Self-Diffusion and Velocity Correlation

Approximate expressions for the self-diffusion coefficients of spherical molecules in solid, liquid, and gas phases are obtained from the relation D=(kT/m) ∫ 0∞ρ(s)ds,where D is the diffusion coefficient and ρ(s) is the velocity correlation function of the spherical molecules. The correlation function is approximated by the function cosαδs/coshαs and the parameters α and δ are expressed in terms of molecular properties for liquids and gases. The approximate diffusion coefficient is found to obey an Arrhenius relation in the solid phase and a Sutherland equation for the gas phase. The results of a crude calculation of the self-diffusion coefficient for liquid neopentane are within a factor of two of the experimental diffusion coefficients. The temperature coefficient of the calculated diffusion coefficients is also within a factor of two of the observed temperature coefficient.