Viscoelasticity complex shear viscosity

Complex shear viscosity of carbon nanofibre reinforced PEEK composites as a function of frequency, at a temperature of 360°C, in the linear viscoelastic regime. The insert shows the resulting shear thinning exponent as a function of nanofibre content. 

A viscoelastic material also possesses a complex dynamic viscosity, rj = rj - - iv( and it can be shown that r = G jiuj-, rj = G juj and rj = G ju), where CO is the angular frequency. The parameter Tj is useful for many viscoelastic fluids in that a plot of its absolute value Tj vs angular frequency in radians/s is often numerically similar to a plot of shear viscosity Tj vs shear rate. This correspondence is known as the Cox-Merz empirical relationship. The parameter Tj is called the dynamic viscosity and is related to G the loss modulus the parameter Tj does not deal with viscosity, but is a measure of elasticity. 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

Figure 8.12 illustrates the effect of complex formation between protein and polysaccharide on the time-dependent surface shear viscosity at the oil-water interface for the system BSA + dextran sulfate (DS) at pH = 7 and ionic strength = 50 mM. The film adsorbed from the 10 wt % solution of pure protein has a surface viscosity of t]s > 200 mPa s after 24 h. As the polysaccharide is not itself surface-active, it exhibited no measurable surface viscosity (t]s < 1 niPa s). But, when 10 wt% DS was introduced into the aqueous phase below the 24-hour-old BSA film, the surface viscosity showed an increase (after a further 24 h) to a value around twice that for the original protein film. Hence, in this case, the new protein-polysaccharide interactions induced at the oil-water interface were sufficiently strong to influence considerably the viscoelastic properties of the adsorbed biopolymer layer. 

Polymer melts are complex fluids. Their viscoelastic properties during flow depend not only on their molecular structure but also on the interactions they are likely to develop at the walls, depending on the physical and chemical features of the interface and the flow conditions. In addition, not all their properties can be determined and the constitutive equations used are in practice often limited to considerations on the shear viscosity. From a theoretical point of view, considerable difficulties are involved and the problem to be studied here has not been solved. In particular, even though the boundary conditions considered in... 

In this book, we review the most basic distinctions and similarities among the rheological (or flow) properties of various complex fluids. We focus especially on their linear viscoelastic behavior, as measured by the frequency-dependent storage and loss moduli G and G" (see Section 1.3.1.4), and on the flow curve— that is, the relationship between the "shear viscosity q and the shear rate y. The storage and loss moduli reveal the mechanical properties of the material at rest, while the flow curve shows how the material changes in response to continuous deformation. A measurement of G and G" is often the most useful way of mechanically characterizing a complex material, while the flow curve q(y ) shows how readily the material can be processed, or shaped into a useful product. The... 

A single-relaxation-time response is also observed for this fluid in other flow histories, including start-up and cessation of steady shearing, if the shear rate y is low enough. At higher shear rates, the viscoelastic response is more complex. Figure 12-11 shows the time-dependence of the shear viscosity r] after start-up of steady shearing for a solution... 

The viscoelasticity in polymer solutions has been investigated for some time but the experimental techniques which enabled measurements at high dilutions have been developed since around 1948 (24). When a polymer solution is subject to a sinusoidally varying shearing stress its response can be expressed in terms of a complex intrinsic viscosity [j ], the imaginary part of which is the rigidity ... 

Abstract Grease lubrication is a complex mixture of science and engineering, requires an interdisciplinary approach, and is applied to the majority of bearings worldwide. Grease can be more than a lubricant it is often expected to perform as a seal, corrosion inhibitor, shock absorber and a noise suppressant. It is a viscoelastic plastic solid, therefore, a liquid or solid, dependent upon the applied physical conditions of stress and/or temperature, with a yield value, ao- It has a coarse structure of filaments within a matrix. The suitability of flow properties of a grease for an application is best determined using a controlled stress rheometer for the frequency response of parameters such as yield, a, complex shear modulus, G phase angle, 5, and the complex viscosity, rj. ... 

For the step from the 3D-rheology to the 2D-state, to the surface rheology, it is best to use the vector treatment for describing the complex variables of strain s , stress complex viscosity T , complex shear modulus G , respectively, ri and G are viscoelastic vectors. The relating vector treatment for strain in a shear deformation is shown in Fig. 3.7. 

Different techniques for the study of shear rheology of interfacial layers have been developed over the years however, they are mostly suited for liquid/gas inter faces. The early instruments were constructed to measure the interfacial shear viscosity under constant shear conditions. In more complex systems, nonlinear effects, shear-rate dependencies of the viscosity, and viscoelastic properties are... 

The attractiveness of dynamic analysis is that an accurate determination of the viscoelastic behavior can be made. A common geometry for dynamic measurements is the cone and plate rheometer. In dynamic analysis, the viscosity components can be measured up to an angular frequency of about 500 radians/s. Cox and Merz [72] found empirically that the steady shear viscosity corresponds to the complex viscosity if the shear rate in s is plotted on the same scale as the angular frequency in radians/s. This can be stated as ... 

Some of the manifestations of viscoelasticity are delayed relaxation of stress after cessation of flow phase shift between stress and strain rate in oscillatory shear flow shear thinning (decrease of viscosity) at shear rates exceeding the reciprocal of the longest relaxation time and normal stress differences in shear flow, whose magnitudes are related to the relaxation time spectrum. A very convenient observation for experimentalists is that there is a close similarity between the shear viscosity and first normal stress difference as functions of shear rate and the corresponding parameters, complex viscosity and storage modulus, as functions of frequency in a small amplitude oscillatory shear. 

The results of investigation of the interfacial properties (thermodynamic and rheological) of the aqueous gelatin/ lecithin mixtures in the wide range of component ratios are presented in this work for the first time. It has been shown that adsorption of gelatin/lecithin complexes (formed in the bulk aqueous phase) at the immiscible liquid interface leads to self-assembly of the interfacial viscoelastic layer. The non-monotonic time-dependent interfacial shear viscosity and elastic modulus evolution were observed. This effect was explained by the phase transitions proceeding in time at the liquid interface in the systems containing lecithin. 

An unfortunate usage of the term bulk viscosity is common among polymer chemists, in the sense of the ordinary shear viscosity of a polymer in bulk, as contrasted with its viscosity in dilute solution. In acoustics, bulk viscosity means the viscosity associated with a change in volume, and this definition fits in best with the nomenclature of viscoelasticity. In this book, the complex dynamic bulk viscosity refers to 77 = K /iu). 

We have reported [66] a limited study of spread polymethyl methacrylates and polyethylene oxide. Figure 12.19 shows the variation in surface tension, shear viscosity and dilational modulus obtained from SQELS data as a function of surface concentration. The viscoelastic moduli both show maximum values at finite values of the surface concentration. As the capillary waves generate oscillatory stress and strain, these are related via the complex dynamic modulus of the surface... 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

The investigations of model compositions, based on linear elastomers and various fillers, have shown that the yield stress also may be characterized by the value of the complex shear modulus measured at various frequencies. The dependence of the dynamic modulus on the filler concentration characterizes critical concentrations of the filler, above which the viscoelastic behavior of composition drastically changes. Dynamic modulus corresponding to the yield stress does not depend on the matrix viscosity or its nature. This fact indicates a predominant role of the structural frame for rheological properties of filled polymers. 

It was these studies of the complex dielectric constant as a function of frequency which led to the search for euialogous methods of studying viscoelasticity hy measuring a complex viscosity or elastic modulus. The first success was observation of shear wave propagation in polymer solutions . The only theoretical treatment of wave propagation which could he found as a clue to analysis of the measurements was in a geophysical journal. From the wave propagation the complex shear modulus and its frequency dependence could be derived. 

The viscoelastic characteristics are usually obtained from the results of dynamic experiments in which knowledge of the law of the change in the molecular orientation with variable loads is even more important for the correct interpretation of the results than in the case of steady-state shear flow. The absence of a homogeneous orientation in each cycle can be the cause of the almost constantly observed difference in the values of the complex dynamic viscosity Tj and the related characteristic in the established flow mode in conditions of the comparison of y = co (co is the angular frequency). Generally speaking, despite the qualitative correlation between the dynamic and steady-state characteristics of LC polymers, quantitative coincidence between them is usually... 

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