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 in the Transport in Solids interface is decomposed as follows
where μext contains all the contributions not related to the diffusion process. Note that the free energy density has to be function of the concentration 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
(3-283)
where M is the mobility, that can be related to the diffusion coefficient D by comparing the definitions in Equation 3-280 and Equation 3-283
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 c
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).