Viscoelastic parameter

Viscoelastic parameters Ki, K2 and q of the model are determined by fitting the experimental curve V(t) to the sum of cosines with constant coefficients ... 

Many other techniques of measuring viscoelastic parameters, such as transient shear, creep and sinusoidally-varying shear, are available. A good description, together with the merits and demerits of each of these techniques, is available in Whorlow(19. ... 

FIGURE 6.9 Dependence of viscoelastic parameters on solvent quality. The (A) static force, (B) drag coefficient at 10 kHz, (C) dynamic spring constant, and (D) dispersion parameter are shown as a function of the surface-sphere distance. The results for water, propanol, and a 50/50 water/propanol mixture are given. Reprinted with permission from Benmouna and Johannsmann (2004). 

Assuming that a number of NMR data sets (e.g., 2-D or 3-D maps of displacement vectors resulting from an external periodic excitation) from an object are acquired, the remaining difficulty is their reconstruction into viscoelastic parameters. As written in Section 2 the basic physical equation is a partial differential equation (PDE, Eq. (3)) relating the displacement vector to the density, the attenuation, Young s modulus and Poisson s ratio of the medium. The reconstruction problem is indeed two-fold ... 

The forward problem is the calculation of displacement fields from input viscoelasticity parameters. The latter describe correctly the investigated object if the calculated and measured displacement images converge. 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

Hooke s Law, which states that a proportional relationship exists between stress and strain, usually holds for a viscoelastic material at a small strain. This phenomenon is called linear viscoelasticity (LVE). Within the LVE region, the viscoelastic parameters G and G" remain constant when the amplitude of the applied deformation is changed. Consequently, parameters measured within the LVE region are considered material characteristics at the observation time (frequency). 

Figure 3.18 shows different surface relaxation modes and the corresponding viscoelastic parameters [59],... 

The dilatational rheology of the poly(vinylacetate) monolayer onto an aqueous subphase has been studied between 1°C and 25°C by Monroy et al. [59], These authors have used the combination of several techniques. By this way, the exploration of a broad frequency range was possible. The relaxation experiments have shown multiexponential decay curves, whose complexity increases with decreasing the temperature. A regularization technique has been used to obtain the relaxation spectra from the relaxation curves and the dilatational viscoelastic parameters have been calculated from the spectra. The shapes of the relaxation spectra agree with the predictions of the theoretical model proposed by Noskov [100],... 

Two other technical issues must be discussed briefly. In deducing the viscoelastic parameters through the dispersion equation from the power spectrum of SLS, it must be corrected for the instrumental broadening. The other... 

It is necessary to state more precisely and to clarify the use of the term nonlinear dynamical behavior of filled rubbers. This property should not be confused with the fact that rubbers are highly non-linear elastic materials under static conditions as seen in the typical stress-strain curves. The use of linear viscoelastic parameters, G and G", to describe the behavior of dynamic amplitude dependent rubbers maybe considered paradoxical in itself, because storage and loss modulus are defined only in terms of linear behavior. 

Tsardaka, K. D., and Rees, J. K. (1990), Relations between viscoelastic parameters and compaction properties of two modified starches, J. Pharm. Pharmacol., 42,77R... 

AW device sensitivity to viscoelastic parameters and electrical pnqieities can be used to advantage in some film characterization techniques. In these situations, a comparison of the AW device response to a model of the AW/thin film interaction is often crucial to the effective evaluation of thin film parameters. These additional interaction mechanisms typically involve changes in both the wave velocity and the wave attenuation for SAW, APM and FPW devices, and changes in both resonant frequency and admittance magnitude in TSM devices. In contrast, mass loading does not contribute to wave attenuation or decreases in admittance since moving mass involves no power dissipation (see Chapter 3). 

One may use the linear viscoelastic data as a pure rheological characterization, and relate the viscoelastic parameters to some processing or final properties of the material inder study. Furthermore, linear viscoelasticity and nonlinear viscoelasticity are not different fields that would be disconnected in most cases, a linear viscoelastic function (relaxation fimction, memory function or distribution of relaxation times) is used as the kernel of non linear constitutive equations, either of the differential or integral form. That means that if we could define a general nonlinear constitutive equation that would work for all flexible chains, the knowledge of a single linear viscoelastic function would lead to all rheological properties. 

We will discuss in this section the variations of the viscoelastic parameters derived from linear viscoelastic measurements all these parameters may be derived from any t3rpe of measurement (relaxation or creep experiment, mechanical spectroscopy) performed in the relevant time or frequency domain. The discussion will be focused however on the complex shear modulus which is the basic function derived from isothermal frequency sweep measurements performed with modem rotary rheometers. 

Some general important remarks may be formulated regarding the characteristic viscoelastic parameters of these polymers with long chain branching ... 

Remembering that three characteristic molecular weights are defined from viscoelastic parameters Mg, the molecular weight between entan ements,... 

Some terminal viscoelastic parameters have also been evaluated at 160°C using a Cole-Cole expression for the dynamic viscosity. Table Ic shows the zero shear viscosity (t]o)> the characteristic relaxation time (ko, corresponding to the... 

Table 3-4 Viscoelastic Parameters from Shear, Simple Extension, and Bulk Compression...

The time-temperature superposition method can be also applied to viscosity data (Ferry, 1980). For any viscoelastic parameter, exact matching of the adjacent curves is an important criterion for the applicability of the method. In addition, when possible, the same values of oy must superpose all the viscoelastic parameters and the temperature dependence of ar should have a reasonable form based on experience. One advantage of the method is that the range of frequencies are extended beyond those available experimentally. The time-temperature method has been also referred to as thermorheological simplicity (Plazek, 1996). 

We note that the creep-compliance parameters can be used to calculate the moduli Ei = 1/J, and viscosities t]i = EiXi. In the following, the magnitudes of the viscoelastic parameters, that is, the moduli and the viscosities, will be discussed. 

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