Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

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.     

Bimolecular self-reactions of 2-arylindandione- 1,3-yl radicals studied by flash photolysis

Kinetic and thermodynamic data for reaction (1) of certain C-centered aromatic radicals (referred to in this paper by the numbers I to X) in chlorobenzene: have been obtained. The k₁ values of radicals varied between (1.1 ± 0.2) × 10⁶M^?1·sec^?1 (radical VIII) and (3.6 ± 0.7) × 10⁹M^?1 sec^?1 (radical VI) at 20°C. An investigation of the relationship between the recombination rates of radicals I–VIII and X and the solvent viscosity (mixture of toluene and dibutylphthalate, 0.6 < η < 18.4 cP) has shown that the recombination reactions involving radicals I–IV are limited by diffusion in solvents having a viscosity η> 10 cP and are activation reactions in solvents having a viscosity η < 10 cP. The recombination of radicals VIII and IX is an activation reaction, while that of radicals V–VII is diffusion-controlled in the entire viscosity range. The recombination of radical X is limited, in the viscosity range of 18.4 to 2 cP, by intrusion into the first coordination sphere of the partner, the effect of viscosity on the radical X recombination rate in the specified range being the same as its effect on diffusion-controlled reactions. The possible reasons of the discrepancies between the experimental fast recombination rate constants and the theoretical values calculated by the Debye–Smoluchowski theory are discussed. The equilibrium constant depends strongly on the nature of the substituent in the phenyl fragment: the substituents which increase unpaired electron delocalization in the radical intensify the dissociation of the respective dimer. Long-wave absorption bands have been recorded for radicals I–X and their extinction coefficients obtained. Dimers I–V are thermo- and photochromic compounds.     

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.     

Properties of amorphous and crystallizable hydrocarbon polymers. II. Rheology of linear and star-branched polybutadiene

Some results are reported on the linear viscoelastic properties of polybutadienes with narrow-molecular-weight distributions. The zero shear viscosity η₀ varies as M^3.4 in the linear samples, and viscosity enhancement is found in star-branched samples with long arms, in good agreement with results reported earlier by Kraus and Gruver. The temperature coefficient of viscosity appears to be slightly larger in stars when the arms become long. The steady state recoverable compliance J is 2.1 × 10 ^?7 cm²/dyn in linear samples of high molecular weight, but it increases to values as much as 10 times larger in the stars. The plateau modulus G, obtained from a composite curve for the linear samples, is 1.32 × 10⁷ dyn/cm². The terminal relaxation spectrum of the stars is too broad to allow an evaluation of plateau modulus.     

Fluorescence polarization anisotropy and kinetics of malachite green measured as a function of solvent viscosity

The fluorescence kinetics and polarization anisotropy of the triphenylmethane dye malachite green were measured as a function of solvent viscosity. The relationshp between the relaxation kinetics and the solvent viscosity was investigated in order to obtain information on the effect of enviromnental changes on the orientational order of dye molecules in solution. It was found that the fluorescence lifetimes follow an η^{$\text{2}\text{3}$} dependence for 1 < η < 60 P, η^{$\text{1}\text{2}$} dependence for 60 P < η < 1000 P and approach a constant for η > 1000 P. The dependence of the fluorescence decay rates on the solvent viscosity was fit to k = 5 × 10¹⁰η^{?$\text{2}\text{3}$} + 5 × 10⁸ s^?1. The fluorescence polarization anisotropy term, R(0), was also measured as a function of solvent viscosity. A marked decrease in R(0) was observed at a viscosity of 1000 P. For η < 1000 P, R(0) was found to be close to the expected value for a random distribution of molecules, 0.4; and for η > 3000 P, R(0) was measured to be ≈0.11. This small value of R(0) may indicate a nonrand The observed change of the polarization anisotropy with increasing viscosity indicates that the dye molecules become ordered at higher viscosities. This may arise through the formation of a long range order due to lack of rotational deexcitation of the malachite green dye molecules at high viscosities.     

Thermoplastic urethane elastomers. VI. Dilute solution properties in various solvents

A thermoplastic urethane elastomer prepared from a polycaprolactone diol, 4,4′-diphenylmethane diisocyanate, and 1,5-pentanediol was fractionated and the solution properties of the fractions were characterized in terms of viscosity and sedimentation. Mark-Houwink relations were established for data obtained at 30° in various solvents: In dimethylacetamide, tetramethylurea, and N-methyl pyrrolidone, the value of K_θ increased systematically in the range (1.7 to 2.0) × 10^?3. Lower values of K_θ were obtained in dimethylformamide (0.8 × 10^?3) and meta-cresol (0.9 × 10^?3). The molecular expansion coefficients in the various solvents were approximated from the experimental viscosity data. Short-range interactions between the solvent molecules and polymer chains are suggested as possible causes for differences in the hydrodynamic parameters.     

Moderately concentrated solutions of polystyrene. I. Viscosity as a function of concentration,temperature, and molecular weight

Data on the viscosity η of moderately concentrated solutions of polystyrene are reported. Several solvents were investigated, including cyclopentane solutions over a temperature span between θ_U = 19.5°C and θ_L = 154.5°C. The data were analyzed in terms of a relation giving η as a function of αφM, where α_φ is the expansion factor for the chain dimensions in a solution with volume fraction φ of polymer with molecular weight M. It is shown that values of α_φ so determined decrease as ? lnα_φ/? lnφ = (1 ? 2μ)/6μ for φ greater than φ^* = 0.2M/s³ for moderately concentrated solutions, where s is the root-mean-square radius of gyration and μ = ? ln[η]/? lnM with [η] the intrinsic viscosity.     

VLPR study of the reaction Br + CH3CHO

The reaction \documentclass{article}\pagestyle{empty}\begin{document}${\rm Br} + {\rm CH}_3 {\rm CHO}\buildrel1\over\rightarrow{\rm HBr} + {\rm CH}_3 {\rm CO}$\end{document} has been studied by VLPR at 300 K. We find k₁ = 2.1 × 10¹² cm³/mol s in excellent agreement with independent measurements from photolysis studies. Combining this value with known thermodynamic data gives k_-1 = 1 × 10¹⁰ cm³/mol s. Observations of mass 42 expected from ketene suggest a rapid secondary reaction: in which step 2 is shown to be rate limiting under VLPR conditions and k₂ is estimated at 10^12.6 cm³/mol s from recent theoretical models for radical recombination. It is also shown that 0 ? E₁ ? 1.4 kcal/mol using theoretical models for calculation of A₁ and is probably closer to the lower limit. Reaction ?1 is negligible under conditions used.     

Properties of amorphous and crystallizable hydrocarbon polymers. I. Melt rheology of fractions of linear polyethylene

The dynamic moduli G′(ω) and G″(ω) for two groups of linear polyethylene fractions (reported M _w/M _n < 1.2) were measured in the melt state using the eccentric rotating disk method. Values of zero shear viscosity η₀ were obtained and compared with published results on similar fractions. Molecular weight data were converted to a common basis through intrinsic viscosities in trichlorobenzene (TCB) at 135°C. With recent data on M _w (light scattering) vs. [η]_TCB, for linear polyethylene, the relationship at 190°C, η₀ = 3.40 × 10^?14(M _w)^3.60, was obtained. The flow activation energy E_a was 6.4 kcal (T = 140–195°C). The plateau modulus G at 190°C was determined from the area under the loss modulus peak in one high-molecular-weight sample. The value obtained, G = 1.5₈ × 10⁷ dyn/cm², corresponds to an apparent molecular weight between entanglements of 1850. The storage compliance J′(ω) becomes anomalously large at low frequencies. The recoverable compliance J could not be determined for any of the fractions.     

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.     

Anionic polymerization of 4-methyl-2-oxetanone (β-butyrolactone)

Polymerization of 4-methyl-2-oxetanone ( 1 ) initiated with potassium acetate-dibenzo-18-crown-6 complex ( 2 ) in THF as solvent, was studied. Transfer reactions, leading to both crotonate anions and carboxylic acid formation, have been observed. Two kinetic effects of these reactions, hampering the living polymerization, have been established. The first results from reinitiation with the crotonate anions and thereby lowers the polymer molecular weight. The second is the decrease in the overall polymerization rate due to complexation of the growing carboxylate anions with carboxylic acid moieties. Kinetic scheme of polymerization involves propagation accompanied by transfer followed by slow reinitiation. This scheme, including complexation of the active species has been solved numerically. The apparent rate and equilibrium constants (k_p, k_tr, k_ri, and K_ass and respectively) have been determined. Although these kinetic parameters depend strongly on the polymerization conditions, but the ratio of the rate constants k_p : k_t : k_ri is fairly constant and equal to 10⁻⁴ : 10⁻⁶ : 10⁻⁶, respectively (at 20°C). Conditions of the controlled anionic synthesis of the amorphous poly(4-methyl-2-oxetanone) with $\bar M_n$ as high as 1.7 × 10⁴ and ${{ \le \bar M_n } \mathord{\left/ {\vphantom {{ \le \bar M_n } {\bar M_n }}} \right. \kern-\nulldelimiterspace} {\bar M_n }} \le 1.20$ have also been elaborated.     

Vapor-liquid equilibria for polyisobutylene solutions

Vapor sorption isotherms in binary solutions of polyisobutylene (PIB), (M_η = 4.7 × 10⁶ g/mol) in hydrocarbons (cyclopentane; cyclohexane; n-heptane; 2,2-dimethyl butane; and 2,2,4-trimethyl pentane) and chlorinated methanes [carbon tetrachloride (CCI₄) and chloroform (CHCI₃)] have been determined at 23.5°C using the piezoelectric sorption method. The polymer-solvent interaction parameter χ obtained agrees with previously published values determined by using gas-liquid chromatography and a quartz-helix vapor sorption apparatus. The Flory theory of corresponding-states has been applied to the experimental results through the χ parameter and affords a good prediction of the concentration dependence of χ for solutions of chloroform, carbon tetrachloride, n-heptane, and 2,2-dimethyl butane in PIB. The experimental values of \documentclass{article}\pagestyle{empty}\begin{document}$ [\partial (a_1 /\psi _1 )/\partial a_1 ]_{T,P} $\end{document} for the PIB solutions are constant over the measured concentration range, for example \documentclass{article}\pagestyle{empty}\begin{document}$ [\partial (a_1 /\psi _1 )/\partial a_1 ]_{T,P} $\end{document} = ?4.1 for CCI₄, ?3.65 for CHCI₃, ?3.0 for 2,2-dimethyl butane and n-heptane, ?2.7 for 2,2,4-trimethyl pentane, ?2.7 for cyclohexane, and ?1.7 for cyclopentane, where a₁ is the solvent activity and ψ₁ is the solvent segment fraction. The correlations between the values of \documentclass{article}\pagestyle{empty}\begin{document}$ [\partial (a_1 /\psi _1 )/\partial a_1 ]_{T,P} $\end{document} and the theories of Guggenheim, Miller, Huggins, and Flory 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.     

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.     

Nonisothermal kinetic analysis of the chemiluminescence from tetramethyl-1,2-dioxetane

A computerized method is given for the evaluation of Arrhenius parameters which describe the chemiluminescent decomposition of tetramethyl-1,2-dioxetane. The parameters were determined in several solvents by linear regression methods and the equation ln ln \documentclass{article}\pagestyle{empty}\begin{document}$ [(\sum\nolimits_0^\infty I - \sum\nolimits_0^t I)/(\sum\nolimits_0^\infty I - \sum\nolimits_0^t I - \sum\nolimits_0^{t + \Delta t} I)] = \ln\, (A_1 \Delta t) - E_1 /RT$\end{document}, where I refers to photons counted by increments of Δt, and E₁ and A are the first-order Arrhenius parameters. The average of E₁ and log A₁ (s^?1) from this method from six runs in CCl₄ with initial concentrations of 4.9 × 10^?5-8.45 × 10^?4M were 27.21 ± 0.88 kcal/mol (113.7 ± 3.7 kJ/mol) and 13.88 ± 0.50, respectively. Simulated curves of chemiluminescence versus time were obtained with the use of a computer program and an auxiliary plotter.     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

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      

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}.