Viscosity measurements theory

Intrinsic Viscosity. Due to the complicating effects of aggregation and selective adsorption on the A2 values determined by light scattering, another means was sought to characterize the quality of solvents for PVB. The alternate means chosen was intrinsic viscosity measurements. Theory relates the intrinsic viscosity to the polymer chain dimensions through the expression (24)... 

Experimental detection of the gel point is not always easy since the equilibrium shear modulus is technically zero at the gel point and any applied stress will eventually relax, but only at infinite time. From the classical theory, the attributes of the gel point are an infinite steady-shear viscosity and a zero equilibrium modulus at zero frequency limit (Figure 6-3) (Flory, 1953). These criteria have been widely employed to detect the gel point of chemical gels. However, because continuous shearing affects gel formation, accurate information from viscosity measurement is not possible in the close vicinity of the gel point. Further, information regarding the transition itself could only be obtained by extrapolation, thereby introducing uncertainties in the determination of the gelation moment. 

The influence of temperature on diffusion coefficients of solutes in liquids has been studied in less detail. Diffusion coefficients often can be estimated from viscosity measurements. Hydrodynamic theory relates self-diffusion coefficients to the viscosity by... 

High-pressure viscosity measurements can also be of considerable practical importance. For example, in the field of lubrication it has been recognized for some time that the fluid in a lubricated contact can experience several giga-pascals of pressure. Theory predicts that the derivative of viscosity with respect to pressure is a critical parameter in determining the metal-metal contact and thus the wear in such a system. However, this derivative is itself a strong function of pressure, and a more accurate estimate of viscosity effects is gained by experimentally determining the entire pressure-viscosity curve up to the actual pressures of operation. 

In air, the mean-free path has an order of 10 m and does not depend on temperature but is inversely proportional to pressure. The expressions given for collision number and mean-free path are useful for understanding chemical reactions (see collision theory in Chapter 4.1.1.2) but have only limited worth for applications because the molecular diameter (or radius) is not directly measurable. However, the molecular diameter is typically determined from viscosity measurements. 

Reiner M (1926) Elow of elastic liquid by means of a capillary. Article on the theory of the viscosity measurements. Kolloid-Zeitschrift 39 80-87... 

Within this system of classification by substance name, there exists a class of pertinent information for which no specific substance name would be appropriate, e.g., Theory of the Thermal Conductivity of Gases or New Technique for the Viscosity Measurement of Liquids or Emissivity of a Black-Body Cavity. Literature covering this class of publications is not reported in this volume but is available at TPRC and a special computer search and retrieval can be made upon request. 

Reliable experimental data on the behaviour of polymer dimensions with increasing solvent quality is too rare, in fact the classical data of Beny is still widely cited. Neutron scattering does provide a new approach (see Chapter 11), but concomitant light scattering/intrinsic viscosity measurements remain the main probe. A recent paper furnishes a novel approach by using bacterium synthesized poly(D-/S-hydroxy-butyrate), PHB, in trifluorethanol. Values of > 7 may be obtained and aj is found to be asymptotically proportional to z. Further, the interpenetration function T [equation (10)] does not increase to an asymptote as a function of as predicted by all current theories but instead reaches a maximum before falling to an asymptotic limit 2 0.22. 

Size-exclusion chromatography fractionation is steric, that is, dimensional. In theory, a SEC system could be calibrated by means of some appropriate standards of known dimensions and, in this way, to measure SEC fractionation depends on the hydrodynamic radius Rh of the macromolecules Rh M[r]] where [17] is the intrinsic viscosity. sY and Rh are two different parameters. I Y is an equilibrium parameter Rif isa dynamic parameter and depends on the method by which it is obtained. Rh becomes the Stokes radius R in diffusion measurements and the Einstein radius R in viscosity measurements. Because SEC fractionation depends on Rh, the method is not appropriate for a direct measure of YY- Convenient experimental methods to measure sY are scattering techniques. 

Making reasonable estimates of the molecular parameters and adjusting d to make theory and experiment coincide when k jk = 0.1 yields the results of Fig. 9.10. The corresponding values of d are given in Table 9.3. The agreement between theory and experiment is gratifying. An indication of the theory s consistency is the behavior of d. Its temperature variation is small and its value is very close to the hard-sphere diameter determined from viscosity measurements, 0.45 nm. 

Below we discuss the present status of the theory of polyelectrolytes. Some of the important experimental results with which there is simulation data to compare are also discussed. We do not mention experiments such as viscosity measurements since no simulation has calculated such quantities. 

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