Cantera  3.1.0a1
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Base class for rate parameterizations that involve interfaces. More...

#include <InterfaceRate.h>

Inheritance diagram for InterfaceRateBase:
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Detailed Description

Base class for rate parameterizations that involve interfaces.

Rate expressions defined for interfaces may include coverage dependent terms, where an example is given by Kee, et al. [15], Eq 11.113. Using Cantera nomenclature, this expression can be rewritten as

\[ k_f = A T^b \exp \left( - \frac{E_a}{RT} \right) \prod_k 10^{a_k \theta_k} \theta_k^{m_k} \exp \left( \frac{- E_k \theta_k}{RT} \right) \]

It is evident that this expression combines a regular modified Arrhenius rate expression \( A T^b \exp \left( - \frac{E_a}{RT} \right) \) with coverage-related terms, where the parameters \( (a_k, E_k, m_k) \) describe the dependency on the surface coverage of species \( k, \theta_k \). In addition to the linear coverage dependence on the activation energy modifier \( E_k \), polynomial coverage dependence is also available. When the dependence parameter \( E_k \) is given as a scalar value, the linear dependency is applied whereas if a list of four values are given as \( [E^{(1)}_k, ..., E^{(4)}_k] \), a polynomial dependency is applied as

\[ k_f = A T^b \exp \left( - \frac{E_a}{RT} \right) \prod_k 10^{a_k \theta_k} \theta_k^{m_k} \exp \left( \frac{- E^{(1)}_k \theta_k - E^{(2)}_k \theta_k^2 - E^{(3)}_k \theta_k^3 - E^{(4)}_k \theta_k^4}{RT} \right) \]

The InterfaceRateBase class implements terms related to coverage only, which allows for combinations with arbitrary rate parameterizations (for example Arrhenius and BlowersMaselRate).

Definition at line 92 of file InterfaceRate.h.

Public Member Functions

void setParameters (const AnyMap &node)
 Perform object setup based on AnyMap node information.
 
void getParameters (AnyMap &node) const
 Store parameters needed to reconstruct an identical object.
 
void setCoverageDependencies (const AnyMap &dependencies, const UnitSystem &units=UnitSystem())
 Set coverage dependencies based on AnyMap node information.
 
void getCoverageDependencies (AnyMap &dependencies) const
 Store parameters needed to reconstruct coverage dependencies.
 
virtual void addCoverageDependence (const string &sp, double a, double m, const vector< double > &e)
 Add a coverage dependency for species sp, with exponential dependence a, power-law exponent m, and activation energy dependence e, where e is in Kelvin, that is, energy divided by the molar gas constant.
 
bool exchangeCurrentDensityFormulation ()
 Boolean indicating whether rate uses exchange current density formulation.
 
void setContext (const Reaction &rxn, const Kinetics &kin)
 Build rate-specific parameters based on Reaction and Kinetics context.
 
void setSpecies (const vector< string > &species)
 Set association with an ordered list of all species associated with a given Kinetics object.
 
void updateFromStruct (const InterfaceData &shared_data)
 Update reaction rate parameters.
 
double voltageCorrection () const
 Calculate modifications for the forward reaction rate for interfacial charge transfer reactions.
 
bool usesElectrochemistry ()
 Boolean indicating whether rate uses electrochemistry.
 
double beta () const
 Return the charge transfer beta parameter.
 
double siteDensity () const
 Return site density [kmol/m^2].
 
void setSiteDensity (double siteDensity)
 Set site density [kmol/m^2].
 

Protected Attributes

double m_siteDensity
 Site density [kmol/m^2].
 
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_chargeTransfer
 Boolean indicating use of electrochemistry.
 
bool m_exchangeCurrentDensityFormulation
 
double m_beta
 Electrochemistry only.
 
double m_deltaPotential_RT
 Normalized electric potential energy change.
 
double m_deltaGibbs0_RT
 Normalized standard state Gibbs free energy change.
 
double m_prodStandardConcentrations
 Products of standard concentrations.
 
map< size_t, size_t > m_indices
 Map from coverage dependencies stored in this object to the index of the coverage species in the Kinetics object.
 
vector< string > m_cov
 Vector holding names of coverage species.
 
vector< double > m_ac
 Vector holding coverage-specific exponential dependence.
 
vector< vector< double > > m_ec
 Vector holding coverage-specific activation energy dependence as a 5-membered array of polynomial coeffcients starting from 0th-order to 4th-order coefficients.
 
vector< bool > m_lindep
 Vector holding boolean for linear dependence.
 
vector< double > m_mc
 Vector holding coverage-specific power-law exponents.
 

Private Attributes

vector< pair< size_t, double > > m_stoichCoeffs
 Pairs of species index and multipliers to calculate enthalpy change.
 
vector< pair< size_t, double > > m_netCharges
 Pairs of phase index and net electric charges (same order as m_stoichCoeffs)
 

Constructor & Destructor Documentation

◆ InterfaceRateBase()

Definition at line 92 of file InterfaceRate.cpp.

Member Function Documentation

◆ setParameters()

void setParameters ( const AnyMap node)

Perform object setup based on AnyMap node information.

Parameters
nodeAnyMap object containing reaction rate specification

Definition at line 106 of file InterfaceRate.cpp.

◆ getParameters()

void getParameters ( AnyMap node) const

Store parameters needed to reconstruct an identical object.

Parameters
nodeAnyMap object receiving reaction rate specification

Definition at line 119 of file InterfaceRate.cpp.

◆ setCoverageDependencies()

void setCoverageDependencies ( const AnyMap dependencies,
const UnitSystem units = UnitSystem() 
)

Set coverage dependencies based on AnyMap node information.

Parameters
dependenciesCoverage dependencies
unitsUnit system

Definition at line 136 of file InterfaceRate.cpp.

◆ getCoverageDependencies()

void getCoverageDependencies ( AnyMap dependencies) const

Store parameters needed to reconstruct coverage dependencies.

Parameters
dependenciesAnyMap receiving coverage information

Definition at line 180 of file InterfaceRate.cpp.

◆ addCoverageDependence()

void addCoverageDependence ( const string &  sp,
double  a,
double  m,
const vector< double > &  e 
)
virtual

Add a coverage dependency for species sp, with exponential dependence a, power-law exponent m, and activation energy dependence e, where e is in Kelvin, that is, energy divided by the molar gas constant.

Reimplemented in InterfaceRate< RateType, DataType >.

Definition at line 199 of file InterfaceRate.cpp.

◆ exchangeCurrentDensityFormulation()

bool exchangeCurrentDensityFormulation ( )
inline

Boolean indicating whether rate uses exchange current density formulation.

Definition at line 122 of file InterfaceRate.h.

◆ setContext()

void setContext ( const Reaction rxn,
const Kinetics kin 
)

Build rate-specific parameters based on Reaction and Kinetics context.

Parameters
rxnReaction associated with rate parameterization
kinKinetics object associated with rate parameterization

Definition at line 279 of file InterfaceRate.cpp.

◆ setSpecies()

void setSpecies ( const vector< string > &  species)

Set association with an ordered list of all species associated with a given Kinetics object.

Definition at line 214 of file InterfaceRate.cpp.

◆ updateFromStruct()

void updateFromStruct ( const InterfaceData shared_data)

Update reaction rate parameters.

Parameters
shared_datadata shared by all reactions of a given type

Definition at line 228 of file InterfaceRate.cpp.

◆ voltageCorrection()

double voltageCorrection ( ) const
inline

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. The correction factor is based on the net electric potential energy change

\[ \Delta E_{p,j} = \sum_i E_{p,i} \nu_{i,j} \]

where potential energies are calculated as \( E_{p,i} = F \phi_i z_i \). Here, \( F \) is Faraday's constant, \( \phi_i \) is the electric potential of the species phase and \( z_i \) is the charge of the species.

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.

Warning
The updated calculation of voltage corrections is an experimental part of the Cantera API and may be changed or removed without notice.

Definition at line 160 of file InterfaceRate.h.

◆ usesElectrochemistry()

bool usesElectrochemistry ( )
inline

Boolean indicating whether rate uses electrochemistry.

If this is true, the Butler-Volmer correction

\[ f_{BV} = \exp ( - \beta * Delta E_{p,j} / R T ) \]

is applied to the forward reaction rate.

See also
voltageCorrection().

Definition at line 195 of file InterfaceRate.h.

◆ beta()

double beta ( ) const
inline

Return the charge transfer beta parameter.

Definition at line 200 of file InterfaceRate.h.

◆ siteDensity()

double siteDensity ( ) const
inline

Return site density [kmol/m^2].

Warning
This method is an experimental part of the Cantera API and may be changed or removed without notice.

Definition at line 212 of file InterfaceRate.h.

◆ setSiteDensity()

void setSiteDensity ( double  siteDensity)
inline

Set site density [kmol/m^2].

Note
This method is used internally, for testing purposes only as the site density is a property of InterfaceKinetics and will be overwritten during an update of the thermodynamic state.
Warning
This method is an experimental part of the Cantera API and may be changed or removed without notice.

Definition at line 225 of file InterfaceRate.h.

Member Data Documentation

◆ m_siteDensity

double m_siteDensity
protected

Site density [kmol/m^2].

Definition at line 230 of file InterfaceRate.h.

◆ m_acov

double m_acov
protected

Coverage contribution to pre-exponential factor.

Definition at line 231 of file InterfaceRate.h.

◆ m_ecov

double m_ecov
protected

Coverage contribution to activation energy.

Definition at line 232 of file InterfaceRate.h.

◆ m_mcov

double m_mcov
protected

Coverage term in reaction rate.

Definition at line 233 of file InterfaceRate.h.

◆ m_chargeTransfer

bool m_chargeTransfer
protected

Boolean indicating use of electrochemistry.

Definition at line 234 of file InterfaceRate.h.

◆ m_exchangeCurrentDensityFormulation

bool m_exchangeCurrentDensityFormulation
protected

Definition at line 235 of file InterfaceRate.h.

◆ m_beta

double m_beta
protected

Electrochemistry only.

Forward value of apparent electrochemical transfer coefficient

Definition at line 236 of file InterfaceRate.h.

◆ m_deltaPotential_RT

double m_deltaPotential_RT
protected

Normalized electric potential energy change.

Definition at line 237 of file InterfaceRate.h.

◆ m_deltaGibbs0_RT

double m_deltaGibbs0_RT
protected

Normalized standard state Gibbs free energy change.

Definition at line 238 of file InterfaceRate.h.

◆ m_prodStandardConcentrations

double m_prodStandardConcentrations
protected

Products of standard concentrations.

Definition at line 239 of file InterfaceRate.h.

◆ m_indices

map<size_t, size_t> m_indices
protected

Map from coverage dependencies stored in this object to the index of the coverage species in the Kinetics object.

Definition at line 243 of file InterfaceRate.h.

◆ m_cov

vector<string> m_cov
protected

Vector holding names of coverage species.

Definition at line 244 of file InterfaceRate.h.

◆ m_ac

vector<double> m_ac
protected

Vector holding coverage-specific exponential dependence.

Definition at line 245 of file InterfaceRate.h.

◆ m_ec

vector<vector<double> > m_ec
protected

Vector holding coverage-specific activation energy dependence as a 5-membered array of polynomial coeffcients starting from 0th-order to 4th-order coefficients.

Definition at line 249 of file InterfaceRate.h.

◆ m_lindep

vector<bool> m_lindep
protected

Vector holding boolean for linear dependence.

Definition at line 250 of file InterfaceRate.h.

◆ m_mc

vector<double> m_mc
protected

Vector holding coverage-specific power-law exponents.

Definition at line 251 of file InterfaceRate.h.

◆ m_stoichCoeffs

vector<pair<size_t, double> > m_stoichCoeffs
private

Pairs of species index and multipliers to calculate enthalpy change.

Definition at line 255 of file InterfaceRate.h.

◆ m_netCharges

vector<pair<size_t, double> > m_netCharges
private

Pairs of phase index and net electric charges (same order as m_stoichCoeffs)

Definition at line 258 of file InterfaceRate.h.


The documentation for this class was generated from the following files: