Shear viscosity modeling, polymer systems

The Rouse and Zimm models provide little direct help in dealing with t](y) since each predicts a viscosity which is independent of shear rate. The principal interest here is in concentrated systems where entanglement effects are prominent. Nevertheless, shear rate can influence the viscosity of polymer systems at all levels of concentration, including infinite dilution (307) and melts with M < Mc (308, 315). It is therefore essential to identify the causes of shear rate dependence in systems of isolated or weakly interactions molecules in order to separate intramole-... 

The presence of polymers at the interface between oil and water makes for excellent stabilization of emulsions (1,4). Figure 13 shows the interfacial shear viscosity of the interfacial film between a model oil and NaOH solution or polymer solution at 45°C. The model oil consisted of 20% Daqing crade oil injet fuel. The contents ofNaOH, ORS41, and a biological surfactant in the NaOH solution were 1.2, 0.5, and 0.15%, respectively. The concentration ofpolymer hydrolyzed polyacrylamide (HPAM) in the solution was 150mg/L. It can be seen that the interfacial shear viscosity of the system with the polymer is three times higher than... 

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

Most of the methods developed in this book are, by themselves, only applicable to amorphous polymers and amorphous polymeric phases. (An exception with obvious relevance to the properties of multiphase materials is the development of a physically robust predictive model for the shear viscosities of dispersions in Section 13.H.) Their combination with other types of methods to predict the properties of multiphase materials from component properties and multiphase system morphology enables us to expand their applications to include the prediction of selected properties of multiphase polymeric systems where one or more of the phases are amorphous polymers. In other words, the methods developed in this book are used to predict the properties of the amorphous polymeric phases of the multiphase system. These properties are then inserted into equations of composite models and into numerical simulation schemes (along with material parameters of the other types of components, obtained from other sources such as literature tabulations) to predict the properties of the multiphase system. We use existing composite models whenever they are adequate, and develop our own otherwise. 

Other equations have been developed to describe the shear thinning behavior of polymer melts, for instance, the Yasuda-Carreau equation, which is written here as Equation 22.19 [41]. In this equation, as in the power-law model, the effect of temperature on viscosity of the system can be taken into account by means of an Arrhenius-type relationship ... 

While Eq. (2.33) is valid for monodispersedathermal polymers, in reality polymers are polydispersed and do interact with each other. Consequently, application of the model to a real system requires that the influence of individual molecular weight fractions on the rheological functions is taken into account. For example, in the simplest case of the zero-shear viscosity-composition dependence for entangled systems [194, 195] the prediction is ... 

To understand and model the flow during the blending process, the bulk shear viscosity of a polymer blend must be understood. The rheology of multiphase systems has been investigated by many researchers (2, 71-73]. Figure 6.2 shows the schematics of both solid particle-filled Uquid (curve a) and polymer blends... 

The Rouse model was initially designed to treat the dynamics of polymers in very dilute solutions [1]. Ironically, however, it turned out that dilute solutions are not appropriate systems for it. Indeed, in the Rouse model the maximal relaxation time, Tchain> and the diffusion coefficient, I>chain> scale with the molecular weight, M, as and M respectively (see Eqs. 57 and 61). Furthermore, it is a straightforward matter to demonstrate that for the Rouse model at = 0 the zero shear viscosity [ ] (0)] is proportional to M, see Eq. 22. All these theoretical findings disagree with the experimental data... 

The shear thinning behavior, as generally observed with polymer systems, is a typical nonlinear viscoelastic effect, so that by combining the Carreau-Yasuda and the Arrhenius equations a general model for the shear viscosity function can be written as follows ... 

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