[Kinetics] Implement rate-specific voltage correction

include/cantera/kinetics/InterfaceKinetics.h

@@ -96,6 +96,9 @@ class InterfaceKinetics : public Kinetics
 
     //! values needed to convert from exchange current density to surface
     //! reaction rate.
+    /*!
+     *  @deprecated  To be removed after Cantera 2.6.
+     */
     void updateExchangeCurrentQuantities();
 
     virtual void getDeltaGibbs(doublereal* deltaG);
@@ -127,6 +130,8 @@ class InterfaceKinetics : public Kinetics
      *
      *  @return Beta parameter. This defaults to zero, even for charge
      *    transfer reactions.
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     doublereal electrochem_beta(size_t irxn) const;
 
@@ -325,6 +330,8 @@ class InterfaceKinetics : public Kinetics
      *
      * @param kfwd  Vector of forward reaction rate constants on which to have
      *              the voltage correction applied
+     *
+     * @deprecated  To be removed after Cantera 2.6.
      */
     void applyVoltageKfwdCorrection(doublereal* const kfwd);
 
@@ -343,6 +350,8 @@ class InterfaceKinetics : public Kinetics
      *
      * @param kfwd  Vector of forward reaction rate constants, given in either
      *              normal form or in exchange current density form.
+     *
+     * @deprecated  To be removed after Cantera 2.6.
      */
     void convertExchangeCurrentDensityFormulation(doublereal* const kfwd);
 
@@ -520,6 +529,8 @@ class InterfaceKinetics : public Kinetics
      * potential energy change due to the reaction.
      *
      *  deltaElectricEnergy_[jrxn] = sum_i ( F V_i z_i nu_ij)
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp deltaElectricEnergy_;
 
@@ -538,6 +549,8 @@ class InterfaceKinetics : public Kinetics
     /*!
      *   Electrochemical transfer coefficient for all reactions that have
      *   transfer reactions the reaction is given by m_ctrxn[i]
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp m_beta;
 
@@ -548,6 +561,8 @@ class InterfaceKinetics : public Kinetics
      *  an index into the m_beta array.
      *
      *        irxn = m_ctrxn[i]
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     std::vector<size_t> m_ctrxn;
 
@@ -560,34 +575,44 @@ class InterfaceKinetics : public Kinetics
      *                            the rate constant as a chemical forward rate constant, a standard format.
      *   m_ctrxn_ecdf[irxn] = 1   this means that the rate coefficient calculator will calculate
      *                            the rate constant as an exchange current density rate constant expression.
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_int m_ctrxn_ecdf;
 
     //! Vector of standard concentrations
     /*!
      *   Length number of kinetic species
      *   units depend on the definition of the standard concentration within each phase
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp m_StandardConc;
 
     //!  Vector of delta G^0, the standard state Gibbs free energies for each reaction
     /*!
      *    Length is the number of reactions
      *    units are Joule kmol-1
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp m_deltaG0;
 
     //! Vector of deltaG[] of reaction, the delta Gibbs free energies for each reaction
     /*!
      *    Length is the number of reactions
      *    units are Joule kmol-1
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp m_deltaG;
 
     //! Vector of the products of the standard concentrations of the reactants
     /*!
      *   Units vary wrt what the units of the standard concentrations are
      *   Length = number of reactions.
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     vector_fp m_ProdStanConcReac;
 
@@ -623,6 +648,8 @@ class InterfaceKinetics : public Kinetics
      *  If this is true, the standard state Gibbs free energy of the reaction
      *  and the product of the reactant standard concentrations must be
      *  precalculated in order to calculate the rate constant.
+     *
+     *  @deprecated  To be removed after Cantera 2.6.
      */
     bool m_has_exchange_current_density_formulation;
 

include/cantera/kinetics/InterfaceRate.h

@@ -95,6 +95,7 @@ class CoverageBase
         if (shared_data.ready) {
             m_siteDensity = shared_data.density;
         }
+
         if (m_indices.size() != m_cov.size()) {
             // object is not set up correctly (setSpecies needs to be run)
             m_acov = NAN;
@@ -110,6 +111,79 @@ class CoverageBase
             m_ecov += m_ec[item.first] * shared_data.coverages[item.second];
             m_mcov += m_mc[item.first] * shared_data.logCoverages[item.second];
         }
+
+        // Update quantities used for exchange current density formulation
+        if (m_exchangeCurrentDensityFormulation) {
+            m_deltaG0 = 0.;
+            m_prodStandardConcentrations = 1.;
+            for (const auto& item : m_stoichCoeffs) {
+                m_deltaG0 +=
+                    shared_data.standardChemPotentials[item.first] * item.second;
+                if (item.second > 0.) {
+                    m_prodStandardConcentrations *=
+                        shared_data.standardConcentrations[item.first];
+                }
+            }
+        }
+    }
+
+    //! Calculate modifications for the forward reaction rate for interfacial charge
+    //! transfer reactions
+    /*!
+     *  For reactions that transfer charge across a potential difference, the
+     *  activation energies are modified by the potential difference. This method
+     *  calculates a correction factor based on the net electric potential energy
+     *  change due to the reaction
+     *  \f[
+     *   deltaElectricEnergy = sum_i ( pot_i nu_ij)
+     *  \f]
+     *  where \f$ pot_i = F phi_i z_i \f$ is passed as an argument to this method.
+     *
+     *  When an electrode reaction rate is specified in terms of its exchange current
+     *  density, the correction factor is adjusted to the standard reaction rate
+     *  constant form and units. Specifically, this converts a reaction rate constant
+     *  that was specified in units of A/m2 to kmol/m2/s.
+     *
+     *  @param pot  Array of potential energies due to voltages
+     *
+     *  @warning  The updated calculation of voltage corrections is an experimental
+     *      part of the %Cantera API and may be changed or removed without notice.
+     */
+    //
+    double voltageCorrection(const double* pot, double RT) {
+        if (!m_chargeTransfer) {
+            return 1.;
+        }
+
+        // Compute the change in electrical potential energy.
+        // This will only be non-zero if a potential difference is present.
+        double deltaElectricEnergy = 0.;
+        for (const auto& item : m_stoichCoeffs) {
+            deltaElectricEnergy += pot[item.first] * item.second;
+        }
+
+        // Calculate reaction rate correction. Only modify those with a non-zero
+        // activation energy.
+        double correction = 1.;
+        if (deltaElectricEnergy != 0.) {
+            // Comments preserved from previous implementation:
+            // Below we decrease the activation energy below zero.
+            // NOTE, there is some discussion about this point. Should we decrease the
+            // activation energy below zero? I don't think this has been decided in any
+            // definitive way. The treatment below is numerically more stable, however.
+            correction = exp(-m_beta * deltaElectricEnergy / RT);
+        }
+
+        // Update correction if exchange current density formulation format is used.
+        if (m_exchangeCurrentDensityFormulation) {
+            // Comment preserved from previous implementation:
+            // We need to have the straight chemical reaction rate constant to
+            // come out of this calculation.
+            double tmp = exp(-m_beta * m_deltaG0 / RT);
+            tmp /= m_prodStandardConcentrations * Faraday;
+            correction *= tmp;
+        }
+        return correction;
     }
 
     //! Return site density [kmol/m^2]
@@ -139,14 +213,19 @@ class CoverageBase
     double m_acov; //!< Coverage contribution to pre-exponential factor
     double m_ecov; //!< Coverage contribution to activation energy
     double m_mcov; //!< Coverage term in reaction rate
-    bool m_electrochemistry; //!< Boolean indicating use of electrochemistry
+    bool m_chargeTransfer; //!< Boolean indicating use of electrochemistry
     double m_beta; //!< Forward value of apparent electrochemical transfer coefficient
     bool m_exchangeCurrentDensityFormulation; //! Electrochemistry only
+    double m_deltaG0; //!< Standard state Gibbs free energy
+    double m_prodStandardConcentrations; //!< Products of standard concentrations
     std::map<size_t, size_t> m_indices; //!< Map holding indices of coverage species
     std::vector<std::string> m_cov; //!< Vector holding names of coverage species
     vector_fp m_ac; //!< Vector holding coverage-specific exponential dependence
     vector_fp m_ec; //!< Vector holding coverage-specific activation energy dependence
     vector_fp m_mc; //!< Vector holding coverage-specific power-law exponents
+
+    //! Pairs of species indices and multiplers to calculate enthalpy change
+    std::vector<std::pair<size_t, double>> m_stoichCoeffs;
 };
 
 
@@ -305,7 +384,7 @@ class InterfaceRate : public RateType, public CoverageBase
     }
 
     virtual bool usesElectrochemistry() override {
-        return m_electrochemistry;
+        return m_chargeTransfer;
     }
 
     //! Update reaction rate parameters
@@ -438,7 +517,7 @@ class StickingRate : public RateType, public StickingCoverage
     }
 
     virtual bool usesElectrochemistry() override {
-        return m_electrochemistry;
+        return m_chargeTransfer;
     }
 
     //! Update reaction rate parameters

include/cantera/kinetics/ReactionData.h

@@ -327,13 +327,17 @@ struct CoverageData : public BlowersMaselData
         coverages.resize(n_species, 0.);
         logCoverages.resize(n_species, 0.);
         partial_molar_enthalpies.resize(n_species, 0.);
+        standardChemPotentials.resize(n_species, 0.);
+        standardConcentrations.resize(n_species, 0.);
         ready = true;
     }
 
     double sqrtT; //!< square root of temperature
 
-    vector_fp coverages; //!< vector holding surface coverages
-    vector_fp logCoverages; //!< vector holding logarithm of surface coverages
+    vector_fp coverages; //!< surface coverages
+    vector_fp logCoverages; //!< logarithm of surface coverages
+    vector_fp standardChemPotentials; //!< standard state chemical potentials
+    vector_fp standardConcentrations; //!< standard state concentrations
 };
 
 }

src/kinetics/InterfaceRate.cpp

@@ -16,9 +16,11 @@ CoverageBase::CoverageBase()
     , m_acov(0.)
     , m_ecov(0.)
     , m_mcov(0.)
-    , m_electrochemistry(false)
+    , m_chargeTransfer(false)
     , m_beta(0.5)
     , m_exchangeCurrentDensityFormulation(false)
+    , m_deltaG0(NAN)
+    , m_prodStandardConcentrations(NAN)
 {
 }
 
@@ -42,7 +44,7 @@ void CoverageBase::getParameters(AnyMap& node) const
         getCoverageDependencies(deps);
         node["coverage-dependencies"] = std::move(deps);
     }
-    if (m_electrochemistry) {
+    if (m_chargeTransfer) {
         if (m_beta != 0.5) {
             node["beta"] = m_beta;
         }
@@ -127,8 +129,16 @@ void CoverageBase::setSpecies(const std::vector<std::string>& species)
 
 void CoverageBase::setContext(const Reaction& rxn, const Kinetics& kin)
 {
-    m_electrochemistry = rxn.checkElectrochemistry(kin);
+    m_chargeTransfer = rxn.checkElectrochemistry(kin);
     setSpecies(kin.thermo().speciesNames());
+
+    m_stoichCoeffs.clear();
+    for (const auto& sp : rxn.reactants) {
+        m_stoichCoeffs.emplace_back(kin.kineticsSpeciesIndex(sp.first), -sp.second);
+    }
+    for (const auto& sp : rxn.products) {
+        m_stoichCoeffs.emplace_back(kin.kineticsSpeciesIndex(sp.first), sp.second);
+    }
 }
 
 StickingCoverage::StickingCoverage()

src/kinetics/ReactionData.cpp

@@ -317,8 +317,15 @@ bool CoverageData::update(const ThermoPhase& phase, const Kinetics& kin)
             logCoverages[n] = std::log(std::max(coverages[n], Tiny));
         }
         for (size_t n = 0; n < kin.nPhases(); n++) {
-            kin.thermo(n).getPartialMolarEnthalpies(
-                partial_molar_enthalpies.data() + kin.kineticsSpeciesIndex(0, n));
+            size_t start = kin.kineticsSpeciesIndex(0, n);
+            const auto& ph = kin.thermo(n);
+            ph.getPartialMolarEnthalpies(partial_molar_enthalpies.data() + start);
+            ph.getStandardChemPotentials(standardChemPotentials.data() + start);
+            size_t nsp = ph.nSpecies();
+            for (size_t k = 0; k < nsp; k++) {
+                // only used for exchange current density formulation
+                standardConcentrations[k + start] = ph.standardConcentration(k);
+            }
         }
         m_state_mf_number = mf;
         changed = true;