +/- 0.11) + (9.04 +/- 0.78) kJ mol(-1)/RT In 10 log(k(THF)(infinity)/cm(3) molecule(-1) s(-1)) = (-10.59 +/- 0.10) + (5.76 +/- 0.65) kJ mol(-1)/RT In 10 Binding-energy values of 77, 97, and 92 kJ mol(-1) have been obtained for the donor-acceptor complexes of SiH2 with oxirane, oxetane, and THF, respectively, by means of quantum chemical (ab initio) calculations carried Out at the G3 level. The use of these values to model the pressure dependences of these reactions, via RRKM theory, provided a good fit only in the case of SiH2 + THF. The lack of fit in the other two cases is attributed to further reaction pathways for the association complexes of SiH2 with oxirane and oxetane. The finding of ethene as a product of the SiH2 + oxirane reaction supports a pathway leading to H2Si=O + C2H4 predicted by the theoretical calculations of Apeloig and Sklenak.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.