Kinetics and mechanism of oxidation of the chromium(III)-DL-aspartic acid complex/periodate reaction. Evidence for iron(II) catalysis

The kinetics of oxidation of the chromium(III)-DL- aspartic acid complex, [CrIIIHL]+ by periodate have been investigated in aqueous medium. In the presence of Fe^II as a catalyst, the following rate law is obeyed:

Effect of long-chain branching on the relation between steady-flow and dynamic viscosity of polyethylene melts

The steady-state viscosity η, the dynamic viscosity η′, and the storage modulus G′ of several high-density and low-density polyethylene melts were investigated by using the Instron rheometer and the Weissenberg rheogoniometer. The theoretical relation between the two viscosities as proposed earlier is:\documentclass{article}\pagestyle{empty}\begin{document}$ \eta \left( {\dot \gamma } \right){\rm } = {\rm }\int {H\left( {\ln {\rm }\tau } \right)} {\rm }h\left( \theta \right)g\left( \theta \right)^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \tau {\rm }d{\rm }\ln {\rm }\tau $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \theta {\rm } = {\rm }{{\dot \gamma \tau } \mathord{\left/ {\vphantom {{\dot \gamma \tau } 2}} \right. \kern-\nulldelimiterspace} 2} $\end{document}; \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} is the shear rate, H is the relaxation spectrum, τ is the relaxation time, \documentclass{article}\pagestyle{empty}\begin{document}$ g\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{\theta \mathord{\left/ {\vphantom {\theta {\left( {1 + \theta ^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 + \theta ^2 } \right)}}} \right] $\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$ h\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} \mathord{\left/ {\vphantom {{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right. \kern-\nulldelimiterspace} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right] $\end{document}. Good agreement between the experimental and calculated values was obtained, without any coordinate shift, for high-density polyethylenes as well as for a low density sample with low n_w, the weight-average number of branch points per molecule. The correlation, however, was poor with low-density samples with large values of the long-chain branching index n_w. This lack of coordination can be related to n_w. The empirical relation of Cox and Merz failed in a similar way.     

Inner-sphere oxidation of a ternary dipicolinatochromium(III) complex involving a malonic acid co-ligand

The oxidation of a ternary complex of chromium(III), [Cr^III(DPA)(Mal)(H₂O)₂]^?, involving dipicolinic acid (DPA) as primary ligand and malonic acid (Mal) as co-ligand, was investigated in aqueous acidic medium. The periodate oxidation kinetics of [Cr^III(DPA)(Mal)(H₂O)₂]^? to give Cr(VI) under pseudo-first-order conditions were studied at various pH, ionic strength and temperature values. The kinetic equation was found to be as follows: \( {\text{Rate}} = {{\left[ {{\text{IO}}_{4}^{ - } } \right]\left[ {{\text{Cr}}^{\text{III}} } \right]_{\text{T}} \left( {{{k_{5} K_{5} + k_{6} K_{4} K_{6} } \mathord{\left/ {\vphantom {{k_{5} K_{5} + k_{6} K_{4} K_{6} } {\left[ {{\text{H}}^{ + } } \right]}}} \right. \kern-0pt} {\left[ {{\text{H}}^{ + } } \right]}}} \right)} \mathord{\left/ {\vphantom {{\left[ {{\text{IO}}_{4}^{ - } } \right]\left[ {{\text{Cr}}^{\text{III}} } \right]_{\text{T}} \left( {{{k_{5} K_{5} + k_{6} K_{4} K_{6} } \mathord{\left/ {\vphantom {{k_{5} K_{5} + k_{6} K_{4} K_{6} } {\left[ {{\text{H}}^{ + } } \right]}}} \right. \kern-0pt} {\left[ {{\text{H}}^{ + } } \right]}}} \right)} {\left\{ {\left( {\left[ {{\text{H}}^{ + } } \right] + K_{4} } \right) + \left( {K_{5} \left[ {{\text{H}}^{ + } } \right] + K_{6} K_{4} } \right)\left[ {{\text{IO}}_{4}^{ - } } \right]} \right\}}}} \right. \kern-0pt} {\left\{ {\left( {\left[ {{\text{H}}^{ + } } \right] + K_{4} } \right) + \left( {K_{5} \left[ {{\text{H}}^{ + } } \right] + K_{6} K_{4} } \right)\left[ {{\text{IO}}_{4}^{ - } } \right]} \right\}}} \) where k ₆ (3.65 × 10^?3 s^?1) represents the electron transfer reaction rate constant and K ₄ (4.60 × 10^?4 mol dm^?3) represents the dissociation constant for the reaction \( \left[ {{\text{Cr}}^{\text{III}} \left( {\text{DPA}} \right)\left( {\text{Mal}} \right)\left( {{\text{H}}_{2} {\text{O}}} \right)_{2} } \right]^{ - } \rightleftharpoons \left[ {{\text{Cr}}^{\text{III}} \left( {\text{DPA}} \right)\left( {\text{Mal}} \right)\left( {{\text{H}}_{2} {\text{O}}} \right)\left( {\text{OH}} \right)} \right]^{2 - } + {\text{H}}^{ + } \) and K ₅ (1.87 mol^?1 dm³) and K ₆ (22.83 mol^?1 dm³) represent the pre-equilibrium formation constants at 30 °C and I = 0.2 mol dm^?3. Hexadecyltrimethylammonium bromide (CTAB) was found to enhance the reaction rate, whereas sodium dodecyl sulfate (SDS) had no effect. The thermodynamic activation parameters were estimated, and the oxidation is proposed to proceed via an inner-sphere mechanism involving the coordination of IO₄ ^? to Cr(III).     

Thermodynamic studies on Pr2TeO6

The standard Gibbs energy of formation of Pr₂TeO₆ $ (\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)) $ was derived from its vapour pressure in the temperature range of 1,400–1,480 K. The vapour pressure of TeO₂ (g) was measured by employing a thermogravimetry-based transpiration method. The temperature dependence of the vapour pressure of TeO₂ over the mixture Pr₂TeO₆ (s) + Pr₂O₃ (s) generated by the incongruent vapourization reaction, Pr₂TeO₆ (s) = Pr₂O₃ (s) + TeO₂ (g) + ½ O₂ (g) could be represented as: $ { \log }\left\{ {{{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} \mathord{\left/ {\vphantom {{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} {{\text{Pa}} \pm 0.0 4}}} \right. \kern-0em} {{\text{Pa}} \pm 0.0 4}}} \right\} = 19. 12- 27132\; \left({\rm{{{\text{K}}}}/T} \right) $ . The $ \Updelta_{\text{f}} G^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ could be represented by the relation $ \left\{ {{{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} \mathord{\left/ {\vphantom {{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} \pm 5.0} \right\} = - 2 4 1 5. 1+ 0. 5 7 9 3\;\left(T/{\text{K}}\right) .$ Enthalpy increments of Pr₂TeO₆ were measured by drop calorimetry in the temperature range of 573–1,273 K and heat capacity, entropy and Gibbs energy functions were derived. The $ \Updelta_{\text{f}} H_{{298\;{\text{K}}}}^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ was found to be $ {{ - 2, 40 7. 8 \pm 2.0} \mathord{\left/ {\vphantom {{ - 2, 40 7. 8 \pm 2.0} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} $ .     

Massenspektrometrische Untersuchungen an Azoverbindungen: I

A number of symmetrical and unsymmetrical azo compounds have been studied by electron impact mass spectrometry. In all cases (except azoisobutyronitrile) the compounds follow a two-step fragmentation mechanism \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm R}^{\rm 1} - {\rm N = N - R}^{\rm 2} } \right]_{}^{_.^ + } $\end{document} → [R¹? N₂]⁺ (+R²˙)→[R¹]⁺(+N₂).     

Mass spectrometry of transition-metal π-complexes. III—a study of an iron-coordinated tautomer of phenol

A study of the fragmentation of the \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{\left({{\rm C}_{\rm 6} {\rm H}_{\rm 6} {\rm O}} \right){\rm Fe}} \right]_{}^{_.^ + } $\end{document} ion formed from two different precursors suggests that the ions adopt different structures over that part of the energy distribution giving rise to decomposition in the ion source.     

Kinetics of the reaction Cl + NO2 + M

The termolecular rate constant for the reaction Cl + NO₂ + M has been measured over the temperature range 264 to 417 K and at pressure 1 to 7 torr in a discharge flow system using atomic chlorine resonance fluorescence at 140 nm to monitor the decay of Cl in an excess of NO₂. The results are\documentclass{article}\pagestyle{empty}\begin{document}$k_1^{{\rm He}} = 9.4{\rm } \times {\rm }10^{ - 31} \left({\frac{T}{{300}}} \right)^{ - 2.0 \pm 0.05} {\rm cm}^6 {\rm s}^{ - {\rm 1}}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$k_1^{{\rm N}2} = (14.8{\rm } \pm {\rm }1.4){\rm } \times {\rm 10}^{ - 31} {\rm cm}^6 {\rm s}^{ - 1}$\end{document} at 296 K where error limits represent one standard deviation. The systematic error of k₁ measurements is estimated to be about 15%. Using a static photolysis system coupled with the FTIR spectrophotometer the branching ratio for the formation of the two possible isomers was found to be ClONO(?75%) and CINO₂(?25%) in good agreement with previous measurements.     

Photoreduction of Thiosulfate in Semiconductor Dispersions

Conduction band electrons produced by band gap excitation of TiO₂-particles reduce efficiently thiosulfate to sulfide and sulfite. \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm 2e}_{{\rm cb}}^ - ({\rm TiO}_{\rm 2}) + {\rm S}_{\rm 2} {\rm O}_3^{2 - } \longrightarrow {\rm S}^{2 - } + {\rm SO}_3^{2 - } $\end{document} This reaction is confirmed by electrochemical investigations with polycrystalline TiO₂-electrodes. The valence band process in alkaline TiO₂-dispersions involves oxidation of S₂O to tetrathionate which quantitatively dismutates into sulfite and thiosulfate, the net reaction being: \documentclass{article}\pagestyle{empty}\begin{document}$ 2{\rm h}^{\rm + } ({\rm TiO}_{\rm 2}) + 0.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } + 1.5{\rm H}_{\rm 2} {\rm O} \longrightarrow {\rm SO}_3^{2 - } + 3{\rm H}^{\rm + } $\end{document} This photodriven disproportionation of thiosulfate into sulfide and sulfite: \documentclass{article}\pagestyle{empty}\begin{document}$ 1.5{\rm H}_{\rm 2} {\rm O } + 1.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } \mathop \to \limits^{h\nu} 2{\rm SO}_3^{2 - } + {\rm S}^{{\rm 2} - } + 3{\rm H}^{\rm + } $\end{document} should be of great interest for systems that photochemically split hydrogen sulfide into hydrogen and sulfur.     

Oxidation of 3-(4-methoxyphenoxy)-1,2-propanediol by bis(hydrogen periodato)argentate(III) complex anion: a kinetic study

Oxidation of 3-(4-methoxyphenoxy)-1,2-propanediol (MPPD) by bis(hydrogenperiodato) argentate(III) complex anion, [Ag(HIO₆)₂]⁵⁻ has been studied in aqueous alkaline medium by use of conventional spectrophotometry. The major oxidation product of MPPD has been identified as 3-(4-methoxyphenoxy)-2-ketone-1-propanol by mass spectrometry. The reaction shows overall second-order kinetics, being first-order in both [Ag(III)] and [MPPD]. The effects of [OH⁻] and periodate concentration on the observed second-order rate constants k′ have been analyzed, and accordingly an empirical expression has been deduced:

Quantitative softness parameters and their application in elucidation of Structure of Bimetallic Tetrathiocyanate Complexes

〉₂M(NCS)₂M′(SCN)₂〈 and [ML₆][M′(SCN)₄], (M = Co(II) and Ni(II), M′ = Zn(II), Cd(II) and Hg(II) and L = aniline(ani), p-toluidine(tol), pyridine(py), nicotinamide(nia), 2,2′-bipyridine(bipy) and 4-aminopyridine (apy)) have been prepared and characterized. Their structure have been proposed on the basis of molar conductance, magnetic moment, group theoretical calculations, ligand field parameters, infrared and electronic spectral studies. The proposed structures have also been supported by quantitative values of softness ?\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm E}_{\rm n}^{_ + ^ +},{\rm E}_{\rm m}^{_{\rm +}^{\rm +}} $\end{document}”?,. Total softness of M and M′ and their difference \documentclass{article}\pagestyle{empty}\begin{document}$ \Delta {\rm TE}_{\rm n}^{_ + ^ +} \left({{\rm M} - {\rm M}'} \right) $\end{document} have also been derived by the following equations and related to the structure of the complexes. .     

Structures and formation of \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm 8}} } \right]_{}^{_.^ + } $\end{document} ions

Several \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm\ 8}} } \right]_{}^{_.^ + } $\end{document} ion isomers yield characteristic and distinguishable collisional activation spectra: \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm 1-butene} } \right]_{}^{_.^ + } $\end{document} and/or \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm 2-butene} } \right]_{}^{_.^ + } $\end{document} (a-b), \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm isobutene} } \right]_{}^{_.^ + } $\end{document} (c) and [cyclobutane]⁺ (e), while the collisional activation spectrum of \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm methylcyclopropane} } \right]_{}^{_.^ + } $\end{document} (d) could also arise from a combination of a-b and c. Although ready isomerization may occur for \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm 8}} } \right]_{}^{_.^ + } $\end{document} ions of higher internal energy, such as d or e → a, b, and/or c, the isomeric product ions identified from many precursors are consistent with previously postulated rearrangement mechanisms. 1,4-Eliminations of HX occur in 1-alkanols and, in part, 1-buthanethiol and 1-bromobutane. The collisional activation data are consistent with a substantial proportion of 1,3-elimination in 1- and 2-chlorobutane, although 1,2-elimination may also occur in the latter, and the formation of the methylcycloprpane ion from n-butyl vinyl ether and from n-butyl formate. Surprisingly, cyclohexane yields the \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm linear butene} } \right]_{}^{_.^ + } $\end{document} ions a-b, not \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm cyclobutane} } \right]_{}^{_.^ + } $\end{document}, e.     

Dissociation Constants for Citric Acid in NaCl and KCl Solutions and their Mixtures at 25 °C

The constants for the dissociation of citric acid (H₃C) have been determined from potentiometric titrations in aqueous NaCl and KCl solutions and their mixtures as a function of ionic strength (0.05–4.5 mol-dm^–3) at 25 °C. The stoichiometric dissociation constants (K_i^*)

Thermochemical properties of di(N,N-di(2,4,6-trinitrophenyl)amino)-ethylenediamine in dimethyl sulfoxide and N-methyl pyrrolidone

The enthalpies of dissolution for di(N,N-di(2,4,6,-trinitrophenyl)amino)-ethylenediamine (DTAED) in dimethyl sulfoxide (DMSO) and N-methyl pyrrolidone (NMP) were measured using a RD496-2000 Calvet microcalorimeter at 298.15?K. Empirical formulae for the calculation of the enthalpies of dissolution (??_diss H) were obtained from the experimental data of the dissolution processes of DTAED in DMSO and NMP. The linear relationships between the rate (k) and the amount of substance (a) were found. The corresponding kinetic equations describing the two dissolution processes were $ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-0em} {{\rm{d}}t}} = 10^{ - 2.68} \left( {1 - \alpha } \right)^{0.84} $ for the dissolution of DTAED in DMSO, and $ {{{\rm{d}}\alpha } \mathord{\left/ {\vphantom {{{\rm{d}}\alpha } {{\rm{d}}t}}} \right. \kern-0em} {{\rm{d}}t}} = 10^{ - 2.79} \left( {1 - \alpha } \right)^{0.87} $ for the dissolution of DTAED in NMP, respectively.     

1,1-Elimination of HCN from propionitrile under electron-impact. Hydrogen migration in the molecular ion

The dominant primary reactions of propionitrile under electron-impact effect loss of HCN and loss of H·. Deuterium labeling shows that the hydrogen atom lost as HCN comes chiefly from C-2, but that lost as a free atom comes chiefly from C-3. Both reactions are probably preceded by a 1,2 hydrogen migration to yield an allylic-like molecular ion, \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm CH}_{\rm 3}{\rm C}^+ {\rm HCH = N}^{\rm .} \leftrightarrow {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm HCH = N}} \right]^+ $\end{document}.     

Kinetics and mechanism of the reactions of the superoxide ion in solutions. II. The kinetics of protonation of the superoxide ion by water and ethanol

The rate constants for the protonation of “free” (that is, solvated) superoxide ions by water and ethanol are equal to 0.5–3.5 ×10^?3M^?1·s^?1 in DMF and AN at 20º. It has been found that the protonation rates for the ion pairs of \documentclass{article}\pagestyle{empty}\begin{document}${\rm O}_{\rm 2}^{\overline {\rm .} }$\end{document} with the Bu₄N⁺ cation are much slower than those for “free” \documentclass{article}\pagestyle{empty}\begin{document}${\rm O}_{\rm 2}^{\overline {\rm .} }$\end{document}. It is suggested that the effects of aprotic solvents on the protonation rates of \documentclass{article}\pagestyle{empty}\begin{document}${\rm O}_{\rm 2}^{\overline {\rm .} }$\end{document} are mainly due to the fact that the proton donors form solvated complexes of different stability in these solvents.     

Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

Amphiphilic block copolymers of vinyl ethers by living cationic polymerization. II. Synthesis and surface activity of macromolecular amphiphiles with pendant amino groups

Amphiphilic block polymers of vinyl ethers (VEs). $\rlap{--} [{\rm CH}_{\rm 2} {\rm CH}\left( {{\rm OCH}_{\rm 2} {\rm CH}_{\rm 2} {\rm NH}_{\rm 2} } \right)\rlap{--} ]_m \rlap{--} [{\rm CH}_{\rm 2} {\rm CH}\left( {{\rm OR}} \right)\rlap{--} ]_n \left( {{\rm R: }n{\rm - C}_{{\rm 16}} {\rm H}_{{\rm 33}} ,{\rm }n{\rm - C}_{\rm 4} {\rm H}_{\rm 9} ;m \simeq 40,{\rm n} = 1 - 10} \right)$ were prepared, each of which consists of a hydrophilic segment with pendant primary amino groups and a hydrophobic poly(alkyl VE) segment. Their precursors were obtained by the HI/I₂-initiated sequential living cationic polymerization of an alkyl VE and a VE with a phthalimide pendant (CH₂ = CHOCH₂CH₂Im; Im; phthalimide group), where the segment molecular weights and compositions (m/n ratio) could be controlled by regulating the feed ratio of two monomers and the concentration of hydrogen iodide. Hydrazinolysis of the imide functions gave the target polymers which were readily soluble in water under neutral conditions at room temperature. These amphiphilic block polymers lowered the surface tension of their aqueous solutions (0.1 wt%, 25°C) to a minimum ? 30 dyn/cm when the hydrophobic pendant R was n-C₄H₉ (n = 4–9). The polymers with n-C₄H₉ pendants in the hydrophobic segment exhibited a higher surface activity than those with n-C₁₆ H₃₃ pendants. The surface activity of the polymers also depended on the pH of the polymer solutions; the surface activity increased in more basic solutions where the ionization of the amino group (? NH₂)2? NH₃^⊕) is suppressed.     

Kinetics and mechanism of oxidation of hydroxylamine by tetrachloroaurate(III) ion

The oxidation of H₂NOH is first-order both in [NH₃OH⁺] and [AuCl₄ ^–]. The rate is increased by the increase in [Cl^–] and decreased with increase in [H⁺]. The stoichiometry ratio, [NH₃OH⁺]/[AuCl₄ ^–], is 1. The mechanism consists of the following reactions.

An entanglement model for the dependence of fracture surface energy on molecular weight

Over the last decade, empirical evidence has indicated that the effective surface energy γ associated with the fracture of noncrystalline is a linear function of the reciprocal of the viscosity–average molecular weight: \documentclass{article}\pagestyle{empty}\begin{document}$ \gamma = \gamma _\infty - b\bar M_v ^{ - 1} $\end{document}. For poly(methyl methacrylate), data of J. P. Berry, G. C. Berry and Fox show that gamma; ～ 0 at about the same value of M?_v that corresponds to the polymer chain-entanglement length. From this fact, we have developed an entanglement network model for fracture, that bears a resemblance to F. Bueche's entanglement model for the melt viscosity of bulk polymers. Our model allows for the expression of the previously empirical constants, γ_∞ and b, in terms of molecular parameters: \documentclass{article}\pagestyle{empty}\begin{document}$ {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } \mathord{\left/ {\vphantom {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } {\bar M_{\rm s} }}} \right. \kern-\nulldelimiterspace} {\bar M_{\rm s} }} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ b = 2({{\bar M_v } \mathord{\left/ {\vphantom {{\bar M_v } {\bar M_n }}} \right. \kern-\nulldelimiterspace} {\bar M_n }})\gamma _\infty M_{\rm f} $\end{document} where M?_n and M?_f are the number-average molecular weights of the polymer and of the free chain ends, M?_v is the viscosity-average molecular weight, γ_s is the average fracture-energy per entanglement in the craze volume, A_s is the average cross-sectional area of the polymer chain, Z_c and ρ_c are the thickness and density of crazed material on the fracture surface, respectively; M?_s is the average strand molecular weight between entanglements, and N_A is AvogadrO's number.     

Products and mechanism for the OH radical initiated oxidation of acrylonitrile,methacrylonitrile, and allylcyanide in the presence of NO

The photooxidation of acrylonitrile, methacylonitrile, and allylcyanide in the presence of NO was studied in parts per million concentration using the long-path Fourier transform IR spectroscopic method. The stoichiometry of the OH radical initiated oxidation of methacrylonitrile was established as \documentclass{article}\pagestyle{empty}\begin{document}$ \left( {{\rm OH}} \right) + {\rm CH}_{\rm 2} = {\rm C}\left( {{\rm CH}_{\rm 3} } \right){\rm CN + 2NO + 2O}_{\rm 2} \mathop {\hbox to 20pt{\rightarrowfill}}\limits^{1.0} {\rm HCHO + CH}_{\rm 3} {\rm COCN + 2NO}_{{\rm 2}} + \left( {{\rm OH}} \right) $\end{document}. The yield of HCHO for acrylonitrile and allylcyanide was found to be ca. 100 and 80%, and the stoichiometric reactions were assessed to proceed, \documentclass{article}\pagestyle{empty}\begin{document}$ \left( {{\rm OH}} \right) + {\rm CH}_{\rm 2} = {\rm CHCN + 2NO + 2O}_{\rm 2} \mathop {\hbox to 20pt{\rightarrowfill}}\limits^{1.0} {\rm HCHO + HCOCN + 2NO}_{\rm 2} + \left( {{\rm OH}} \right) $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \left( {{\rm OH}} \right) + {\rm CH}_{\rm 2} = {\rm CHCH}_{\rm 2} {\rm CN + 2NO + 2O}_{\rm 2} \mathop {\hbox to 20pt{\rightarrowfill}}\limits^{0.8} {\rm HCHO + HCOCH}{\rm 2} {\rm CN + 2NO}_{\rm 2} + \left( {{\rm OH}} \right) $\end{document}, respectively. These results revealed that the reaction mechanism for these unsaturated organic cyanides are analogous to that of olefins.