Viscosity Exponent Research Articles

Nonuniversal nature of dynamic critical anomaly in polymer solutions.

Critical anomaly of viscosity has been studied for ideal polymer solutions, focusing on its dependence on the molecular weight of polymer M(w). According to the conventional understanding that polymer solutions should belong to the same dynamic universal class as classical fluids, the critical exponent of viscosity y(c) should be a universal constant (approximately 0.04). Contrary to this, we find that y(c) significantly decreases with increasing M(w). This unusual behavior can be explained by the dynamic coupling of critical concentration fluctuations with an additional slow viscoelastic mode intrinsic to polymer solutions. Our dynamic light scattering measurements support this picture.

Critical dynamics of gelation.

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation k=straight phi-beta for the critical exponent of the shear viscosity. Here beta is the thermal exponent for the gel fraction, and straight phi is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.

Frequency-dependent viscosity of xenon near the critical point

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity eta of xenon near its critical density rho(c) and temperature Tc. In microgravity, useful data were obtained within 0.1 mK of Tc, corresponding to a reduced temperature t=(T-Tc)/Tc=3 x 10(-7). Because they avoid the detrimental effects of gravity at temperatures two decades closer to T(c) than the best ground measurements, the data directly reveal the expected power-law behavior eta proportional, variant t(-nuz(eta)). Here nu is the correlation length exponent, and our result for the viscosity exponent is z(eta)=0.0690+/-0.0006. (All uncertainties are one standard uncertainty.) Our value for z(eta) depends only weakly on the form of the viscosity crossover function, and it agrees with the value 0.067+/-0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)]. The measurements spanned the frequency range 2 Hz< or = f < or =12 Hz and revealed viscoelasticity when t < or = 10(-5), further from Tc than predicted. The viscoelasticity's frequency dependence scales as Aftau, where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0+/-0.3 times the result of a one-loop perturbation calculation. Near Tc, the xenon's calculated time constant for thermal diffusion exceeded days. Nevertheless, the viscosity results were independent of the xenon's temperature history, indicating that the density was kept near rho(c) by judicious choices of the temperature versus time program. Deliberately bad choices led to large density inhomogeneities. At t>10(-5), the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.

Viscoelastic scaling in polymer gels

New scaling laws for chain networks are derived to describe the fundamental relationships between the viscosity exponent (k), viscoelastic exponent (m), stretched exponent (β), spatial dimension (d). fractal dimension (df), and a universal constant (γ). The scaling of the total number of monomers and the radius of gyration is defined by df. We have discovered γ = m/β to be a universal constant which relates the shear modulus of a polymer gel melt to the shear modulus near the glass transition. Analyzing the size-dependent shear viscosity, we have determined γ = 3dfcd/(7d−5dfc) = 2.647 for d = 3 where dfc is the fractal dimension of critical clusters at the gel point. By using γ, the present theory extends previous work pertaining to systems near the sol-gel transition, and shows how properties far from the critical point can be explained. The theoretical prediction is in good agreement with viscoelastic measurements.

Critical behavior of viscosity for alginate solutions near the gelation threshold induced by cupric ions

The critical behavior of relative viscosity and intrinsic viscosity near the gelation point was experimentally examined for 1 g/100 mℓ alginate solution induced by cupric ions. The critical exponent of relative viscosity was found to be 1.27, which is in good agreement with the prediction of the percolation model based on a Rouse cluster approximation gives the exponent as 1.3. Critical behavior of intrinsic viscosity reveals that the constant of Huggins equation k′ for alginate clusters formed near the gelation point was considerably higher than that of linear alginate polychains in aqueous solution. Typically intramolecular crosslinking between polychains in the low cupric concentration could be detected in the plots of [η] vs molar fraction of cupric ions for the system. The weak divergence of intrinsic viscosity resembles the critical behavior of Zimm clusters predicted by the three-dimensional percolation theory rather than clusters of classical theory.

Reptation theory: geometrical and topological aspects

AbstractThis paper discusses topological and geometrical aspects of reptation theory which are common to all versions of reptation theory. These are: the postulated existence of the tube, the functional relationship between the tube diameter a and the polymer/monomer density p, the crossover from the Rouse to reptation regime. Statistical mechanics of the geometrically confined polymer chain is reanalyzed by careful separation of the diffusive motion of the chain into the longitudinal and transversal parts. Connection between old results and the new formalism is established. It is shown that the longitudinal motion resembles that known for directed polymers. This provides a source of the effective rigidification of the reptating chain's backbone thus facilitating the viscosity exponent to be larger than 3. The transversal motion is also reanalyzed. It is shown that the diffusion on the Bethe lattice used before to describe the transversal (planar) motion (conformational statistics) of the trapped chain is actually the diffusion on the universal covering of the corresponding Riemannian surface. This fact allows to reanalyze the tube stability using topological arguments. Detailed numerical comparison of the obtained new theoretical results with available experimental and Monte Carlo data is provided. Very good agreement between theory and experiment is found. It is also shown that the emerging physical picture of the tube destruction is isomorphic to that which was developed earlier with the help of the quantum Hall effect analogy (J. Phys. I 4, 843 (1994)). Remarkable connections between the reptation theory and the theory of quantum chaotic/mesoscopic systems are established thus making the reptation theory part of the more general theory of quantum chaotic systems.

Experimental folding and boudinage under pure constrictional conditions

Constrictional folds are characterized by true fold-axis parallel extension if the rock-volume does not vary during deformation. Studies of such folds in experiments, using plasticine layers of different apparent viscosity and power-law exponent, clearly indicate that fold-axis parallel stretch may be accompanied by plastic elongation as well as boudinage of the competent layer. Characteristic aspects of the experimentally folded competent layers are: (1) coeval development of folds and boudins; (2) layer thickness not changing during deformation; (3) layer-parallel shortening in sections perpendicular to the fold (stretching) axis; (4) enlargement of the initial thickness of the competent layer results in increasing fold wavelength and decreasing number of boudins. The ratio of dominant wavelength to layer thickness of the constrictional folds can be described mathematically approximately by the equation developed for plane strain folding of power-law materials

Solution Properties and Chain Stiffness of Poly(Acenaphthylene)

Abstract Solution properties of poly(acenaphthylene) (PACN) were investigated in a theta solvent (1,2-dichloroethane) and a good solvent (chloroform). The viscosity exponent α was found to be 0.50 at both 35 and 41 °C in 1,2-dichloroethane. Unperturbed dimensions found from viscometric measurements were compared with those of other vinyl aromatic polymers. Calculation of the chain flexibility parameters led to the conclusion that PACN is a rather stiff chain compared to other vinyl polymers with its characteristic ratio C∞ of 18.2 and chain flexibility parameter λ of 7.

Thermal and Inertia Effects in Hydrodynamic Lubrication of Rollers by a Power Law Fluid Considering Cavitation

A theoretical aspect of hydrodynamic lubrication of two symmetric rollers by power law fluids is analyzed. The effect of fluid convective inertia, which is significant in case of high speed bearing, is taken into account. The effect of hydrodynamic pressure and temperature on the lubricant consistency m is assumed to vary with pressure and the mean temperature. The squeezing motion of the surfaces is also incorporated along with inertia and thermal effects. The Reynolds equation and the energy equation (with convection and conduction), which are coupled through m, are solved simultaneously. Various bearing characteristics such as pressure, temperature, load and drag etc. are obtained and a comparison between results (with and without inertia) is also made. It is noted that the effect of inertia is to increase pressure, temperature, load and drag etc. and to displace the position of pressure peak slightly towards the center line of contact of the rollers. An attempt is also made to study the variation of film thickness with load, speed, Eckert number, pressure, and temperature viscosity exponents.

Concentration Dependence of Mechanical Properties of Gelatin near the Sol-Gel Transition Point

The concentration dependence of mechanical properties for gelatin near the sol–gel transition point was analyzed by the scaling law derived from the percolation theory, and compared with the results previously obtained for polyacrylamide. The critical concentration at the sol–gel transition point, ϕg, was estimated from the concentration (ϕ) vs. the reciprocal of viscosity (η) plots by extrapolating 1/η to zero. The critical exponent for sol viscosity, s, was estimated from the slope of a log(ϕg–ϕ) vs. log η plot. The critical exponent s was about 1.1, being larger than the value predicted by the percolation theory assuming the superconductor model. The critical exponent for gel elasticity, t, was estimated from the slope of a log(ϕ–ϕg) vs. log G′ plot, where G′ is the dynamic shear modulus at a frequency of 2Hz. The critical exponent t was about 2, being similar to the value predicted by the percolation theory.

Concentration Dependence of Mechanical Properties of Polyacrylamide near the Sol-Gel Transition Point

The scaling law derived from the percolation theory was applied to the concentration dependence of mechanical properties of polyacrylamide measured near the sol–gel transition point. The critical concentration of the sol–gel transition, ϕg, was estimated from the plot of concentration (ϕ) vs. the reciprocal of viscosity (η) by extrapolating 1/η to zero. The critical exponent for the sol viscosity, s, which was estimated from the slope of the log(ϕg–ϕ) vs. log η plot was about 0.7. The estimated value of s was similar to the value predicted by the percolation theory based on the superconductor–normal conductor mixture model. The critical exponent for the gel elasticity, t, as estimated from the slope of the log(ϕ–ϕg) vs. log G′ plot, where G′ was the dynamic shear modulus of the gel at a frequency of 2Hz. The value of t was about 2, which was also similar to the value predicted by the percolation theory. These results indicated the at the concentration dependences of η and G′ of polyacrylamide near the sol...

Empirical Correlations of Saturated Steam Properties

Summary Both steamdrive and steam stimulation processes for EOR involve thermodynamic and transport properties of steam. These properties have roles in the fluid flow, heat transfer, and mass and heat balances of recovery processes. Hence, they affect, not only the operation of the process, but also the economics and management of the oil recovery project. This paper presents empirical correlations of thermodynamic and transport properties of saturated steam in dimensionless forms as functions of either reduced temperature or reduced pressure. The pressure range of the correlations extends from atmospheric to 3, 000 psia [20.7 MPa]. The properties include saturation temperature, saturation pressure, specific volume, specific enthalpy, specific entropy, isobaric specific heat, dynamic viscosity, thermal conductivity, dielectric constant, surface tension, and isentropic expansion exponents. Compared with values listed in current steam tables, the calculated properties are accurate within ±0.02 % for saturation temperature and pressure, within ±0.12 % for thermodynamic properties, and within ±0.27% for transport properties.

The influence of a third constituent in binary solutions on critical properties studied by viscosity measurements

Abstract Using shear viscosity measurements, the influence of adding a small amount of a third constituent to a critical binary solution of nitrobenzene in n-hexane on the critical temperature of the solution and the critical exponent of viscosity ⊘ has been studied.

Sol—gel transition of alginate solution by additions of various divalent cations: critical behavior of relative viscosity

The critical behavior of viscosity near the gelation point was experimentally investigated for alginate solutions by additions of four different divalent cations. The critical exponent for viscosity was found to lie in the range 0.88–1.14 and is in good agreement with the predictions of percolation theory. The results are also comparable with those of several experiment systems reported in the literature.

Critical exponent for viscosity.

The critical exponent y characterizing the divergence of the viscosity for carbon dioxide and xenon has been measured. The values of y for both fluids fall within the range y = 0.041 + or - 0.001 and are consistent with the range y = 0.042 + or - 0.002 spanned by earlier data for four binary liquid mixtures. This agreement is the strongest evidence that pure fluids and binary liquids are in the same dynamic universality class; however, the results for y are inconsistent with the recent theoretical value of 0.032.

Critical behavior of the specific viscosity of poly(vinyl alcohol) solutions near the gelation threshold

The critical exponent of the specific viscosity, near the sol-gel transition point was examined for poly(vinyl alcohol) solutions and found to be 1.67. This value is larger than those reported previously for various polymerizing systems, and for a gelatin system.

Scaling of the shear viscosity of the system nitrobenzene —n-heptane in the critical region

The temperature dependence of shear viscosity of the system nitrobenzene-n-heptane has been studied near the critical concentration. The critical exponent of the shear viscosity Φ was calculated from the empirical formula $$\eta = \eta _{id} \varepsilon _{sp} ^{ - \Phi } $$ and compared with the theoretical and experimental results obtained for other critical systems. The shear viscosity satisfies scaling law relations similar to those previously established for equilibrium properties.

The thermodynamics of hydrogen isotope exchange in lysozyme: The influence of glycerol

AbstractThe temperature dependence of hydrogen isotope exchange rates for lysozyme in 5 molal aqueous glycerol and for poly (D,L‐alanine) in a range of glycerol concentrations from 0 molal to 8 molal have been determined. The activation enthalpy of base‐catalyzed exchange for poly (D,L‐alanine) in water is 4 kcal/mol and passes through a minimum at about 2 molal glycerol before returning to a value of 4 kcal/mol at 4 molal glycerol. Exchange rates for lysozyme have been analyzed with transition state and Kramers's theories. The activation parameters for exchange of protons in lysozyme in the presence of 5 molal glycerol show a similar qualitative behavior to those determined for exchange in the absence of glycerol [R. B. Gregory et al. (1982) Biochemistry 24, 6523–6530]. The activation enthalpies and entropies for the fast‐exchanging protons show a gentle increase as H(t), the number of hydrogens remaining unexchanged, decreases. By contrast, the activation parameters for the slowest exchanging protons [H(t) &lt; 20] increase dramatically as H(t) decreases. As in water, the activation parameters for exchange of the fast‐ and slow‐exchanging protons in glycerol solution are characterized by two distinct compensation temperatures (510 ± 100 K for the fast protons and 340 ± 40K for the slow protons). These values are not significantly different from those determined for exchange in water.The activation parameters, ΔH‡, and TΔS‡, are both several kcal/ mol lower for exchange in glycerol solutions compared with water. Enthalpy and entropy changes for the thermal unfolding of lysozyme in glycerol solutions [results of K. Gekko (1982) J. Biochem. 19, 1197–1204] are larger than those determined for unfolding in water. This suggests that exchange does not involve local unfolding of segments of the protein. There is evidence for a contribution from thermal unfolding for exchange of the slowest protons in glycerol solutions which is not observed in water.Analysis of exchange rates for the fast protons as a function of temperature and viscosity with Kramers' equation provides values of the viscosity exponent. This is found to increase with decreasing values of H(t). These results are not easily rationalized with Gavish's model [(1980) Phys. Rev. Lett. 44, 1160] of a “position‐dependent, internal protein viscosity” and suggest that the Gavish model of the friction coefficient is incorrect. A dissection of the effect of glycerol on exchange of the fast protons into viscosity and thermodynamic contributions is not possible with the present data. Both factors are suggested to influence exchange of the fast protons.

Scaling of the shear viscosity of the system nitrobenzene—n-hexane in the critical region

Abstract The shear viscosity of the system nitrobenzene—n-hexane was measured along the isochores near the critical concentration. By applying the empirical formula η = ηidε-Φ sp, the critical exponent of the shear viscosity Φ was determined.

A reevaluation of the viscosity exponent for binary mixtures near the consolute point

A reevaluation of the critical exponent of the viscosity anomaly for binary mixtures close to the consolute point is presented. Using published data we make a systematic, consistent study in which corrections due to shear gradients and frequency effects are included and the effect of the functional form for the background viscosity is critically examined. The result is that the value of the exponent is generally found to be larger than reported and larger than the most recent theoretical predictions.