Diffusion-controlled processes among partially absorbing stationary sinks

A general linear response theory is presented to calculate the zero-wavevector and zero-frequency reaction rate coefficient for particles diffusing into absorbing spheres. Allowance is made for possible incomplete particle absorption. A Faxén-like theorem for chemical reactions is derived. The problem is solved completely for a simple regular array of sinks. Exact analytic expressions for the rate coefficient as a function of sink volume fraction are obtained for the sc and fcc lattices. The case of a disordered array of sinks is also considered and the leading order nonanalytic density dependence of the rate coefficient is calculated. In both cases an increase in the rate coefficient with sink density in a local region of the system is found. The general formalism is extended to examine the modification to the particle diffusion coefficient due to the presence of the spheres. For regular arrays of spheres, the mean field result is reproduced.Research supported in part by a grant from the National Research Council of Canada.     

The mercury-sensitized oxidation of carbon monoxide

The mercury-photosensitized oxidation of CO was studied at 275°C over a wide range of [O₂]/[CO] ratios in the absence and presence of the oxygen atom scavenger 2-trifluoromethylpropene (TMP) and at 25°C at low [O₂]/[CO] ratios in the presence of TMP. By following the quantum yield of CO₂ production, Φ {CO₂}, as a function of the [O₂]/[CO] ratio, the reactions of vibrationally excited CO (v υ 9) and electronically excited O₂, probably in the c¹Σ^?_u state, were studied. At low [O₂]/[CO] ratios the predominant reactions are of vibrationally excited CO (v υ 9). Relative rate constants for chemical reaction versus deactivation of CO (v υ 9) were obtained. At higher [O₂]/[CO] ratios, the principal reactions are of electronically excited O₂. Relative rate constants for chemical reactions and deactivation of this electronically excited O₂ with CO, O₂, and TMP were obtained. From the effect of total pressure on Φ {CO₂}, it is proposed that an intermediate CO₃ is formed in the reaction of electronically excited O₂ with CO.     

The reaction of O(3P) with C2HCl3

The reaction of O(³P), prepared from the Hg photosensitization of N₂O, with C₂HCl₃ was studied at 25°C. The products of the reaction in the absence of O₂ were CO, CHCl₃, and polymer (as well as N₂ from the N₂O). The quantum yields of CO and CHCl₃ were 0.23 ± 0.01 and 0.14 ± 0.05, is respectively independent of reaction conditions. The reaction mechanism is with k_14a/k₁₄ = 0.23, where k_14a + k_14b. Most of the HCl and CCl₂ combine to form CHCl₃, but some other products must also be formed to account for the difference in the CO and CHCl₃ quantum yields. The C₂HCl₃O* adduct polymerizes without involving additional C₂HCl₃ molecules, since the quantum yield of C₂HCl₃ disappearance, ? Φ{C₂HCl₃}, was about 1.0 at high values of [N₂O]/[C₂HCl₃]. The rate coefficient for the reaction of O(³P) with C₂HCl₃ is 0.10 that for the reaction of O(³P) with C₂F₄. In the presence of O₂ the free radical chain oxidation occurs because of the reaction The main product is CHCl₂CCl(O) with smaller amounts of CO and CCl₂O, and some CO₂. The chain lengths were long and values of ? Φ {C₂HCl₃} up to 90 were observed.     

Mössbauer measurement of the hyperfine magnetic field AT sp site in Heusler alloys Rh2 Mn Z (Z=In and Sb)

We have investigated the systematics of hyperfine magnetic field on a fixed probe at the Z-site in Heusler alloys Rh₂MnZ as the valence of Z (sp element) is varied. The hmf on¹¹⁹Sn in Rh₂MnIn_.98 ¹¹⁹Sn₀₂ has been measured at 293K and 77K. In Rh₂Mn_1.12Sb_.86 ¹¹⁹Sn_.02 the hmf on¹²¹Sb has been measured at 77 K, and on¹¹⁹Sn at 293 K and 77 K. The results are compared with the hmf on¹¹⁹Sn in Rh₂Mn Ge_.98 ¹¹⁹Sn_.02 Rh₂Mn Sn, and Rh₂Mn Pb_.98 ¹¹⁹Sn_.02.Supported by the University Research Council, University of CincinnatiSupported by the Natural Sciences and Engineering Research Council of Canada     

Reactions of ozone with olefins: Ethylene,allene, 1,3-butadiene,and trans- 1,3-pentadiene

The reactions of O₃ with ethylene, allene, 1,3-butadiene, and trans-1,3-pentadiene have been studied in the presence of excess O₂ over the temperature range 232 to 298 K. The initial O₃ pressure was varied from 4–18 mtorr, and the olefin pressure was varied from 0.1 to 4.5 torr (ethylene), 2.8 to 39.6 torr (allene), 52.7 to 600 mtorr (1,3-butadiene) or 26.2 to 106 mtorr (trans-1,3-pentadiene). The O₃ decay was monitored by ultraviolet absorption. The reactions are first order in both O₃ and olefin, and the rate coefficients are independent of the O₂ pressure. For the O₃-ethylene system, various diluent gases (O₂, N₂, air) were used and the rate coefficients were found to be independent of the nature of the diluent gas. The various rate coefficients fit the Arrhenius expressions (k in cm³ s^?1): where the reported uncertainties are one standard deviation and R is in cal/mol K.     

Note on group consistency in analytic hierarchy process

We study the paper of Xu [Z. Xu, On consistency of the weighted geometric mean complex judgement matrix in AHP, European Journal of Operational Research 126 (2000) 683–687] for the group consistency in analytic hierarchy process of multicriteria decision-making. The purpose of this note is threefold. First, we point out the questionable results in this paper. Second, for three by three comparison matrices, we provide a patchwork for his method. Third, we constructed a counter example to show that in general his method is wrong. Numerical examples are provided to illustrate our findings. If there are four or more alternatives, then we may advise researchers to ignore his results to avoid questionable estimation of group consistency.     

Constitution der β-Chinolinderivate und derm-Chlorchinoline

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