Viscosity is the resistance to flow. As shown in Table 1.5,
polymer melts have viscosities of 100 to 1,000,000 Pa-s, whereas water has a viscosity of 0.001 Pa-s.11 These high viscosities result from the long polymer chains and cause the polymer melt to exhibit laminar flow; that is, the melt moves in layers. Although, these melt layers may move at the same velocity, thereby producing plug flow, the melt layers typically flow at different the different velocities to provide shear. Changes in the cross-sectional area of the melt channel or drawing processes stretch or allow relaxation of the polymer chains, giving rise to elongation or extension. The shear viscosity of polymer melts generally decreases with increasing shear rate. This pseudoplastic behavior contrasts with the shear-rate independent viscosity of fluids, such as water, solvents, and oligomers. The decrease in the viscosity of pseudoplastic fluids, however, does not occur immediately. At low shear rates, the polymer molecules flow as random coils, and the constant viscosity is called the zero-shear rate viscosity (.o). With increasing shear rate, the polymer chains align in the direction of flow, and the viscosity decreases (Fig. 1.12).
The shear rate corresponding to the onset of chain alignment or shear thinning increases with decreasing polymer molecular weight. When the viscosity decreases is proportional to the increase in shear rate, the viscosity can be modeled using:(1.8)
where k is the consistency index and n is the power law index. The power law index is an indicator of a material’s sensitivity to shear (rate), or the degree of non-Newtonian behavior. For Newtonian fluids n = 1, and for pseudoplastic fluids n < 1, with smaller values indicating greater shear sensitivity. Since shear rate varies considerably with the processing method (Table 1.6),
the degree of alignment, shear thinning, and material relaxation varies considerably with the process. Compression and rotational molding typically induce very little alignment of the polymer chains and thus produce low levels of orientation and retained stress. In contrast, the polymer chains are highly oriented during injection molded, and such parts exhibit high levels of residual stress. As illustrated in Fig. 1.12,
shear viscosity also decreases with temperature, since the polymer chains are more mobile. This temperature dependence of viscosity can be expressed using an Arrhenius equation: (1.9)
where A is a material constant, Ea is the activation energy (which varies with polymer and shear rate), R is a constant, and T is the absolute temperature. Since the activation energy depends on the difference between a polymer’s processing and glass transition temperatures, materials such as polyethylene have activation energies less than 20 kJ/mol, whereas higher-temperature polymers, such as polycarbonate, exhibit activation energies that are greater than 50 kJ/mol. Pressure increases viscosity, but the effects are relatively insignificant when the processing pressures are less than 35 MPa (5,000 psi).14 At higher pressures, the increase in viscosity is given by15 (1.10)
where .r is the viscosity at a reference Pr, and ap is an empirical constant with values of 200 to 600 MPa–1. Shear viscosity increases with more rigid polymer structures, higher molecular weights, and additives such as fillers and fibers. Long chain branching and broader molecular weight distributions increase the shear sensitivity of viscosity. Blending two polymers can significantly alter polymer viscosity, but the effect depends on the two polymers. Additives such as lubricants typically decrease viscosity, whereas the effect of colorants and impact modifiers varies with type of additive. In contrast, the effect of strain rate on extensional viscosity varies with the polymer structure. Branched polymers generally exhibit extensional thickening and a corresponding increase in viscosity. Linear polymers, such as LLDPE, undergo extensional thinning in which the viscosity decreases as the polymer sample necks. Generally, extensional viscosity is greater than shear viscosity and depends primarily on the molecular weight of the polymer.
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