Chemical Potential
The chemical potential μ is the driving force for transport processes and it is related to the concentration c through the free energy density, ψ, as follows
The free energy density can have contributions from different sources like the elastic energy due to deformation, or the mixing energy of a solvent in the solid
The chemical potential is decomposed as follows
(3-293)
where μext contains all the contributions not related to the diffusion process. Note that the free energy density, ψ, has to be function of the concentration c to define the chemical potential.
For instance, the Flory–Huggins free energy often used to describe diffusion in polymeric gel reads
It is possible to define the diffusive flux as a function of the chemical potential gradient
(3-294)
where M is the mobility, that can be related to the diffusion coefficient D by comparing the definitions in Equation 3-290 and Equation 3-294
thus the diffusion coefficient is related to the mobility by
The mobility tensor M is the proportionality factor between the gradient of the chemical potential and the diffusive flux, and it is often a function of the concentration
For a linear mobility, it is written as
where ηc is the mobility coefficient (SI unit: s·mol/kg).
For a quadratic dependency on the concentration, it is written as
where cmax is the concentration level at which there is no diffusive flux.
It is also possible to enter a value or expression for the mobility tensor M (SI unit: s·mol2/(kg·m3).