Zero shear viscosity, concentration dependence

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The rheological behavior of storage XGs was characterized by steady and dynamic shear rheometry [104,266]. Tamarind seed XG [266] showed a marked dependence of zero-shear viscosity on concentration in the semi-dilute region, which was similar to that of other stiff neutral polysaccharides, and ascribed to hyper-entanglements. In a later paper [292], the flow properties of XGs from different plant species, namely, suspension-cultured tobacco cells, apple pomace, and tamarind seed, were compared. The three XGs differed in composition and structural features (as mentioned in the former section) and... 

Taking into account the relevance of the range of semi-dilute solutions (in which intermolecular interactions and entanglements are of increasing importance) for industrial applications, a more detailed picture of the interrelationships between the solution structure and the rheological properties of these solutions was needed. The nature of entanglements at concentrations above the critical value c leads to the viscoelastic properties observable in shear flow experiments. The viscous part of the flow behaviour of a polymer in solution is usually represented by the zero-shear viscosity, rj0, which depends on the con-... 

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. 

In Sect. 6.3, we have neglected the intermolecular hydrodynamic interaction in formulating the diffusion coefficients of stiff-chain polymers. Here we use the same approximation by neglecting the concentration dependence of qoV), and apply Eq. (73) even at finite concentrations. Then, the total zero-shear viscosity t 0 is represented by [19]... 

The motion of polymers in concentrated solution and bulk is of major theoretical and practical concern. For example, the strong dependence of zero-shear viscosity on molecular weight (approximately the 3.4 power) and the marked decrease of viscosity 1) with shear rate y not only bespeak some of the unusual properties of long-chain molecules but also are of essential importance in virtually every processing operation. Yet the reasons for these unusual behaviors have become clear only recently. The reptation con-... 

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. 

Concentration Dependence of the Zero-Shear Viscosity of Amylopectin Solutions... 

Stable particle suspensions exhibit an extraordinarily broad range of rheological behavior. which depends on particle concentration, size, and shape, as well as on the presence and type of stabilizing surface layers or surface charges, and possible viscoelastic properties of the suspending fluid. Some of the properties of suspensions of spheres are now reasonably well understood, such as (a) the concentration-dependence of the zero-shear viscosity of hard-sphere suspensions and (b) the effects of deformability of the steric-stabilization layers on the particles. In addition, qualitative understanding and quantitative empirical equations... 

For some surfactant/salt combinations, the dependence of viscosity on added salt concentration is even more peculiar than that shown in Fig. 12-16. Rehage and Hoffmann (1988) found that the zero-shear viscosity of CPyCl has two maxima in viscosity as a... 

Dynamic mechanical strain-controlled measurements for both concentrated fabric softeners are shown in Figure 4.26. There are significant differences between the two products as regards the magnitude of the complex viscosity and complex modulus components and their strain dependence. Product B exhibits a higher viscosity and markedly longer linear region. The zero shear viscosity of product B is approximately 95 mPa s whereas that of product A is approximately half of this value at 50 mPa s. 

The average molecular weight, polydispersity, temperature, hydrostatic pressure, and shear rate dependences of polymer melt viscosity will be discussed in Chapter 13, resulting in a set of correlations which can be used to obtain a rough estimate of melt viscosity as a function of all of these variables. A new correlation will be presented for the molar viscosity-temperature function. The dependences of the zero-shear viscosity of concentrated polymer solutions on the average molecular weight and on the temperature will also be discussed. Finally, a new model that was developed to predict the shear viscosities of dispersions of particles in both polymeric fluids and ordinary molecular fluids will be presented. 

Step 22. Calculate the viscosity of a polymer melt and/or the zero-shear viscosity of a concentrated polymer solution. The molecular weight dependence of the zero-shear viscosity is given by equations 13.2 and 13.3, where the critical molecular weight Mcr (Equation 13.6) is... 

The zero-shear viscosities of PS in the poorer solvent trans-decalin depend on a higher exponent of c than in the better solvent toluene. Although it has been assumed in the literature that r 0°cc4-M3-5 [66], experimental investigations show higher exponents for c [67]. In the high molar mass region and at high concentration, the rio M3,4 relationship was established [62]. 

Figure 7.27. Concentration dependence of zero shear viscosity of polypropylene blends with two linear low density polyethylenes at 190°C. Points are experimental with error bars indicating the standard deviation [Dumoulin, 1988]. Lines are computed from Eq 7.125.

Figure 7.29 Concentration dependence of zero shear viscosity at 260, 280 and 300°C of polyethyleneterephthalate blended with polyamide-6,6. Points are experimental with the error bars indicating the error of measurements 2% ]Utracki et al, 1982].

Figure 7.31. Concentration dependence of zero shear viscosity at 200°C of PS/LDPE blends without (solid line) and with (broken line) 5 wt% SEE. Points — experimental error bars of measurement 3% [Austin et al., 1987].

FIGURE 1.13 Concentration dependence of the zero-shear viscosity of 1,4-polyisoprene linear (N250K, A/ = 256,900g/mol), three-arm symmetric star (SIOIK, aim = 101,000 g/mol), and three-arm asymmetric star (A2B73K, = 73,000g/mol,... 

Dreval, V. E., Malkin, A. Y., and Botvinnik, G. O., Approach to generalization of concentration dependence of zero-shear viscosity in polymer solutions, J. Polym. Sci. Polym. Phys. Ed., 11,1055-1076(1973). 

Figures 7.3a and b show shear-rate dependences of the viscosity at 35 °C and 40°C, respectively, for different concentrations. The viscosity is almost constant in the shear rate range up to 10-100 s , depending on the concentration and temperature. So, the viscosity at 1 s is regarded as the zero-shear viscosity and plotted against the concentration in Figures 7.4 and 7.5. The data in the lower concentration range in Figure 7.4 have been already reported before [21].

The concentration dependences of the apparent aggregation number (Figure 7.1), the cooperative diffusion coefficient (Figure 7.2), and the zero-shear viscosity (Figure 7.4) strongly suggest entanglement of worm-like micelles. The overlap concentrations are obtained to be about 0.7, 0.4, and 0.2 wt% at 35, 40, 45 °C, respectively, from the concentrations above which the zero-shear viscosity increases rapidly. 

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