Calculation of Built-in Equilibrium and Thermoneutral Potentials

The change of enthalpy for an electrode reaction is (Ref. 1)

where Hi = Hi(T) are the enthalpies of formation of the reacting species of index i, and νi the stoichiometric coefficients.

Similarly, the change of entropy is

Where Si = Si(T) is the (absolute) molar entropy.

Hi and Si are generally known for liquids and gases, whereas for ions the values will depend on the nature of the electrolyte in use, and are hence hard to measure experimentally.

The corresponding change of Gibbs free energy of a reaction is

The equilibrium potential for an electrode reaction is

and the thermoneutral voltage, required to compute electrode reaction heat sources, is

where n is the number of electrons included in the electrode reaction.

Temperature dependent thermodynamic expressions for gaseous species of Hi(T) and Si(T), at standard partial pressures of 1 atm, are based on Ref. 6.

For the charge-conducting ion in the electrolyte, entropy and enthalpy values are however generally not known and need to be set by the user. The stoichiometric coefficient of the charge-carrying ion is derived from the number of electrons participating in the charge transfer reaction and the charge carrying ion charge as

For convenience, the built-in equilibrium potentials are defined versus a reversible reference hydrogen electrode (RHE) for the same electrolyte type, for a specified reference temperature. This will have the effect that the HOR/HER will have an equilibrium potential in a model close to 0 V, and the ORR/OER reaction will have an equilibrium potential ranging from around 1.2 (at room temperature) to 1.0 V (at 800°C). This shift facilitates setting for instance initial values for the potential dependent variables in a model.

The reference equilibrium and thermoneutral potentials used by the electrode reaction node, versus the RHE, are defined as

and

where

with ΔSref being the change in entropy at the chosen reference conditions (typically 1 atm).

Note that due to cancellation in the equation for Eeq, ref, the values of the ion entropy (0 by default) has no impact on the equilibrium potentials values (nor the overall cell voltage and energy balance), but it will impact how the thermoneutral voltage Etherm and corresponding heat sources for the individual electrode reactions are computed.

The fc/we interface defines the water vapor pressure, pvap (Pa), and the enthalpy of vaporization Hvap (J/mol), by the use of an experimental correlations (interpolation) functions vs temperature. The pvap(T) correlation is based on Ref. 5, whereas Hvap(T) is defined using the same source data as in the Thermodynamics node (See Using Thermodynamic Properties).

The enthalpy of formation of liquid water, HH2O(l) (J/mol), is then defined as

Assuming that the vapor behaves as an ideal gas, and that the liquid water is incompressible, the following equation for the entropy of liquid water can be derived

The relative humidity, RH (1), is defined as