Viscosity Of Dilute Solutions Research Articles

Viscometric titration of a linear polyelectrolyte

Viscosities of dilute solutions of linear poly(2-vinyl pyridine) with molecular weights ranging from 3.0×104 to 1.0×106 have been measured under conditions where the polymer can be charged by protonation. By employing weakly acidic solvents, large reduced viscosities typical of polyelectrolytes in low-salt solutions are observed. They exhibit a pronounced maximum occurring at a concentration which is independent of molecular weight. Separate pH titrations are used to calculate polyion charge density and electrostatic screening lengths. The origin of the viscosity maximum is explained by consideration of changing electrostatic persistence lengths on dilution, resulting in polyion coil expansion and contraction. Investigations of limiting conditions of low charge density and full electrostatic screening with basic and high acid or salt solutions reveal expected normal polymer behavior in concentration extrapolations to the intrinsic viscosity.

High temperature capillary viscometer

A new high-temperature capillary viscometer for measuring the viscosity of dilute polymer solutions has been designed, constructed, and extensively tested. The viscometer has combined several valuable capabilities: high-temperature operation (potentially to 280 °C and tested up to 250 °C), high precision (∼10−3 s with a temperature control of ±0.001 °C), variable shear rates (by changing the orientation of the capillary), and differential measurements (by using a twin viscometer arrangement). A description of the high-temperature viscometer and tests of its capabilities are presented.

Renormalization-group study of the dynamical viscosity of dilute solutions of self-avoiding polymer chains.

The first-order excluded-volume correction to the dynamical viscosity of dilute polymer solutions is studied within the path-integral formulation of the Kirkwood diffusion equation. The renormalization of the dynamical viscosity [\ensuremath{\eta}(\ensuremath{\Omega})] is explicitly performed in two limits: (a) zero frequency \ensuremath{\Omega}=0, and (b) \ensuremath{\Omega}\ensuremath{\ne}0, large contour length L (or finite L and \ensuremath{\Omega}\ensuremath{\rightarrow}\ensuremath{\infty}). The effect of screening the hydrodynamic interaction by increasing the excluded-volume strength is predicted. The renormalization at the \ensuremath{\Omega}-dependent renormalization point enabled us to derive the scaling law for the dynamical viscosity [\ensuremath{\eta}(\ensuremath{\Omega})]\ensuremath{\approxeq}${\ensuremath{\Omega}}^{\mathrm{\ensuremath{-}}(d\ensuremath{\nu}\mathrm{\ensuremath{-}}1)/d\ensuremath{\nu}}$ within the renormalization group.

Viscosity–temperature relationships for linear and 12‐arm star polystyrenes in dilute solution

AbstractThe actual viscosities (cP) of dilute solutions of linear and 12‐arm star polystyrenes were measured in benzene, a good solvent, and cyclohexane, a poor to moderate solvent, as a function of temperature. The equations of Moore, previously established for solutions of linear polymers, were also found to be valid for star polystyrenes. A branching parameter b was defined which is essentially the same as g′ = [η]br/[η]1. The values of b found in benzene are close to the value of g′ for 12‐arm star polystyrene in toluene, another thermodynamically good solvent. It thus appears that Moore's relationships have at least limited utility in studying branching in polymers.

Functional polymers. XLIX. Copolymerization of ω‐alkenoates with α‐olefins and ethylene

AbstractThe 2,6‐dimethylphenyl ester of 10‐undecenoic acid was copolymerized with 1‐dodecene, 1‐octene, 1‐hexene, propylene, and ethylene using coordination initiation systems based on “aluminum‐activated” titanium trichloride and dialkylaluminum chlorides. The copolymerizations with higher α‐olefins proceeded smoothly and gave copolymers incorporating from 60 to 90% of the 10‐undecenoate feed. Copolymerization with propylene gave incorporation of 5 mol % of 2,6‐dimethylphenyl 10‐undecenoate; with ethylene only 3 mol % of the ω‐alkenoate was readily incorporated. All copolymers were characterized by elemental analysis, dilute solution viscosity, and by their IR 1H‐ and 13C‐NMR spectra.

Viscosity of dilute polyelectrolyte solutions: concentration dependence on sodium chloride, magnesium sulfate and lanthanum nitrate

Mesures de viscosite de poly(styrene sulfonate) completement neutralise par Na + par un dispositif permettant des mesures precises pour des concentrations faibles (< 1 ppm). Le passage d'un ion monovalent (Na + ) a un ion divalent (Mg 2+ ) puis trivalent (La 3+ ) deplace la position de la viscosite maximale vers les concentrations de polymere elevees et diminue la valeur absolue de la viscosite reduite. Bon accord entre les valeurs experimentales et theoriques

Chain Dimensions and Rheology of Poly(arylene ethers)

Dilute solution and melt viscosities of two poly(arylene ether ketones) were compared. One polymer contained all para linkages in the backbone and the other contained one meta linkage per repeat unit. Molecular dimensions were shown to agree with calculated values and entanglement spacings could be predicted using the semi-empirical formula of Graessley and Edwards. Frictional properties in the two melts differed considerably when compared in ‘corresponding states' at Tg+100°C.

On the role of thermal treatments on the properties of xanthan solutions

The aim of the present study was to determine the effect on the xanthan molecule of the thermal treatment applied to the xanthan broth after the fermentation processes. The influence of xanthan and salt concentrations, pH, temperature and time were tested. After the treatments, the xanthan was characterized by measuring the broth and dilute solution viscosities, the intrinsic viscosity, the molecular weight and the substituent contents. Three mechanisms are suggested to explain the experimental results. The viscosity increase may be due to the conversion of the native ordered xanthan conformation to a renatured more viscous one, or to aggregation. The aggregates seem to be reversible when they are formed from the native ordered xanthan conformation and irreversible from the denatured one. The loss in viscosity is due to xanthan degradation; this process increases with the temperature and time of treatment when the temperature is higher than 60°C.

Hydrodynamic Behavior of Semirigid Polymer at a Solid‐Liquid Interface

The apparent viscosity of dilute and semidilute xanthan solutions flowing through small cylindrical pores, under conditions where there is no adsorption effect, were accurately determined in Newtonian and shear‐thinning regimes. The analysis of the results using a two‐fluid flow model shows that the hydrodynamic thickness of the depletion layer near the pore wall is closely related to the equivalent rod length of the macromolecule, but seems to be insensitive to the persistence length. The hydrodynamic thickness does not depend on polymer concentration as expected for a semirigid polymer and decreases slightly as shear rate increases.

Rheological properties of the liquid crystalline poly(γ‐benzyl α, L‐glutamate) gels in benzyl alcohol

AbstractWe have determined the degree of stiffness of a poly(γ‐benzyl α, L‐glutamate) (PBLG) chain in benzyl alcohol by measuring the intrinsic viscosities of dilute Solutions with differing molecular weights. Viscoelastic properties in oscillatory shear flow have been studied and the dependence of the loss and storage moduli on temperature, composition, and frequency are reported. We have also studied the transient shear stress relaxation behavior of the PBLG gel at different temperatures and concentrations. A comparison has been made between these gels and a classical poly(dimethyl siloxane) (PDMS) network, as well as, typical glassy polymers. Shear creep and recovery measurements have been made for this system. Some extensional step strain experiments using lubricated squeezing have been investigated. Tensile experiments have been made to determine stress‐strain relationship during elongation. Preliminary experiments using the impulse approach to viscoelasticity further indicate the high elastic contribution in the gel.

On the dynamical viscosity of dilute polymer solutions in theta solvents

The path integral formulation of the Kirkwood diffusion equation is used to derive the perturbation expansion of the intrinsic viscosity in powers of the hydrodynamic interaction. Within the preaveraging approximation the perturbation expansion yields the Zimm formula for the intrinsic viscosity. The renormalization of the dynamical viscosity [η(ω)] has been explicitly carried out for both zero and large frequencies. At intermediate frequencies the renormalization of [η(ω)] has been performed in an approximate manner. A simple analytical expression for the dynamical viscosity is given. For low ω the real part of [η(ω)] has a plateau, while for large ω the Zimm behavior ([η(ω)]∼ω−1/3) is obtained.

Thermodynamics and high‐pressure viscosity of dilute solutions of poly(decyl methacrylate) and how the free volume influences them

AbstractLight scattering and viscometric measurements were performed for the system isooctane/poly(decyl methacrylate) of weight‐average molecular weight M̄w = 250 000 within the concentration regime of pair interaction between the macromolecules in the temperature range from 25°C to 100°C. In case of the intrinsic viscosities [η], the pressure was varied up to 3500 bar. Under isobaric conditions, the osmotic second virial coefficients A2, the z‐average radii of gyration rz and [η] pass through a maximum, the Huggins coefficient kH through a minimum, with variation of temperature. These extrema indicate a change in the heat of dilution from endothermal at low, to exothermal at high temperature T. The calculation of the temperature dependence of the intrinsic viscosity [η] (T) for isochoric conditions does not yield a maximum, provided the pressure at the lowest temperature is chosen close to atmospheric pressure; it can, therefore, be concluded that the change in the sign of the enthalpy is in this case only due to the free volume of the system which increases markedly with increasing T. For pressures larger than ≈700 bar, maxima are always observed, no matter whether the temperature is changed isobarically or isochorically. All parameters under investigation are closely interdependent: A one‐to‐one correspondence exists between [η] and A2 at 1 bar, and kH and [η] interrelate linearly for constant T.

Effect of chain association on the viscosity of dilute ionomer solutions

Etude theorique de la structure des chaines agregees. Application au polystyrenesulfonate de sodium

Viscosity of dilute polyelectrolyte solutions

We have developed an apparatus which enables us to perform accurate measurements of the shear viscosity of low ionic strength, dilute polyelectrolyte solutions, down to polymer concentrations below one part per million. We have shown that a theoretical expression for the viscosity of such solutions can be derived using the mode–mode coupling approximation to the hydrodynamics of charged Brownian spheres. Very good agreement between the predicted and observed polymer and salt concentration and molecular weight dependence of the viscosity is observed in the low-added salt, dilute solution range. Furthermore, it appears that the theory gives a qualitatively correct description of the viscosity of semidilute solutions, indicating that independent of polyion concentration, the hydrodynamics of low ionic strength polyelectrolyte solutions is dominated by electrostatic repulsion between polyions.

Transient extensional viscosity of dilute flexible polymer solutions

A tubeless siphon apparatus was designed and constructed in order to measure the transient extensional viscosity of dilute flexible polymer solutions. The stretch rate was found to be practically constant in the higher portion of the fluid threadline. However, these constant values of the stretch rate are rather low, but slightly higher than the reciprocals of the relaxation times of the macromolecules. By systematically varying instrument parameters (flow rate, threadline length and nozzle diameter) we observed a strong dependence of the transient extensional viscosity on the strain. The data obtained for polymer concentrations ranging from 280 to 840 ppm suggest that even at these low concentrations hydrodynamic interactions, between stretched macromolecules exist.

Some special features in estimating the molecular weight of cellulose acetates

The slope of the lines which show the concentration dependence of the viscosity of dilute CDA solutions is different from fractions from the very same specimen, and also depends on the technological parameters of the preparation process.

Uniaxial and biaxial extensional viscosity measurements of dilute and semi-dilute solutions of rigid rod polymers

Effective uniaxial extensional and biaxial extensional viscosities of dilute and semi-dilute solutions of collagen, a rigid rod molecule, have been measured with an opposing jet apparatus. The concentration of collagen in the glycerin/water solvent ranged from 50 to 2300 ppm. The data agree quantitatively with a theory developed by Batchelor describing the extensional viscosity of perfectly aligned rigid rods. The viscosity measured for the dilute rigid rod solutions is independent of the rate of strain as predicted by Batchelor's theory. Data taken on the semi-dilute, strain-thinning solutions at strain rates sufficiently high to align the rods in the extension direction also agree with the predictions of Batchelor's theory. The measured viscosity of semi-dilute solutions at low strain rates agree qualitatively with a theory developed by Doi and Edwards describing the strain-thinning behavior of semi-dilute rigid rod solutions.

Solution properties of poly(methyl methacrylate) in methyl methacrylate, 1. Viscosities from the dilute to the concentrated solution regime

AbstractThe viscosities of samples of poly(methyl methacrylate), PMMA, with narrow molecular weight distributions and with molecular weights in the range 1,75·104 &lt; M̄w &lt; 1,60.106 were measured in methyl methacrylate, MMA, as solvent at 20, 40, and 60°C in the dilute and in the semi‐dilute concentration regime. By extrapolation to zero polymer concentration the limiting viscosity numbers and therefrom the Mark‐Houwink‐Kuhn‐Sakurada parameters for PMMA in MMA were obtained. In addition, unperturbed dimensions were determined from dilute solution viscosity data. Together with some published results for more concentrated solutions of PMMA in MMA the viscosities of the semi‐dilute systems were analysed in terms of scaling theories. It was found that irrespective of temperature, polymer concentration, and molecular weight all data could be quite well fitted by a single master curve when the relative viscosity η/η0 was plotted as a function of the product of the intrinsic viscosity and mass concentration [η]·c. No sharp transitions between different concentration regimes were observed, however, and the scaling law exponents for the entangled solution are significantly higher than predicted by theory.

Influence of acetyl and pyruvate contents on rheological properties of xanthan in dilute solution

In this paper, we investigate the role of acetyl and pyruvate groups on rheological properties of xanthan in dilute solutions. For this purpose, a series of xanthan derivatives were prepared by chemical hydrolysis from the same original sample, i.e. acetyl-free, pyruvate-free, acetyl and pyruvate-free xanthans. Conformational transitions of the four samples (native and modified xanthans) were followed by measuring optical rotation as a function of temperature. Values of midpoint transition ( T m ) thus obtained indicate that acetyl groups have a stabilizing effect on the ordered form of xanthan whereas pyruvate groups have an opposite effect. After partial depolymerization by sonication, viscosities of the four samples were studied as a function of polymer concentration (below overlap concentration C * and molecular weight. Unique curves were obtained for [η] versus M w and specific viscosity versus the overlap parameter C[η] for the four samples. This result shows that acetyl and pyruvate contents have no influence either on xanthan dilute solution viscosity or on its intrinsic viscosity at a given molecular weight.

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

AbstractWe present an analysis of data on the intrinsic viscosity [η] of sulfo‐polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 &lt; ε &lt; 18, [η] decreases from the base polymer value [η]0 with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]0 was found to depend on a single reduced variable αAαSx, where x is the fractional substitution, αA depends only on the counterion, and αS ∝ ε−1 depends only on the solvent. For solvents of high dielectric constant, 36 &lt; ε &lt; 47, [η] increases approximately as x3, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association‐induced gelation behavior and possible generalizations of the reduced variables approach.