Viscoelastic properties of liquid crystals of aqueous biopolymer solutions

The formation of aqueous, lyotropic phases of the biopolymers xanthan (M = 1.6·10⁶) and schizophyllan (M _W = 335 000) is investigated with stationary shear flow and oscillatory measurements, as well as with the aid of polarization microscopy, because these polymers show very different viscoelastic properties from coiled vinyl polymers. Xanthan and schizophyllan exhibit the same typical behavior observed in anisotropic solutions when the viscosity is plotted as a function of concentration and of shear rate. It has also been observed that the first normal stress difference for concentrated xanthan solutions shows a saturation effect at increasing shear rate. In oscillatory measurements only schizophyllan exhibits an maximum for the storage modulus. The absence of a such an elasticity maximum in the case of the xanthan solution may be attributed to the significantly higher flexibility of the xanthan helix. A comparison of the critical concentrations calculated according to Flory's theory and the experimentally determined values shows that the two-phase region is distinctly broader than the theory predicts. This deviation cannot be attributed to the flexibility of the polymer, but can, however, be explained by intermolecular interactions. In contrast to the non-charged schizophyllan the polyelectrolyte xanthan is affected in addition to the attractive interactions (H-bonds) by electrostatic repulsion forces.This paper was partly presented at the 198th ACS National Meeting in Miami Beach, Florida, Sept. 10–15, 1989 .     

Viscoelastic properties of semidilute poly(methyl methacrylate) solutions

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G _N . Two time constants, _s and ₁, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant _k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios ₁/ _s and _k / _s were determined solely by N for each polymer species. The ratio ₁/ _s was proportional to N ^4.5 and N ^3.5 for PMMA and PS solutions, respectively. The ratio _k / _s was approximately proportional to N ^2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants _s and G _N are known.     

Quantitative description of rheological properties of dilute polymer solutions

The Rouse-Zimm model has been generalized to describe the rheology of dilute polymer solutions at moderate shear rates by allowing for a reduced-shear-rate dependent slippage of the carrier solvent in the neighbourhood of the polymer coil with respect to the macroscopic continuum. A comparison of the theoretical predictions with published viscosity data for monodisperse polymer systems shows good agreement. Thus it appears to be sufficient to measure the intrinsic viscosity in order to estimate all the material functions of interest for the steady and dynamic shear flow of dilute polymer solutions.     

Viscoelastic solutions for conical indentation

The aim of indentation analysis is to link indentation data, typically an indentation force vs. indentation depth curve, P–h, to meaningful mechanical properties of the indented material. While well established for time independent behavior, the presence of a time dependent behavior can strongly affect both the loading and the unloading responses. The paper presents a framework of viscoelastic indentation analysis based on the method of functional equations, developed by Lee and Radok [1960, The contact problem for viscoelastic bodies, J. Appl. Mech. 27, 438–444]. While the method is restricted to monotonically increasing contact areas, we show that it remains valid at the very beginning of the unloading phase as well. Based on this result, it is possible to derive closed form solutions following the classical procedure of functional formulations of viscoelasticity: (1) the identification of the indentation creep function, which is the indentation response to a Heaviside load; and (2) a convolution integral of the load history over the indentation creep function. This is shown here for a trapezoidal loading by a conical indenter on three linear isotropic viscoelastic materials with deviator creep: the 3-parameter Maxwell model, the 4-parameter Kelvin–Voigt model and the 5-parameter combined Kelvin–Voigt–Maxwell model. For these models, we derive closed form solutions that can be employed for the back-analysis of indentation results from the loading and holding period and for the definition of unloading time criteria that ensure that viscous effects are negligible in the unloading response.     

Steady and dynamic shear properties of non-aqueous drag-reducing polymer solutions

The steady and dynamic shear properties of two non-aqueous drag-reducers (a medium molecular weight polyisobutylene and a commercial organic drag-reducer) in kerosene solutions over a wide range of temperature and concentration were presented. The intrinsic and zero-shear viscosity results were used to identify the concentrate regimes of these solutions. A characteristic time constant λ₀, which was based on the spring-bead model for dilute solutions, was employed as the scaling parameter for both steady-shear and dynamic data over a wide range of concentration and temperature. The inadequacy of the Graessley reduced-variable method in the dilute region was illustrated. The shear-thinning behaviour of these polymer solutions could be described by the Carreau model. The dynamic data followed the Zimm and Rouse-like behaviour in the low and high frequency limits. The Cox-Merz rule was obeyed in the low shear rate and frequency regions. The Carreau and the zero-frequency Maxwell time constants appeared to be related to λ₀ by a constant factor over a wide range of polymer concentrations. The finding provides a method for extrapolating viscoelastic information into the drag reduction regime, and could be useful for interpretation of drag reduction results.     

Viscoelastic properties of human cornea

Viscoelastic response of intact human cornea subjected to physiological intraocular pressure was determined from local deformations measured by a flying spot micrometer. One eye of a paired specimen was prepressurized at 15 mmHg for at least 8 hr while the other eye was left unpressurized before testing. Test results of five paired eyes showed that, in prepressurized enucleated eyes, the viscoelastic response was insignificant while significant viscoelastic response existed in the nonpressurized eyes. The latter viscoelastic properties were characterized by a five-element linear viscoelastic model and a nonlinear hereditary integral by Fung.     

Viscoelastic properties of fractal media

Temporal fractal sets for analysis of viscoelastic properties of nonhomogeneous media are considered. A fractional derivative directly related to fractal dimension is constructed. The relationship between the diffusion of the relaxation spectrum and the fractal dimension is established. Odessa State Polytechnical University, Odessa 270044, Ukraine. Institute of Molecular Physics, Polish Academy of Sciences, Poznan, Poland. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 162–172, January–February, 2000.     

Viscoelastic properties of laminated bodies

In this paper we define a class of two-phase laminate composites for which the constituent elements are either linearly elastic or exhibit viscoelastic effects. We determine the viscoelastic behaviour of the equivalent homogeneous transversely isotropic medium by a single time-independent memory function.     

Viscoelastic properties of magnetorheological fluids

We have studied the rheological properties of some magnetorheological fluids (MRF). MRF are known to exhibit original rheological properties when an external magnetic field is applied, useful in many applications such as clutches, damping devices, pumps, antiseismic protections, etc. While exploiting parameters such as magnetic field intensity, particle concentration and the viscosity of the suspending fluid, we highlighted the importance of each one of these parameters on rheology in the presence of a magnetic field. We made this study by conducting rheological experiments in dynamic mode at very low strain which facilitates the comprehension of the influence of the structure on MRF rheology. Our results confirmed the link between the magnetic forces which ensure the cohesion of the particles in aggregates, and the elastic modulus. Moreover, we found that the loss modulus varies with the frequency in a similar manner than the elastic modulus. The system, even with the smallest deformations, was thus not purely elastic but dissipates also much energy. Moreover, we demonstrated that this dissipation of energy was not due to the matrix viscosity. Actually, we attributed viscous losses to particle movements within aggregates.     

Rheological properties of dilute polymer solutions: An extended thermodynamic approach

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.     

Measurement of dynamic properties of dilute polymer solutions with a Laser-Doppler velocimeter

The complex velocity field of an oscillating Couette flow is measured with a Laser-Doppler velocimeter. Different evaluation methods are used for the determination of material functions such as relaxation times and the dynamic complex viscosity.     

Viscoelastic properties of butadiene-styrene block copolymers

Summary The viscous properties of SBS block copolymers (of Cariflex TR-1102 in this work) have been determined with the rate of shear being varied by 10⁸ times. It has been shown that in the region of low shear rates the polymer behaves as a structured highly concentrated disperse system which exhibits sharply pronounced thixotropy. In the region of high shear rates, the viscous properties of the polybutadiene matrix are of decisive importance. At low values of shear stress the compliance of the SBS block copolymer exceeds that of the polybutadiene matrix almost by a decimal order.At high shear stresses, just as in the case of viscous properties, the elastic behaviour of the SBS block copolymer approaches that of the polybutadiene matrix. Measurements of the dynamic characteristics at frequencies, which vary by a million times, most spectacularly point to the specificity of the viscoelastic properties over a wide temperature range. Under conditions of low temperatures the SBS block copolymer behaves as a rubber, while at temperatures above the glass transition temperature of polystyrene, at low loading intensities (low amplitudes and small deformations) the block copolymer shows low fluidity. This is most clearly seen from the frequency dependence of the loss modulus, especially in comparison with the relation typical of polybutadiene.

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Zusammenfassung Die viskosen Eigenschaften von SBS-Block-Copolymeren (hier Cariflex TR-1102) werden in einem Bereich von acht Zehnerpotenzen der Schergeschwindigkeit untersucht. Es wird gezeigt, daß im Bereich niedriger Schergeschwindigkeiten das Polymer sich wie ein strukturiertes hochkonzentriertes disperses System verhält, das eine ausgeprägte Thixotropie besitzt. Im Bereich hoher Schergeschwindigkeiten sind dagegen die viskosen Eigenschaften der Polybutadien-Matrix von entscheidender Bedeutung. Bei niedrigen Schubspannungswerten übersteigt die Komplianz des SBS-Block-Copolymeren diejenige der Polybutadien-Matrix höchstens um etwa 10%.Bei hohen Schubspannungen nähert sich das elastische Verhalten analog wie bei den viskosen Eigenschaften demjenigen der Polybutadien-Matrix an. Die Messung der dynamischen Charakteristiken über einem Frequenzbereich von sechs Zehnerpotenzen lassen die spezifischen viskoelastischen Eigenschaften in einem weiten Temperaturbereich sehr deutlich erkennen. Bei tiefen Temperaturen verhält sich das Polymer wie ein Gummi, während bei Temperaturen oberhalb der Glasübergangstemperatur des Polystyrols unter geringer Belastung (d.h. kleinen Amplituden bzw. Deformationen) das Polymer eine geringe Fluidität zeigt. Dies erkennt man am deutlichsten an der Frequenzabhängigkeit des Verlustmoduls, insbesondere durch Vergleich mit derjenigen bei Polybutadien.

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Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

Viscoelastic properties of polymerlike reverse micelles

A dramatic increase in the viscosity of reverse micellar solutions of lecithin in a variety of organic solvents of up to a factor of 10⁶ upon the addition of a small amount of water can be observed. The formation of viscoelastic solutions can be explained by a water-induced aggregation of lecithin molecules into flexible cylindrical reverse micelles and the subsequent formation of a transient network of entangled micelles. The viscoelastic properties of these solutions are characterized as a function of water content and temperature for different organic solvents by means of dynamic shear viscosity measurements. The results are interpreted by making analogies to the behavior of semidilute polymer solutions and living polymers.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

Viscoelastic plastic rheological model for particle filled polymer melts

A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.     

Some general rheological properties of dilute polymer solutions predicted from intrinsic viscosity measurements

Expressions for the rheological properties of dilute polymer solutions at low and moderate deformation rates are established through the computation and analysis of exact Zimm's eigenvalues. It is shown that they can be expressed in terms of measurable parameters from intrinsic viscosity data. Under moderate deformation rates one needs to introduce a slippage between the solvent and the smoothed polymer to be able to describe shear-thinning behaviour.