Transient and steady rheology of polydisperse entangled melts. Predictions of a kinetic network model and data comparisons

The kinetic network (KN) model discussed previously in the context of monodisperse and bimodal polymer systems is extended to polymers of arbitrary molecular weight distribution. A generalization is proposed for the flow-dependent entanglement loss term in the structure equation, replacing the shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} by a new variable \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \Gamma $\end{document} which reduces to\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} for simple shear and is more appropriate for elongational and other flows. New data are obtained on shear stress transients of many kinds, using a recently developed parallel-plate rheometer. These data and others on steady and transient flows of well-characterized polydisperse polymers in shear and in elongation are used to demonstrate that the KN model predictions are valid. Comparisons with predictions for monodisperse polymers having the same as M _w polydisperse systems show that transient behavior—especially stress overshoot—is particularly sensitive to details of the molecular weight distribution. Further possible improvements in the theory are suggested, and the relationship of the KN model to other recent network models is discussed. The KN model has greater data fitting capabilities, with fewer parameters, than any other model available at present.     

Flow behavior of narrow-distribution polydimethylsiloxane

The flow behavior of α,ω-dihydroxypolydimethylsiloxanes, having a weight-average number-average molecular weight ratio of 1.1–1.2, was studied with a Cannon-Manning viscometer and an Instron rheometer. Comparison of the flow behavior of samples with narrow and broad molecular weight distributions indicated that the onset of non-Newtonian behavior occurred at a much higher shear rate for narrow-distribution polydimethylsiloxanes than for polydisperse polydimethylsiloxanes. A plot of reduced viscosity versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \eta _0 {M \mathord{\left/ {\vphantom {M T}} \right. \kern-\nulldelimiterspace} T} $\end{document} gave two experimental master curves, one for polymer of narrow distribution and the other for polydisperse polymer. The experimental master curve obtained from the narrow-distribution polymer was found to fit the theoretical master curve derived from Graessley's entanglement theory. The viscosity–molecular weight relationship for the higher molecular weight polydimethylsiloxanes was found to be the same for both hydroxydimethylsilyl- and trimethylsilyl-endblocked polymers. However, at low molecular weight, the viscosity–molecular weight curve deviated from linearity because of the association of polydimethylsiloxanols, which apparently is not significant at higher molecular weights. The critical molecular weight of entanglement, M_c, was found to be about 30,000.     

Flow-induced chain fracture of isolated linear macromolecules in solution

The recently developed elongational flow technique is applied to the examination of flow-induced chain rupture of macromolecules in solution. For both closely monodisperse atactic polystyrene (a-PS) and poly(ethylene oxide) (PEO), the critical strain rate for extension (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c $\end{document}) is found to depend upon molecular weight M as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c \simeq M^{ - 1.5} $\end{document}, consistent with ideal Zimm dynamics. When the chains are subjected to strain rates beyond \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f $\end{document} the scission products correspond closely to one-half of the initial molecular weight. The critical fracture stress depends upon molecular weight as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f \simeq M^{ - 2} $\end{document}, enabling the prediction of the ultimate chain length which can be extended without fracture (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c = \dot \varepsilon _f $\end{document}). For a-PS this corresponds to M = 3 × 10⁷. These findings are well accounted for by Stokes' Law applied to an extended bead–rod model. The calculated flow-induced force in the chain corresponds closely to the rupture force of a covalent backbone bond calculated from a modified Arrhenius rate equation. During the prefracture stage (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f > \dot \varepsilon > \dot \varepsilon _c $\end{document}) a-PS shows anomalies in the flow-induced birefringence, which suggest that the Phenyl side groups are becoming reoriented due to the progressive increase in free volume as the chemical backbone bonds stretch and the bond angles open.     

Solution properties of ethylene-vinyl acetate copolymers

High-pressure ethylene–vinyl acetate copolymers of four different chemical compositions(9%, 15%, 45%, and 70% VA) were characterized to determine molecular weight and distribution. The four samples were fractionated by solvent–nonsolvent precipitation methods. Light-scattering, osmometry, and viscosity measurements were made on these fractionated copolymers to determine weight-average molecular weight \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {M_w } $\end{document}, number-average molecular weight \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {M_n } $\end{document}, molecular size in solution, and interaction constants. Dilute solution viscosity was measured on the fractions to determine intrinsic viscosity and Huggins' constant k′. Viscosity–molecular weight equations were established for the four copolymer compositions. The log intrinsic viscosity versus log molecular weight diagrams were analyzed and the average length of branches calculated. The composition of the polymer fractions, determined by C and H combustion analysis, was found not to vary significantly with molecular weight. The uniformly random character of the E/VA copolymers was thereby confirmed. The density of the fractions was determined by density-gradient column method. Chain sequence distribution of monomer units for the four copolymers was calculated by using IBM 704 computations involving the actual monomer reactivity ratios. Long sequences of either ethylene or vinyl acetate are improbable, except at the extremes of copolymer composition.     

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.     

Stereochemical regulation of polypropylenes prepared with various Ziegler-Natta catalysts

The 220-MHz proton magnetic resonance and infrared spectra of stereoregular polypropylenes polymerized with a number of Ziegler-Natta catalysts and isotactic polymers of low molecular weight obtained by thermal degradation of a highly isotactic polypropylene were measured in an attempt to obtain some information on the local regularity. The fraction of thermally degraded polymer soluble in diethyl ether shows stereorandomness (tactie sequence length is quite short), and the portion soluble in n-pentane has stereoblock character. The results so obtained provide strong evidence that racemic dyads of whole polymer consist of two models of racemic dyad isolated and racemic dyads in groups. The polymers prepared with vanadium catalyst systems show stereorandom character and these polymers have \documentclass{article}\pagestyle{empty}\begin{document}$\hbox{-\hskip-1pt-}\hskip-4pt({\rm CH}_2 \rlap{--} )$\end{document} groups formed by two propylene units in a tail-to-tail linkage. Syndiotactic polypropylene has head-to-head and tail-to-tail arrangements of two propylene units and this is the origin of randomness of syndiotacticity.     

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.     

A basis for the determination of branching in polymers by use of gel-permeation chromatography

The technique for determining branching in polymers by using a combination of GPC and intrinsic viscosity data has been extended beyond current methods. Equations used in these analyses are presented. The derivations are based upon the assumption that branching is present only when there is a measurable reduction in the intrinsic viscosity. Techniques for calculating the functionality of the star branch point in starbranched polymers are given. Three random-branching parameters are calculated from a knowledge of the average branching density, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar \lambda $\end{document}: (a) the lowest molecular weight branched polymer that can be measured, M?^*; (b) the average molecular weight between branch points, M?_bp; (c) the weight percentage of polymer that is branched. The applicability of this technique is demonstrated by using an analysis of published data on characterized fractions of a randomly branched polystyrene.     

The Radical Anions and Trianions of 1,8-Diphenylnaphthalene and of Some of its Derivatives Containing a Cyclophane Substructure

The radical anions of 1,8-diphenylnaphthalene ( 1 ) and its decadeuterio-(D₁₀- 1 ) and dimethyl-( 2 ) derivatives, as well as those of [2.0.0] (1,4)benzeno(1,8)naphthaleno(1,4)benzenophane ( 3 ) and its olefinic analogue ( 4 ) have been studied by ESR and ENDOR spectroscopy, At a variance with a previous report, the spin population in \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {2}^{-\kern-4pt {.}} $\end{document} is to a great extent localized in the naphthalene moiety. A similar spin distribution is found for \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {3}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {4}^{-\kern-4pt {.}} $\end{document}. The ground conformations of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document}-\documentclass{article}\pagestyle{empty}\begin{document}$ \rm {4}^{-\kern-4pt {.}} $\end{document} are chiral of C₂ symmetry. For \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document}, an energy barrier between these conformations and the angle of twist about the bonds linking the naphthalene moiety with the phenyl substituents were estimated as ca. 50 kJ/mol and ca. 45°, respectively. The radical trianions of 1 , D₁₀- 1 , and 2 , have also been characterized by their hyperfine data. In \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{3-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {2}^{3-\kern-4pt {.}} $\end{document}, the bulk of the spin population resides in the two benzene rings so that these radical trianions can be regarded as the radical anions of ‘open-chain cyclophanes’ with a fused naphthalene π-system bearing almost two negative charges. The main features of the spin distribution in both \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{3-\kern-4pt {.}} $\end{document} are correctly predicted by an HMO model of 1 .     

Separation of dextrans by gel permeation chromatography

The role of the intrinsic viscosity [η] as separation parameter in gel permeation chromatography (GPC) was studied for dextrans (from Leuconostoc mesenteroids B512) dissolved in water with deactivated silicagel (Porasil) as the column-filling material. For that purpose specific viscosities of dextran fractions eluted by GPC were measured as a function of the elution volume v. Provided that the elution volumes are corrected for zonal spreading, they are related to the intrinsic viscosities in an unambiguous way, probably reflecting a unique relationship between degree of branching and molecular weights. This was further investigated by developing an iteration method to prepare two calibration curves γ(v) and g(v), respectively, relating ln[\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] and InM (M is the molecular weight) to v. It required that the weight-average molecular weight M _w, the number-average molecular weight M _n, and the average intrinsic viscosity [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] for a number of dextran samples (broad distributions) be previously known. The calibration curves found lead to consistent values of the above-mentioned averages. Moreover, they allow-establishment of the [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}]-M relationship over the range 5000 < M < 500,000.     

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.     

Gas phase ion chemistry of methyl acetate,methyl propanoate and their enolic tautomers. An experimental approach

From a combination of isotopic substitution, time-resolved measurements and sequential collision experiments, it was proposed that whereas ionized methyl acetate prior to fragmentation rearranges largely into \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 \mathop {\rm C}\limits^ + ({\rm OH}){\rm O}\mathop {\rm C}\limits^{\rm .} {\rm H}_2 $\end{document}, in contrast, methyl propanoate molecular ions isomerize into \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_2 {\rm CH}_2 \mathop {\rm C}\limits^ + ({\rm OH}){\rm OCH}_3 $\end{document}. Metastably fragmenting methyl acetate molecular ions are known predominantly to form H₂?OH together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}, whereas ionized methyl propanoate largely yields H₃CO˙ together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm CH}_2 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}. The observations were explained in terms of the participation of different distonic molecular ions. The enol form of ionized methyl acetate generates substantially more H₃CO˙ in admixture with H₂?OH than the keto tautomer. This is ascribed to the rearrangement of the enol ion to the keto form being partially rate determining, which results in a wider range of internal energies among metastably fragmenting enol ions. Extensive ab initio calculations at a high level of theory would be required to establish detailed reaction mechanisms.     

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.     

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.     

Stable [C2H7O2]+ isomers: Experimental and theoretical evidence for the existence of protonated peroxides and proton-bound dimers in the gas phase

Evidence is presented for the gas phase generation of at least eight stable isomeric [C₂H₇O₂]⁺ ions. These include energy-rich protonated peroxides (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_2 {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (e), \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm (H)OH} $\end{document} (f) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm (H)CH}_{\rm 3} {\rm (g)),} $\end{document} (g)), proton-bound dimers (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm 3} \cdot \cdot \cdot {\rm OH}_{\rm 2} $\end{document} (h) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH2 = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm + } \cdot \cdot \cdot {\rm HOCH}_{\rm 3} $\end{document} (i)) and hydroxy-protonated species (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 2} {\rm (OH)CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} (a), $\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH(OH)}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (b) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm OCH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (c)). The important points of the present study are (i) that these ions are prevented by high barriers from facile interconversion and (ii) that both electron-impact- and proton-induced gas phase decompositions seem to proceed via multistep reactions, some of which eventually result in the formation of proton-bound dimers.     

Flow-dependent rejection of polystyrene from microporous membranes

Dilute solutions of polystyrene (molecular weight 1 × 10⁵?2 × 10⁷) in a mixed solvent of 90% carbon tetrachloride-10% methanol were filtered through track-etched porous mica membranes. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was measured as a function of polymer size r_s, pore radius r_o, and solvent flow rate q through each pore. Polymer size was characterized by the Stokes-Einstein radius, as determined from diffusion coefficients measured by quasielastic light scattering, and chain relaxation times τ were estimated from measured intrinsic viscosities. In the case of chains whose unperturbed radius was smaller than the pore, σ depended on the ratio r_s/r_o in the manner predicted by a hard-sphere theory, as long as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \tau < < 1 $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q, toward zero at high q. The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r_s > r_o by a single similarity variable \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} \mathord{\left/ {\vphantom {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} {(\dot \gamma \tau)^n}}} \right. \kern-\nulldelimiterspace} {(\dot \gamma \tau)^n}} \sim ({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})^{1 - 3n} q^{- n} $\end{document}; a least-squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.     

Structures and relative energies of gas-phase [C2H7N]+˙ radical cations

Ab initio molecular orbital calculations with split-valence plus polarization basis sets and incorporating electron correlation and zero-point energy corrections have been used to examine possible equilibrium structures on the [C₂H₇N]⁺˙ surface. In addition to the radical cations of ethylamine and dimethylamine, three other isomers were found which have comparable energy, but which have no stable neutral counterparts. These are \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm }, $\end{document} with calculated energies relative to the ethylamine radical cation of ?33, ?28 and 4 kJ mol^?1, respectively. Substantial barriers for rearrangement among the various isomers and significant binding energies with respect to possible fragmentation products are found. The predictions for \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H}_{\rm 3} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3}$\end{document} are consistent with their recent observation in the gas phase. The remaining isomer, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm },$\end{document}is also predicted to be experimentally observable.     

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.