Polystyrene Zero-shear viscosity

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-... 

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. 

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. 

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. ... 

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... 

Shown in Fig. 4.12 are the data of steady-state compliance J° of nearly monodisperse polystyrene samples obtained by different laboratories. Similar to the case with zero-shear viscosity, J° shows two regions with drastically different molecular-weight dependences, separated by a transition point M. Above M, J° is basically independent of molecular weight, and the data points fluctuate mainly because J° is very sensitive to the small variations among the molecular-weight distributions, even though all nearly monodisperse, of the studied samples. Below M, the relation of log(Jg) to log(Miu) has an apparent slope of one. The explanation for the... 

Comet [12] proposed equating c to c where the lo rithm of zero shear viscosity plotted against c begins to follow a linear relation and obtained c = 0.614/[ /]e for polystyrene in cyclohexane. Since [j ] this relation... 

McKerma, G. B., Hadziioarmou, G., Lutz, P., Hild, G., Strazielle, C., Straupe, C., Rempp, P., and Kovacs, A. J., 1987. Dilute-solution characterization of cyclic polystyrene molecules and their zero-shear viscosity in the melt. Macromolecules, 20 498-512. 

It is now important to calculate the stress exerted by the particles. This stress is equal to aApgfZ. For polystyrene latex particles with radius 1.55 pm and density 1.05 g cm , this stress is equal to 1.6 x 10 Pa. Such stress is lower than the critical stress for most EH EC solutions. In this case, one would expect a correlation between the settling velocity and the zero shear viscosity. This is illustrated in Chapter 7, whereby v/a is plotted versus 7(0). A linear relationship between log( /a ) and log 7(0) is obtained, with a slope of —1, over three decades of viscosity. This indicated that the settling rate is proportional to [7(0)] . Thus, the settling rate of isolated spheres in non-Newtonian (pseudo-plastic) polymer solutions is determined by the zero shear viscosity in which the particles are suspended. As discussed in Chapter 7, on rheological measurements, determination of the zero shear viscosity is not straightforward and requires the use of constant stress rheometers. 

Master curves (7b = 25 °C) for the complex viscosity of two nearly monodisperse 1,4-polybutadiene melts [28] are shown in Fig. 3.24. One is linear rjo = 4.8 X 10 Pa s, J° = 2.1 X 10 Pa ), the other a three-arm star rjo = 2.8 x 10 Pa s, J° - 1. 4 X 10 Pa ). Their zero-shear viscosities are similar, but their recoverable compliances differ by a factor of seven and the shapes of their curves are obviously different, too. Figures 3.25(a) and (b) compare those results with steady-shear-viscosity data for nearly monodisperse polymers, showing master curves at 183 °C for five linear polystyrene samples [29] (48 500 < M < 242 000) in Fig. 3.25(a), and master curves at 106 °C for seven polybutadiene stars [30] (45 000 < M < 184000) in Fig. 3.25(b). Values of t]o were available for all samples, so knowledge of rj y)/r o was always available. Values of J° were not generally available, so Tq for the shear-rate reduction was estimated from the onset of shear-rate dependence. Agreement with the Cox-Merz rule is evident even in this rather severe test of using different samples and even different species. The... 

Utracki and Roovers report the zero-shear viscosity of solutions of 24 different linear and four- and six-arm star polystyrenes in diethylbenzene(56). Polymer molecular weights extended from 34 kDa to 1.8 MDa, polymer concentration was fixed at 255 g/1, and rj was determined using calibrated Cannon-Ubbelohde capillary viscometers. Eight polymers were studied at a range of temperatures others were examined only at 30°C. Taking the solvent viscosity to be known and fixed, stretched exponentials in M are shown by Figure 12.26b to fit t] at high accuracy for each arm number. 

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