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Self-diffusion describes the diffusive motions of molecules within themselves e.g. the movement of a water molecule in water. According to the IUPAC definition, the self-diffusion coefficient ${\displaystyle D_{i}^{*}}$ of medium ${\displaystyle i}$ is the diffusion coefficient ${\displaystyle D_{i}}$ of a chemical species in said medium when the concentration of this species is extrapolated to zero concentration. It can be described by the equation:

$${\displaystyle D_{i}^{*}=D_{i}{\frac {\partial \ln c_{i}}{\partial \ln a_{i}}}}$$

Here, ${\displaystyle a_{i}}$ is the activity of the medium ${\displaystyle i}$ in the solution and ${\displaystyle c_{i}}$ is the concentration of medium ${\displaystyle i}$. Due to challenges observing it directly it is commonly assumed to be equal to the diffusion of an isotope in the medium of interest. However modern simulations are able to estimate it directly without the need for isotope labeling.

See also

• Brownian motion
• Diffusion
• Molecular diffusion

References

1. S. J. Chalk (1997). A. D. McNaught, A. Wilkinson (ed.). "IUPAC Compendium of Chemical Terminology 'The Gold Book'" (2 ed.). Blackwell Scientific Publications.
2. Everett, D. H. (1972-01-01). "Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry". Pure and Applied Chemistry. 31 (4): 577–638. doi:10.1351/pac197231040577. ISSN 1365-3075.
3. Mills, R. (1973-03). "Self-diffusion in normal and heavy water in the range 1-45.deg". The Journal of Physical Chemistry. 77 (5): 685–688. doi:10.1021/j100624a025. ISSN 0022-3654. {{cite journal}}: Check date values in: |date= (help)
4. Bizzarri, Anna Rita (1996). "Molecular dynamics simulation evidence of anomalous diffusion of protein hydration water". Physical Review E. 53 (4): R3040 – R3043. doi:10.1103/PhysRevE.53.R3040.

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