Rheology of poly(vinyl chloride) melts. II. Shear rate-dependent properties

Four samples containing 40, 60, 80, and 97 wt-% of poly(vinyl chloride), the rest being plasticizer and stabilizer, were tested by using the Weissenberg Rheogoniometer in the steady-shearing mode at temperatures between 155 and 235°C and rates of shear \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma = 0.01 - 400 $\end{document} sec^?1. The viscosity η versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} follows Graessley's theoretical dependence for infinitely entangled system. The primary normal-stress difference coefficient ψ versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is well described by the same theoretical function, used with the square of its argument. The temperature dependence of η₀ and ψ₀ shows discontinuities at T = T_b. The numerical values of T_b can be calculated from the theory of the melting point depression due to diluent. The activation energy of viscous flow E_η below T_b is 5–9 times as large as above this temperature. The activation energy of normal stress is found to be Eψ ≈ 5E_η. The characteristic relaxation times τ_o, ψ_p, calculated from superposition of η versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} and ψ versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} data, respectively, onto Graessley's master curves, and τ_N, computed from zero shear parameters η₀ and ψ₀, differ in their sensitivity to the melting of microcrystalline regions. It is postulated that in the systems investigated, aggregates with long lifetimes are being formed, increasing the effective molecular weight and introducing changes in the effective polydispersity.     

The gas-phase pyrolysis of alkyl nitrites. III. Isopropyl nitrite

The rate of decomposition of isopropyl nitrite (IPN) has been studied in a static system over the temperature range of 130–160°C. For low concentrations of IPN (1–5 × 10^?5M), but with a high total pressure of CF₄ (～0.9 atm) and small extents of reaction (～1%), the first-order rates of acetaldehyde (AcH) formation are a direct measure of reaction (1), since k₃ » k₂(NO): \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {\rm IPN}\begin{array}{rcl} 1 \\ {\rightleftarrows} \\ 2 \\ \end{array}i - \Pr \mathop {\rm O}\limits^. + {\rm NO},i - \Pr \mathop {\rm O}\limits^. \stackrel{3}{\longrightarrow} {\rm AcH} + {\rm Me}. $\end{document} Addition of large amounts of NO (～0.9 atm) in place of CF₄ almost completely suppressed AcH formation. Addition of large amounts of isobutane – t-BuH – (～0.9 atm) in place of CF₄ at 160°C resulted in decreasing the AcH by 25%. Thus 25% of \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^{\rm .} $\end{document} were trapped by the t-BuH (4): \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + t - {\rm BuH} \stackrel{4}{\longrightarrow} i - \Pr {\rm OH} + (t - {\rm Bu}). $\end{document} The result of adding either NO or t-BuH shows that reaction (1) is the only route for the production of AcH. The rate constant for reaction (1) is given by k₁ = 10^{16.2±0.4–41.0±0.8}/θ sec^?1. Since (E₁ + RT) and ΔH°₁ are identical, within experimental error, both may be equated with D(i-PrO-NO) = 41.6 ± 0.8 kcal/mol and E₂ = 0 ± 0.8 kcal/mol. The thermochemistry leads to the result that \documentclass{article}\pagestyle{empty}\begin{document}$ \Delta H_f^\circ (i - {\rm Pr}\mathop {\rm O}\limits^{\rm .} ) = - 11.9 \pm 0.8{\rm kcal}/{\rm mol}. $\end{document} From ΔS°₁ and A₁, k₂ is calculated to be 10^10.5±0.4M^?1·sec^?1. From an independent observation that k₆/k₂ = 0.19 ± 0.03 independent of temperature we find E₆ = 0 ± 1 kcal/mol and k₆ = 10^9.8+0.4M^?;1·sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + {\rm NO} \stackrel{6}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} In addition to AcH, acetone (M₂K) and isopropyl alcohol (IPA) are produced in approximately equal amounts. The rate of M₂K formation is markedly affected by the ratio S/V of different reaction vessels. It is concluded that the M₂K arises as the result of a heterogeneous elimination of HNO from IPN. In a spherical reaction vessel the first-order rate of M₂K formation is given by k₅ = 10^9.4–27.0/θ sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm IPN} \stackrel{5}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} IPA is thought to arise via the hydrolysis of IPN, the water being formed from HNO. This elimination process explains previous erroneous results for IPN.     

Pyrolysis of dimethyl peroxide

By using isobutane (t-BuH) as a radical trapit has been possible to study the initial step in the decomposition of dimethyl peroxide (DMP) over the temperature range of 110–140°C in a static system. For low concentrations of DMP (2.5 × 10^?5?10^?4M) and high pressures of t?BuH (～0.9 atm) the first-order homogeneous rate of formation of methanol (MeOH) is a direct measure of reaction (1): \documentclass{article}\pagestyle{empty}\begin{document}${\rm DMP}\mathop \to \limits^1 2{\rm Me}\mathop {\rm O}\limits^{\rm .},{\rm Me}\mathop {\rm O}\limits^{\rm .} + t{\rm - BuH}\mathop \to \limits^4 {\rm MeOH} + t{\rm -}\mathop {\rm B}\limits^{\rm .} {\rm u}$\end{document}. For complete decomposition of DMP in t-BuH, virtually all of the DMP is converted to MeOH. Thus DMP is a clean thermal source of Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document}. In the decomposition of pure DMP complications arise due to the H-abstraction reactions of Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document} from DMP and the product CH₂O. The rate constant for reaction (1) is given by k₁ = 10^15.5?37.0/θ sec^?1, very similar to other dialkyl peroxides. The thermochemistry leads to the result D(MeO? OMe) = 37.6 ± 0.2 kcal/mole and /H(Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document}) = 3.8 ± 0.2 kcal/mole. It is concluded that D(RO? OR) and D(RO? H) are unaffected by the nature of R. From ΔS and A₁, k₂ is calculated to be 10^10.3±0.5 M^?1· sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2{\rm Me}\mathop {\rm O}\limits^{\rm .} \mathop \to \limits^2 {\rm DMP}$\end{document}. For complete reaction, trace amounts of t-BuOMe lead to the result k₂ ～ 10⁹ M^?1 ·sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2t{\rm - Bu}\mathop \to \limits^5$\end{document} products. From the relationship k₆ = 2(k₂k_5a)^1/2 and with k_5a = 10^8.4 M^?1 · sec^?1, we arrive at the result k₆ = 10^9.7 M^?1 · sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2t{\rm - u}\mathop {\rm B}\limits^{\rm .} \to (t{\rm - Bu)}_{\rm 2}{\rm,}t{\rm -}\mathop {\rm B}\limits^{\rm .} {\rm u} + {\rm Me}\mathop {\rm O}\limits^{\rm .} \mathop \to \limits^6 t{\rm - BuOMe}$\end{document}.     

The gas-phase pyrolysis of alkyl nitrites. IV. Ethyl nitrite

The rate of decomposition of methyl nitrite (MN) has been studied in the presence of isobutane-t-BuH-(167-200°C) and NO (170-200°C). In the presence of t-BuH (～0.9 atm), for low concentrations of MN (～10^?4M) and small extents of reaction (4-10%), the first-order homogeneous rates of methanol (MeOH) formation are a direct measure of reaction (1) since k₄(t-BuH) »k₂(NO): . The results indicate that the termination process involves only \documentclass{article}\pagestyle{empty}\begin{document}$ t - {\rm Bu\, and\, NO:\,\,}t - {\rm Bu} + {\rm NO\stackrel{e}{\longrightarrow}} $\end{document} products, such that k_e ～ 10¹⁰ M^?1 ～ sec^?1.Under these conditions small amounts of CH₂O are formed (3-8% of the MeOH). This is attributed to a molecular elimination of HNO from MN. The rate of MeOH formation shows a marked pressure dependence at low pressures of t-BuH. Addition of large amounts of NO completely suppresses MeOH formation. The rate constant for reaction (1) is given by k₁ = 10^{15.8°0.6-41.2°1}/· sec^?1. Since (E₁ + RT) and ΔH^Δ₁ are identical, within experimental error, both may be equated with D(MeO - NO) = 41.8 + 1 kcal/mole and E₂ = 0 ± 1 kcal/mol. From ΔS¹₁ and A₁, k₂ is calculated to be 10^10.1°0.6M^?1 · sec^?1, in good agreement with our values for other alkyl nitrites. These results reestablish NO as a good radical trap for the study of the reactions of alkoxyl radicals in particular. From an independent observation that k₆/k₂ = 0.17 independent of temperature, we conclude that \documentclass{article}\pagestyle{empty}\begin{document}$ E_6 = 0 \pm 1{\rm kcal}/{\rm mol\, and\,}\,k_6 = 10^{9.3} M^{- 1} \cdot {\rm sec}^{- 1} :{\rm MeO} + {\rm NO}\stackrel{6}{\longrightarrow}{\rm CH}_2 {\rm O} + {\rm HNO} $\end{document}. From the independent observations that k₂:k_2→: k_6→ was 1:0.37:0.04, we find that k_2→ = 10^9.7M^?1 ? sec^?1 and k_6→ = 10^8.7M^?1 ? sec^?1. In addition, the thermodynamics lead to the result In the presence of NO (～0.9 atm) the products are CH₂O and N₂O (and presumably H₂O) such that the ratio N₂O/CH₂O ～ 0.5. The rate of CH₂O formation was affected by the surface-to-volume ratio s/v for different reaction vessels, but it is concluded that, in a spherical reaction vessel, the CH₂O arises as the result of an essentially homogeneous first-order, fourcenter elimination of \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm HNO}:{\rm MN\stackrel{5}{\longrightarrow}CH}_{\rm 2} {\rm O} + {\rm HNO} $\end{document}. The rate of CH₂O formation is given by k₅ = 10^{13.6°0.6-38.5-1}/? sec^?1.     

The gas-phase pyrolysis of alkyl nitrites. II. s-butyl nitrite

The rate of decomposition of s-butyl nitrite (SBN) has been studied in the absence (130–160°C) and presence (160–200°C) of NO. Under the former conditions, for low concentrations of SBN (6 × 10^?5 ? 10^?4M) and small extents of reaction (～1.5%), the first-order homogeneous rates of acetaldehyde (AcH) formation are a direct measure of reaction (1) since k_3c » k₂(NO): . Unlike t-butyl nitrite (TBN), d(AcH)/dt is independent of added CF₄ (～0.9 atm). Thus k_3c is always » k₂ (NO) over this pressure range. Large amounts of NO (～0.9 atm) (130–160°C) completely suppress AcH formation. k₁ = 10^16.2–40.9/θ sec^?1. Since (E₁ + RT) and ΔH°₁ are identical, within experimental error, both may be equated with D(s-BuO-NO) = 41.5 ± 0.8 kcal/mol and E₂ = 0 ± 0.8 kcal/mol. The thermochemistry leads to the result ΔH°_f (s-\documentclass{article}\pagestyle{empty}\begin{document}${\rm Bu}\mathop {\rm O}\limits^{\rm .}$\end{document}) = ? 16.6 ± 0.8 kcal/mol. From ΔS°₁ and A₁, k₂ is calculated to be 10^10.4 M^?1 · sec^?1, identical to that for TBN. From an independent observation that k₆/k₂ = 0.26 ± 0.01 independent of temperature, \documentclass{article}\pagestyle{empty}\begin{document}${\rm s - Bu}\mathop {\rm O}\limits^{\rm .} + {\rm NO}\mathop \to \limits^{\rm 6} {\rm MEK} + {\rm HNO}$\end{document}, we find E₆ = 0 ± 1 kcal/mol and k₆ = 10^9.8M^?1 · sec^?1. Under the conditions first cited, methyl ethyl ketone (MEK) is also a product of the reaction, the rate of which becomes measurable at extents of conversion >2%. However, this rate is ～0.1 that of AcH formation. Although MEK formation is affected by the ratio S/V for different reaction vessels, in a spherical reaction vessel, this MEK arises as the result of an essentially homogeneous first-order 4-centre elimination of HNO. \documentclass{article}\pagestyle{empty}\begin{document}${\rm SBN}\mathop \to \limits^{\rm 5} {\rm MEK} + {\rm HNO}$\end{document}; k₅ = 10^12.8–35.8/θ sec^?1. Sec-butyl alcohol (SBA), formed at a rate comparable to MEK, is thought to arise via the hydrolysis of SBN, the water being formed from HNO. The rate of disappearance of SBN, that is, d(MEK + SBA + AcH)/dt, is given by k_global = 10^15.7–39.6/θ sec^?1. In NO (～1 atm) the rate of formation of MEK was about twice that in the absence of NO, whereas the SBA was greatly reduced. This reaction was also affected by the ratio S/V of different reaction vessels. It was again concluded that in a spherical reaction vessel, the rate of MEK formation was essentially homogeneous and first order. This rate is given by k_obs = 10^12.9–35.4/θ sec^?1, very similar to k₅. However, although it is clear that the rate of formation of MEK is doubled in the presence of NO, the value for k_obs makes it difficult to associate this extra MEK with the disproportionation of s-\documentclass{article}\pagestyle{empty}\begin{document}${\rm Bu}\mathop {\rm O}\limits^{\rm .}$\end{document} and NO: s-\documentclass{article}\pagestyle{empty}\begin{document}$s{\rm - Bu}\mathop {\rm O}\limits^{\rm .} + {\rm NO}\mathop \to \limits^{\rm 6} {\rm MEK} + {\rm HNO}$\end{document}. NO at temperatures of 130–160°C completely suppresses AcH formation. AcH reappears at higher temperatures (165–200°C), enabling k_3c to be determined. Ignoring reaction (6), d(AcH)/dt = k₁k₃ (SBN )/[k_3c + k₂(NO)]; k_3c = 10^14.8–15.3/θ sec^?1. Inclusion of reaction (6) into the mechanism makes very little difference to the result. Reaction (3c) is expected to be a pressure-dependent process.     

Quasielastic scattering by dilute polymer solutions

The scattering law S( k ,w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ω(k) of S( k ,w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse–Zimm model) using the “spring-bead” model ignoring memory effects. For small (ka\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} ? 1) and large (ka ? 1) values of k we find Ω = 0.195 k²/β α η₀ \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} and Ω = k²/βξ, respectively, indicating that the width is governed mainly by the viscosity η₀ for small k values and by the friction coefficient ξ for large k values. For intermediate k values which are of importance in neutron scattering we find that in the Rouse limit Ω = k⁴a²/12βξ. When the hydrodynamic effects are included, Ω(k) becomes 0.055 k³/βη₀. Using the Rouse–Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Ω(k). The implications of the theoretical predictions for scattering experiments are discussed.     

Tensile stress and recoverable strain measurements on polystyrene melts. Interpretation of results in terms of rubberlike elasticity

Extensional tests at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document} have been carried out on polystyrene melts with different molecular weight distributions at various temperatures and strain rates. The true tensile stress is found to be well approximated by the sum of two contributions: (1) a neo-Hookean expression involving the recoverable strain and (2) a contribution rapidly reaching a steady-state value. Two experimental parameters can be defined: an elasticity modulus \documentclass{article}\pagestyle{empty}\begin{document}$ G(\dot \varepsilon ) $\end{document} from (1) and a viscosity \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{\rm v} (\dot \varepsilon ) $\end{document} from (2). It is further shown that time-temperature equivalence applies not only to the stress but also to the recoverable strain and to G and η_v. The dependence of G and η_v on strain rate is then discussed. For high strain rates, G is close to the linear viscoelastic plateau modulus of PS melts and decreases with decreasing strain rate. The value of η_v is found to a good approximation to be equal to three times the shear viscosity taken at a shear rate equivalent to the elongational strain rate.     

Laser-induced chemical kinetics: Absolute rate constants for the reactions Ċ2F2 + Br2 → C2F5Br + Ḃr and n-Ċ3F7 + Br2 → n-C3F7Br + Ḃr

Absolute rate constants at room temperature for the metathesis reaction have been measured under VLPP conditions: k₁ = (2.0 ± 0.5) × 10⁸M^?1·s^?1, k₂ = (3.0 ± 0.7) × 10⁸M^?1·s^?1. The radicals were generated through collisionless infrared-multiphoton decomposition of the corresponding iodides by irradiation from a high-power CO₂-TEA laser. The reaction of ?₂F₅ and ?₃F₇ with \documentclass{article}\pagestyle{empty}\begin{document}$$\mathop {\rm N}\limits^{\rm .} {\rm O}_{\rm 2} $$\end{document} are briefly discussed in relation to the reaction of ?₃ with \documentclass{article}\pagestyle{empty}\begin{document}$$\mathop {\rm N}\limits^{\rm .} {\rm O}_{\rm 2} $$\end{document}, which had been measured previously.     

Rate constants for alkyl radical recombination. II. The isopropyl radical

Products of radical combination from the free-radical buffer system \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$${{\rm R}^{\rm .} + {\rm R}^{\rm '} {\rm I}\mathop {\leftrightharpoons}\limits^{{\rm K}_{{\rm RR}}}{\rm RI} + {\rm R}^{'}}$$\end{document}. have been analyzed for the two cases, R = Me, R′ = iPr and R = Et, R′ = iPr. Results are consistent with the previously examined system where R = Me, R′ = Et, and give a value of k_P for iPr· combination of 10^8.6±1.1 M^?1 sec^?1.     

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.     

Temperature dependence of viscosity–shear rate behavior in undiluted polystyrene

The time—temperature superposition principle is well-established for linear viscoelastic properties of polymer systems. It is generally supposed that the same principle carries over into nonlinear phenomena, such as the relationship between viscosity η and shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}. Guided by this principle and the forms of various molecular theories, one would expect that η—\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} data on the same polymer at different temperatures would superimpose when plotted as η/η0 versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}η0/ρT, η0 being the limiting viscosity at low shear rates, ρ the polymer density, and T the absolute temperature. Data on polystyrene melts, obtained in a plate-cone viscometer, appear systematically to violate this principle in the range 140–190°. Such anomalies are absent in concentrated solutions of polystyrene. The trends are similar to those reported by Plazek in the steady-state compliance of polystyrene melts near T_g, but they appear to persist to higher temperatures than the compliance anomaly.     

The gas phase pyrolysis of alkyl nitrites. I. t-butyl nitrite

The rate of decomposition of t-butyl nitrite (TBN) has been studied in a static system over the temperature range of 120–160°C. For low concentrations of TBN (10^?5- 10^?4M), but with a high total pressure of CF₄ (～0.9 atm) and small extents of reaction (～1%), the first-order homogeneous rates of acetone (M₂K) formation are a direct measure of reaction (1), since k₃» k₂ (NO): TBN . Addition of large amounts of NO in place of CF₄ almost completely suppresses M₂K formation. This shows that reaction (1) is the only route for this product. The rate of reaction (1) is given by k₁ = 10^16.3–40.3/θ s^?1. Since (E₁ + RT) and ΔH are identical, both may be equated with D(RO-NO) = 40.9 ± 0.8 kcal/mole and E₂ = O ± 1 kcal/mole. From ΔS and A₁, k₂ is calculated to be 10^10.4M^?1 ·s^?1, implying that combination of t? BuO and NO occurs once every ten collisions. From an independent observation that k₂/k₂′ = 1.7 ± 0.25 independent of temperature, it is concluded that k₂′ = 10^10.2M^?1 · s^?1 and k₁′ = 10^15.9?40.2/θ s^?1; . This study shows that MeNO arises solely as a result of the combination of Me and NO. Since NO is such an excellent radical trap for t-Bu\documentclass{article}\pagestyle{empty}\begin{document}${\rm Me\dot O}$\end{document}, reaction (2) may be used in a competitive study of the decomposition of t? Bu\documentclass{article}\pagestyle{empty}\begin{document}${\rm Me\dot O}$\end{document} in order to obtain the first absolute value for k₃. Preliminary results show that k₃ (∞) = 10^15.7–17.0/θ s^?1. The pressure dependence of k₃ is demonstrated over the range of 10^?2?1 atm (160°C). The thermochemistry for reaction (3) implies that the Hg 6(³P₁) sensitised decomposition of t-BuOH occurs via reaction (m): In addition to the products accounted for by the TBN radical split, isobutene is formed as a result of the 6-centre elimination of HONO: TBN \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \to \limits^7 $\end{document} isobutene + HONO. The rate of formation of isobutene is given by k₇ = 10^12.9–33.6/θ s^?1. t-BuOH, formed at a rate comparable to that of isobutene–at least in the initial stages–is thought to arise as a result of secondary reactions between TBN and HONO. The apparent discrepancy between this and previous studies is reconciled in terms of the above parallel reactions (1) and (7), such that k + 2k₇ = 10^14.7–36.2/θ s^?1.     

Methyl thiirane: Kinetic gas-phase titration of sulfur atoms in SX OY systems

The reaction SO + SO →l S + SO₂(2) was studied in the gas phase by using methyl thiirane as a titrant for sulfur atoms. By monitoring the C₃H₆ produced in the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm S} + {\rm CH}_3\hbox{---} \overline {{\rm CH\hbox{---}CH}_2\hbox{---} {\rm S}} \to {\rm S}_2 + {\rm C}_3 {\rm H}_6 (7) $\end{document}, we determined that k₂ ? 3.5 × 10^?15 cm³/s at 298 K.     

Relaxation spectra of polymer melts from relaxation and steady-state flow data

Accurate measurements of stress relaxation after steady-state flow have been carried out, in the Newtonian flow region, for a polystyrene and a poly(methyl methacrylate) melt, with a cone-and-plate rotational rheometer. From the stress relaxation σ(t) versus t curves the relaxation spectra H were calculated by means of the first approximation equation: \documentclass{article}\pagestyle{empty}\begin{document}$ H = - ({1 \mathord{\left/ {\vphantom {1 {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}} \right. \kern-\nulldelimiterspace} {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}\ln t $\end{document}. The shear stress–shear rate curves, σ versus \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} were also measured, in large ranges of shear rates, for the same melts, and from these data the relaxation spectra H were obtained by means of equations given by Faucher and Ferry. The Faucher equation, \documentclass{article}\pagestyle{empty}\begin{document}$ H = - \dot \gamma ^2 d{\sigma \mathord{\left/ {\vphantom {\sigma d}} \right. \kern-\nulldelimiterspace} d}\dot \gamma ^2 $\end{document}, has been found to give results which compare satisfactorily with those obtained from the first approximation equation. It has been found that the Ferry equation has to be modified for comparable agreement.     

A Modified Kinetic Model for the Peroxydisulfate-Iodide Reaction

One kinetic model for the oxidation of iodide ion by peroxydisulfate ion in aqueous solution is proposed. The reaction is regarded as \documentclass{article}\pagestyle{empty}\begin{document} {\rm S}_2 {\rm O}_8^{2 -} + {\rm I}^ - {\rm IS}_2 {\rm O}_8^{3 -} \end{document}, followed by the reaction \documentclass{article}\pagestyle{empty}\begin{document} {\rm IS}_2 {\rm O}_8^{3 -} + {\rm I}l_2 + 2{\rm SO}_4^{2 -} \end{document}. If the initial rates V are obtained from the formation of the iodine molecules, the reaction rate constant k₁ and the ratio k₂/k_-1 can be estimated by plotting the values of [S₂O₈^2?][I^?]/V against that of 1/[I^?]. The extrapolated value for k₁ is 2.20×10^?2 L/mol-sec and k₂/k_-1 is calculated to be 4.25×10² mol/L at 27°C in a solution with an ionic strength of 0.420.     

Linear polymers in nonhomogeneous flow fields. II. The cross-stream migration velocity

The cross-stream migration velocity v _⊥ is that part of the velocity of a particle which has no component in the direction of the undistrubed flow. In order to obtain v _⊥ for bead–spring model macromolecules, it is necessary to compute the trace of the matrix product \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell \cdot \underline {{\rm \hat C}} $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell $\end{document} denotes the migration matrix and \documentclass{article}\pagestyle{empty}\begin{document}$ \underline {{\rm \hat C}} $\end{document} is the modified Kramer's matrix. In this paper this is done via an eigenvalue calculation, where the eigenvalues are estimated by using the Rouse eigenfunctions. The results are then checked against the few known exact results and excellent agreement is found. It turns out that v _⊥ depends on the third power of the molecular weight for free-draining polymers. The dependence upon molecular weight becomes weaker with increasing hydrodynamic interaction until, in the nondraining limit, v _⊥ ∝ M^2.5. A simple yet accurate formula for v _⊥ is proposed. In conjunction with the results for D (of Part I), purely rotational flow fields are shown to be characterized by a single parameter, the particle Peclet number Pe. Up to a constant of order one (actually a function of the hydrodynamic interaction parameters h^* and h, which can vary only between 0.8 and 2.057), Pe depends only upon D, the mean-square equilibrium extension R, and q₀, the magnitude of the maximum shear rate for the flow.     

Origin of the irrational part contained in the angular numerical factors of matrix elements of the Coulomb operator

By means of second quantization formalism and angular momenta coupling techniques, we show the reason why the irrational part of the coefficients of the Slater integrals R^k(ab, cd) in the expression \documentclass{article}\pagestyle{empty}\begin{document}$ (\Psi |\sum\limits_{i < j} {e^2 /r_{ij} |\Psi } ') $\end{document} is common to all values of k, a, b, c, d, and depends only on (Ψ∣ and ∣Ψ′).     

Application of a new structural theory to polymers. I. Uniaxial stress in crosslinked rubbers

A continuum rheological theory, endowed with generalized structural significance, has recently been developed. Based on nonequilibrium thermodynamics, it relates stress σ, strain rate \documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document} and temperature in terms of material evolution through a series of structural states. The theory has previously had success in dealing with crystalline metals and surface physics, and here it is applied to crosslinked rubbery polymers in the nominally amorphous condition. Structure is believed to be related to interchain associations, chain entanglements, chain ends, and other defects in the hypothetical ideal network which by itself would lead to neo-Hookean predictions in uniaxial deformation, σ^nH ∝ λ² — λ^?1, where λ is the stretch ratio. Predictions are made for σ(λ) in both tension and compression and shown to be more compatible with data than either σ^nH(λ) or the Mooney—Rivlin expression σ^MR(λ). Only two parameters are required, moduli G_o (reflecting initial structure) and G_s (the steady-state condition), and rate effects are incorporated through G_o(\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document}) and G_s(\documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document}). The phenomena of yielding and stress softening in cyclic tensile loading are also predicted, suggesting advantages to this approach relative to conventional viscoelastic continuum models.     

Kinetics of the thermal dimerization and isomerization of cis,trans-1,5-cyclooctadiene in the gas phase and of related reactions. A simple algorithm to determine the rate constants of competing first- and second-order reactions

In the gas phase, cis,trans-1,5-cyclooctadiene (\documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 1\limits_\sim} $\end{document}) undergoes a unimolecular rearrangement to cis,cis-1,5-cyclooctadiene (\documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 2\limits_\sim} $\end{document}) and bimolecular formation of dimers \documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 3\limits_\sim}-{\mathop 5\limits_\sim} $\end{document} $\end{document}. The Arrhenius parameters are E_A = 135.7 ± 4.4 kJ mole^?1 and log(A/sec^?1) = 12.9 ± 0.6 for the first reaction and E_A = 66.1 ± 6.0 kJ mole^?1 and log[A/(liter mole^?1 sec^?1)] = 5.5 ± 0.8 for the second reaction. Using thermochemical kinetics, the first reaction is shown to proceed via a rate determining Cope rearrangement of \documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 1\limits_\sim} $\end{document} to cis? 1,2-divinylcyclobutane (\documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 6\limits_\sim} $\end{document}), E_A = 136.2 - 4.4 kJ mole^?1 and log(A/sec^?1) = 13.0 ± 0.6. The corresponding back reaction, \documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 6\limits_\sim}{\rightarrow}{\mathop 1\limits_\sim} $\end{document}, which was investigated separately, shows E_A = 110.2 ± 1.2 kJ mole^?1 and log(A/sec^?1) = 10.9 ± 0.2. The heat of formation of \documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 6\limits_\sim} $\end{document} is determined to 188 ± 5.5 kJ mole^?1. The mechanism of formation of dimers \documentclass{article}\pagestyle{empty}\begin{document}$ {\mathop 3\limits_\sim}-{\mathop 5\limits_\sim} $\end{document} is discussed. To allow the formal analysis of the kinetic problem, a simple algorithm to obtain the rate constants of competing first- and second-order reactions was developed.