The reactions of alkoxy radicals with O2. II. n-C3H7O radicals

n-C₃H₇ONO was photolyzed with 366 nm radiation at ?26, ?3, 23, 55, 88, and 120°C in a static system in the presence of NO, O₂, and N₂. The quantum yields of C₂H₅CHO, C₂H₅ONO, and CH₃CHO were measured as a function of reaction conditions. The primary photochemical act is and it proceeds with a quantum yield ?₁ = 0.38 ± 0.04 independent of temperature. The n-C₃H₇O radicals can react with NO by two routes The n-C₃H₇O radical can decompose via or react with O₂ via Values of k₄/k₂ ? k_4b/k₂ were determined to be (2.0 ± 0.2) × 10¹⁴, (3.1 ± 0.6) × 10¹⁴, and (1.4 ± 0.1) × 10¹⁵ molec/cm³ at 55, 88, and 120°C, respectively, at 150-torr total pressure of N₂. Values of k₆/k₂ were determined from ?26 to 88°C. They fit the Arrhenius expression: For k₂ ? 4.4 × 10^?11 cm³/s, k₆ becomes (2.9 ± 1.7) × 10^?13 exp{?(879 ± 117)/T} cm³/s. The reaction scheme also provides k_4b/k₆ = 1.58 × 10¹⁸ molec/cm³ at 120°C and k_8a/k₈ = 0.56 ± 0.24 independent of temperature, where      

Casimir self-stress on a perfectly conducting spherical shell

The Casimir stress on a perfectly conducting uncharged sphere, due to occurrence of fluctuations in the electromagnetic field, is calculated using a source theory formulation. Two independent methods are employed: we compute (1) the total Casimir energy inside and outside the sphere, and (2) the radial component of the stress tensor on the surface. It is necessary to exercise care in allowing the field points to overlap; a correct limiting procedure supplies a “cutoff” in the frequency integration. In spite of numerous technical improvements, the result of Boyer, that the self-stress is repulsive (and not attractive as Casimir hoped), is confirmed unambiguously. The magnitude of the Casimir energy of a sphere of radius a is found, by numerical and analytic techniques, to be $\text{E = (}\text{h}\text{?}\text{c}\text{2a}\text{)(0.09235)}$, also in agreement with the very recent result of Balian and Duplantier.     

Pyrolysis of vinylacetylene between 300 and 450°C

Vinylacetylene was pyrolyzed at 300–450°C in a packed and an unpacked static reactor with a pinhole bleed to a quadrupole mass spectrometer. The reactant and C₈H₈ products were monitored continuously during a reaction by mass spectrometry. In some runs, the products were also analyzed by gas chromatography after the run. In these runs CH₄, C₂H₆, C₃H₆, and C₂H₄ were also detected. The reaction for vinylacetylene removal and C₈H₈ formation is homogeneous, second order in reactant, and independent of the presence of a large excess of N₂ or He. However, C₈H₈ formation is about half-suppressed by the addition of the free-radical scavengers NO or O₂. The rate coefficient for total vinylacetylene removal is 1.7 × 10⁶ exp(?79 ± 13 kJ/mol RT) L/mol · s. The major reaction for C₄H₄ removal is polymerization. In addition four C₈H₈ isomers, carbon, and small hydrocarbons are formed. The three major C₈H₈ isomers are styrene, cyclooctatetraene (COT), and 1,5? dihydropentalene (DHP). The C₈H₈ compounds are formed by both molecular and free-radical processes in a second-order process with an overall k ? 3 × 10⁸ exp(?122 kJ/mol RT) L/mol · s (average of packed and unpacked cell results). The molecular process occurs with an overall k = 8.5 × 10⁷ exp (?118 kJ/mol RT) L/mol · s. The COT, DHP, and an unidentified isomer (d), are formed exclusively in molecular processes with respective rate coefficients of 4.4 × 10⁴ exp(?77 kJ/mol RT), 1.7 × 10⁵ exp(?89 kJ/mol RT), and 3.1 × 10⁹ exp(? 148 kJ/mol RT) L/mol · s. The styrene is formed both by a direct free-radical process and by isomerization of COT.     

Modifications to the hole-drilling technique of measuring residual stresses for improved accuracy and reproducibility

The hole-drilling technique is a relatively well established and straightforward semidestructive method for measuring residual stresses in fabricated components. However, a number of factors can have a marked influence on the accuracy of this technique. Some of the factors evaluated in the present work were the method of drilling the hole, the size and shape of the hole, and the equations used to calculate the principal residual stresses from the relaxed-strain measurements. In this investigation, air-abrasive hole drilling using a 0.062-in.-ID stationary nozzle gave the most reproducible and accurate results. Of the three approaches used to calculate the residual stresses, one method proved to be superior, especially in a biaxial-stress field.     

Sample size determination for comparing two therapies taking both the α (type I or false positive) error and the β (type II or false negative) error into consideration

The sample size required for determination of a given degree of difference between two therapies or modalities A and B being compared with each other, supposing that the sample sizes are equal, is given by Here C_α/2 is the upper α/2 percentile point of the standard normal distribution, C_1?β is the abscissa cutting off the proportion 1?β in its upper tail and β in its lower tail; p_A and p_B are the probabilities of favorable response to A and B; if p?_A and p?_B are the corresponding measured proportions, then $\text{p}$ = $\text{1}\text{2}$(p?_A + p?_B); and the Q's are 1 minus the p's. When it is desirable to use unequal size groups, the sample sizes n₁     

Light absorption at high intensities. Comparison of quantum theory and semi-classical results

An error in the author's previous treatment of the interaction of an absorber with high intensity light is noted. The correct development of Mower is applied to determine the amplitude of the initial state of the radiation-matter system. Comparison of the quantum theory solution for a damped absorber exposed to a square light pulse with the results of semiclassical theories based on the undamped optical Bloch equations is effected by determining the effective in- and out-of-phase components of the transition dipole response. In general, the out-of-phase (or absorptive) part of the transition dipole is zero at the outset and strongly time-dependent at short times, evolving to a steady-state value at longer times. For resonance radiation the system exhibits either overdamped irreversible decay or underdamped oscillations, depending upon the relative magnitudes of the incident light intensity and the radiative damping rate. Specific results are presented for a variety of limiting values of the physical parameters, including light intensity, damping rate, and amount of off-resonance.     

Theory of dynamic light scattering by polymers and gels

It is shown under very general conditions that the intermediate scattering function for the generalized Rouse—Zimm model always takes the simple form G(K, t) α exp[?K²(k_BT/f)t], when the scattering vector K becomes sufficiently large. (Here k_B is Boltzmann's constant, T is the absolute temperature and f is the individual bead friction factor.) A microscopic formulation for the bulk modulus and friction factor density of a gel network is incorporated into the viscoelastic continuum model of Tanaka et al. The resulting expression for the apparent long-wavelength diffusion coefficient of the gel is D_G = (k_BT/f)2(1 - 2/Φ), where Φ is the network functionality.