Viscosity of poly(vinyl acetate) and its concentrated solutions

Data on the viscosity of poly(vinyl acetate) (PVOAc) and its concentrated solutions in diethyl phthalate (DEP) and cetyl alcohol (CeOH) are examined over the molecular weight range 8 × 10³ < M < 1.3 × 10⁶, the range 0.15 < φ < 1.0 of the volume fraction φ of polymer, the temperature range 308 to 430°K for PVOAc and its solutions in DEP, and at 396°K in CeOH. The latter is the θ temperature for dilute solutions of PVOAc in CeOH. The data are analyzed with the relation η = KX_c(αφM/M_c)^a exp[1/β(T – T₀)], where a is 1 or 3.4 for αφM less than or greater than a constant M_c, respectively, and X_C, is a constant. The expansion factor α_φ of the chain dimension is found to be essentially unity for φ > ca. 0.25, increasing with decreasing φ for smaller φ. Both β and T₀ depend on φ, and T₀ also depends on M at low M.     

Leading‐order behavior of the correlation energy in the uniform electron gas

We show that, in the high‐density limit, restricted Møller‐Plesset (RMP) perturbation theory yields E = π^?2(1 ? ln 2) ln r_s + O(r) for the correlation energy per electron in the uniform electron gas, where r_s is the Seitz radius. This contradicts an earlier derivation which yielded E = O(ln|ln r_s|). The reason for the discrepancy is explained. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Dilute-solution properties of trans-1,4-polyisoprene

Trans-1,4-polyisoprene was fractionated by both fractional precipitation and preparative gel permeation chromatography to obtain possibly sharp fractions of narrow molecular weight distribution. Selected fractions were characterized by light scattering, viscosity, and gel permeation chromatography. Necessary corrections for molecular heterogeneity were applied. Some of the characteristic relations between [η] and M _w are [η] = 1.81 × 10^?4 M in benzene at 30°C, [η] = 1.38 × 10^?4 M in n-hexane at 30°C, which are found to be in good agreement with literature data when corrected for molecular heterogeneity.     

Inorganic reactions of iodine(III) in acidic solutions and free energy of iodous acid formation

An analysis of the former works devoted to the reactions of I(III) in acidic nonbuffered solutions gives new thermodynamic and kinetic information. At low iodide concentrations, the rate law of the reaction IO + I^? + 2H⁺ ? IO₂H + IOH is k_+B [IO][I^?][H⁺]² – k_?B [IO₂H][IOH] with k_+B = 4.5 × 10³ M^?3s^?1 and k_?B = 240 M^?1s^?1 at 25°C and zero ionic strength. The rate law of the reaction IO₂H + I^? + H⁺ ? 2IOH is k_+C [IO₂H][I^?][H⁺] – k_?C [IOH]² with k_+C = 1.9 × 10¹⁰ M^?2s^?1 and k_?C = 25 M^?1s^?1. These values lead to a Gibbs free energy of IO₂H formation of ?95 kJ mol^?1. The pK_a of iodous acid should be about 6, leading to a Gibbs free energy of IO formation of about ?61 kJ mol^?1. Estimations of the four rate constants at 50°C give, respectively, 1.2 × 10⁴ M^?3s^?1, 590 M^?1s^?1, 2 × 10⁹ M^?2s^?1, and 20 M^?1 s^?1. Mechanisms of these reactions involving the protonation IO₂H + H⁺ ? IO₂H and an explanation of the decrease of the last two rate constants when the temperature increases, are proposed. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 647–652, 2008     

Dynamic mechanical properties of moderately concentrated polystyrene solutions

The storage (G′) and loss (G″) shear moduli have been measured in the frequency range from 0.04 to 630 Hz for solutions of narrow distribution polystyrenes with molecular weights (M) 19,800 to 860,000, and a few of poly(vinyl acetate), M = 240,000. The concentration (c) range was 0.014–0.40 g/ml and the viscosities of the solvents (diethyl phthalate and chlorinated diphenyls) ranged from 0.12 to 70 poise. Data at different temperatures (0–40°C) were combined by the method of reduced variables. Two types of behavior departing from the usual frequency dependence describable by the Rouse-Zimm-Tschoegl theories were observed. First, for M ? 20,000, the ratio (G″ ? ωη_s)/G′ in the neighborhood of ωτ₁ = 1 was abnormally large and the steady-state compliance J was abnormally small, especially at the lowest concentrations studied. Here ω is circular frequency, η_s solvent viscosity, and τ₁ terminal relaxation time. Related anomalies have been observed by others in undiluted polymers at still lower molecular weights. Second, at the highest concentrations and molecular weights, a “crossover” region of the logarithmic frequency scale appeared in which G″ ? ωη_s < G′. The width of this region is a linear function of log c; the frequency dependence under these conditions can be represented by a sequence of Rouse relaxation times grafted on to a sequence of Zimm relaxation times. For each molecular weight, the terminal relaxation time τ₁ was approximately a single function of c for different solvents of widely different η_s. At lower concentrations, τ₁ was close to the Rouse prediction of 6ηM/π²cRT, where η is the steady-flow viscosity; but at higher concentrations, τ₁ was proportional to η/c² and corresponded, according to a recent theory of Graessley, to an average molecular weight of 20,000 between entanglement coupling points in the undiluted polymer.     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.     

Dilute solutions of poly(vinyl alcohol) derived from vinyl trifluoroacetate

The dilute-solution behavior of poly(vinyl alcohol) (PVA_VTFA), derived from vinyl trifluoroacetate, in water-dimethylsulfoxide (DMSO) mixtures was investigated. With solvent mixtures ranging from 10 to 20 vol % DMSO, the relation between the reduced viscosity η_sp/C and the polymer concentration C was linear for polymer concentrations above 0.2 g/dL, whereas in solutions in mixed solvents of other compositions the dependence was linear for polymer concentrations above 0.1 g/dL. The relation between the intrinsic viscosity [η] obtained for aqueous solutions of PVA_VTFA and the molecular weight M estimated from viscosity measurements in solutions of poly(vinyl acetate) (PVA_VTFA), obtained by acetylation of PVA_VTFA, was given by [η] = 7.34 × 10^?4 M^0.63. The value of [η] was greatest for the solvent mixture with 10 vol % DMSO and smallest for about 50 vol % DMSO, and Huggins constants k were smallest and greatest for these two cases, respectively. The turbidity of the solutions of low-molecular-weight PVA_VTFA, was higher than that of high-molecular-weight PVA_VTFA up to 30 vol % DMSO, and the reverse relation held for 40-70 vol % DMSO.     

Lactone polymers. II. Hydrodynamic properties and unperturbed dimensions of poly-ε-caprolactone

Poly-ε-caprolactone prepared by a dibutylzinc-catalyzed bulk polymerization process was fractionated, and the solution properties of the fractions were studied in benzene and in dimethylformamide. In these solvents at 30°C the Mark-Houwink relations were [η] = 9.94 × 10^?5 M and [η] = 1.91 × 10^?4 M , respectively. The value of K_Θ was found to vary from 1.1 to 1.2 × 10^?3 when determined by three known extrapolation techniques. Poly-ε-caprolactone chains appear to be quite flexible in solution, and the steric hindrance parameter σ had the low value of 1.37. Root-mean-square end-to-end dimensions were approximated from the experimental data and calculated from the Debye-Bueche and the Kirkwood-Riseman theories.     

On the resolution of a double determinant

The resolution of a double determinant into a sum of spin-free orthogonal spin eigenfunctions is presented; its equivalent resolution of a spin function product θ^M₀ is also given. Furthermore, a more general resolution of a Slater determinant into all spin eigenfunctions with S ≥ M is also obtained. Present work has also provided a method to calculate the linear coefficients in the expression of the primitive θ^M_i in terms of the linear combination of spin eigenfunctions X? (S, M).     

Rheological studies of moderately concentrated polystyrene solutions. I. A new method for the extrapolation of the zero-shear viscosity

Measurements of the viscosity coefficient η of solutions of polystyrene (M_w = 6.0 × 10⁵ and 1.77 × 10⁶) in trans-decalin (TD, θ solvent) and toluene (TL, good solvent) as function of shear rate (11?10⁴ s^?1), concentration (4.24?11.21 wt %), and temperature (10–50°C) are reported. As a new theoretically grounded method for the determination of the zero-shear viscosity η₀ it is proposed to plot η as a function of $\left({\eta \dot \gamma} \right)^3$. The intercepts of the straight lines obtained by this procedure give η₀ in good agreement with directly measured values.     

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.     

Entanglement friction and dynamics in blends of starlike and linear polymer molecules

We investigate relaxation dynamics in a series of six‐arm star/linear 1,4‐polybutadiene blends with mechanical rheometry measurements. Blend systems are formulated to systematically probe constraint release and arm relaxation dynamics. Zero shear viscosity and terminal relaxation times of star/linear polymer blends with fixed star arm molecular weights (M_a) and compositions (?_S) are found to follow nonmonotonic dependencies on the linear polymer molecular weight (M_L). At low values of ?_S, at least two scaling regimes are apparent from the data (ξ₀ ～ M and ξ₀ ～ M), where ξ₀ refers to the zero shear viscosity or terminal relaxation time of the blend. The two regimes are separated by a critical linear polymer molecular weight M^* that is more than 20 times larger than the critical molecular weight for entanglements. When the linear polymer contribution to blend properties is removed, a clear transition from dilution dynamics, ξ₀ ～ M, to Rouse‐like constraint‐release dynamics, ξ₀ ～ M, is apparent at low values of ?_S. At higher ?_S values, a new activated constraint‐release dynamic regime is evident in which ξ₀ ～ M and ξ₀ ～ ?, where α changes continuously from approximately 2 to 0.5 as ?_S increases and β varies from 2.0 to 1.0 as M_L increases. The experimental results are compared with theoretical predictions based on a drag coupling model for entangled polymer liquids. All features observed experimentally are captured by this model, including the value of M^* for the transition from dilution to Rouse constraint‐release dynamics. Predictions of the drag coupling model are also compared with published data for the zero shear viscosity and terminal relaxation time in bidisperse linear polymer blends and pure entangled starlike molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2501–2518, 2001     

Über hexagonale Perowskite mit Kationenfehlstellen. XXXI. Die Systeme BaO?Re2O7?MO5 mit MV = Nb,Ta

On Hexagonal Perovskites with Cationic Vacancies. XXXI. Systems BaO? Re₂O₇? M O₅ with M^V = Nb, Ta In the systems BaO? Re₂O₇? MO₅ three quaternary oxides are formed, which belong to the perovskite stacking polytypes with cationic vacancies: Ba₈Re_7/2M□₃O₂₄ (M^V = Nb, Ta; rhombohedral 24 L type; sequence (hhhhchhc)₃; space group R3 m), Ba₄Re_9/8Ta_13/8□_5/4O₁₂ (rhombohedral 12 L type; sequence (hhcc)₃; space group R3 m) and the phases Ba₅BaRe_3/2?xM □O_15?x□_x (M^V = Nb, Ta; variants of a hexagonal 5 L type).     

Rheology of polystyrene solutions around the coil overlapping concentration: A phenomenological description of stresses in simple shear flow

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τ_RZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τ_L > τ_RZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ₁) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ²)^?1/2, where γ is the magnitude of shear. Contributions to η and Ψ₁ from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τ_st = τ + (τ_RZ ? τ)/(1 + 0.35τ_RZ γ˙) instead of τ_RZ. Here, γ˙ is the rate of shear, and τ is the τ_RZ value at the infinite dilution limit. η and Ψ₁ at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol^?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002     

Strong nonadiabatic effects in reactions of photoisomerization

Reactions of photoisomerization proceeding through a “funnel” are discussed (Fig. 1a, θ ? θ*, where θ is the angle of isomerization). Strong nonadiabatic interactions in the region of conical intersection of the multidimensional adiabatic potentials U_s and U_s0 are supposed to be responsible for the ultrafast nonradiative transition S → K₂ S₀ (K₂ ? 10¹⁰-10¹² s^?1). The K₂ dependence on the solvent viscosity (isomerization of t-stilbene in series ethanol--octanol) and polarity (isomerization of cyanine dyes in polar solvents) was determined to be in a good agreement with experiments.     

Syndiospecific polymerization of styrene. II. Monocyclopentadienyltributoxy titanium/methylaluminoxane catalyst

Syndiospecific polymerization of styrene was catalyzed by monocyclopentadienyltributoxy titanium/methylaluminoxane [CpTi (OBu)₃/MAO]. The atactic and syndiotactic polystyrenes were separated by extracting the former with refluxing 2-butanone. The activity and syndiospecificity of the catalyst were affected by changes in catalyst concentration and composition, polymerization temperature, and monomer concentration. Extremely high activity of 5 × 10⁷ g PS (mol Ti mol S h)^?1 with 99% yield of the syndiotactic product were achieved. The concentration of active species, [C^*], has been determined by radiolabeling. The amount of the syndiospecific and nonspecific catalytic species, [C] and [C] respectively, correspond to 79 and 13% of the CpTi(OBu)₃. The rate constants of propagation for C and C at 45°C are 10.8 and 2.0 (M s)^?1, respectively, the corresponding rate constants for chain transfer to MAO are 6.2 × 10^?4 and 4.3 × 10^?4s^?1. There was no deactivation of the catalytic species during a batch polymerization. The rate constant of chain transfer with monomer is 6.7 × 10^?2 (M s)^?1; the spontaneous β-hydride transfer rate constant is 4.7 × 10^?2 s^?1. The polymerization activity and stereospecificity of the catalyst are highest at 45°C, both decreasing with either higher or lower temperature. The stereoregular polymer have broad MW distributions, M?_w/M?_n = 2.8–5.7, and up to three crystalline modifications. The T_m of the s-PS polymerized at 0–90°C decreased from 261.8 to 241°C indicating thermally activated monomer insertion errors. The styrene polymerization behaviors were essentially insensitive to the dielectric constant of the medium.     

Fractionation and characterization of a protein–polysaccharide complex from Pleurotus tuberregium sclerotia

A water‐soluble sample (TM4b), extracted from sclerotia of Pleurotus tuberregium, was analyzed using elemental analysis, one‐ and two‐dimensional ¹H and ¹³C NMR. The results indicated that TM4b was protein–polysaccharide complex, and the polysaccharide moiety was hyperbranched β‐D ‐glucan with residuals branched at C3, C2, C4, and C6 positions. A preparative size‐exclusion chromatography (SEC) column combined with nonsolvent addition method was used to fractionate TM4b, and nine fractions were obtained. Solution properties of TM4b in 0.15 M aqueous NaCl were studied using static laser light scattering and viscometry at 25 °C. The dependences of intrinsic viscosity ([η]) and radius of gyration (〈S²〉) on weight–average molecular weight (M_w) for TM4b in the M_w range from 1.89 × 10⁴ to 2.58 × 10⁶ were found to be [η] = 0.21M and 〈S²〉 = 3.63M. It indicated that TM4b existed as compact sphere conformation in the aqueous solution. Atomic force microscopy image further confirmed that the TM4b molecules exhibited globular shape in the solution. This work gave valuable information on fractionation and chain conformation characterization of the globular protein–polysaccharide complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2546–2554, 2007     

Schwingungsspektren der Clusterverbindungen (M6X)X · 8 H2O,M = Nb,Ta; Xi = CI,Br; Xa = CI,Br, I

Vibrational Spectra of the Cluster Compounds (M₆X₁₂ⁱ) · 8H₂O, M = Nb, Ta; Xⁱ = Cl, Br; X^a = Cl, Br, I IR and, for the first time, Raman spectra at 80 K of the cluster compounds (M₆X)X · 8H₂O; M = Nb, Ta; Xⁱ = Cl, Br; X^a = Cl, Br, I, have been recorded, characterized by typical frequencies of the (M₆X) unit, which are only slightly influenced by the terminal X^a ligands. The most intense line with the depolarisation ≈? 0.2 in all Raman spectra is caused by inphase movement of all atoms and assigned to the symmetric metal-metal vibration v₁, observed for the clusters (Nb₆Cl) at 233–234, for (Nb₆Br) at 186–187, for (Ta₆Cl) at 199–203, and for (Ta₆Br) at 176–179 cm^?1. The IR spectra exhibit in the same series intense bands at 233, 204, 207, and 179 cm^?1, assigned to the antisymmetric metal-metal vibration. The metal-metal frequencies are significantly higher than discussed before. The tantalum clusters show on excitation with the krypton line 647.1 nm in the region of a d–d transition at 645 nm a resonance Raman effect with series of overtones and combination bands. In case of (Ta₆Br) another polarisized band is observed at 229 cm^?1 and assigned to the Ta? Brⁱ vibration v₂. From the progressions of v₁ and v₂ anharmonicity constants of about ?3 cm^?1 are calculated indicating a strong distortion of the potential curves.     

Magnesium chloride supported high mileage catalysts for olefin (decene-l) polymerization XIV. Propagation and chain transfer

Decene-l was polymerized with the MgCl₂/ethylebenzoate/p-cresol/AIEt₃/TiCl₄-AlEt₃/methyl-p-toluate catalyst at 50° using an A/T ratio of 167 and a range of monomer concentration. The concentration of the two kinds of active sites are [Ti] = 12% and [Ti] = 4% of the total titanium. The rate constants of propagation are 24 M^?1 s^?1. Chain transfers to AIEt₃, monomer, and by β-hydride elimination have rate constant values of 1.7 × 10^?3 M^?1 s^?1, 1.34 × 10^?2 M^?1 s^?1, and 1.7 × 10^?2 s^?1, respectively. Poly(decene-l) have relatively narrow MW which are unchanged during the course of a polymerization. Therefore, the active site concentrations in the CW catalyst for propylene and decene polymerization are identical and their rate constant values agree within a factor of 2. However, the rate of decene polymerization depends on fractional order of monomer concentration and decreases with the increase of activator concentration. Furthermore, the formation of metal polymer bonds has a rate independent of these concentrations. These kinetic behaviors are a manifestation of absorption processes of these species which are not seen in propylene polymerizations.