Viscosity concentration relation for

Figure 7. Reduced viscosity-concentration relations for FS, C-PS, and S-PS in hexanol/xylene (5% Hexanol/xylene (%) PS (V) S-PS 0.32% ...

In accordance with Staudinger we will consider solutions below the limiting con- Fig- H- Viscosity concentration relation for centration as dilute solutions. Some years nitrocellulose of different polymerisation degrees... 

Theoretical treatment of the viscosity-concentration relationship for polyelectrolyte solutions would involve both the cumbersome statistics of highly elongated chains beyond the range of usefulness of the Gaussian approximation and the even more difficult problem of their electrostatic interactions when highly charged. There appears to be little hope for a satisfactory solution of this problem from theory. Fuoss has shown, however, that experimental data may be handled satisfactorily through the use of the empirical relation ... 

This viscosity-concentration relation is shown in Fig. 11 for a series of nitrocellulose of various polymerisation degrees. 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

Utracki,L., Simha,R. Corresponding states relations for the viscosity of moderately concentrated polymer solutions. J. Polymer Sci. Pt. A1,1089-1098 (1963). 

Simha,R., Chan,F.S. Corresponding states relations for the newtonian viscosity of concentrated polynier solutions. Temperature dependence. J. Phys. Chem. 75,256-267... 

Only at very low concentrations can the coils be considered as separate spheres. In that case Einstein s relation for the viscosity of suspensions can be applied ... 

The ambiguity of definition of Re encountered in the concentric annulus case is compounded here because of the fact that no viscosity is definable for non-Newtonian fluids. Thus, in the literature one encounters a bewildering array of definitions of Re-like parameters. We now present friction factor results for the non-Newtonian constitutive relations used above that are common and consistent. Many others are possible. 

Another very useful approach to molar mass information of complex polymers is the coupling of SEC to a viscosity detector [55-60]. The viscosity of a polymer solution is closely related to the molar mass (and architecture) of the polymer molecules. The product of polymer intrinsic viscosity [r ] times molar mass is proportional to the size of the polymer molecule (the hydrodynamic volume). Viscosity measurements in SEC can be performed by measuring the pressure drop AP across a capillary, which is proportional to the viscosity r of the flowing liquid (the viscosity of the pure mobile phase is denoted as r 0). The relevant parameter [r ] is defined as the limiting value of the ratio of specific viscosity (qsp= (n-noVflo) and concentration c for c—> 0 ... 

Being able to determine [r ] as a function of elution volume, one can now compare the hydrodynamic volumes Vh for different polymers. The hydrodynamic volume is, through Einstein s viscosity law, related to intrinsic viscosity and molar mass by Vh=[r ]M/2.5. Einstein s law is, strictly speaking, valid only for impenetrable spheres at infinitely low volume fractions of the solute (equivalent to concentration at very low values). However, it can be extended to particles of other shapes, defining the particle radius then as the radius of a hydrody-namically equivalent sphere. In this case Vjj is defined as the molar volume of impenetrable spheres which would have the same frictional properties or enhance viscosity to the same degree as the actual polymer in solution. 

Because of strong interactions in polyelectrolyte solutions without added salt, the use of the well-known Stokes-Einstein relation for free particle diffusion D = kBT/6Trr)Rh, where 17 is viscosity and Rh is hydrodynamic radius, is rather limited. Even at very low concentrations, where intermo-lecular interactions can be neglected due to large intermolecular separations, the friction factor contains in addition to the Stokes-Einstein contribution /SE = 67717/4 also a contribution from electrolyte dissipation, so that the total friction factor / = /SE + /eidiS, where the electrolyte dissipation term reflects the retardation of the polyion motion due to the instantaneous distortion of the surrounding ion atmosphere as the polyion moves through the solvent [27,28],... 

B. (3.0) Ratio Polymers Effect of Urethane Group Concentration. Figure 5 shows the polymerization viscosity-time-temperature relations for a (3.0 ratio) thermoplastic poly(ester-urethane) elastomer, Polymer 9. This polymer was made from reactants VI, IV, and X (Table I) the polyester glycol component being intermediate acid number PTAd (0.30). 

Macroscopic viscosity, in contrast to microscopic viscosity, should not depend on the size of the protein molecules, but only on the volume fraction ij>. This is well known in the limit of low concentration of protein where the Einstein relation for spherical particles ( ) holds... 

To check the theoretical prediction for the nonequilibrium enhancement of the concentration fluctuations, as given by Eq. (4), we need in addition to D and ST also values for the kinematic viscosity v and for (d/ i/dw)p.T. The latter quantity is related to the concentration derivative of the osmotic pressure [22] which can be deduced from information provided by Noda et al. [31,32]. To obtain the kinematic viscosity v = rj/p the concentration dependence of the shear viscosity t can be represented by the Huggins relation... 

Simha, R., and Chan, F. S., Corresponding state relations for the Newtonian viscosity of concentrated polymer solutions temperature dependence, J. Phys. Chem., 75, 256-267 (1971). 

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