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 ${\displaystyle D_{i}^{*}}$ 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.