Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

New insights in the properties of cellulose in phosphoric acid: viscometric study

Measurements of viscosity were carried out using several solutions of cellulose in different concentrations of phosphoric acid at different temperatures. The intrinsic viscosity [η]₀, a measure for the size of a single chain and the Huggins constant k_H, a measure for the interaction between chains were derived.     

Molecular weight influence on viscosimetric parameters of poly(4-vinylpyridine) polymers

This work describes the effect of the molecular weight on the viscosimetric parameters of poly(4-vinylpyridine) (P4VP) polymers in ethanolic solution. Numerous studies concerning this question have been reported in very separate intervals of molecular weight. We have observed a discordance (discontinuity) in the variation of the intrinsic viscosity as a function of the molecular weight of these polymers ([η]=f(M_w)). In order to establish a general relationship between viscosimetric parameters and M_w, we have considered 10 P4VP samples in a wide interval of molecular weights: 0.75×10⁴ to 153×10⁴. These results have been compared and completed with that of the literature. We have observed that:

(i)

All viscosimetric parameters (intrinsic viscosity [η], Huggins constant k_H, second virial coefficient, viscosimetric expansion coefficient α_η, and critical concentration) change according to a continuous function without a break.

(ii)

The lower is the molecular weight of P4VP; the higher are the variations of the expansion coefficient and the interaction effects.

(iii)

The variation of the intrinsic viscosity versus the molecular weight follows a unique relation in the whole M_w range. In fact, the Berkowitz equation (1), described for a limited range of relatively high M_w (10⁵ to 18.5×10⁵) is extended for all M_w interval values.

(iv)

Empiric laws for [η], k_H, A₂ and C^* and variations as a function of molecular weight were proposed for the P4VP in ethanol.

     

A viscometric study of dilute aqueous solutions of poly(vinylalcohol)-polyacrylamide mixtures

The viscosity interaction coefficient, k_AB, for the system poly(vinylalcohol)-polyacrylamide-water was determined at 25° by two methods: (a) estimation of the Huggins slope coefficients for mixtures of polymers in different proportions; (b) determination of the intrinsic viscosity of polymer (A) in aqueous solutions of polymer (B). The result, k_AB = 0.3, indicates a low degree of overlapping of unlike polymer molecules.     

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.     

Conformational behavior of nylon 6 in mixed solvents

The intrinsic viscosity [η], Huggins constant (K_H), laser light scattering, UV and IR measurements of Nylon 6 are made in m‐cresol and its mixture with 1,4‐dioxane at 20–60 °C. The intrinsic viscosity, R_g, A₂, (<S>²)^1/2 (calculated from viscosity data), R_H, and UV absorbance initially increase and then decrease with the rise in 1,4‐dioxane contents. The K_H and the transmittance of ? OH group in IR spectra show an opposite trend to that of [η]. The dielectric constant calculated from the refractive index of the solvent (m‐cresol with 1,4‐dioxane) and polymer solution shows a continuous decrease with the amount of 1,4‐dioxane. Activation energy shows a minimum while linear expansion coefficient (α³) maximum with the addition of 1,4‐dioxane. Change in [η], K_H, and other characteristics of the polymer solutions with alterations in solvent composition and temperature are the result of variation in the thermodynamic quality of the solvent, its selective adsorption, hydrogen bonding, and conformational transitions. It has been concluded that the addition of 1,4‐dioxane first enhances the quality of the solvent, encourages hydrogen bonding, and specific adsorption, and then deteriorates, bringing conformational transitions in the polymer molecules. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 534–541, 2005     

Streaming birefringence. VII. Influence of the intermolecular hydrodynamic interaction on the viscosity and streaming birefringence of polymer solutions

The cavity model used in the theory of dielectrics was applied to hydrodynamics to calculate the force exerted by a system of soft dumbbells on a reference dumbbell in a hydrodynamic field. The influence of this force on the viscosity and flow birefringence and its dependence on both the concentration and velocity gradient were calculated. The system of equations has a real solution only for values of β = M[η]η₀γ/RT which are smaller than a critical value rapidly decreasing with increasing concentration. At zero concentration the results obtained agree with the theory of a single isolated dumbbell model. The calculated Huggins constant is k′ = 0.4. The extinction angle is connected with the relative viscosity very nearly as derived from experiments. However, the theory fails at higher concentrations and gradients yielding an increase in viscosity with the gradient and infinite zero-shear viscosity for the concentration c = 2.5/[η].     

VISCOSITY BEHAVIOR OF LACQUER POLYSACCHARIDE IN AQUEOUS SOLUTION

The dependence of measured viscosity on NaCl concentration (0.1 to 3.0M), pH (range of 2—13) and cadoxen composition w_(cad) (from 2% to 100%) for the lacquer polysaccharide in NaCl/cadoxen/H_2O mixture containing HCl or without were obtained. All the viscosity exponents γin the Mark-Houwink equations under three different solvent condition arc close to 0.5. The w_(cad) dependence of reduced viscosity ηsp/c confirms the single strand chain of the polysaccharide. As the γvalues close to 0.5 and values of unperturbed dimension _θ/M and [η] much smaller than those for usual linear polymers, these facts suggest that the polysaccharide chains in the aqueous solutions should be dense random coil owing to the highly branched structure.     

Evaluation of Huggins' Constant,Kraemer's Constant and Viscosity Concentration Coefficient of Polymer Dextran in Urea,Glycine and Glucose

Abstract

Reduced viscosity (η_sp/c) and Inherent viscosity (In η_rel/c) of dilute solution of water soluble polysaccharide polymer “Dextran” has been calculated by measuring the flow time of the polymer solution in solvents like 6(M) Urea, 2(M) Glycine and 50% Glucosc at three different temperatures ? 25°C, 30°C and 35°C. From extrapolation of curve (η_sp/c) versus (c) and (In η_rel/c) versus (c), thermo viscosity parameters like Huggins' constant (k′_H) Kraemer's constant (k″_H) and viscosity concentration coefficient (a ₂) have been estimated which enable us to know the fate of the polymer molecules in these solvents.     

Molecular structure of a water-polyethylene glycol-KOH system, according to densitometry and viscometry data

The dynamic viscosity and density of a water-polyethylene glycol-KOH system are measured at temperatures of 293.15 to 323.15 K in concentrations ranging from 0.00001 and 0.001 (mole fractions). The activation parameters of viscous flow (ΔG _η ^≠ , ΔH _η ^≠ , and ΔS _η ^≠ ), structural temperature (T ₀), the partial molar volume of polyethylene glycol (PEG) in solution $\left( {\tilde V} \right)$ , intrinsic viscosity([η]), and the Huggins constant (K _H), are calculated. It is found that PEG has a structuring effect on water in water-PEG and water-PEG-KOH systems, with the PEG structuring effect in the latter being somewhat attenuated by the destructuring influence of KOH.     

Viscosity of aqueous solutions of polysaccharides and hydrophobically modified polysaccharides: Application of Fedors equation

Amphiphilic polysaccharides have been obtained by hydrophobic modification of a neutral bacterial polysaccharide, dextran. Various amounts and types of aliphatic hydrocarbon groups have been attached to dextran.The solution behaviour of unmodified dextran samples and amphiphilic dextran derivatives is characterized by viscometric measurements. The overall viscosity behaviour of unmodified polysaccharides is described up to C × [η] = 3, using the equation of Fedors [Fedors RF. Polymer 1979;20:225] which involves only a concentration parameter. The latter is shown to depend on the hydrodynamic volume of the macromolecules in solution.The equation of Fedors is shown to conveniently estimate the viscosity behaviour of amphiphilic dextran derivatives up to C × [η] = 1. The interdependence between Fedors parameter and other viscometric characteristics (intrinsic viscosity, Huggins coefficient) is evidenced. These results are extended to the data of other authors.     

Thermodynamic properties of aqueous polyacrylamide solutions as a function of pressure and temperature

The viscosities of dilute aqueous solutions of polyacrylamide were measured at temperatures from 20 to 60.4° and pressures up to 150 MPa using a falling-body viscometer. The viscosity coefficient, ν, increases exponentially with increasing pressure at a given temperature and concentration. The rate of increase of the apparent energy of activation. E≠, with pressure becomes more rapid as the concentration of the solutions increases. Intrinsic viscosity, [ν], increases with increasing pressure at a given temperature but almost levels off at pressures above 100 MPa while the Huggins constant, k_H, decreases. The Flory-Huggins interaction parameter, _X1, decreases at a greater rate with increasing pressure as the temperature decreases indicating that the effect of pressure on improving the compatability between the polymer and solvent is greater near the θ-temperature. The second virial coefficient, A₂, was calculated from the intrinsic viscosity data and compared with the results obtained by light scattering technique.     

Rheological properties of wheat gliadins in aqueous propanol

Rheological properties of wheat gliadins in 50%(V/V) aqueous propanol were carried out as a function of gliadin concentration c and temperature.The solutions at 20 g L 1 to 200 g L 1 behave as Newtonian fluids with an flow activation energy of 23.5 27.3 kJ mol 1.Intrinsic viscosity [η] and Huggins constant k H are determined according to Huggins plot at c ≤ 120 g L 1.The results reveal that gliadins are not spherical shaped and the molecular size tends to increase with temperature due to improved solvation.     

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.     

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.     

Anionic polymerization of caprolactam. XLIII. Relationship between osmometric molecular weight,viscosity, and endgroups of a polymer

For unfractionated anionic polymers, the following relationship between the osmometric molecular weight and intrinsic viscosity is valid: M?_n = 13200[η]^1.115 (cresol), or M?_n = 13000[η]^1.021 (93.8% H₂SO₄). A comparison of the osmometric and viscometric data with the number of endgroups of a polymer confirmed the finding that under certain conditions, moderately branched molecules can be formed; the above parameters depend on the type of the activator used.     

Viscosity Molecular Weight Determination of Polyadenylic Acid

Abstract

In this study viscosity measurements of polyadenylic acid (PolyA) in aqueous solution were carried out under different conditions. In the absence of any additives, the polymer degraded during flow through the capillary of a viscometer or when standing still. Degradation during the former was more severe. The degradation of polyadenylic acid can be prevented by addition of an electrolyte such as KCl to increase the ionic strength. However, in this case the deviation from linearity was still considerable at most ionic strength values. The best fit to the Huggins and Kraemer equations was obtained using a Tris–EDTA buffer solution with a final pH of 7.65. Estimation from intrinsic viscosity and weight-average molecular weight values gave k and α as 2.04 × 10^?5 and 0.89 from the equation η = kM ^α. The difference between Huggins (k ₁) and Kraemer (k ₁′) constants was close to 0.50 for all measurements.     

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.     

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.