Viscoelastic properties frequency dependence

Very dilute solutions of axisymmetric rigid molecules exhibit not only frequency-dependent viscoelastic properties but also an apparent viscosity which depends on shear rate. This non-Newtonian flow is predicted by theory for elongated ellipsoids and rigid dumbbells,and the theoretical results have been widely applied for certain biological macromolecules. The shear-rate dependent viscosity r) is defined as the ratio of shear stress a to shear rate 7, and the intrinsic viscosity as defined by equation 5 with 77 substituted for rjo is then in general a function of 7. At low shear rates, the shear-dependent intrinsic viscosity has the form... 

Agee, B. L. and L. D. Mitchell, Frequency dependent viscoelastic property measurement via modal analysis techniques, 9th International Conference on Experimental Mechanics, Copenhagen, Denmark, pp. 1978-1988, 1990. 

Dynamic mechanical measurements for elastomers that cover wide ranges of frequency and temperature are rather scarce. Payne and Scott [12] carried out extensive measurements of /a and /x" for unvulcanized natural mbber as a function of test frequency (Figure 1.8). He showed that the experimental relations at different temperatures could be superposed to yield master curves, as shown in Figure 1.9, using the WLF frequency-temperature equivalence, Equation 1.11. The same shift factors, log Ox. were used for both experimental quantities, /x and /x". Successful superposition in both cases confirms that the dependence of the viscoelastic properties of rubber on frequency and temperature arises from changes in the rate of Brownian motion of molecular segments with temperature. 

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

The results of measurements of the dependencies G (w,t) for three circular frequencies w0 = 27tf0, wi= 4rcwo, and w2 = 16jtwo are shown in Fig. 3.1. The lack of coincidence in the shapes of die time dependencies of the dynamic modulus components for different frequencies is obvious. This phenomenon is especially true for G", because the position of the maximum differs substantially along the time axis. In the most general sense, this reflects the contributions of the main relaxation mechanisms of the material to its measured viscoelastic properties. 

The relaxation spectrum H(0) completely characterizes the viscoelastic properties of a material. H(0) can be found from the measured frequency dependence of the dynamic modulus of elasticity G (co) by means of the following integral equation ... 

In the event that the film is not rigid, the EQCM response is a function of both the film mass and its rheological characteristics. Application of the Sauerbrey equation under these circumstances is inappropriate it underestimates the mass change, to an extent that is dependent on the viscoelastic properties of the film. Under these circumstances, there are two questions to be addressed first, how does one diagnose film (non-)rigidity and, second, how does one interpret responses from a non-rigid film The answers to both questions can be found from crystal impedance measurements. This is a technique in which one determines the admittance (or impedance) of the loaded crystal as a function of frequency in the vicinity of resonance. Effectively, one determines the shape (width and height) and position (on the frequency axis) of the resonance, rather than just its position (as in the simple EQCM technique). 

Because of the time-temperature (or frequency-temperature) relation for the viscoelastic properties of polymers there is of course also a corresponding frequency dependence of the acoustic properties of polymers. In Table 14.2 frequency derivatives of sound speeds and absorptions are listed. 

Wu et al. (73) studied the viscoelastic properties, viz. storage modulus (GO and complex viscosity (r 0 with respect to frequency (co) of PLA-carboxylic-acid-functionalized MWCNTs nanocomposites using a rheometer (HAAKE RS600, Thermo Electron Co., USA). The dynamic frequency sweep measurements were carried out at the pre-strain level of 1%. They observed that the addition of carboxylic-acid-functionalized MWCNTs weakened the dependence of G on go, especially at higher loading levels (Figure 9.12). This indicates... 

One further point regarding this mechanism should be made the temperature dependency of the viscoelastic properties. If the impact condition—e.g.9 frequency and temperature—corresponds to an up-slope region of the loss peaks with temperature, then the temperature will continue to rise at an increasing rate, assuming no heat losses. However, examination of the loss peaks would indicate that the temperature rise caused by this effect should be less than 100 °C since for these materials there is a negative slope above 70°-80°C. 

Wetton XSl has described the mechanical characteristics for vibration damping materials in terms of the frequency and temperature dependence of the viscoelastic properties of polymeric materials. Use of polymeric materials in free-layer and constrained layer damping configurations has been discussed in the literature by Ungar (10-12). Kerwin (13.14). and others (15.16). 

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... 

The time-dependent rheological properties of disordered smectics are also peculiar. Figure 10-37 shows apparent G and G" data (labeled MD ) measured for 8CB after a quench from the isotropic state. Quenched samples contain a very high density of smectic defects, which produce elastic-like behavior in G at low frequencies of oscillation. The apparent moduli G and G" in Fig. 10-37 are not true linear viscoelastic moduli, since they were... 

Strictly speaking, there are no static viscoelastic properties as viscoelastic properties are always time-dependent. However, creep and stress relaxation experiments can be considered quasi-static experiments from which the creep compliance and the modulus can be obtained (4). Such tests are commonly applied in uniaxial conditions for simphcity. The usual time range of quasi-static transient measurements is limited to times not less than 10 s. The reasons for this is that in actual experiments it takes a short period of time to apply the force or the deformation to the sample, and a transitory dynamic response overlaps the idealized creep or relaxation experiment. There is no limitation on the maximum time, but usually it is restricted to a maximum of 10" s. In fact, this range of times is complementary, in the corresponding frequency scale, to that of dynamic experiments. Accordingly, to compare these two complementary techniques, procedures of interconversion of data (time frequency or its inverse) are needed. Some of these procedures are discussed in Chapters 6 and 9. 

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