Self-diffusion

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]

$D_{i}^{*}=D_{i}{\frac {\partial \ln c_{i}}{\partial \ln a_{i}}}$ {\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} in the 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 isotope in the medium of interest.^[3] However modern simulations are able to estimate it directly without the need for isotope labeling.^[4]