Contribution of Polymer‐Solvent Interactions to Dynamics of Linear Polymers in Dilute Solutions

In this work a theoretical approach to dynamics of linear vinyl polymers in dilute solutions of high viscosity solvents is presented. The calculations for the relaxation time spectra, polymer intrinsic viscosity [η (ω)], complex elastic modulus G*(ω), total intrinsic viscosity [η^T (ω)] and specific heat capacity C (ω) were carried out in the non‐free‐draining limits. The relaxation time spectrum calculated for dynamics of low frequency modes exhibits a Rouse‐like character. Its position and shape corresponds to the ultrasonic relaxation time spectrum observed in the system at 10⁶ Hz. On the other hand, the relaxation time spectrum associated with moderate frequency mode dynamics is narrower and typical for ultrasonic relaxation observed at 10⁷ Hz. The polymer intrinsic viscosity [η (ω)] and elastic modulus G*(ω) are shown to be represented by the model within a low‐frequency range. In turn, the specific heat capacity C (ω) is displayed as a representation of the model in the acoustic region mentioned above. In the high‐frequency range the dynamics is described by the total intrinsic viscosity [η^T (ω)] tending to a plateau where the value is equal to the sum of the single‐bead intrinsic viscosity [η_N] and effective solvent viscosity [η_eff].     

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.     

二元无机物标准熵 So298的拓扑研究

为了预测二元无机物的标准熵,基于分子图的连接矩阵和离子参数gi、qi,提出了一种新的连接性指数mQ, mG及其逆指数mQ’, mG’。 qi、gi定义为：qi=(1.1+Zi1.1) /(1.7+ni), gi=(1.4+Zi) /(0.9+ri+ri-1),其中Zi 、ni和 ri分别代表离子i的电荷数、最外层主量子数和半径。从0Q, 0Q’, 1G,和1G’,利用多元线性回归分析方法和人工神经网络方法,可以构建优良的QSPR模型。对371个二元无机物,其多元线性模型及神经网络模型的相关系数、标准偏差和平均绝对偏差分别是：0.9905, 8.29 J.K-1.mol-1, 6.48 J. K-1.mol-1, 0.9960, 5.37 J.K-1.mol-1 和 3.90 J.K-1.mol-1。留一法交叉验证表明,其多元线性模型具有良好的稳定性。两个模型对187个未进入模型的二元无机物的标准熵的预测值和实验值之间的相关系数、标准偏差和平均绝对偏差分别是：0.9897, 8.64 J. K-1.mol-1, 6.84 J. K-1.mol-1, 0.9957, 5.63 J.K-1.mol-1, 和 4.18 J.K-1.mol-1。研究表明,本文方法在预测二元无机物标准熵时比文献方法更有效,两种模型均能较精确的预测二元无机物的标准熵,且神经网络模型的预测结果更精确。     

Electric birefringence and conformation of polychlorohexylisocyanate in solutions

Electric birefringence was investigated for solutions of polychlorohexylisocyanate fractions for molecular weights 30·6 × 10⁴–1·2 × 10⁴ in tetrachloromethane.Experimentally found dispersion of the Kerr effect is used for estimating the coefficients of rotatory diffusion D_r of molecules. A comparison of rotatory diffusion D_r values with molecular weights M and intrinsic viscosities [η] of fractions shows that the value of D_rM[η] decreases with M. This illustrates the change in the conformation of molecules from a random coil to a rod.On the basis of experimental dependences of D_r and the Kerr constants K on M, the main structural parameters of the polymer investigated were determined: the number of monomer units in a segment, the projection of the length of the monomer unit on the axis of the molecule, the value of the dipole moment μ₀ of the monomer unit and the angle formed by μ₀ and the chain direction.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

The Regioselective Methylation of Polycyclic Aromatic Hydrocarbons through Tricarbonylchromium Coordination

Deprotonation, methylation, and air oxidation of polycyclic arenes coordinated to chromium(0), (η⁶-arene)Cr(CO)₃, produced ring-methylated products with high selectivity and in good yield. This procedure gave 3-methylbenz[a]anthracene from (η⁶-benz[a]anthracene)Cr(CO)₃, 3-methylphenanthrene from (η⁶-phenanthrene)Cr(CO)₃, 2-acetyl-6-methylphenanthrene from (η^6?2-acetylphenanthrene)Cr(CO)₃, and 3,7,12-trimethylbenz[a]anthracene from (η^6?7,12-dimethylbenz[a]anthracene)Cr(CO)₃.     

Ensemble evaluation of polydisperse nanocellulose dimensions: rheology,electron microscopy,X-ray scattering and turbidimetry

Six types of CNCs with different sizes were prepared from tunicins by sulfuric acid hydrolysis and subsequent sonication in water. The size distributions of CNCs were comprehensively evaluated by turbidimetry, small angle X-ray scattering, and microscopy to predict their intrinsic viscosities. Experimental intrinsic viscosities [η] of the CNC dispersions were evaluated by shear viscosity measurement, and then compared with their theoretical [η] values based on theories for rotational motions of rigid rods. The experimental [η] values for the straight CNCs were in good agreement with their theoretical [η] values, irrespective of the size and distributions. On the other hand, the experimental [η] value of the kinked CNC was higher than the theoretical [η] value, in agreement with a theoretical calculation giving higher intrinsic viscosities for bent fibers.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Mono and Bimetallic Complexes of Molybdenum(ii) and Tungsten(ii) Containing 4,4′-Diphenylenecarbonitrile

The complexes [MI₂(CO)₃(NCMe)₂] (M=Mo or W) react in CH₂Cl₂ at room temperature with two equivalents of 4,4'-diphenylenecarbonitrile (dpc) to afford the new seven-coordinate complexes, [MI₂(CO)₃(4,4'-dpc-N)₂] (1 and 2) in good yield. Equimolar quantities of [MI₂(CO)₃(NCMe)₂] and PPh₃ give [MI₂(CO)₃(NCMe)(PPh₃)], which react in situ with 4,4'-dpc to yield the mono-4,4'-diphenylenecarbonitrile complexes, [MI₂(CO)₃(4,4'-dpc-N)(PPh₃)] (3 and 4). Treatment of the bis(alkyne) complexes, [WI₂(CO)(NCMe)(η ²-RC₂R)₂] (R=Me and Ph) with one equivalent of 4,4'-dpc in CH₂Cl₂ at room temperature affords the acetonitrile displaced products, [WI₂(CO)(4,4'-dpc-N)(η ²-RC₂R)₂] (5 and 6). Reaction of equimolar quantities of [WI₂(CO)(NCMe)(η ²-PhC₂Ph)₂] and 2 in CH₂Cl₂ at room temperature gives the 4,4'-dpc-bridged complex, [WI₂(CO){WI₂(CO)₃(4,4'-dpc-N)(4,4'-dpc- N,N')}(η ²-PhC₂Ph)₂] (7) in good yield. Similarly, equimolar amounts of [WI₂(CO)(NCMe)(η ²-RC₂R)₂] (R=Me and Ph) and (4) react in CH₂Cl₂ to afford the bimetallic complexes, [WI₂(CO){WI₂(CO)(4,4'-dpc-N,N')(PPh₃)}(η ²-RC₂R)₂] (8 and 9). The new bimetallic 4,4'-dpc-bridged alkyne complexes, [WI₂(CO){WI₂(CO)(4,4'-dpc-N,N')(η ²-MeC₂Me)₂}(η ²-MeC₂Me)₂] [(10), [WI₂(CO){WI₂(CO)(4,4'-dpc-N,N')(η ²-PhC₂Ph)₂}(η ²-PhC₂Ph)₂] (11) and [WI₂(CO){WI₂(CO)(4,4'-dpc-N,N')(η ²-MeC₂Me)₂}(η ²-PhC₂Ph)₂] (12) are also described.     

Cationic Functionalisation by Phosphenium Ion Insertion

The reaction of [Cp′′′Ni(η³-P₃)] ( 1 ) with in situ generated phosphenium ions [RR′P]⁺ yields the unprecedented polyphosphorus cations of the type [Cp′′′Ni(η³-P₄R₂)][X] (R=Ph ( 2 a ), Mes ( 2 b ), Cy ( 2 c ), 2,2′-biphen ( 2 d ), Me ( 2 e ); [X]⁻=[OTf]⁻, [SbF₆]⁻, [GaCl₄]⁻, [BAr^F]⁻, [TEF]⁻) and [Cp′′′Ni(η³-P₄RCl)][TEF] (R=Ph ( 2 f ), tBu ( 2 g )). In the reaction of 1 with [Br₂P]⁺, an analogous compound is observed only as an intermediate and the final product is an unexpected dinuclear complex [{Cp′′′Ni}₂(μ,η³:η¹:η¹-P₄Br₃)][TEF] ( 3 a ). A similar product [{Cp′′′Ni}₂(μ,η³:η¹:η¹-P₄(2,2′-biphen)Cl)][GaCl₄] ( 3 b ) is obtained, when 2 d [GaCl₄] is kept in solution for prolonged times. Although the central structural motif of 2 a – g consists of a “butterfly-like” folded P₄ ring attached to a {Cp′′′Ni} fragment, the structures of 3 a and 3 b exhibit a unique asymmetrically substituted and distorted P₄ chain stabilised by two {Cp′′′Ni} fragments. Additional DFT calculations shed light on the reaction pathway for the formation of 2 a – 2 g and the bonding situation in 3 a .     

Polyelectrolytes Revisited: Reliable Determination of Intrinsic Viscosities

The linear extrapolation of (η − η₀)/(η₀c) towards c → 0 constitutes the basis of traditional methods to determine intrinsic viscosities [η], where η is the viscosity of polymer solutions of concentration c and η₀ is the viscosity of the pure solvent. With uncharged macromolecules this procedure works well; for polyelectrolytes it fails because of the pronounced non‐linearity of the above dependence at high dilution resulting from the increasing electrostatic interactions. This contribution presents a new method for the determination of [η]. It rests upon the application of the laws of phenomenological thermodynamics to the viscosity of polymer solutions and introduces a generalized intrinsic viscosity enabling a comparison of differently charged and uncharged polymers.

     

Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity

In order to explain the observed nonvanishing limiting value of dynamic intrinsic viscosity of polymer solutions at ω = ∞ one has considered the necklace model with finite resistance to the rate of coil deformation introduced long ago by Cerf for the study of gradient dependence of intrinsic viscosity and streaming birefringence. The calculation need not take into account change of hydrodynamic interaction as a consequence of coil deformation because the experimental data are always either obtained at very low gradient or extrapolated to zero gradient so that in the experiment the macromolecule has the same conformation as in the solution at rest. The model indeed yields a finite [η]′_{ω = ∞} in good agreement with experiments on polystyrene in Aroclor. According to the theory [η]′_{ω = ∞}/[η]₀ decreases with increasing molecular weight as M^?1 and M^?1/2 for the free-draining and impermeable coil, respectively. The absolute limiting value [η]_∞′, therefore turns out to be nearly independent of M, at least for small values of internal viscosity. From the observed value [η]_∞′/[η₀] one can obtain the coefficient of internal viscosity of the macromolecule. The value for polystyrene in Aroclor calculated from dynamic experiments on rather concentrated solutions is close to that derived by Cerf from streaming birefringence observations of polystyrene in a series of solvents of widely differing viscosity.     

Molecular dimensions of polydipropylsiloxamer

The molecular dimensions of polydipropylsiloxamer were studied by intrinsic viscosity measurements in toluene and in 2-pentanone. The relationships between the molecualr weight and the intrinsic viscosity were found to be: [η]_25°C., toluene = 4.35 × 10^?4 M^0.58; [η]_θ(10°C.), toluene = 1.09 × 10^?3 M^0.5; [η]_θ(76°C.), 2-pentanone = 8.71 × 10^?4 M^0.5. This held reasonably well for molecular weights from 25,000 to 3000,000. The root-mean-square end-to-end length ratio, (r₀² /M)^1/2 as calculated from the constant K, exceeds the free rotation value by approximately 100%. The disparity is greater than that found with polydimethylsiloxamer, indicating a lower degree of flexibility for the polydipropylsiloxamer. This is largely due to the short range steric interaction between near neighboring units of the chain. Gel permeation chromatography was also employed to demonstrate the lower degree of flexibility for polydipropylsiloxamer as compared with polydimethylsiloxamer.     

Ein beitrag zur strukturviskosität von polyisobutylen in verdünnter lösung

The viscosities of dilute solutions of polyisobutylene were measured as function of concentration and rate of shear (0–2500 sec^?1). For computing intrinsic viscosity, the Huggins relation was chosen. For the Huggins constant k_Hu, as a function of the hydrodynamic expansion coefficient α_η³ using the theoretical relation of Imai at the theta point, a value of 0·63 was obtained. The corresponding Hellers constant was found to be 0·50 in agreement with the value reported by Bohdanecký. The plot of relative intrinsic viscosity [η]_q/[η]_O against M[η]_Oη_sq/RT for polyisobutylene in cyclohexane, n-heptane and toluene at 25° and in benzene at 24° indicates, by shifting the M[η]_Oη_sq/RT axis, that the deformable polyisobutylene molecule behaves as expected for a Scheragas rigid molecule. The curves are equivalent to that of a rigid molecule with ellipsoid axis ratio p = 3. Moreover, the magnitude of the shift is proportional to the molecular weight. Also, polyisobutylene in benzene at 24° (theta point) has a weak non-Newtonian intrinsic viscosity and the magnitude of [η]_q/[η]_O ? M[η]_Oη_sq/RT agrees with those reported previously.Si è misurata la viscosità di soluzioni diluite di poliisobutilene in funzione della concentrazione e del fattore di taglio (0–2500 sec^?1). Per il calcolo della viscosità intrinseca si è scelta la relazione di Huggins. Per la costante di Huggins k_Hu, come funzione del coefficiente di espansione idrodinamica α_η³, impiegando la relazione teorica di Imai al punto teta, si è ottenuto un valore di 0,63. Si è trovato che la corrispondente costante di Hellers è di 0,50, concordante cioè con il valore comunicato da Bohdanecky. Il diagramma per punti della viscosità intrinsica relativa [η]_q/[η]_O in funzione di M[η]_Oη_sq/RT del poliisobutilene in cicloesano, n—eptano e toluene a 25° e in benzene a 24° indicano, spostando l'asse M[η]_Oη_sq/RT, che la molecola deformabile di poliisobutilene si comporta come previsto per una molecola a stella di Scheragas. Le curve sono equivalenti a quelle di una molecola a stella con rapporto degli assi di elissoide p = 3. Inoltre la grandezza dello spostamento è proporzionale al peso molecolare. Per di più, il poliisobutilene in benzene a 24° (punto teta) possiede una debole viscosità intrinseca non Newtoniana e la grandezza di [η]_q/[η]_O ? M[η]_Oη_sq/RT concorda con quelle comunicate precedentemente.