Molecular models for diffusion

The starting point for a molecular theory of diffusion is the analysis of a random walk of an atom or molecule. In Chapter 3, we dealt with the possible shapes of a one-dimensional polymer chain Eq. (3.13) gave the number of distinguishable chains of end-to-end length r as 

This solution can be adapted for diffusion as follows The diffusing species is assumed to take v steps per second, so, in a time t, has traced out a walk oin = vt steps. The step length I becomes the jump distance of the diffusing species. The one-dimensional polymer chain becomes a planar diffusion problem, in which the concentration C only varies in the x direction, and is constant in the yz plane. The equivalent of Eq. (A.3) then is 

This describes the diffusion of an initially planar source of impurity atoms (Fig. A.l). M is the total amount of the impurity per unit cross-sectional area, and the diffusion distance x replaces the random walk length r. With increasing time, the Gaussian distribution spreads and the peak diminishes in magnitude. 

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The model of Meares is only of historical interest because it was the first molecular model for diffusion in polymers. Meares (12) found that the activation energy for diffusion correlates linearly with the square of the penetrant diameter, but not with the diameter cubed. Therefore, he inferred that the elementary... 

Microstructure and Engineering Appiications 3E A. I Molecular models for diffusion... 

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