Viscoelastic behavior Polymer , displacement

Accordingly, given the necessity from equilibrium coil dimensions that bt> 1, the shear rate and frequency departures predicted by FENE dumbbells are displaced from each other. Moreover, the displacement increases with chain length. This is a clearly inconsistent with experimental behavior at all levels of concentration, including infinite dilution. Thus, finite extensibility must fail as a general model for the onset of nonlinear viscoelastic behavior in flexible polymer systems. It could, of course, become important in some situations, such as in elongational and shear flows at very high rates of deformation. 

The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. 

This chapter discnsses this new concept. It first reviews some flnid viscoelastic properties. Then it presents the evidence of polymer viscoelastic behavior in the laboratory and in the field. In addition, this chapter discnsses the displacement mechanisms of polymer solntion and the effect of viscoelastic polymer solntion on held facilities and operations. 

Wang, D.-M., Xia, H.-E, Liu, Z.-C., Yang, Q.-Y, 2001b. Study of the mechanism of polymer solution with viscoelastic behavior increasing microscopic oil displacement efficiency and the forming of steady Oil Thread flow channels. Paper SPE 68723 prepared at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, 17-19 April. 

S.3.2 Dynamic Mechanical Analysis (DMA) Storage and Loss Modulus Dynamic mechanical analysis (DMA) is typically performed to measure the viscoelastic behavior of polymer networks. A sinusoidal force (stress) is applied to a material and the resulting displacement (strain) is measured, allowing one to determine the complex modulus. 

When a plastics (polymer) is subjected to stress, the structure can react in a number of ways. In the first reaction the bonds are stressed by stretching or bending which is the elastic response. Unlike the more ordered structures, adjustment of the strain in the materials is hindered by the interference between molecules so that all but the very initial response is hindered by frictional effects and the material shows a delay between the application of the stress and the resulting strain. This behavior is referred to as viscoelastic behavior. From Fig. 1-9 it can be seen how the molecules slide past each other to increase spacings and reduce the elastic load on the bonds. Sustained stress causes actual displacement of the molecular chains with extensive movement of the chains past each other and results in flow-like behavior which is referred to as creep or cold flow. At constant initial strain the slippage of the molecules and the adjustment of position lead to another condition which is called stress relaxation. The level of the resistance of the structure to applied deformation drops and the material assumes a lower energy configuration. 

This section considers the behavior of polymeric liquids in steady, simple shear flows - the shear-rate dependence of viscosity and the development of differences in normal stress. Also considered in this section is an elastic-recoil phenomenon, called die swell, that is important in melt processing. These properties belong to the realm of nonlinear viscoelastic behavior. In contrast to linear viscoelasticity, neither strain nor strain rate is always small, Boltzmann superposition no longer applies, and, as illustrated in Fig. 3.16, the chains are displaced significantly from their equilibrium conformations. The large-scale organization of the chains (i.e. the physical structure of the liquid, so to speak) is altered by the flow. The effects of finite strain appear, much as they do when a polymer network is deformed appreciably. 

Furthermore, the magnitude of the relaxation modulus is a function of temperature to more fuUy characterize the viscoelastic behavior of a polymer, isothermal stress relaxation measurements must be conducted over a range of temperatures. Figure 15.6 is a schematic log ,(f)-versus-log time plot for a polymer that exhibits viscoelastic behavior. Curves generated at a variety of temperatures are included. Key features of this plot are that (1) the magnitude of EXt) decreases with time (corresponding to the decay of stress. Equation 15.1), and (2) the curves are displaced to lower EXt) levels with increasing temperature. 

There is considerable evidence that all the hysteresis effects observed in these materials and most of the viscoelastic behavior can be caused by the time dependent failure of the polymer on a molecular basis and are not due to internal viscosity [1,2]. At near equilibrium rates and small strains filled polymers exhibit the same type of hysteresis that many lowly filled, highly cross-linked rubbers demonstrate at large strains [1-8]. This phenomenon is called the "Mullins Effect" and has been attributed to micro-structural failure. Mullins postulated that a breakdown of particle-particle association and possibly also particle-polymer breakdown could account for the effect [3-5]. Later Bueche [7,8] proposed a molecular model for the Mullins Effect based on the assumption that the centers of the filler particles are displaced in an affine manner during deformation of the composite. Such deformations would cause a highly non-uniform strain and stress gradient in the polymer... 

Much more information can be obtained by examining the mechanical properties of a viscoelastic material over an extensive temperature range. A convenient nondestmctive method is the measurement of torsional modulus. A number of instmments are available (13—18). More details on use and interpretation of these measurements may be found in references 8 and 19—25. An increase in modulus value means an increase in polymer hardness or stiffness. The various regions of elastic behavior are shown in Figure 1. Curve A of Figure 1 is that of a soft polymer, curve B of a hard polymer. To a close approximation both are transpositions of each other on the temperature scale. A copolymer curve would fall between those of the homopolymers, with the displacement depending on the amount of hard monomer in the copolymer (26—28). 

Polymer properties exhibit time-dependent behavior, which is dependent on the test conditions and polymer type. Figure 1.7 shows a typical viscoelastic response of a polymer to changes in testing rate or temperature. Increases in testing rate or decreases in temperature cause the material to appear more rigid, while an increase in temperature or decrease in rate will cause the material to appear softer. This time-dependent behavior can also result in long-term effects such as stress relaxation or creep. These two time-dependent behaviors are shown in Fig. 1.8. Under a fixed displacement, the stress on the material will decrease over time, and this is called stress relaxation. This behavior can be modeled nsing a... 

Although the experiments described in the foregoing section are very helpful for developing our intuition about the behavior of viscoelastic fluids such as polymers, they are not suitable for obtaining and cataloging information about specific polymeric materials. For the characterization of polymers it is necessary to make careful measurements of stresses in systems where the velocity or displacement field is known within rather strict limits. These rheometric experiments provide information about one or more of the stress components as functions of shear rate, frequency, or of other controllable variables these functions are generally referred to as material functions , since they are different for each material. Once these material functions have been measured, they can be used to test various empirical or molecular expressions for the stress tensor (that is, the constitutive equation), or they can be used to establish the values of the parameters that appear in these stress-tensor expressions. 

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