self-diffusion

{{short description|Mass diffusivity of a chemical species without a chemical potential gradient}}

{{one source |date=March 2024}}

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,{{cite web|url=https://goldbook.iupac.org/terms/view/S05582|title=IUPAC Compendium of Chemical Terminology 'The Gold Book'|edition=2|date=1997|publisher=Blackwell Scientific Publications|author=S. J. Chalk|doi=10.1351/goldbook.S05582 |editor=A. D. McNaught, A. Wilkinson}} the self-diffusion coefficient $D\_i^*$ of medium $i$ is the diffusion coefficient $D\_i$ 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:{{Cite journal |last=Everett |first=D. H. |date=1972-01-01 |title=Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry |url=https://www.degruyter.com/document/doi/10.1351/pac197231040577/html |journal=Pure and Applied Chemistry |language=en |volume=31 |issue=4 |pages=577–638 |doi=10.1351/pac197231040577 |issn=1365-3075|url-access=subscription }}

$$$$

D_i^* = D_i\frac{\partial\ln c_i}{\partial\ln a_i}

Here, $a\_i$ is the activity of the medium $i$ in the solution and $c\_i$ is the concentration of medium $i$. Due to challenges observing it directly it is commonly assumed to be equal to the diffusion of an isotope in the medium of interest.{{Cite journal |last=Mills |first=R. |date=March 1973 |title=Self-diffusion in normal and heavy water in the range 1-45.deg. |url=https://pubs.acs.org/doi/abs/10.1021/j100624a025 |journal=The Journal of Physical Chemistry |language=en |volume=77 |issue=5 |pages=685–688 |doi=10.1021/j100624a025 |issn=0022-3654|url-access=subscription }} However modern simulations are able to estimate it directly without the need for isotope labeling.{{Cite journal |last=Bizzarri |first=Anna Rita |date=1996 |title=Molecular dynamics simulation evidence of anomalous diffusion of protein hydration water |url=https://journals.aps.org/pre/abstract/10.1103/PhysRevE.53.R3040 |journal=Physical Review E |volume=53 |issue=4 |pages=R3040–R3043 |doi=10.1103/PhysRevE.53.R3040|pmid=9964761 |bibcode=1996PhRvE..53.3040B |url-access=subscription }}