Electrochemical, Internal, External, and Total Chemical Potential
The abstract definition of chemical potential given above—total change in free energy per extra mole of substance—is more specifically called total chemical potential. If two locations have different total chemical potentials for a species, some of it may be due to potentials associated with "external" force fields (Electric potential energy differences, gravitational potential energy differences, etc.), while the rest would be due to "internal" factors (density, temperature, etc.) Therefore the total chemical potential can be split into internal chemical potential and external chemical potential:
where
i.e., the external potential is the sum of electric potential, gravitational potential, etc. (q and m are the charge and mass of the species, respectively, V and h are the voltage and height of the container, respectively, and g is the acceleration due to gravity.) The internal chemical potential includes everything else besides the external potentials, such as density, temperature, and enthalpy.
The phrase "chemical potential" sometimes means "total chemical potential", but that is not universal. In some fields, in particular electrochemistry, semiconductor physics, and solid-state physics, the term "chemical potential" means internal chemical potential, while the term electrochemical potential is used to mean total chemical potential.
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