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,¹ 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:²

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

Here, ${\displaystyle a_{i}}$ is the activity of the medium ${\displaystyle i}$ (e.g. water) in the system (e.g. 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 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