Viscosity theory

Flory s viscosity theory also furnishes confirmation of the w temperature as that in which a=V.2, and it permits the determination of the unperturbed dimensions of the Polymer chain. Even if a Q solvent is not available, several extrapolation techniques can be used for the estimating the unperturbed dimensions from viscosity data in good solvents. The simplest of these techniques seems to be that of Stockmayer. 

Bowen, W. R. and Williams, P. M. Chem. Eng. Sci. 56 (2001) 3083. Prediction of the rate of cross-flow ultrafiltration of colloids with concentration-dependent diffusion coefficient and viscosity-theory and experiment. 

Intermolecular distances in Eyring s viscosity theory (Part 6). 

By considering that the applied stress induces molecular flow, which can be treated along the lines of the Eyring viscosity theory, the strain rate, e, and yield stress, oy, are related by the so-called Eyring equation ... 

In an analogous manner, it is possible to show, from the viscosity theory developed by Fujita and Kishimoto (1961), that the viscosity at zero diluent concentration, rj (0,T), is represented in terms of f(0,T) as... 

In summarizing the intrinsic viscosity relations presented in this section, it must be admitted that they represent nothing more than rather small semi-empirical refinements of the Flory excluded volume theory and the Flory-Fox viscosity theory. For a large fraction of the existing body of experimental data, they offer merely a slight improvement in curve-fitting. But for polymers in good solvents it is believed that a more transcendental result has been achieved. The new equations permit more reliable assessment of unperturbed chain dimensions in such cases, and in some instances (e. g., certain cellulose derivatives see Section III B) they offer possible explanations of heretofore paradoxical solution behavior. 

With the development of the non-Newtonian viscosity theories it is now possible to compare the rotary diffusion coefficient and thereby the calculated length (or diameter) of the rigid particles as obtained from this technique with that from the commonly used flow birefringence method. Since both measurements depend upon the same molecular distribution function (Section III) they should give an identical measure of the rotary diffusion coefficient. Differences, however, will arise if the system under study is heterogeneous. The mean intrinsic viscosity is calculated from Eq. (7) whereas the mean extinction angle, x, for flow birefringence is defined by the Sadron equation (1938) ... 

B. Ottar. Acta Chem. Scand. 9, 344-5 (1955) (in English). Diffusion, viscosity, theory H2O, D2O. 

Therefore, the intrinsic viscosity theories discussed in this paper are based on small particle correlations. 

MCT is a popular liquid viscosity theory (Gee, 1970 Gotze et al., 1981 Leutheuser, 1984, Jackie, 1989). It is based on the description of the dynamical properties of density fluctuations in terms of a dynamical structure factor. There are inherent density fluctuations in liquids, which decay with characteristic relaxation times. The decay becomes slower as the temperature is lowered due to increase of viscosity. It is controlled by dynamically correlated collisions. The equations governing the decay are non-linear. Analysis of the non-linear equation of motion of the density fluctuations gives a density correlation function of the type... 

For liquid viscosity, theory is lacking and correlations are largely empirical. The main variation is with temperature the effect of pressure is small for liquids well removed from the critical point. It is common to correlate the viscosity (or sometimes the kinematic viscosity, v = 11/p) with a logarithmic dependence in reciprocal temperatnre ... 

When compared with lyotropic liquid crystalline polymers, the viscosity theory associated with thermotropic liquid crystalline polymers is far less studied except for a very few works done in theory (de Gennes, 1982) and experiment (Martins et al, 1986). More work should be carried out in this respect. 

Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

However, the Equation (2) has not take into account the specificity of the polymeric chain, that is why, it was not win recognized in the viscosity theory of the polymeric solutions. 

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