Base class for rate parameterizations that involve interfaces. More...

#include <InterfaceRate.h>

Inheritance diagram for InterfaceRateBase:

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()

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

node	AnyMap 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

node	AnyMap 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

dependencies	Coverage dependencies
units	Unit system

Definition at line 136 of file InterfaceRate.cpp.

◆ getCoverageDependencies()

void getCoverageDependencies ( AnyMap & dependencies ) const

Store parameters needed to reconstruct coverage dependencies.

Parameters

dependencies AnyMap 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

rxn	Reaction associated with rate parameterization
kin	Kinetics 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_data data 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:

Detailed Description

Public Member Functions

Protected Attributes

Private Attributes

Constructor & Destructor Documentation

◆ InterfaceRateBase()

Member Function Documentation

◆ setParameters()

◆ getParameters()

◆ setCoverageDependencies()

◆ getCoverageDependencies()

◆ addCoverageDependence()

◆ exchangeCurrentDensityFormulation()

◆ setContext()

◆ setSpecies()

◆ updateFromStruct()

◆ voltageCorrection()

◆ usesElectrochemistry()

◆ beta()

◆ siteDensity()

◆ setSiteDensity()

Member Data Documentation

◆ m_siteDensity

◆ m_acov

◆ m_ecov

◆ m_mcov

◆ m_chargeTransfer

◆ m_exchangeCurrentDensityFormulation

◆ m_beta

◆ m_deltaPotential_RT

◆ m_deltaGibbs0_RT

◆ m_prodStandardConcentrations

◆ m_indices

◆ m_cov

◆ m_ac

◆ m_ec

◆ m_lindep

◆ m_mc

◆ m_stoichCoeffs

◆ m_netCharges