Theory for Electrochemical Power Losses
Most Electrochemistry interfaces define power loss variables that can be used to analyze the performance of electrochemical cells. The power loss variables are derived using similar principles as for the electrochemical heat source variables, but with the fundamental difference that the power loss variables are based on interfacial changes and domain gradients in the Gibbs free energy, rather than the enthalpy. In the absence of entropy changes, the power loss and the heat source variables are identical.
Kinetic Activation Power Losses
On an electrode surface, the local power loss (A/m2) equals the local electrode reaction current density times the overpotential
(4-48)
whereas in a homogenized porous electrode model, the local power loss (A/m3) equals the volumetric electrode reaction current density times the overpotential
(4-49)
Electrolyte transport power losses
Power loss associated with transport is based on gradients in the chemical potentials of the transported species. (The chemical potential equals the Gibbs free energy per mole of that species). For an electrolyte species i, the electrochemical potential gradient (J/mol/m) is defined as
(4-50)
This definition assumes that the Nernst–Einstein equation applies for the definition of the electrolyte mobility, and that the equilibrium potential of all electrode reactions exhibit a Nernstian (logarithmic) concentration dependency. For non-ideal activities, the ci is replaced by ai.
The electrolyte power loss associated with the transport of the species i is then defined as
(4-51)
where Nmd,i is the migrative-diffusive flux of species i with respect to the mass-averaged, or solvent, convective velocity of the electrolyte which relates to the total molar flux Ntot,i as
(4-52)
where v is the velocity.
The total power loss due to electrolyte transport is defined as
(4-53)
Recognizing that the total electrolyte current vector equals
(4-54)
it is possible to split the total power loss into an entropic and ohmic part defined as
(4-55)
and
(4-56)
Electrolyte Transport Losses in the Lithium-Ion Battery and Battery with Binary Electrolytes interfaces
For a binary 1:1 concentrated electrolyte, neglecting the contribution from the solvent, the transport power loss is defined as
(4-57)
The concentrated electrolyte transport model for the binary electrolyte defines a non-ideal activity coefficient for the neutral salt rather than the individual ions, which does not allow for defining the chemical potential gradients individually. However, for the lithium-ion case, the above expression may be rewritten as
(4-58)
using the relations , and .
Similarly, for the Battery with Binary Electrolyte interface, the local electrolyte transport power loss becomes
(4-59)