Corrected compared with self-diffusivity

Optional At 273 K, 7 23 (for He-Ar) is 0.653 cm s . From Du, Di, and D23 at room temperature, calculate c/12, c/13, and c/23. (To correct diffusion constants from one temperature to another, assume a dependence if the temperature change is small. This is only approximate, since the ds may vaiy in some degree with the temperature.) Then obtain d-[, di, and c/3 and use these to calculate D, Di, and D, from Eq. (V-35). Determine the ratios of the self-diffusion constants to their respective viscosities. How do these compare with the theoretical ratios discussed in the introductory section of Chapter V ... 

Dubbeldam et al.46S use random walk theory and extended dynamically corrected transition state theory in order to compute the self-diffusivity of adsorbed molecules in nanoporous confined systems at nonzero loading. The results are compared with MD simulation results with good agreement. 

NMR PFG measurements determine the tracer or self-diffusivity (D ) under equilibrium conditions with no concentration gradient. n any sorption rate measurement it is the transport diffusivity under the influence of a concentration gradient which is measured. In general these two quantities are not the same but the relationship between them can be established from irreversible thermodynamics. (17,18) In the low concentration limit the thermodynamic correction factor vanishes and the transport and self diffusivities should approach the same limit. Since ZLC measurements are made at low concentrations within the Henry s Law region the diffusivity values should be directly comparable with the NMR self-dif fusivities. ... 

Figure 8. Dj for heat corrected data in unfilled, crosslinked, natural rubber sample, versus volume fraction of solvent, compared with empirical extrapolation (dashed line) to the self-diffusion constant for toluene.

As shown in Fig. 12, a monotonous decrease in the self-diffusion coefficient was measured by PPG NMR for a series of n-alkanes in Na-X [50]. A similar trend was observed in ZSM-5 by QENS. From the NSE experiments performed in 5A, one finds that Dt drops to a minimum at Cs and has a clear maximiun at Ci2. A similar variation is obtained for Do after correcting from the thermodynamic correction factor (the number of carbon atoms per cavity is the same). Recent PEG NMR results indicate also a small minimum for Ds at Cg and a small maximum at Cm [51]. The NSE data obtained for longer n-alkanes in 5A are in contradiction with simulations which predict increasing diffusivities from C12 to Ci7 [52] whereas a decreasing trend is observed (Fig. 12). Finally, the activation energies derived from the NSE measurements show a minimum for C12, in agreement with the explanation in terms of the window effect. These results are related to similar concepts such as resonant diffusion [53] or the levitation effect, which corresponds to a maximum in self-diffusivity when the size of the diffusant is comparable to the diameter of the void [54]. 

FIGURE 8.11 (a) Circles represent diffusivities from the synthetic boundary method, squares from DLS, and triangles are NMR self-diffusion coefficients. The system is ovalbumin with very little electrolyte and close to the isoelectric point, (b) Mutual diffusivities corrected for the solution nonideality compared to NMR results (line). Reprinted from Gibbs et al. (1991) with permission. Copyright 1978 American Chemical Society. 

NMR techniques provide a somewhat more convenient and widely used method for the measurement of self-diffusivities. The method is, however, restricted to species such as hydrocarbons which contain a sufficiently hi concentration of unpaired nuclear spins. In comparing the results of NMR and uptake rate measurements it follows from Eqs. (5.6) and (5.9) that one should compare the NMR self-diffusivity with the corrected diffusivity from the uptake rate measurements. Exact agreement can be expected only when the cross coefficient is zero, but this is normally a good approximation at low concentrations. 

When quantitatively comparing simulation results with experimental data, the choice of force field is crucial. Because our focus is the dynamics of hydration water, we use the widely familiar TlP4P-Ew model. It has a computed self-diffusion constant that agrees well with experimental values and with the T scale (its density maximum is at 274K, only 3K below the correct value) down to 230K. Thus, we... 

Fast activationless reactions, such as recombination of atoms and radicals, of course, occur more slowly in liquid than in gas because they are limited by the rate of particle self-diffusion, and diffusion in liquid occurs more slowly than in gas. Therefore, it is of interest to compare slow reactions, which are not limited by diffusion in liquid, to those with rate constants A < 1 o l/(mol s) in the gas phase. As we will see further, the solvation effects and formation of molecular complexes influence strongly on the chemical reaction in liquid. Since solvation is absent ftom the gas phase, for the correct comparison we have to consider reactions in which at least one reactant is a nonpolar particle, for example, hydrocarbon. Reactions of radicals with nonpolar C—H bonds are most suitable for this comparison. The data on such... 

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