Thermodynamic diffusion coefficient fractional free volume

Fujita (ljD related the thermodynamic diffusion coefficient, D, to the fractional free volume, v, by... 

The theory is based on the assumption that a diffusing molecule can only move from one place to another when the local free volume around that molecule exceeds a certain critical value. The probability of finding such sufficient free volume is proportional to exp( —Ff), where is a parameter describing the amount of free volume needed and is proportional to d, the Lennard-Jones size parameter, 0 is the volume fraction of permeant and is the fractional free volume of the system. The thermodynamic diffusion coefficient Dj may be related to this probability by... 

The dimensionless parameters that define the thermodynamic state of this system are the total volume fraction ( ) = (nl6)n (with n being the total number concentration, n = n, + n, the relative concentrations = njn, and the potential parameters K2, and z. The free-diffusion coefficients D° are also assumed identical for both species, that is, D = D = D°. Explicit values of the parameters a and D are not needed, since the dimensionless dynamic properties, such as t), only depend on the dimensionless parameters specified above, when expressed in terms of the scaled variables ka and t/to, where to = a /D . Besides solving the SCGLE scheme, in reference [21] Brownian dynamics simulations were generated for the static and dynamic properties of the system above. 

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