Filled polymers shear viscosity function

The suppression of the Newtonian plateau in the shear viscosity function when the filler content is above 12-13% can be seen as the extension in the low rate range of the nonlinear viscoelastic character, otherwise observed on pure, homogeneous polymers in the high rate range. However such a nonlinearity is "internal" (i.e., morphology induced, or "intrinsic") to filled compounds, a part of their basic character, in contrast to the "external" (i.e., strain induced) nonlinear viscoelasticity of pure polymers that appear when stress conditions overcome a certain limit. With respect to Figure 5.16, it is easy to understand that as the applied stress or rate of strain reduce, the system responds more and more as an elastic network and, therefore, the... 

There is however an aspect which is qualitatively common to all filler-thermoplastic systems the linear viscoelastic behavior exhibited by most pure polymers at sufficiently low strain or low rate of deformation disappear above a sufficient filler level. For instance, the so-called Newtonian plateau on the shear viscosity function is no longer observed, the d5mamic modulus is strongly strain dependent and the terminal region in the elastic modulus function disappears and is replaced by a low frequency plateau. As we have seen, such typical effects are also observed with filled rubber compounds. 

Modeling the shear viscosity function of filled polymer systems by combining two Carreau-Yasuda equations the curve was calculated with the following model parameters Tioj = 8x10 Pa.s X = 500 s Aj = 1.9 = 0.4 rioj = 3x10 Pa.s - O l s = 3 Wj = 0.33. 

Capabilities of Equation 6.14 in meeting the typical features of the shear viscosity function of filled polymer systems fixed parameters r o = 3 kPa.s, n = 0.3 = 0.74 variable parameters O, a, a. ... 

A6.2 Modeling the Shear Viscosity Function of Filled Polymer Systems... 

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. 

Menges et al. [44] have proposed a method for converting the viscosity curves for filled systems into those for the unfilled base polymer by a shift factor under a constant shear stress. Although their viscosity function is temperature and concentration invariant, their approach requires a knowledge of the shift factor in the case of each system. 

The empirical rule of Cox-Merz describes similarities between the steady state shear viscosity as a function of shear rate and the dynamic viscosity as a function of angular velocity. The rule states that at equal values of frequency and shear rate the steady state values of the dynamic viscosity closely approach the steady state shear viscosity. As pointed out by Booij[Booij] etal the Cox-Merz rule is not applicable to strongly nonlinear melts. Utracki[Utracki] also discnssed the Cox-Merz rule and showed that it does not apply to immiseible polymer blends and filled polymer systems. Therefore, it is not surprising that the plots in Figure 4 do not coincide. More important that attempting to invoke the Cox-Merz rule is the fact that capillary date are needed to make viscosity... 

Fig. 18 Viscosities of mixtures of a 3-CD polymer (P-cyclodextrinyl-PIBMA) and a guest polymer (tert-butyl anilide of PIBMA) as functions of the molar fraction of guest groups in water for different shear rates D (s-1) of 66 (filled diamonds), 131 (filled squares), 196 (filled circles), 393 (open triangles), and 590 (open circles) at constant total polymer concentration of 2 wt% [202]...

Capillary and slit-die rheometers are used to determine the dependency of viscosity on shear rate. Since most molten polymers exhibit non-Newtonian behavior, it is important to be able to characterize this behavior. Measurements are made using a piston-driven cylinder that drives the molten polymer through a die of precise dimensions. The pressure drop across the die is measured, as is the flow rate through the die. Temperature is precisely controlled throughout the measurement. This test yields precise viscosity measurements as a function of temperature and shear rate. However, measurements tend to have artifacts in them, which need to be corrected in order to obtain true viscosity using Bagley and Rabinowitsch corrections. Capillary rheometers are also used to determine the effects of slip, a phenomenon in which the velocity of the melt at the capillary wall is nonzero. Slip has important implications for highly filled materials. 

While melt flow rate information is helpful, it is insufficient for complete characterization of viscosity since it is a function of temperature, pressure and shear stress for a given polymer, for example, melt flow during mold filling and in the runners at or above the melting point of the resin and at shear rates in excess of 1000 sec. The viscosity behavior as a function of shear rate depends on the polymer structure (e.g.,... 

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