Viscoelasticity linear regime

The viscoelastic nature of polymers generally determines rate and temperature dependence of their mechanical properties. At low strain levels, i.e. in a linear regime, this dependence is well described by intrinsic material properties defined within constitutive viscoelastic laws [1]. At high strains, in presence of failure processes, such as yielding or fracture, it is more difficult to establish a constitutive behaviour as well as to define material properties able to intrinsically characterise the failure process and its possible viscoelastic features. 

Doi molecular theory adds a probability density function of molecular orientation to model rigid rodlike polymer molecules. This model is capable of describing the local molecular orientation distribution and nonlinear viscoelastic phenomena. Doi theory successfully predicts director tumbling in the linear regime and two sign changes in the first normal stress difference,as will be discussed later. However, because this theory assumes a uniform spatial structure, it is unable to describe textured LCPs. 

Because of the complications caused by the stress-induced orientation of clay platelets resulting in different rheological responses, the studies of CPNC flow focus on smaU-amplitude oscillatory shear flow (SAGS). As the discussion on the steady-state flow indicates, there is a great diversity of structures within the CPNC family. Whereas some nanocomposites form strong three-dimensional structures, others do not thus while nonlinear viscoelastic behavior is observed for most CPNCs, some systems can be smdied within the linear regime. 

At this point the reptation theory makes some strong predictions about the viscoelastic response in the linear regime, viz, the viscosity varies as and the ratio of Js°/Gn = 6/5 = 1.2. Note that the molecular weight dependence of the viscosity has already been discussed above, and recall that, experimentally, the viscosity varies as N -. In addition, the ratio is observed experimentally... 

An alternative way to learn about viscoelastic properties of polymer melts in the linear regime is to conduct MD simulations of preoriented polymer melt... 

The breadth of the scope of nonlinear phenomena can be grasped in part by considering the various time-dependent probes of linear viscoelasticity cited in Table 3.3.2 sinusoidal oscillation, creep, constrained recoil, stress relaxation after step strain, stress relaxation after steady shearing, and stress growth after start-up of steady shearing. In the linear regime— that is, at small strains or small strain rates—the experimental results of any one of these probes (in simple shear, for example) can be used to predict results for any of the other probes, not only for simple shearing defor-... 

Dispersed systems, i.e. suspensions, emulsions and foams, are ubiquitous in industry and daily life. Their mechanical properties are often tested using oscillatory rheological experiments in the linear regime as a function of temperature and frequency [29]. The complex response function is described in terms of its real part (G ) and imaginary part (G"). Physical properties like relaxation times or phase transitions of the non-perturbated samples can be evaluated. The linear rheology is characterized by the measurement of the viscoelastic moduli G and G" as a function of angular frequency at a small strain amplitude. The basics of linear rheology are described in detail in several textbooks [8, 29] and will not be repeated here. The relations between structure and linear viscoelastic properties of dispersed systems are well known [4,7, 26]. 

In Chapter 4 it was explained that the linear elastic behavior of molten polymers has a strong and detailed dependency on molecular structure. In this chapter, we will review what is known about how molecular structure affects linear viscoelastic properties such as the zero-shear viscosity, the steady-state compliance, and the storage and loss moduli. For linear polymers, linear properties are a rich source of information about molecular structure, rivaling more elaborate techniques such as GPC and NMR. Experiments in the linear regime can also provide information about long-chain branching but are insufficient by themselves and must be supplemented by nonlinear properties, particularly those describing the response to an extensional flow. The experimental techniques and material functions of nonlinear viscoelasticity are described in Chapter 10. 

The melt rheologieal properties of the sanq)les were determined using a TA Instruments Advanced Rheometrics Expansion System (ARES) with 25 mm parallel plates at 380°C under a nitrogen blanket. The strain was 15%. Strain sweeps were performed to determine the linear viscoelastic (LVE) regime. The apphed strain was selected from the LVE region. 

The outlined scheme is shown to yield stable solutions for non-zero Weissenberg number flows in a number of benchmark problems (Swarbric and Nassehi, 1992b). However, the extension of this scheme to more complex problems may involve modifications such as increasing of elemental subdivisions for stress calculations from 3 x 3 to 9 x 9 and/or the discretization of the stress field by biquadratic rather than bi-linear sub-elements. It should also be noted that satisfaction of the BB condition in viscoelastic flow simulations that use mixed formulations is not as clear as the case of purely viscous regimes. 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

Figure 2.34 Schematic of Newtonian, elastic, linear, and non-linear viscoelastic regimes as a function of deformation and Deborah number during deformation of polymeric materials.

Experimentally a variety of quantities are used to characterise linear viscoelasticity (Ferry 1980). There is no need to consider all the characteristics of linear viscoelastic response of polymers which are measured under different regimes of deformation in linear region, they are connected with each other. The study of the reaction of the system in the simple case, when the velocity gradients are independent of the co-ordinates and vary in accordance with the law... 

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