Volume fraction dependence self-diffusion coefficients

To illustrate the effects, corrections to the diffusion coefficient data were made using an empirically chosen value for the heat transfer coefficient. When these results were converted to solvent mobilities, the extrapolation as a function of the volume fraction of solvent appeared to be consistent with the self-diffusion coefficient for toluene. However, this comparison is dependent on the method used to reduce the diffusion data. 

Figure 9 Relative self-diffusion coefficients of water and oil as a function of the oil volume fraction

Figure 37 Relative zero-shear viscosity (normalized to the solvent tis) as a function of the effective volume fraction

M. Watzlawek, G. Niigele, Self-diffusion coefficients of charged particles Prediction of nonlinear volume fraction dependence. Phys. Rev. E 56(1), 1258-1261 (1997). doi 10.1103/PhysRevE. 56.1258... 

As shown above, we can easily determine a hydro-dynamic radius at high dilution where interactions are negligible. The situation, however, becomes more problematic at higher concentrations, where, for example, diffusion coefficients depend on both size and on interactions. As seen in Figure 17.14, the droplet self-diffusion coefficient decreases with increasing volume fraction. Is this decrease due to interactions only or is it also a consequence of droplet growth ... 

Translational motions of solvent and other small molecules in polymer solutions are quite different from their behaviors in viscous liquids. The self-diffusion coefficient of the solvent has a transition at a polymer volume fraction 0.4. At smaller (j), Ds follows a simple exponential exp(-a) in polymer concentration, but at larger Ds(c) follows a stretched exponential with large exponent. The exponential factor a is independent of polymer molecular weight, while rj depends strongly on M, so Ds and A must be nearly independent of solution rj. Probes somewhat... 

FIGURE 4.12 Volume fraction dependence of the short- (squares) and long-time (circles) self-diffusion coefficients. Both coefficients are normalized by the free diffusion coefficient... 

Inhibition of self-diffusion becomes apparent at timescales A short compared jD, where d is the characteristic pore diameter, because a fraction of molecules is always close to the walls, and their diffusion is hindered. This fraction depends on the surface-to-volume ratio (S/V) of the sample and the observation time A of the diffusion. This simple model leads to a fraction of 2DAf 5/V molecules being restricted in their motion. An analytical derivation [Mitl, Mit2, Mit6, Mit7] confirms an approximately linear dependence of the effective diffusion coefficient Deff(A) on... 

Figure 16 Variation of the water self-diflfusion coefficient with the water + surfactant volume fraction <1> for three different dilution lines corresponding to different water/surfactant ratios in the ternary DDAB-water-dodecane system. Above a certain concentration, which depends on the water/surfactant ratio, the water diffusion coefficient increases dramatically, indicating a water droplet-to-bicontinuous transition. (Data from Ref. 48.)...

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