Diffusion

The diffusion coefficient, is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D = \frac{1}{3} \int_0^\infty \langle v_i(t) \cdot v_i(0)\rangle ~dt}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_i(t)} is the center of mass velovity of molecule Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} .

Einstein relation

$D=\lim _{t\rightarrow \infty }{\frac {1}{6}}\langle \vert \mathbf {r} _{i}(t)\cdot \mathbf {r} _{i}(0)\vert ^{2}\rangle$

References

1. G. L. Aranovich and M. D. Donohue "Limitations and generalizations of the classical phenomenological model for diffusion in fluids", Molecular Physics 105 1085-1093 (2007)