Prediction of diffusivity

Indeed, it is worth noting that by itself, a permeation rate proportional to p°50 could be consistent with any value whatever for the ratio of monatomic to diatomic species in the solid, if the diatomic species is very immobile. For in such case, the permeation flux would be carried entirely by the monatomic species, whose concentration always goes as p0 50. However, a sizable diatomic fraction would significantly modify the transient behavior of the permeation after a change in gas pressure. Although neither Van Wieringen and Warmholtz nor Frank and Thomas published details of the fit of their observed transients to the predictions of diffusion theory, it is unlikely that any large discrepancies would have escaped their attention. 

Hayduk, W. and Laudie, H. Prediction of diffusion coefficients for nonelectrolytes in dilute aqueous solution, Am. Inst. Chem. Eng., 20(3) 611-615, 1974. 

Hayduk, W., and H. Laudie, Prediction of diffusion coefficients for non-electrolytes in dilute aqueous solutions , AlChE J., 20,611-615 (1974). 

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

Fig. 8.8 Free volume theory prediction of mutual binary diffusion coefficient for the toluene-PS system based on parameters (19). [Reproduced by permission from J. L. Duda, J. S. Vrentas, S. T. Ju and H. T. Liu, Prediction of Diffusion Coefficients, A.I.Ch.E J., 28, 279 (1982).]...

From the point of view of earlier discussions, namely the true prediction of diffusion coefficients for volatile and nonvolatile organic penetrants in glassy polymers, the diffusion equations derived in the framework of the DST have only a limited usefulness. That means that, because the parameters of the DST models are not directly related to first principles , the equations can be used with success to correlate experimental results, but not to truly predict diffusion coefficients. 

Two atomistic approaches have been presented briefly above molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the ab initio character of the method. However MD and TSA are valuable achievements, they are complementary in several... 

Prediction of diffusion coefficients in gases, liquids, amorphous solids and plastic materials using an uniform model... 

From a detailed analysis of molecular motion in dilute gases a much better prediction of diffusion coefficients results with the Chapman-Enskog equation. This equation, which describes a mixture of two solutes A and B (binary gas system) is ... 

In general, diffusion coefficients in gases can be often be predicted accurately. Predictions of diffusion coefficients in liquids are also possible using the Stokes-Einstein equation or its empirical parallels. On the contrary in solids and polymers, models allow coefficients to be correlated but predictions are rarely possible. 

Diffusion coefficients are required to interpret all the data, but measured values are not available in most cases. The method of Wilke and Chang [33] represents the widely accepted standard for prediction of diffusion coefficients ... 

The objective was to develop a mathematical model allowing the prediction of diffusion coefficients for different solutes in various solvents, based... 

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