Polystyrene shear thinning

When water (a Newtonian liquid) is in an open-ended pipe, pressure can be applied to move it. Doubling the water pressure doubles the flow rate of the water. Water does not have a shear-thinning action. However, in a similar situation but using a plastic melt (a non-Newtonian liquid), if the pressure is doubled the melt flow may increase from 2 to 15 times, depending on the plastic used. As an example, linear low-density polyethylene (LLDPE), with a low shear-thinning action, experiences a low rate increase, which explains why it can cause more processing problems than other PEs. The higher-flow melts include polyvinyl chloride (PVC) and polystyrene (PS). 

The Newtonian viscosity of some polymers increases essentially linearly with the weight average molecular weight, and for other polymers the Newtonian viscosity increases with an exponential power of the molecular weight. The exponential power is found to be about 3.4, but this power does deviate for some polymers. These two transitions, Newtonian to pseudo-plastic and linear to 3.4 power in the Newtonian range are often related to molecular structure as demonstrated in Fig. 3.31 [22]. The polystyrene data used to develop the Adams-Campbell viscosity function showed almost no shear thinning at [18]. That is why the power law slope, s, is a function of and M. At the slope is zero and the material would be essentially Newtonian. 

Sample balancing problem. Let us consider the multi-cavity injection molding process shown in Fig. 6.54. To achieve equal part quality, the filling time for all cavities must be balanced. For the case in question, we need to balance the cavities by solving for the runner radius R2. For a balanced runner system, the flow rates into all cavities must match. For a given flow rate Q, length L, and radius R, solve for the pressures at the runner system junctures. Assume an isothermal flow of a non-Newtonian shear thinning polymer. Compute the radius R2 for a part molded of polystyrene with a consistency index (m) of 2.8 x 104 Pa-s" and a power law index (n) of 0.28. Use values of L = 10 cm, R = 3 mm, and Q = 20 cm3/s. 

Isothermal draw resonance is found to be independent of the flow rate. It occurs at a critical value of draw ratio (i.e., the ratio of the strand speed at the take-up rolls to that at the spinneret exit). For fluids that are almost Newtonian, such as polyethylene terephthalate (PET) and polysiloxane, the critical draw ratio is about 20. For polymer melts such as HDPE, polyethylene low density (LDPE), polystyrene (PS), and PP, which are all both shear thinning and viscoelastic, the critical draw ratio value can be as low as 3 (27). The maximum-to-minimum diameter ratio decreases with decreasing draw ratio and decreasing draw-down length. 

The influence of molar mass distribution on the viscosity function is shown in Fig. 3.16 on the basis of dynamic viscosities of different polystyrenes (PS), which were normalized with respect to their zero shear viscosity. A wider molar mass distribution results in a higher shear thinning in the normalized viscosity function, i. e., the drop in viscosity starts at lower normalized angle frequencies and/or shear rates. 

This can be clearly seen in the comparison of viscosity functions of polystyrene 1 and polystyrene 2. If we add a very high-molecular weight component to polystyrene 2, we obtain polystyrene 3. It is therefore evident that the bimodal molar mass distribution causes the shear thinning to increase further, although not as far as the polydispersity change of the molar mass distribution between polystyrene 1 and polystyrene 2. In the case of higher shear rates, all flow curves proceed to similar viscosity functions. 

Ethylene-styrene interpolymers exhibit a novel balance of properties that are uniquely different from polyethylenes and polystyrenes. In contrast to other ethylene-a-olefin copolymers, ESI display a broad range of material response ranging from semicrystalline, through elastomeric to amorphous. The styrenic functionality and unique molecular architecture of ESI are postulated to be the basis of the versatile material attributes such as processability (shear thinning, melt strength and thermal stability), viscoelastic properties, low-temperature toughness and broad compatibility with other polymers, fillers and low molecular weight materials. 

Figure 9.12 Droplet radius versus wt% dispersed polystyrene (PS) in a blend with polypropylene (PP) at an average shear rate of 10 sec in a single twin screw extruder at T = 200°C. The viscosities of pure PS and PP at these conditions are about 5 x 10 and 2 X 10 Pa-s, respectively both melts are modestly shear thinning (power-law slopes —1/3). The interfacial tension T was measured to be 4.9 dyn/cm. The predicted Taylor limit, a = 0.5 T/rfsy, is shown. (From Elmendorp and van der Vegt 1986, reprinted with permission from the Society of Plastics Engineers.)...

Different polymer blends like PE (polyethylene)/PS (polystyrene) [10-11] and PMMA (polymethylmethacrylate)/PS [12-13] have been produced using supercritical C02-assisted extrusion. Fully intermeshing twin-screw extruders have been used in these studies. A decreased shear thinning behavior on dissolution of supercritical CO2 into blends was observed. The obtained reduction in viscosity ratio resulted in a finer dispersion of the minor phase, which is desirable to create a good polymer blend. The effect of supercritical CO2 on the dispersion of the minor phase for a PMMA/PS blend can be seen clearly in Fig. 12.5. 

Most common thermoplastics exhibit shear thinning, which means that the melt viscosity drops substantially in the runners of the tool, and thus makes moulding to shape much easier (Fig. 10.19). Thus, LDPE and polystyrene... 

Fig. 2.10 Relative intrinsic viscosity as a function of the shear rate poly(a-methylstyrene) in toluene with molecular weight is (1) 690k, (2) 1240k, (3) 1460k (4) 1820k, (5) 7500k, polystyrene with a molecular of weight 13 000 k in toluene, (6) and in decalin (7) The viscosity exhibits shear thinning phenomena. The Newtonian plateau region depends on the molecular weight. (Reprinted with permission from Noda, I. Yamada, Y Nagasawa, M., /. Phys. Chem. 72, 2890 (1968).)...

Typical melt viscosity behavior as a function of shear rate is shown in Fig. 13.9 for polysulfones and some other polymers. As illustrated in these plots, the shear thinning characteristics of polysulfones are much more muted than they are for aliphatic backbone polymers, such as the polyethylene and polystyrene shown to illustrate this point. The rheological behavior of polysulfones is fundamentally more similar to that of polycarbonate. 

Figure 19-11. Reduced viscosities as a function of the reduced shear stress of colloidal silica suspensions (diameter of 100 nm) in the presence of addedpolymer (polystyrene). The solvent used is decalin which is a near theta solvent for polystyrene. The size ratio of the polymer radius of gyration to the colloid radius (Rg/R) is 0.02S. The colloid volume fraction ((f>) is kept fixed at 0.4. In the absence of added polymer (Cp/c = 0), the particles behave as hard spheres and as more polymer is added to the system, the particles begin to feel an attraction. The colloid-polymer suspensions at (p of 0.4 shear thin between a zero rate viscosity of r o and a high shear rate plateau viscosity r]x,. The shear thinning behavior (in the absence and presence of polymer) is well captured by equation (19-10) with n = 1.4. Note rjo, rjao and cTc are functions of volume fraction and strengths of attraction but weakly dependent on range of attraction (Shah, 2003c Rueb, 1997).

Ye and Sridhar report dynamic moduli and shear thinning in solutions of three-arm star polystyrenes dissolved in di-n-butylphthalate(29). Unlike many other authors. Ye and Sridhar identified each point as to its measmement temperature, permitting testing of refinements to simple time-temperature superposition. Figure 13.19 shows G oo) oo and G" oo)joo. The G" co)lco accurately follows the ansatz forms. With increasing c the power-law exponent and the exponential prefactor a increase and the stretching exponent v decreases. The G [Pg.417]

Figure 13.20 Shear thinning in (a) 3.47 MDa polystyrene three-arm stars (concentrations above and below 12 and 10 wt%) in di-n-butylphthalate, based on Ye and Sridhar(29), and (b) 1.19, (c) 1.82, and (d) 3.30 MDapoly-a-methylstyrene in a-chloronaphthalene at concentrations 268, 192, and 188 gd, respectively, using...

Graessley, et al. measured shear thinning in polystyrene n-butylbenzene(33). Seven polymer samples had 19.8 kDa < < 2.4 MDa six samples had... 

Figure 13.22 Shear thinning for (a) narrow-molecular-weight-distribution polymers 255 g/1 polystyrene n-butylbenzene having Mw (top to bottom) 2.4 MDa, 860 kDa, and 411 kDa, and (b) broad-molecular-weight-distribution polystyrene n-butylbenzene at (c, Mw) (top to bottom) of (1.9 MDa, 255 g/1), (677 kDa, 400 g/1), (418 kDa, 300 g/1), and (13% 1.6 MDa mixed with 87% 241 kDa, 300 g/1), using data of Graessley and Segal(34).

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