Polystyrene shear viscosity

A6.4.9 Fitting the Filled Polystyrene Shear Viscosity Data Model equation ... 

The experimental zero-shear viscosities obtained for polystyrene (PS) of different molar masses (with a very narrow molar mass distribution Mw/Mn=1.06-1.30) and different concentrations in toluene and fra s-decalin are plotted as log r sp vs. log (c- [r ]) in Fig. 6. 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

For the unfilled polystyrene melt at low elongational rates a constant value of Tjg is achieved given by three times the zero shear viscosity according to Trou-... 

Wyman and co-workers (120) studied the viscosity of narrow MWD linear and 4-armed star polystyrenes as a function of shear rate. At low shear rates, the star polymers (of MW 204000 and 430000) had low-shear viscosities much lower than linear ones of the same MW it may be remarked that the branch length... 

Fig. 8.1. Dynamic viscosity t] (a>) and steady state viscosity f](y) for undiluted narrow distribution polystyrenes. The data are plotted in reduced form to facilitate comparison. The dimensionless shear rate or frequency is t]0Mwy/gRT >r r/ M co/gRT. [See Eq.(8.3)]. The dynamic viscosities are for Mw = 215000 (O) and Mw = 581000 ( ) at 160° C (312). The steady shear viscosity is for Mw = 411000 (A) at 176° C (313). The shapes in the onset region are similar for the three curves, but the apparent limiting slope for the dynamic...

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

At this point it seems of interest to include a graph obtained on a quite different polymer, viz. cellulose tricarbanilate. Results from a series of ten sharp fractions of this polymer will be discussed in Chapter 5 in connection with the limits of validity of the present theory. In Fig. 3.5 a double logarithmic plot of FR vs. is given for a molecular weight of 720000. This figure refers to a 0.1 wt. per cent solution in benzophenone. It appears that the temperature reduction is perfect. Moreover, the JeR-value for fiN smaller than one is very close to the JeR value obtained from Figure 3.1 for anionic polystyrenes in bromo-benzene. As in the case of Fig. 3.1, pN is calculated from zero shear viscosity. The correspondence of Figs. 3.1 and 3.5 shows that also the molecules of cellulose tricarbanilate behave like flexible linear chain molecules. For more details on this subject reference is made to Chapter 5. 

Figure 3.15 Influence of molecular mass on zero shear viscosity for polystyrene and polycarbonate melts at different reference temperatures T0 ([91, [11], [12])...

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. 

FIG. 15.13 Non-Newtonian shear viscosity r/(q) at 170 °C vs. shear rate, q, for the polystyrene mentioned in Fig. 15.12, measured in a cone and plate rheometer (O) and in a capillary rheometer ( and ) and the dynamic and complex viscosities, rj (w) (dotted line), rj (w) (dashed line) and i (< ) (full line), respectively, as functions of angular frequency, as calculated from Fig. 15.12. From Gortemaker (1976) and Gortemaker et al. (1976). Courtesy Springer Verlag. 

Fig. 40. Steady shear viscosities of aqueous dispersions of polystyrene latices in nonadsorbing dextran solutions (Patel and Russel, 1989b) (a) a/r, = 6.9, 0 = 0.20. A, single phase, 4nR J/3pb = 0.15 B, two-phase, 4jtR /3pb = 0.30 C, two-phase, 4jtRj/3pb = 0.45 D, two-phase, 4jtRj/3pb = 0.65. (b) a/R, = 1.9, 0 = 0.10. F, single phase, 4jtR /pb = 0.65 G, fluid-fluid, 4jtR /3pb = 0.75 H, fluid-solid, 4nR /3p = 0.95 I, fluid-solid, 4jiR3/3p = 1.25.

The increase in gel strength with increase in bentonite concentration above the gel point is consistent with the increase in yield value and modulus. On the other hand, the limited creep measurements carried out on the present suspension showed a high residual viscosity Oq of the order of 9000 Nm s when the bentonite concentration was 45g dm. As recently pointed out by Buscall et al (27) the settling rate in concentrated suspensions depends on 0. With a model system of polystyrene latex (of radius 1.55 vim and density 1.05 g cm ) which was thickened with ethyl hydroxy ethyl cellulose, a zero shear viscosity of lONm was considered to be sufficient to reduce settling of the suspension with = 0.05. The present pesticide system thickened with bentonite gave values that are fairly high and therefore no settling was observed. 

FIGURE 12.12 Steady shear viscosity as a function of Peclet number for polystyrene lattices of radii of 54, 70, 90, 37, and 55 nm at 50% Iqr volume in different solvents (—, H2O O, benzyl alcohol and, meta-cresol), where tjq = 24.7tjn, >, = 13.97, . Data from Kreiger [42]. 

The zero shear viscosities of these randomly branched polystyrenes were measured and compared with those of linear polystyrenes and it was found that t]0 for all of the branched polymers were far lower than that of linear homologues of the same overall molecular weight. In addition, a scaling of fJo was observed for the first two generations of each branched series of... 

Figure 23 Data of zero-shear viscosities of polystyrene firactions ranging from 900 g.mol l to 30 000 g.mol as a function of temperature [29-37]. The master curve is obtained by experimental shifts from the data of a reference mass of 110 000 g. mole-1, includes more than one hundred experiments lying within the experimental bar error. A least squares analysis gives the parameters of the reference mass and the other ones are deduced fiem the shift frictors.

From the correspondence between the calculated and experimental curves we can extract other information. For example the temperature (ca. 72 °C) at which x = 1/2 is shown on Fig. 14b. Above this temperature no more chains break at this temperature and higher, the craze growth is disentanglement dominated. We can use the fact that = 1/2 and Eq. (19) to extract a value for the corresponding to disentanglement of chains at the void interface under these conditions this value is 1.5 x 10" N-s/m, a value that is only reached for polystyrene melts (from zero shear viscosity or diffusion measurements) at a temperature of about 120 °C, or 20° above T. ... 

The superimposition of the shear rate dependence of steady shear viscosity, that is, t]a(o)), and of the frequency dependence of the complex viscosity, that is, i ( >), at equal values of frequency and shear rate was first reported by Cox and Merz (1958) for polystyrene samples, and is known as the Cox-Merz rule. 

Figure 6-29 shows that this simple model gives a good fit to the concentration-dependence of the shear viscosity data for polystyrene latices in 5 x 10" M NaCl. 

Fig. 3 Zero-shear viscosity at 169.5°C as a function of weight-averaged molecular weight for polystyrene melts. Open and closed circles and squares, linear triangles, H-polymers. (From Ref.. )...

Utracki, L.A. Roovers, J.E.L. Viscosity and normal stresses of linear and star branched polystyrene solution. I. Application of corresponding states principle to zero-shear viscosities. Macromolecules 1973, 6 (3), 366-372. 

Figure 13.6. Zero-shear viscosity (N-sec/m2) of polystyrene as a function of T and Mw.

Figure 13.11. Comparison of observed [7] and predicted zero-shear viscosities (N-sec/m2) of concentrated solutions of polystyrene with Mw=3.7-105 in xylene, as functions of the polymer concentration (g/cc), at two different temperatures (T=287K and T=318K).

The effect of overall molecular weight or the number of blocks on rheological properties for the samples from the second fractionation can be illustrated as a plot of reduced viscosity vs. a function proportional to the principal molecular relaxation time (Figure 2). This function includes the variables of zero shear viscosity, shear rate, y, and absolute temperature, T, in addition to molecular weight, and allows the data to be expressed as a single master curve (10). All but one of the fractions from the copolymer containing 50% polystyrene fall on this... 

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