Reactions of alkoxy radicals with O2. III. i-C4H9O radicals

i-C₄H₉ONO was photolyzed with 366-nm radiation at ?8, 23, 55, 88, and 120°C in a static system in the presence of NO, O₂, and N₂. The quantum yield of i-C₃H₇CHO, Φ{i-C₃H₇CHO}, was measured as a function of reaction of reaction conditions. The primary photochemical act is and it proceeds with a quantum yield ?₁ = 0.24 ± 0.02 independent of temperature. The i-C₄H₉O radicals can react with NO by two routes The i-C₄H₉O radical can decompose via or react with O₂ via Values of k₄/k₂ ? k_4b/k₂ were determined to be (2.8 ± 0.6) × 10¹⁴, (1.7 ± 0.2) × 10¹⁵, and (3.5 ± 1.3) × 10¹⁵ molec/cm³ at 23 55, and 88°C, respectively, at 150-torr total pressure of N₂. Values of k₆/k₂ were determined from ?8 to 120°C. They fit the Arrhenius expression: For k₂ ? 4.4 × 10¹¹ cm³/s, k₆ becomes (3.2 ± 2.0) × 10^?13 exp{?(836 ± 159)/T} cm³/s. The reaction scheme also provides k_4b/k₆ = 3.59 × 10¹⁸ and 5.17 × 10¹⁸ molec/cm³ at 55 and 88°C, respectively, and k_8b/k₈ = 0.66 ± 0.12 independent of temperature, where      

Effect of temperature and molecular weight on the rate of spreading of polystyrene melts on plane soda lime glass surfaces

The effect of temperature T and weight-average molecular weight M?_w on the rate of spreading of polystyrene melts on plane solid surfaces has been examined. The activation energy E of spreading was estimated to be 25.2 ± 3 kcal/mole, which is of the same magnitude as the activation energy for flow of polystyrene melts. The rate of spreading was found to be inversely proportional to M?_w raised to the 1.5 power. This rate of spreading, measured as the time rate of increase in the liquid–solid contact area, dA/dt, could be expressed as where γ_1v is the melt surface tension and θ_d and θ_s are the dynamic and static contact angles, respectively. The numerical value of K has been calculated to be (6.025 ± 3.693) × 10^?14 in the temperature range of 110–260°C and for the values of M?_w from 2000 to 37000.     

Reactions of the iso-butyl radical during 1,1′-azoisobutane pyrolysis

Quantitative analysis of the products formed in 1,1′-azoisobutane pyrolyses in the temperature range of 553°–602°K has shown that the major reactions of the iso-butyl radical are Analysis of initial rate data gave log₁₀k₄/(k_c)^1/2(cm^?3/2.mol ^1/2.sec^?1/2) = 7.54±0.44 ? (136.5 + 4.8) kJ/mol/2.303RT, the Arrhenius parameters obtained being in good agreement with thermodynamic data for reaction (4). Measured values of k_a/(k_c)^1/2 where k_a is the rate constant of the reaction iC₄H₉ + AIB → iC₄H₁₀ +. AIB were consistent with published parameters determined by photolysis of 1,1′-azoisobutane. Combination of photolysis and pyrolysis data gave log₁₀ k_a/(k_c)^1/2(cm^3/2.mol^?1/22.sec^?1/2) = 3.68 ± 0.15 ? (27.2 ± 1.2) kJ/mol/2.303RT. The crosscombination ratio for methyl and iso-butyl radicals has been found to be 0.25, indicating that the geometric mean rule does not hold for methyl and iso-butyl radicals.     

A shock tube study of the OH + OH → H2O + O reaction

The rate coefficient for the reaction has been determined in mixtures of nitric acid (HNO₃) and argon in incident shock wave experiments. Quantitative OH time-histories were obtained by cw narrow-linewidth uv laser absorption of the R₁(5) line of the A² σ⁺ ← X² Π_i (0,0) transition at 32606.56 cm^?1 (vacuum). The experiments were conducted over the temperature range 1050–2380 K and the pressure range 0.18–0.60 atm. The second-order rate coefficient was determined to be with overall uncertainties of +11%, ?16% at high temperatures and +25%, ?22% at low temperatures. By incorporating data from previous investigations in the temperature range 298–578 K, the following expression is determined for the temperature range 298–2380 K © 1994 John Wiley & Sons, Inc.     

Synthesis,characterization and thermal behaviour of four homoleptic titanium silanolates

Four titanium silanolates Ti(OSiR₂R′)₄ (1, R = Ph, R′ = ^tBu; 2, R = R′ = Ph; 3, R = R′ = ⁱPr; 4, R = Me, R′ = ^tBu) were synthesised starting from Ti(OⁱPr)₄ and the corresponding silanol, and their thermally induced decomposition was studied. Colourless single crystals of Ti(OSiPh Bu) CHCl C₇H₈ ( CHCl C₇H₈) were obtained from a mixture of chloroform and toluene (1:1) at ?20 °C. The compound crystallizes in the space group R3 c with Z = 18. The metal atom shows an almost ideal tetrahedral coordination, as is demonstrated by the O? Ti? O angles of 108.4(1)–111.1(1)°. Copyright © 2005 John Wiley & Sons, Ltd.     

A shock tube study of reactions of atomic oxygen with isocyanic acid

Reactions of atomic oxygen with isocyanic acid (HNCO) have been studied in incident and reflected shock wave experiments using HNCO/N₂O/Ar mixtures. Quantitative time-histories of the NH(X³Σ^?) and OH(X²Π_i) radicals were measured behind the shock waves using cw, narrow-linewidth laser absorption at 336 nm and 307 nm, respectively. The second-order rate coefficients of the reactions: and were determined from early-time NH and OH formation rates, with least-squares two-parameter fits of the results given by: and cm³ mol^?1 s^?1. The minimum and maximum rate constant factors (?,F) define the lower and upper uncertainty limits, respectively. An upper limit on the rate coefficient of was determined to be: .     

Another look at the degree‐Kirchhoff index

Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees d_i ≤ D, for fixed D and all i, then for the index R′(G) = ∑_{i < j}d_id_jR_ij we show that We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N² ? 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Zur Thermodynamik der Metallcarbonate 3. Mitteilung [1]. Löslichkeitskonstanten und Freie Bildungsenthalpien von ZnCO3 und Zn5(OH)6(CO3)2 bei 25°

The solubilities of ZnCO₃ and Zn₅(OH)₆(CO₃)₂ have been investigated at 25°C in solutions of the constant ionic strength 0,2 M consisting primarily of sodium perchlorate. From experimental data the following values for equilibrium constants and GIBBS free energies of formation are deduced: A predominance area diagram for the ternary system Zn²⁺–H₂O–CO_2(g) including ZnO, ZnCO₃, Zn₅(OH)₆(CO₃₎₂, and Zn²⁺ is given.     

Temperature and shear dependencies of rheology of poly(acrylonitrile‐co‐itaconic acid) dope in DMF

Poly(acrylonitrile‐co‐itaconic acid) (poly(AN‐co‐IA)) precursor required for carbon fiber production is made into a dope and spun into fibers using a suitable spinning technique. The viscosity of the resin dope is decided by the polymer concentration, polymer molecular weight, temperature, and shear force. The shear rheology of concentrated poly(AN‐co‐IA) polymer solutions in N,N‐dimethylformamide (DMF), in the range of 1 × 10⁵–1 × 10⁶ g mol^?1, has been investigated in the shear rate (γ′) range of 1 × 10¹–5 × 10⁴ min^?1. The zero shear viscosity (η₀) has been evaluated at different temperatures. The temperature dependence of zero shear viscosity conformed to the Arrhenius–Frenkel–Eyring model. The free energy of activation of viscous flow (ΔG_V) values were in the range 5–32 kJ mol^?1 and this value increased with increase in polymer concentration and molecular weight. A master equation for the ΔG_V value of the polymer solution of any and concentration (c) is suggested. The power law fitted well for the shear dependency of viscosity of these polymer solutions. The pseudoplasticity index (n) diminished with increase in polymer concentration and molecular weight. An empirical relation between viscosity (η) and was found to exist at constant shear rate, concentration and temperature. For each , the equation relating n, c, and T was established. Copyright © 2008 John Wiley & Sons, Ltd.     

Configuration-Dependent properties of the poly(dimethylsilmethylene) chain in the third-order interaction approximation

On the basis of rotational isomeric state theory, first-order, second-order, and third-order conformation energies E_σ, E_ω and E_φi respecively, are calculated for poly(dimethylsilmethylene) (CH₂—Si(CH₃)₂)_x using the Lennard–Jones potential function. With the third-order interaction included, the characteristic ratios and temperature coefficients 〈R²〉₀ and 〈μ²〉₀ are obtained: These results are in satisfactory agreement with the experimental data previously reported. © 1993 John Wiley & Sons, Inc.     

Zur Thermodynamik der Metallcarbonate. 4. Mitteilung. Potentiometrische Untersuchungen am System Mn2+?CO2?H2O

The solubility and the complex equilibria in the system Mn²⁺-CO₂-H₂O have been investigated at 25°C in solutions of the constant ionic strength 3 M (Na)ClO₄. From experimental data the following values for equilibrium constants and Gibbs free energies of formation are deduced: A predominance area diagram for the system Mn²⁺-H₂-CO_2(g)-H₂S_(g) including MnCO_3(ppt.), α-MnS and Mn²⁺ is given.     

The reaction of OH with CO

Hydroxyl radicals were prepared from the photolysis of N₂O at 213.9 nm in the presence of excess H₂. The O(¹D) produced in the primary photolytic act reacts with H₂ to produce OH radicals. If CO is also present, then OH can react either with H₂ or CO: The competition between reactions (1) and (2) was measured by measuring the CO₂ yield at various values of the ratio [CO]/[H₂] at 217–298°K. At 298°K the ratio of the rate coefficients k₁/k₂ increased with pressure from a low-pressure limiting value of 14 to a high-pressure limiting value of 50. The low-pressure limiting value agrees well with the low-pressure values found by others. At lower temperatures our high-pressure values of k₁/k₂ were larger than deduced from the accepted low-pressure Arrhenius expression and could be fitted to the expression The mechanism which seems to fit the results best is with k₁° = k_ak_b/k_-a and k₁^∞ = k_a.     

The oxidation of CFClCFCl and CF2CCl2

The oxidation of CFClCFCl and CF₂CCl₂ were studied at room temperature by chlorine- and oxygen-atom initiation. The chlorine-atom initiated oxidation of CFClCFCl yields CCl₂FCF(O) as the exclusive product. Its quantum yield is ～420, which gives k_3a/k_3b=210 where reactions (3a) and (3b) are The O(³P)? CFClCFCl reaction gives CClFO with a quantum yield of 0.80, polymer, and small amounts of an unidentified product which is probably cyclo-(CFCl)₃. Thereaction paths are with k_9a/k₉=0.80. The overall reaction of O(³P) with CFClCFCl proceed one fifth as fast as the O(³P)-C₂F₄ reaction. When O₂ is also present, the same free-radical chain oxidation occurs by O(³P)initiation as by chlorine-atom initiation. The chlorine-atom initiated oxidation of CF₂CCl₂ gives CF₂ClCCl(O) as the major product, with quantum yields ranging from 42 to 85. Smaller amounts of CF₂O and CCl₂O are produced in equal amounts with quantum yields of ～3.5. The reactions responsible for the products are The O(³P)-CF₂CCl₂interaction yields CF₂O and with quantum yields of 1.0 and ～0.85, respectively. In thepresence of O₂ the radical chain products are observed, but the mechanism is different than that for other chloroolefins.     

Liquid-phase oxidation of isobutane—a reanalysis of the data

Data on the liquid-phase oxidation of isobutane at 50 and 100°C have been reexamined, using a modified mechanism to take into account the termination by isobutylperoxy radicals. Algebraic expressions are derived from steady-state methods. Using Arrhenius parameters fitted by transition-state A factors and activation energies derived from observed “best” rate constants, new sets of parameters are derived for the rate constants for propagation by t? BuO₂ + t? BuH → t-BuO₂H + t? Bu^?: where θ = 2.303RT in kcal/mol. This, together with new values for the termination parameters and rates of i-butyl production by k_4B, is shown to give good agreement with the published data. An important reaction: is shown to quench the possible contributions to termination of adventitious radicals such as CH₃O^?₂.     

Kinetics and mechanism of the gas-phase reaction of O(3P) atoms with acetone

The kinetics of the reaction of O(³P) atoms with acetone were investigated using fast flow methods. The reaction was studied over a temperature range of 298 to 478°K. The specific rate constant obtained was (1.9 ± 0.4) × 10¹² exp(—5040 ± 180/1.987 T) cm³/mol·sec. The observation of a sizable primary H/D kinetic isotope effect in comparing rates of CH₃COCH₃ and CD₃COCD₃ led to the conclusion that the major reaction channel involves H atom abstraction, namely, The rather low Arrhenius preexponential factor obtained in this reaction is compared and contrasted with those reported for other reactions of O(³P) with low molecular weight compounds.     

The self-inhibited pyrolysis of isobutane

The pyrolysis of isobutane was investigated in the ranges of 770° to 855°K and 20 to 150 Torr at up to 4% decomposition. The reaction is homogeneous and strongly self-inhibited. A simple Rice-Herzfeld chain terminated by the recombination of methyl radicals is proposed for the initial, uninhibited reaction. Self-inhibition is due to abstraction of hydrogen atoms from product isobutene giving resonance-stabilized 2-methylallyl radicals which participate in termination reactions. The reaction chains are shown to be long. It is suggested that a previously published rate constant for the initiation reaction (1) is incorrect and the value k₁ = 10^16.8 exp (?81700 cal mol^?1/RT)s^?1 is recommended. The values of the rate constants for the reactions (4i) (4t) (8) are estimated to be and From a recalculation of previously published data on the pyrolysis of isobutane at lower temperatures and higher pressures, the value k_11c, = 10^9.6 cm³ mol^?1 s^?1 is obtained for the rate constant of recombination of t-butyl. A calculation which is independent of any assumed rate constants or thermochemistry shows that the predominant chain termination reaction is the recombination of two methyl radicals in the conditions of the present work and the recombination of two t-butyl radicals in those of our previous study at lower temperatures and higher pressures.     

Influence of butadiene-1,3 on ethanal pyrolysis at 495°C

At 495°C and a low extent of reaction, ethanal pyrolysis is slightly inhibited by the addition of small quantities of butadiene-1,3, whereas it is accelerated by more important quantities. The inhibiting effect is interpreted in terms of a free-radical chain mechanism in which the main chain carriers of ethanal pyrolysis (CH₃.free radicals) reversibly add to butadiene-1,3 and yield penten-2-yl (R.) free radicals. These free radicals either react in a metathetical step: or in terminating steps. But butadiene-1,3 also gives rise to new initiation steps: which account for the accelerating effect. Process (i₃) seems to be more important than process (i₂) in the experimental conditions, but its nature could not be identified. The results are consistent with literature data and the following value of k₆: (4.57T in cal/mol).     

The reaction of O(1D) with H2O and the reaction of OH with C3H6

N₂O was photolyzed at 2139 Å to produce O(¹D) atoms in the presence of H₂O and CO. The O(¹D) atoms react with H₂O to produce HO radicals, as measured by CO₂ production from the reaction of OH with CO. The relative importance of the various possible O(¹D )–H₂O reactions is The relative rate constant for O(¹D) removal by H₂O compared to that by N₂O is 2.1, in good agreement with that found earlier in our laboratory. In the presence Of C₃H₆, the OH can be removed by reaction with either CO or C₃H₆: From the CO₂ yield, k₃/k₂ = 75,0 at 100°C and 55.0 at 200°C to within ± 10%. When these values are combined with the value of k₂ = 7.0 × 10^?13exp (–1100/RT) cm³/sec, k₃ = 1.36 × 10^?11 exp (–100/RT) cm³/sec. At 25°C, k₃ extrapolates to 1.1 × 10^?11 cm³/sec.     

Light-scattering study of the molecular weight distribution of polypropylene

A light-scattering study is presented of two isotactic polypropylene samples with broad molecular weight distributions (M _w/M _n = 8.1 and 8.7, respectively) dissolved in α-chloronaphthalene at 147°C. Incident radiation of 5460, 4358, and 3650 A. was used. The reciprocal intramolecular scattering function, P^?1(u) is expressed as a function of the variable [sin(θ/2)/λ′]². This provides a wider range of experimental values of the variable u = 16π²(b²/6) [sin(θ/2)/λ′]² than is accessible by the usual technique of using only one wavelength. The shape of the function P^?1(u) is closer to that predicted theoretically if the weight distribution function f(N) in the equation is given by the log-normal distribution rather than the distribution function of Schulz and Zimm. The method is applicable to polymer samples for which the average molecular weights are too low to be measured by the light-scattering method of Benoit and Loucheux.     

Diluent effects on molecular motions and glass transition in polymers. I. Polystyrene–toluene

The effects of diluent on molecular motions and glass transition in the polystyrene–toluene system was studied by means of dielectric, thermal, and NMR measurements. Three dielectric relaxations were observed between 80 and 400°K. On the basis of NMR measurements on solutions in toluene and in deuterated toluene, relaxation processes were assigned to segmental motions of polystyrene, rotations of toluene, and the local motions of polystyrene and toluene in order of appearance from the high-temperature side. The concentration dependence of the relaxation strength and of the activation energy for the primary relaxation (that at the highest temperature) show a step increment at about 50% by weight. The activation plots for the primary process were expressed by the Vogel–Tamman equation. With this equation, the temperatures at which the mean dielectric relaxation time becomes 100 sec is determined. This agrees well with the glass-transition temperature T_g and hence T_g in concentrated solution is expressed by in terms of the parameters A, B, and T₀ of the Vogel–Tamman equation. The values of A and B are, respectively, about 12 and 0.65 and independent of the concentration. The physical meaning of these parameters is discussed.