Free-Volume Model for Liquids

1 FREE-VOLUME MODEL FOR SELF-DIFFUSION IN LIQUIDS 

Self-diffusion in simple monatomic liquids at temperatures well above their glass-transition temperatures may be interpreted in a simple manner.1 Within such liquids, regions with free volume appear due to displacement fluctuations. Occasionally, the fluctuations are large enough to permit diffusive displacements. 

1This section closely follows Cohen and Turnbull s original derivation [1], The original paper should be consulted for further details. 

Kinetics of Materials. By Robert W. Balluffi, Samuel M. Allen, and W. Craig Carter. 229 Copyright 2005 John Wiley Sons, Inc. 

According to the kinetic theory of gases, the self-diffusivity of a hard-sphere gas is given by DG = (2/5)(u)L, where (u) is the average velocity and L is the mean free path [4]. Because the mean free path of a confined particle in the liquid is about equal to the diameter of its confining volume, the contribution of the confined particle to the self-diffusivity of the liquid may be written 

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The value of a may be taken as unity, while r/ may be estimated from free volume models for liquids. Values of r/ in the range of 0.3 A (or about 10 per cent of vas) seem to fit the data for many liquids to within a factor of about 3." ... 

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