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.     

Laser light scattering studies of poly(L-lysine HBr) in aqueous solutions

A simple theory for the relaxation of concentration fluctuations in polyelectrolyte solutions is presented, and particular results for the high-salt and no-salt limiting cases are discussed. Autocorrelation functions for the fluctuating intensity of scattered light from dilute aqueous solutions of poly(L -lysine HBr) (PLL-HBr) with and without added salt have been observed over a wide range of pH. The observed autocorrelation functions are in general very satisfactorily represented by single exponentials except at high pH (>10.5), where considerable aggregation is manifested. Solutions of PLL HBr without added salt exhibit extraordinary behavior, evident at low pH, involving a species with a very slowly decaying autocorrelation function. Though this species is readily annealed to a more ordinary individual free-molecule form by cycling the pH to 9.5 or higher and back, the resulting molecules are found to require unusually long times to reach internal configuration equilibrium under low pH conditions. Solutions of PLL-HBr in 0.2M NaBr and 0.1M NaCl are apparently free of similar extraordinary effects and show the normal isothermal helix–coil transition accompanied by a 15–30% rise in the diffusion coefficient to a maximum at pH 10.5, which is interpreted in terms of a change in molecular dimension of an interrupted helix. The predicted K² dependence of the reciprocal relaxation time and enhancement of the apparent diffusion coefficient of the polyelectrolyte in the absence of salt is confirmed.     

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.     

Multichain copoly(α-amino acid). II. Preparation and properties of multi-Nϵ-poly(γ-benzyl-L-glutamyl)copoly(L-lysine γ-methyl-L-glutamate)

A number of multi-N^?-poly(γ-benzyl-L -glutamyl)copoly(L -lysine γ-methyl-L -glutamate)s with branches having various degrees of polymerization and with various intervals of the grafting sites in the core molecule were prepared in N,N-dimethylformamide containing dimethyl sulfoxide by the reaction of N-carboxy anhydride of γ-benzyl L -glutamate with random copoly(L -lysine γ-methyl-L -glutamate)s of different composition with various anhydride-initiator ratios. The relationship between the intrinsic viscosity measured in a coil solvent, dichloroacetic acid (DCA), and the number-average molecular weight determined by osmometry was found to be expressed by the Mark–Houwink–Sakurada equation for the multichain copoly(α-amino acid)s which were made from the same polymeric initiator. The observed α values of the multichain copoly(α-amino acid)s in the equation were lower than that of linear poly(γ-benzyl-L -glutamate). The solvent induced helix–coil transition of the multichain copolymer was investigated in the chloroform?DCA system by the ORD technique. Two kinds of transition regions were clearly distinguished: The α-helices of the core molecules underwent the transition at lower DCA concentration and those of the branch chains at higher DCA concentration. The reduced viscosity of the multichain copoly-(α-amino acid) increased slightly between the two transition regions, in contrast to the large decrease in the reduced viscosity of linear poly(γ-benzyl-L -glutamate) during the helix–coil transition.     

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.     

Strain criterion in nonlinear creep and recovery in concentrated polymer solutions

Transient and steady-state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cM/ρM_c < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and M_c the molecular weight between entanglements as determined from zero-shear viscosity. The polystyrene used had M_w = 410,000 and M_w/M_n < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger M_w/M_n. The results give a critical strain γ′ ∝ c⁻¹ such that linear viscoelastic behavior was obtained in a simple shear deformation with shear less than γ′. A simplified version of the constitutive equation of Bernstein, Kearsley, and Zapas is used with an empirical strain function F (γ) which contains γ′ as a parameter to discuss transient and steady-state behavior in terms of the distribution of relaxation (or retardation) times determined for linear viscoelastic responce. Features of the dependence of the steady-state viscosity η_k, recoverable compliance R_k, the first-normal stress function N_k⁽¹⁾ on shear rate k are discussed in terms of F (γ) and the distribution of relaxation times to conclude that the latter plays a dominant role in the behavior observed in the range of k usually studied. The results predict that the reduced functions η_k/η₀, R_k/R₀, and N_k⁽¹⁾/N₀⁽¹⁾ should depend on η₀R_0k, and that the functional form depends markedly on the distribution of relaxation times, at least in the range η₀R₀k < 10². Comparison with the mechanistic model of Doi and Edwards shows a similar F (γ) but substantial differences in the reduced functions caused by a very narrow distribution of relaxation times in the model.     

The crystal structure of the CeNA:RNA hybrid ce(GCGTAGCG):r(CGCUACGC)

Cyclohexenyl nucleic acids (CeNA) are characterised by the carbon–carbon double bond replacing the O4′‐oxygen atom of the natural D ‐2′‐deoxyribose sugar ring in DNA. CeNAs exhibit a high conformational flexibility, are stable against nuclease activity and their hybridisation is RNA selective. Additionally, CeNA has been shown to induce an enhanced biological activity when incorporated in siRNA. This makes CeNA a good candidate for siRNA and synthetic aptamer applications. The crystal structure of the synthetic CeNA:RNA hybrid ce(GCGTAGCG):r(CGCUACGC) has been solved with a resolution of 2.50 Å. The CeNA:RNA duplex adopts an anti‐parallel, right‐handed double helix with standard Watson–Crick base pairing. Analyses of the helical parameters revealed the octamer to form an A‐like double helix. The cyclohexenyl rings mainly adopt the ³H₂ conformation, which resembles the C3′‐endo conformation of RNA ribose ring. This C3′‐endo ring puckering was found in most of the RNA residues and is typical for A‐family helices. The crystal structure is stabilised by the presence of hexahydrated magnesium ions. The fact that the CeNA:RNA hybrid adopts an A‐type double helical conformation confirms the high potential of CeNAs for the construction of efficient siRNAs which can be used for therapeutical applications.     

Regenerated protein fibers. II. Viscoelastic behavior of silk fibroin solutions

The dynamic viscoelastic behavior of a concentrated solution of silk fibroin dissolved in the “MU” solvent is measured. The dynamic viscosity η′ and dynamic elasticity G′ increase with increasing concentration of silk fibroin at constant frequency; however, the increasing frequency decreases η′ and G′ at a constant concentration of silk fibroin. When the mixing ratio of C₂H₅OH/H₂O in the “MU” solvent is increased at a constant concentration of LiBr·H₂O, η′ and G′ sharply increase at constant frequency. If the LiBr·H₂O concentration is varied in the “MU” solvents whose ratio of C₂H₅OH/H₂O is kept constant at 100 : 0, both η′ and G′ are greater for LiBr·H₂O concentrations of 50% by weight compared to concentrations of 40% by weight. The dependence of η′ on the temperature of the solution can be predicted by Andrade's viscosity equation. Spinnability improves when the SF concentration is increased. © John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1955–1959, 1997     

Fluorine-containing poly(vinyl alcohol): A helix or a random coil

Substitution of several mole per cent of the hydroxyl groups of poly(vinyl alcohol) by fluorine results in marked changes in polymer properties. These fluoro poly(vinyl alcohols) (PVAF) form thermally reversible gels in water at low polymer concentrations. In solution, a helical conformation or a random coil containing helical sequences is more in accord with the experimental observations than the random coil structure of poly(vinyl alcohol). This helical hypothesis is supported by high heats of crosslinking of the aqueous thermally reversible gels, the difficult solubility of PVAF in H₂O, the insolubility of the PVAF–iodine complex under conditions where the PVA–iodine complex remains soluble, the temperature-independent high value for the Huggins k ′ slope constant, the greater stability of the PVAF–iodine complex, the shear dependence of the solution viscosity and our inability to form thermally reversible gels by the introduction of fluorine into other water-soluble polymers which are capable of hydrogen bond formation. Infrared dichroism and deuteration measurements do not differentiate between PVA and PVAF. If this conclusion is correct, PVAF is the first vinyl polymer of which we are aware that maintains a helical conformation in solution.     

Amyloid formation from an α-helix peptide bundle is seeded by 3(10)-helix aggregates

Transformation of proteins and peptides to fibrillar aggregates rich in β sheets underlies many diseases, but mechanistic details of these structural transitions are poorly understood. To simulate aggregation, four equivalents of a water‐soluble, α‐helical (65 %) amphipathic peptide (AEQLLQEAEQLLQEL) were assembled in parallel on an oxazole‐containing macrocyclic scaffold. The resulting 4α‐helix bundle is monomeric and even more α helical (85 %), but it is also unstable at pH 4 and undergoes concentration‐dependent conversion to β‐sheet aggregates and amyloid fibrils. Fibrils twist and grow with time, remaining flexible like rope (>1 μm long, 5–50 nm wide) with multiple strings (2 nm), before ageing to matted fibers. At pH 7 the fibrils revert back to soluble monomeric 4α‐helix bundles. During α→β folding we were able to detect soluble 3₁₀ helices in solution by using 2D‐NMR, CD and FTIR spectroscopy. This intermediate satisfies the need for peptide elongation, from the compressed α helix to the fully extended β strand/sheet, and is driven here by 3₁₀‐helix aggregation triggered in this case by template‐promoted helical bundling and by hydrogen‐bonding glutamic acid side chains. A mechanism involving α?α₄?(3₁₀)₄?(3₁₀)_n?(β)_n?m(β)_n equilibria is plausible for this peptide and also for peptides lacking hydrogen‐bonding side chains, with unfavourable equilibria slowing the α→β conversion.     

Poly(γ-alkyl L-glutamates). II. Optical rotatory dispersion studies in organic solvents

Conformations of a series of poly(γ-alkyl L -glutamates) (ethyl, n-propyl, n-butyl, isobutyl, and isoamyl) were studied by ORD and infrared absorption methods. All except the n-propyl ester were found to be in helical form in nonpolar non-aromatic solvents such as ethyl acetate, chloroform, ethylene dichloride, methylene chloride, carbon tetrachloride, 2-chloroethanol, dimethylformamide, and dioxane. In such cases, the Cotton effects due to the n–π* transition of peptide bonds occurred near 234 mμ and were of a magnitude similar to those found for poly(γ-benzyl L -glutamate) and poly-L -methionine in nonpolar non-aromatic organic solvents. These four polypeptides in aromatic nonpolar solvents, such as benzene, benzyl alcohol, pyridine, and m-cresol, were also found to be in helical form, although the ORD parameters differed considerably from the values in non-aromatic solvents. An essential cause seems to be the interaction of π electrons on peptide bonds with π electrons in the solvents. Helix-coil transitions of these esters in chloroform-dichloroacetic acid mixtures (dichloroacetic acid seems to be a random coil-forming solvent) were expressed by the Shechter-Blout formulation. This was not true, however, for helix–coil transitions in benzyl alcohol–dichloroacetic acid mixtures. The dependence of the helical stability of these polypeptides in chloroform solution upon the side-chain length and upon temperature is discussed.     

Viscosity of Aqueous Solutions of n-butylamine,sec-butylamine and tert-butylamine

Abstract

Viscosities of the systems, water (W) + n-butylamine (NBA), W + sec-butylamine (SBA) and W + tert-butylamine (TBA) have been measured in the temperature range 298.15–323.15K. The viscosities (η) and excess viscosities (η^E) have been plotted against mole fraction of amines (X ₂). On addition of amines to water, viscosities first increase rapidly, then pass through maxima at 0.2 mole fraction of amines and then decline continuously as the addition of amines is continued. η^E show large positive values, with maxima also at 0.2 mole fraction of amines. The maxima of the curves of η and η^E vs. mole fraction of butylamines follow the order, W + TBA > W + SBA > W + NBA. The ascending part of the η vs. X ₂ curves in the water-rich region is explained by the hydrophobic hydration caused by the hydrocarbon tails and the hydrophilic effect due to — NH₂ group of amines. Following the maxima, amine - amine association is preferred, which accounts for the steady decrease of viscosity up to the pure state of amines.     

Excluded volume study of a sulfonate-containing polyelectrolyte in salt solutions

Chain characteristics of a linear sulfonate-containing homopolymer, sodium poly(3-methacryloyloxypropane-1-sulfonate), in aqueous salt solutions (ionic strength, C_s = 0.01N to 5N NaCl) have been investigated by light scattering and intrinsic viscosity. The molecular weight (M?_w)–viscosity relation can be well described by the Mark–Houwink and the Stockmayer–Fixman equations. The coil is highly expanded even in the most concentrated NaCl solution (6N), and no 1:1 electrolyte was found to precipitate this polymer. A linear relation was observed between the viscosity expansion factor, α^3η, and (M?_w/C_s)^1/2. Examination of the data in terms of theories for excluded volume and hydrodynamic interaction suggests that the coil experiences dominant hydrodynamic interaction, corresponding to a nondraining coil, and the second virial coefficient and coil expansion at high C^s can be correlated by the Flory–Krigbaum–Orofino equation. Results for this polymer are compared with those for other polyelectrolytes, and are discussed in terms of chain structure, flexibility, and hydrophobicity.     

catena‐Poly[[disilver(I)(Ag—Ag)‐bis[μ‐1,1′‐(butane‐1,4‐diyl)diimidazole‐κ2N3:N3′]] bis(perchlorate)]: a double helix stabilized by ligand‐unsupported argentophilic interactions

The title compound, {[Ag₂(C₁₀H₁₄N₄)₂](ClO₄)₂}_n, is a one‐dimensional coordination polymer formed by Ag^I atoms linearly bridged by 1,1′‐(butane‐1,4‐diyl)diimidazole molecules. The chains have a helical arrangement and pairs of chains are held together by the rarely reported ligand‐unsupported Ag—Ag interaction [2.966 (1) Å], which results in a double‐helix structure. The double helix contains twisted 24‐membered metallomacrocycles, which are composed of four Ag atoms and two ligands. The Ag atoms lie on twofold axes.     

Variation of polymer chain dimensions with temperature below the theta point

The temperature dependence of the intrinsic viscosity [η] for the system polystyrene-cyclohexane in the interval ?20 < (T ? ψ) ≤ 0 near the ideal temperature ψ has been investigated. The observed diminution in size of the molecular coil with decreasing temperature is attributable to attractive net polymer-solvent interactions, denoted by negative values for the excluded volume parameter z. The data thus comprise an interesting selection for comparison with the predictions of various excluded volume theories. Among the approximate, closed-form expressions the functional relationship of Flory (x⁵ ? α³ ～ z) appears to describe best the variation of [η] with temperature in the region examined. The behavior of the Huggins constant k′ derived from the intrinsic viscosity plots is also examined, in accordance with the Peterson-Fixman model, suitably extended to the temperature region below ψ.     

Viscosity dependent radiationless relaxation rate of cyanine dyes. A picosecond laser spectroscopy study

The viscosity dependent radiationless relaxation of several cyanine dyes has been studied by picosecond laser spectroscopy. It was found that the relaxation rate is proportional to η^?α. The value of α, however, is not constant for a certain dye molecule, but is strongly dependent on the kind of solvent used. In n-alcohols for instance α is typically about 1. In glycerol/methanol or glycerol/water mixtures on the other hand α ≈ 0.5. A comparison is made with literature data on orientational relaxation lifetimes of some dyes in similar solvents. It is shown that the radiationless relaxation of cyanine dyes and the orientational relaxation of for instance xanthene dyes changes in roughly the same way as the solvent is changed. This is taken as proof of the proposal that a torsional motion of the heterocyclic quinolyl rings is the main course of the viscosity dependent relaxation of the cyanine dyes studied.     

Longitudinal volume viscosity of poly(methyl methacrylate)

Volume flow of poly(methyl methacrylate) (PMMA) (M?_n = 43,000 and T_g = 384) has been measured in an Instron Capillary Rheometer. Elastic modulus of the longitudinal wave, longitudinal volume viscosity, initial longitudinal volume viscosity, and retardation times are described at temperatures above T_g (418–483K) and compression rates of about 1.00–200.00 × 10⁵ s^?1. An initial increase followed by a decrease in longitudinal volume viscosity has been observed as the compression rate increases and the volume deformation decreases, this last behavior being at the lowest values of the compression rate (6.0 and 30.0 × 10^?5 s^?1) a typical nonequilibrium one. η_L also increases with increasing temperature (T_g decreases 0.18°C/MPa), and volume flow activation energy decreases as the volume deformation increases.     

A chiral interdigitated supramolecular network assembled from single‐stranded helical tubes

The amino‐functionalized helical chiral one‐dimensional coordination polymer catena‐poly[[bis(pyridine‐κN)zinc(II)]‐μ‐2‐aminobenzene‐1,4‐dicarboxylato‐κ⁴O¹,O^1′:O⁴,O^4′], [Zn(C₈H₅NO₄)(C₅H₅N)₂]_n, has an extended structure that is assembled from 2‐aminobenzene‐1,4‐dicarboxylate anions and Zn²⁺ cations and which presents a left‐handed 4₃ helix with a pitch of 25.6975 (9) Å. All the pyridine rings and all the amino groups point away from the helix to generate a hollow tube with a cross‐section of approximately 8 × 8 Å running parallel to the crystallographic c direction. Each single‐stranded helix is interdigitated with four neighbouring helices via N—H...O hydrogen bonds, which gives rise to a dense homochiral three‐dimensional supramolecular network.     

Viscosity of the systems m-xylene, +1-propanol, +2-propanol, +1-butanol, +t-butanol

Viscosities, η, of the systems, m-xylene, +1-propanol, +2-propanol, +1-butanol and +t-butanol have been measured for the whole range of composition at 303.15, 308.15, 313.15, 318.15 and 323.15?K. The variation of viscosities has been plotted against mole fraction of alkanols. Viscosities have been found to increase slowly up to a considerable concentration of alkanols, followed by a rapid rise of viscosities at higher concentrations. The slow rise of viscosity is attributed to dissociation of alkanols in m-xylene, while the rapid rise of viscosity is ascribed to self-association of alkanols. Excess viscosities, η^E, have been plotted as a function of mole fraction of alkanols. The curves show negative values for the whole range of composition, with minima occurring in alkanol-rich region.?η?and η^E have been fitted to appropriate polynomial equations. The study shows the effect of branching and chain length of alkanols on?η?and η^E.     

Rheological behavior of thermotropic flexible main-chain polyesters based on 4,4′-dioxy-2,2′-dimethyl azoxybenzene mesogens. I. Oscillatory shear behavior

The rheological properties of fractionated thermotropic nematic polyesters 4,4′-dioxy-2,2′-dimethyl azoxybenzenenonanediyl (n = 7) (AZA-9) and dodecanediyl (n = 10) (DDA-9) have been determined under oscillatory shear in the nematic and isotropic phase. A markedly more pronounced shear thinning characterizes the polydisperse DDA-9 polymer as compared to the fractionated polymer in the nematic state. This difference becomes less pronounced in the isotropic phase. In all cases, the elastic compliance J′ in the isotropic state is much lower than in the nematic state. The values of relaxation time λ, although lower in the isotropic state, are not very different in the nematic state. The loss tangent tan δ is significantly higher in the isotropic phase for lower molecular weights. For molecular weights of 13,000 and above, this difference becomes smaller and shifts to lower angular frequencies. For AZA-9 and DDA-9, η→₀ the limit of the dynamic viscosity can be represented by η^* = M with a value of α similar for both phases and approximately equal to 4.