Complex viscoelastic functions viscosity

The appropriate viscoelastic functions are ordinarily the complex modulus or the complex viscosity, and the corresponding quantities extrapolated to infinite dilution are the intrinsic storage and loss moduli... 

Time and frequency do not enter the above calculations. However, the solutionlike-meltlike transition suggested a structure for fixed points of the Altenberger-Dahler renormalization group. An ansatz extending the structure from a single concentration variable to a two-variable concentration-time plane indicated a possible form for the complex viscosity(14). Chapter 13 successfully compares the ansatz predictions with experiment. This two-parameter temporal scaling approach has since been applied successfully to describe viscoelastic functions of linear polymers and soft-sphere melts(15), of star polymers(16), and of hard-sphere colloids(17). 

For some materials the linear constitutive relation of Newtonian fluids is not accurate. Either stress depends on strain in a more complex way, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known collectively as non-Newtonian. Many different types of behavior have been observed, ranging from fluids for which the viscosity in the Navier-Stokes equation is a simple function of the shear rate to the so-called viscoelastic fluids, for which the constitutive equation is so different that the normal stresses can cause the fluid to flow in a manner opposite to that predicted for a Newtonian fluid. 

A particular question of interest is whether the DNA torsional motions observed on the nanosecond time scale are overdamped, as predicted by simple Langevin theory, and as observed for Brownian motions on longer time scales, or instead are underdamped, so that damped oscillations appear in the observed correlation functions. A related question is whether the solvent water around the DNA exhibits a normal constant viscosity on the nanosecond time scale, or instead begins to exhibit viscoelastic behavior with a time-, or frequency-, dependent complex viscosity. In brief, are the predictions for... 

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... 

Dynamic-shear measurements are of the complex viscosity rj ) as a function of the dynamic oscillation rate (o), at constant temperature. These tests are defined as isothermal dynamic frequency sweeps. Since the dynamic frequency sweeps are conducted at a given amplitude of motion, or strain, it is necessary to ensure that the sweeps are conducted in the region where the response is strain-independent, which is defined as the linear viscoelastic region. This region of strain independence is determined by an isothermal strain sweep, which measures the complex viscosity as a function of applied strain at a given frequency. This ensures that a strain at which the dynamic frequency sweep may be conducted in the linear viscoelastic region is selected. 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

Sensitivity of the Techniques with Respect to Phase Separation. Simultaneous cloud-point and viscoelastic measurements were made at 130 °C. Figure 3 shows that phase separation is not detected at the same time by these two techniques. Complex viscosity is more sensitive to the beginning of phase separation. Cloud-point sensitivity is a function of the wavelength of the light. For our experiment, the use of white light determines the sensitivity at approximately 0.1 xm. However, in the last step of phase separation (when the transmitted light intensity still varies), the increase of viscosity due to gelation of the resin hides the end of the phenomenon. 

Thus either G (to) or G"(co) as a function of to gives the information equivalent to that included in G(t) as a function of t. The complex modulus is experimentally a more convenient quantity to describe the linear viscoelasticity of low-viscosity fluids than the relaxation modulus (1). The complex modulus is related to the complex viscosity / (co) and the complex compliance J (to) ... 

This test method employs nonresonant forced vibration techniques for determining the complex viscosity (see below) and viscoelastic characteristics of thermoplastic resins as a function of frequency, strain amplitude, temperature, and time. A wide range of frequencies can be used, typically from 0.01 to 100 Hz. 

The viscosity of a liquid is a parameter that measures the resistance of that liquid to flow. For example, water has a very low viscosity, while honey has a much larger or thicker viscosity. Newtonian fluids have constant values of viscosity, which means that the stress in a flowing liquid is proportional to the rate of strain of the flow. Non-Newtonian liquids do not have constant viscosity, but rather have viscosities that can be functions of the rate of strain, the total amount of strain, and other flow characteristics. Huids are usually non-Newtonian as a result of microscopic additives such as polymers or particles. These additives alter the viscosity of a liquid and impart nonlinear flow behavior, such as viscoelasticity. The non-Newtonian behavior of many complex liquids is described thoroughly in several texts, for example [1]. In this entry we focus on behavior and applications of polymer solutions in microfluidic devices. For example, DNA is a biopolymer that is common in microfluidics applications such as gene sequencing and amplification. 

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 system can be further characterised by measurement of the mechanical spectrum at a strain within the linear viscoelastic region defined by the strain sweep. Here the storage (G ) and loss (G") modulus, and complex viscosity (r) ) are measured as a function of frequency (u)) and plotted on double logarithmic plots. Typical mechanical spectrum of entanglement solutions are shown in Figure 2.9. 

The cone and plate viscometer can be used for oscillatory shear measurements as well. In this case, the sample is deformed by an oscillatory driver which may be mechanical or electromagnetic. The amplitude of the sinusoidal deformation is measured by a strain transducer. The force deforming the sample is measured by the small deformation of a relatively rigid spring or tension bar to which is attached a stress transducer. On account of the energy dissipated by the viscoelastic polymer system, a phase difference develops between the stress and the strain. The complex viscosity behavior is determined from the amplitudes of stress and strain and the phase angle between them. The results are usually interpreted in terms of the material functions, p, G, G" and others [33-40]. 

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