Self-diffusion

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 D i ∗ {\displaystyle D_{i}^{*}} of medium i {\displaystyle i} is the diffusion coefficient D i {\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: D i ∗ = D i ∂ ln ⁡ c i ∂ ln ⁡ a i {\displaystyle D_{i}^{*}=D_{i}{\frac {\partial \ln c_{i}}{\partial \ln a_{i}}}} Here, a i {\displaystyle a_{i}} is the activity of the medium i {\displaystyle i} (e.g. water) in the system (e.g. solution) and c i {\displaystyle c_{i}} is the concentration of medium i {\displaystyle i} . Due to challenges observing it directly it is commonly assumed to be equal to the diffusion of an isotopically different molecule of the medium in the medium of interest e.g. a molecule of deuterated water in water. However modern simulations are able to estimate it directly without the need for isotope labeling.

Mass diffusivity of a chemical species without a chemical potential gradient

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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,^[1] the self-diffusion coefficient D i ∗ {\displaystyle D_{i}^{*}} of medium i {\displaystyle i} is the diffusion coefficient D i {\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:^[2]

D i ∗ = D i ∂ ln ⁡ c i ∂ ln ⁡ a i {\displaystyle D_{i}^{*}=D_{i}{\frac {\partial \ln c_{i}}{\partial \ln a_{i}}}}

Here, a i {\displaystyle a_{i}} is the activity of the medium i {\displaystyle i} (e.g. water) in the system (e.g. solution) and c i {\displaystyle c_{i}} is the concentration of medium i {\displaystyle i} . Due to challenges observing it directly it is commonly assumed to be equal to the diffusion of an isotopically different molecule of the medium in the medium of interest e.g. a molecule of deuterated water in water.^[3] However modern simulations are able to estimate it directly without the need for isotope labeling.^[4]

See also

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• Brownian motion
• Diffusion
• Molecular diffusion

References

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1. ^ S. J. Chalk (1997). A. D. McNaught, A. Wilkinson (ed.). "IUPAC Compendium of Chemical Terminology 'The Gold Book'" (2 ed.). Blackwell Scientific Publications. doi:10.1351/goldbook.S05582.
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. (March 1973). "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.
4. ^ Bizzarri, Anna Rita (1996). "Molecular dynamics simulation evidence of anomalous diffusion of protein hydration water". Physical Review E. 53 (4): R3040–R3043. Bibcode:1996PhRvE..53.3040B. doi:10.1103/PhysRevE.53.R3040. PMID 9964761.

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