Kinetics of chemically activated ethane

Chemically activated ethane, with an excitation energy of 114.9 ± 2 kcal/mole, was formed by reaction with methane of excited singlet methylene radicals produced by the 4358 Å photolysis of diazomethane. A decomposition rate constant of (4.6 ± 1.2) × 10⁹ sec^?1 was measured for the chemically activated ethane. This result agrees, via RRKM theory, with most other chemically activated ethane data, and the result predicts, via RRKM and absolute rate theory for E₀ = 85.8 kcal/mole, E* = 114.9 kcal/mole, and k_E = 4.6 × 101 sec^?1, a thermal A-factor at 600°K of 10^16.6±0.2 sec^?1, in approximate agreement with the more recent experimental values. Combining 2 kcal/mole uncertainties in E₀ and E* with the uncertainty in our rate constant yields an A-factor range of 10^16.6±0.7 sec^?1. It is emphasized that this large uncertainty in the A-factor results from an improbable combination of uncertainty limits for the various parameters. These decomposition results predict, via absolute rate theory (with E₀(recombination) = 0) and statistical thermodynamic equilibrium constants, methyl radical recombination rates at 25°C of between 4.4 × 10⁸ to 3.1 × 10⁹ l.-mole^?1-sec^?1, which are 60 to 8 times lower, respectively, than the apparently quite reliable experimental value. A value of E₀(recombination) greater than zero offers no improvement, and a value less than zero would be quite unusual. Activated complexes consistent with the experimental recombination rate and E₀(recombination) = 0 greatly overestimate the experimental chemical activation and high pressure thermal decomposition rate data. Absolute rate theory as it is applied here in a straightforward way has failed in this case, or a significant amount of internally consistent data are in serious error. Some corrections to our previous calculations for higher alkanes are discussed in Appendix II.     

Reactivity ratios of styrene and methyl methacrylate at 90°C

From the conversion–composition data of Gruber and Elias, the reactivity ratios of styrene (M₁) and methyl methacrylate (M₂) were calculated to be r₁ = 0.55 ± 0.02 and r₂ = 0.58 ± 0.06 at 90°C. The least-squares method was then used on these and literature values at other temperatures to obtain the Arrhenius expressions: In r₁ = 0.04736 – (235.45/T), and ln r₂ = 0.1183 – (285.36/T). Using literature values for the homopolymerization steps, A₁₁ = 2.2 × 10⁷l./mole-sec., E₁₁ = 7.8 kcal./mole, and A₂₂ = 0.51 × 10⁷ l./mole-sec.^?1, E₂₂ = 6.3 kcal./mole, activation energies and frequency factors were then calculated for the cross-polymerization steps: A₁₂ = 2.1 × 10⁷ l./mole-sec., E₁₂ = 7.3 kcal./mole, and A₂₁ = 0.45 × 10⁷ l./mole-sec., E₂₁ = 5.7 kcal./mole.     

Lateral thermal expansion of cellulose Iβ and IIII polymorphs

Measurements of the thermal expansion coefficients (TECs) of cellulose crystals in the lateral direction are reported. Oriented films of highly crystalline cellulose I_β and III_I were prepared and then investigated with X‐ray diffraction at specific temperatures from room temperature to 250 °C during the heating process. Cellulose I_β underwent a transition into the high‐temperature phase with the temperature increasing above 220–230 °C; cellulose III_I was transformed into cellulose I_β when the sample was heated above 200 °C. Therefore, the TECs of I_β and III_I below 200 °C were measured. For cellulose I_β, the TEC of the a axis increased linearly from room temperature at α_a = 4.3 × 10^?5 °C^?1 to 200 °C at α_a = 17.0 × 10^?5 °C^?1, but the TEC of the b axis was constant at α_b = 0.5 × 10^?5 °C^?1. Like cellulose I_β, cellulose III_I also showed an anisotropic thermal expansion in the lateral direction. The TECs of the a and b axes were α_a = 7.6 × 10^?5 °C^?1 and α_b = 0.8 × 10^?5 °C^?1. The anisotropic thermal expansion behaviors in the lateral direction for I_β and III_I were closely related to the intermolecular hydrogen‐bonding systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1095–1102, 2002     

Polymerization of Cyclosiloxanes. I. Kinetic Studies on Living Polymer—Octamethylcyclotetrasiloxane Systems

The kinetics of the anionic polymerization of octamethylcyclotetrasiloxane (D₄) initiated by α-methylstyrene living polymer in tetrahydrofuran was studied. The following kinetic scheme was postulated: Initiation: Propagation: where S^- and M represent the initiator and D₄, respectively. At a living end concentration of 0.0377 mole/l. and a monomer concentration of 1.5 mole/l. in tetrahydrofuran at 25°C. the following kinetic data were obtained: k₁ = 2.3 × 10^?4 l./mole-sec., k₂ < 2.3 × 10^?5 sec.^?1, k₃ = 2.75 × 10^?2l./mole-sec. k₄ ≈ 1.17 × 10^?2 sec.^?1, K₁ > 10 l./mole and K₂ ≈ 2.35 l./mole. The rate constants k₁ and k₃ were found to be dependent on the concentration of anions. This is attributed to the dissociation of ion pairs to free ions at lower concentration. Under the experimental conditions studied the majority of the anions were present in the form of ion pairs. The reactivity of the free ions is about 100 times greater than that of ion pairs. There is no temperature effect on K₂, indicating zero ΔH and positive ΔS in the propagation reaction.     

X‐ray diffraction study of the thermal expansion behavior of cellulose triacetate I

Highly crystalline samples of cellulose triacetate I (CTA I) were prepared from highly crystalline algal cellulose by heterogeneous acetylation. X‐ray diffraction of the prepared samples was carried out in a helium atmosphere at temperatures ranging from 20 to 250 °C. Changes in seven d‐spacings were observed with increasing temperature due to thermal expansion of the CTA I crystals. Unit cell parameters at specific temperatures were determined from these d‐spacings by the least squares method, and then thermal expansion coefficients (TECs) were calculated. The linear TECs of the a, b, and c axes were α_a = 19.3 × 10^?5 °C^?1, α_b = 0.3 × 10^?5 °C^?1 (T < 130 °C), α_b = ?2.5 × 10^?5 °C^?1 (T > 130 °C), and α_c = ?1.9 × 10^?5 °C^?1, respectively. The volume TEC was β = 15.6 × 10^?5 °C^?1, which is about 1.4 and 2.2 times greater than that of cellulose I_β and cellulose III_I, respectively. This large thermal expansion could occur because no hydrogen bonding exists in CTA I. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 517–523, 2009     

The very-low-pressure pyrolysis (VLPP) of n-propyl nitrate,tert-butyl nitrite,and methyl nitrite. Rate constants for some alkoxy radical reactions

The pyrolysis of n-propyl nitrate and tert-butyl nitrite at very low pressures (VLPP technique) is reported. For the reaction the high-pressure rate expression at 300°K, log k₁ (sec^?1) = 16.5 ? 40.0 kcal/mole/2.3 RT, is derived. The reaction was studied and the high-pressure parameters at 300°K are log k₂(sec^?1) = 15.8 ? 39.3 kcal/mole/2.3 RT. From ΔS_1,?1⁰ and ΔS_2,?2⁰ and the assumption E_?1 and E_?2 ? 0, we derive log k_?1(M^?1·sec^?1) (300°K) = 9.5 and log k_?2 (M^?1·sec^?1) (300°K) = 9.8. In contrast, the pyrolysis of methyl nitrite and methyl d₃ nitrite afford NO and HNO and DNO, respectively, in what appears to be a heterogeneous process. The values of k_?1 and k_?2 in conjunction with independent measurements imply a value at 300°K for of 3.5 × 10⁵ M^?1·sec^?1, which is two orders of magnitude greater than currently accepted values. In the high-pressure static pyrolysis of dimethyl peroxide in the presence of NO₂, the yield of methyl nitrate indicates that the combination of methoxy radicals with NO₂ is in the high-pressure limit at atmospheric pressure.     

Arrhenius parameters for the reactions CH3. + C4H10 → CH4 + C4H9. and C2H5. + C4H10 → C2H6 + C4H9.

Study of n-butane pyrolysis at high temperature in a flow system allows measurement of the sum of the rate constants of the initiation reactions and of the Arrhenius parameters of the reactions Established data for k₁/k₂ allow estimation of k₁ for 951°K and this, with recent thermochemical data, yields the result log k_?1 (l.mole s^?1) = 8.5, in remarkable agreement with a recent measurement [20] but over si×ty times smaller than conventional assumption. The product k₃k₄ (l.²mole^?2s^?2) is found to be associated with the Arrhenius parameters log (A₃A₄) = 21.90 ± 0.6 and (E₃ + E₄) = 38.3 ± 2.7 kcal/mole. These values are much higher than would be e×pected on the basis of low temperature estimates. Independent evaluation gives log A₄ = 10.5 ± 0.4 (l.mole^?1s^?1) and E₄ = 20.1 ± 1.7 kcal/mole, hence log A₃ = 11.4 ± 0.8 (l.mole^?1s^?1) and E₃ = 18.2 ± 3.2 kcal/mole. These values are shown to be entirely consistent with a wide range of results from pyrolytic studies, and it is argued that they further confirm the view that Arrhenius plots for alkyl radical–alkane metathetical reactions are strongly curved, in part due to tunneling and, appreciably, to other as yet unidentified effects. Since there is published evidence that metathetical reactions involving hydrogen atoms show even greater curvature, it is suggested that this may be a characteristic of many metathetical reactions.     

The rate of the gas phase iodination of cyclobutane. The heat of formation of the cyclobutyl radical

The gas phase iodination of cyclobutane was studied spectrophotometrically in a static system over the temperature range 589° to 662°K. The early stage of the reaction was found to correspond to the general mechanism where the Arrenius parameters describing k₁ are given by log k₁/M^?1 sec^?1 = 11.66 ± 0.11 – 26.83 ± .31/θ, θ = 2.303RT in kcal/mole. The measured value of E₁, together with the fact that E_?1 = 1 ± 1 kcal/mole, provides ΔH(c-C₄H_7.) = 51.14 ± 1.0 kcal/mole, and the corresponding bond dissociation energy, D(c-C₄H₇? H) = 96.8 ± 1.0 kcal/mole. A bond dissociation energy of 1.8 kcal/mole higher than that for a normal secondary C? H bond corresponds to one half of the extra strain energy in cyclobutene compared to cyclobutane and is in excellent agreement with the recent value of Whittle, determined in a completely different system. Estimates of ΔH and entropy of cyclobutyl iodide are in very good agreement with the equilibrium constant K₁₂ deduced from the kinetic data. Also in good agreement with estimates of Arrhenius parameters is the rate of HI elimination from cyclobutyl iodide.     

Kinetics of the reactions Br2 + HCN,BrCN + I−, S(CN)2 + I− in aqueous acid solution

Spectrophotometric methods have been used to obtain rate laws and rate parameters for the following reactions: with k_a, k_b, E_a, E_b having the values 85±5 l./mole · s, 5.7±0.2 s^?1 (both at 298.2°K), and 56±4 and 66±2 kJ/mole, respectively. with k_c=0.106±0.004 l./mole ·s at 298.2°K and E_c=67±2 kJ/mole. with k_d=(3.06 ±; 0.15) × 10^?3 l./mole ·s at 298.2°K and E_d=66±2 kJ/mole. Mechanisms for these reactions are discussed and compared with previous work.     

Alternating copolymerization of the styrene–methyl methacrylate system complexed with diethylaluminum chloride

The rate and molecular weight profiles were obtained for the spontaneous alternating copolymerizations conducted with diethylaluminum chloride. The rate formally fitted an expression, R = k_p[MMA][Sty], and the rate constant was established by two distinct methods: (1) from the yield versus time data and (2) from initial rate over a range of initial concentrations; it was determined as 5.4 × 10^?6 l./mole-sec with E_a = 4.2 kcal/mole. Molecular weights were determined by gel-permeation chromatography. No increase in molecular weight was observed with increased reaction time. Thus living centers or diradicals are not involved in the process. The M?_n shows a steady decrease with increase in monomer-diethylaluminum chloride concentration but the rate is maximum at equimolar monomer concentrations. The data are interpreted on a chain-transfer mechanism and show close agreement to a model in which the excess complexed acceptor monomer is the transfer agent. The chain-transfer constant of 7.1 × 10^?4 l./mole-sec is several orders of magnitude greater than for uncomplexed systems.     

Kinetics of the I2-catalyzed isomerization of allyl chloride to cis- and trans-1-chloro-1-propene. The stabilization energy of the chloroallyl radical

The I₂-catalyzed isomerization of allyl chloride to cis- and trans- l-chloro-l-propene was measured in a static system in the temperature range 225–329°C. Propylene was found as a side product, mainly at the lower temperatures. The rate constant for an abstraction of a hydrogen atom from allyl chloride by an iodine atom was found to obey the equation log [k,/M^?1 sec^?1] = (10.5 ± 0.2) ?; (18.3 ± 10.4)/θ, where θ is 2.303RT in kcal/mole. Using this activation energy together with 1 ± 1 kcal/mole for the activation energy for the reaction of HI with alkyl radicals gives DH⁰ (CH₂CHCHCl? H) = 88.6 ± 1.1 kcal/mole, and 7.4 ± 1.5 kcal/mole as the stabilization energy (SE) of the chloroallyl radical. Using the results of Abell and Adolf on allyl fluoride and allyl bromide, we conclude DH⁰ (CH₂CHCHF? H) = 88.6 ± 1.1 and DH⁰ (CH₂CHCHBr? H) = 89.4 ± 1.1 kcal/ mole; the SE of the corresponding radicals are 7.4 ± 2.2 and 7.8 ± 1.5 kcal/mole. The bond dissociation energies of the C? H bonds in the allyl halides are similar to that of propene, while the SE values are about 2 kcal/mole less than in the allyl radical, resulting perhaps more from the stabilization of alkyl radicals by α-halogen atoms than from differences in the unsaturated systems.     

Water-absorption properties of an acetal copolymer

The kinetics of sorption from the liquid phase to equilibrium and desorption were studied over the temperature range 0–80°C. Equilibrium uptake was found to increase linearly with concentration in this range. Sorption-desorption kinetics showed the diffusion coefficients to decrease with increasing concentration, although the extent of this dependence did not appear in itself to be temperature-dependent. The apparent diffusion coefficient obeyed the law D = D₀ exp {? E/RT} over the temperature range studied, giving E = 9.9 kcal./mole and D₀ = 0.45 cm.² sec.^?1. These values are compared with corresponding values for other polymers.     

Chemistry of trifluorostyrenes and their dimmers: 3. Solvent effect on the kinetic parameters of the thermal cyclodimerization of α, β, β-trifluorostyrene1

Rate constants for the thermal cyclodimerization of α, β, β-trifluorostyrene (TFS) were determined in six solvents at 393°K. The products of this reaction were mixtures of roughly equal amounts of cis-trans isomers. The rate constants in 3 solvents, were calculated according to Arrhenius equation. In n-hexane, log A = 6.02±0.18, E_a= 19.5±0.3 kcal.mol^?1; in glyme, logA = 5.31 ± 0.19, E_a= 18.0±0.3 kcal.mol^?1; in methanol, IogA=4.93±0.13, E_a=17.1±0.3 kcal mol^?1. All data are consistent with a stepwise radical mechanism, and our reaction in this solvent series obeys an isokinetic relationship, with β = 478°K.     

Kinetic interpretation of the glass transition: Glass temperatures of n-alkane liquids and polyethylene

On the basis of an isoviscosity criterion for the glass transition (η_g ? 10¹³ poise) in liquids of low molecular weight, theoretical T_g values were calculated for the n-alkane series by the equation log η = log A + B/(T ? T₀), with the use of values reported by Lewis for the parameters. The T_g/T₀ ratio reaches a limiting value of 1.25 and ?_g = (T_g ? T₀)/2.3B = 0.027, a constant. Extrapolation to (CH₂)_∞ gives T_g = 200°K., T₀ = 160°K., and B = 640°K. This T_g is consistent with other estimates for poly-ethylene, and T₀ coincides with the temperature at which the “excess” liquid entropy for (CH₂)_∞ becomes zero from thermodynamic data. For polymer liquids it is proposed that E₀ = 2.3RB is determined by the internal barriers to rotation for the “isolated” polymer chains. Thus, E₀ = 2.9 kcal./mole for polyethylene, 3.0 kcal./mole for polystyrene, 5.7 kcal./mole for polyisobutylene, and 1.9 kcal./mole for polydimethylsiloxane.     

A Complication in the thermal reactions of 1,1,2,2-tetramethylcyclopropane

Reinvestigation of the gas phase thermal reaction of 1,1,2,2-tetramethylcyclopropane (699-759°K) gave for the unimolecular disappearance of reactant, k_(TMC) = 10^{15.27–63.93/θ} sec^?1, in good agreement with the original results of Frey and Marshall. However, evidence for a high activation energy (E = 79 ± 5 kcal/mole), competitive unimolecular decomposition to 2,3-dimethyl-1 and -2-butenes was also obtained. It is proposed that the serious discrepancy noted [1] between the experimentally observed Arrhenius parameters for the overall reaction kinetics, and those predicted by transition state calculations assuming a biradical mechanism for the isomerization reactions (previously believed to be the only primary reaction mode) can be explained in terms of the increasing importance of the decomposition reactions at higher reaction temperatures.     

Further studies on the dissociation of HBr behind shock waves

Previously reported shock tube studies of the dissociation of HBr in the temperature range of 2100–4200°K have been extended to lower temperatures (1450–2300°K) in pure HBr. The course of reaction was followed by monitoring the radiative recombination emission in the visible spectrum from Br atoms. The results imply that, in the lower range of temperatures, the activation energy of dissociation, E in the expression AT^?2e^?E/RT, can be approximated by the HBr bond energy (88 kcal/mole). It was also found that, in this temperature range, the rate of HBr dissociation is sensitive to the Br₂ dissociation rate and the HBr + Br exchange rate. When these rates were adjusted to bring computed reaction profiles into agreement with experimental ones, it was found that the higher-temperature data could also be fitted reasonably well with an HBr dissociation activation energy of 88 kcal/mole, contrary to the conclusions of our previous work, which favored an activation energy of 50 kcal/mole. The “best value” for k₁^Ar, the rate coefficient for HBr dissociation in the presence of Ar as chaperone, appears to be 10^{21.78 ± 0.3} T^?2 10^?88/θ cc/mole sec, where θ = 2.3 RT/1000; that for k₁^HBr, is 10^22.66T^?210^?88/θ. A detailed review is given of the rate coefficients for the other pertinent reactions in the H₂–Br₂ system, viz., Br₂ dissociation and reactions of HBr with H and Br.     

The carbon–hydrogen bond strength in dimethyl ether and some properties of iodomethyl methyl ether

The kinetics and mechanism of the reaction between iodine and dimethyl ether (DME) have been studied spectrophotometrically from 515–630°K over the pressure ranges, I₂ 3.8–18.9 torr and DME 39.6–592 torr in a static system. The rate-determining step is, where k₁ is given by log (k₁/M^?1 sec^?1) = 11.5 ± 0.3 – 23.2 ± 0.7/θ, with θ = 2.303RT in kcal/mole. The ratio k₂/k_?1, is given by log (k₂/k_?1) = ?0.05 ± 0.19 + (0.9 ± 0.45)/θ, whence the carbon-hydrogen bond dissociation energy, DH° (H? CH₂OCH₃) = 93.3 ± 1 kcal/mole. From this, ΔH°_f(CH₂OCH₃) = ?2.8 kcal and DH°(CH₃? OCH₂) = 9.1 kcal/mole. Some nmr and uv spectral features of iodomethyl ether are reported.     

Addition of ethyl radicals to carbon monoxide. Kinetic and thermochemical properties of the propionyl radical

Azoethane was irradiated in the presence of carbon monoxide in the temperature range of 238 to 378 K. Kinetic parameters for the addition of ethyl radicals to carbon monoxide and for the decomposition of propionyl radicals were determined. The rate constants were found to be log k(cm³ mol^?1 sec^?1) = 11.19 - 4.8/θ and log k(sec^?1) = 12.77 - 14.4/θ, respectively. Estimated thermochemical properties of the propionyl radical are ΔH_f⁰ = -10.6 ± 1.0 kcal mol^?1, S⁰ = 77.3 ± 1.0 cal K^?1 mol^?1, and D(C₂H₅CO? H) = 87.4 kcal mol^?1.