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.

See also