IdealSolidSolnPhase.h

Go to the documentation of this file.

/**
 * @file IdealSolidSolnPhase.h Header file for an ideal solid solution model
 *      with incompressible thermodynamics (see @ref thermoprops and
 *      @link Cantera::IdealSolidSolnPhase IdealSolidSolnPhase@endlink).
 *
 * This class inherits from the %Cantera class ThermoPhase and implements an
 * ideal solid solution model with incompressible thermodynamics.
 */
 
// This file is part of Cantera. See License.txt in the top-level directory or
// at https://cantera.org/license.txt for license and copyright information.
 
#ifndef CT_IDEALSOLIDSOLNPHASE_H
#define CT_IDEALSOLIDSOLNPHASE_H
 
#include "ThermoPhase.h"
 
namespace Cantera
{
 
/**
 * Class IdealSolidSolnPhase represents a condensed phase ideal solution
 * compound. The phase and the pure species phases which comprise the standard
 * states of the species are assumed to have zero volume expansivity and zero
 * isothermal compressibility. Each species does, however, have constant but
 * distinct partial molar volumes equal to their pure species molar volumes. The
 * class derives from class ThermoPhase, and overloads the virtual methods
 * defined there with ones that use expressions appropriate for ideal solution
 * mixtures.
 *
 * The generalized concentrations can have three different forms depending on
 * the value of the member attribute #m_formGC, which is supplied in the
 * constructor and in the input file. The value and form of the generalized
 * concentration will affect reaction rate constants involving species in this
 * phase.
 *
 * @ingroup thermoprops
 */
class IdealSolidSolnPhase : public ThermoPhase
{
public:
    //! Construct and initialize an IdealSolidSolnPhase ThermoPhase object
    //! directly from an input file
    /*!
     * This constructor will also fully initialize the object.
     * The generalized concentrations can have three different forms
     * depending on the value of the member attribute #m_formGC, which
     * is supplied in the constructor or read from the input file.
     *
     * @param infile File name for the input file containing information
     *               for this phase. If blank, an empty phase will be
     *               created.
     * @param id     The name of this phase. This is used to look up
     *               the phase in the input file.
     */
    explicit IdealSolidSolnPhase(const string& infile="", const string& id="");
 
    string type() const override {
        return "ideal-condensed";
    }
 
    bool isIdeal() const override {
        return true;
    }
 
    bool isCompressible() const override {
        return false;
    }
 
    //! @name Molar Thermodynamic Properties of the Solution
    //! @{
 
    /**
     * Molar entropy of the solution. Units: J/kmol/K. For an ideal, constant
     * partial molar volume solution mixture with pure species phases which
     * exhibit zero volume expansivity:
     * @f[
     * \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T)  - \hat R \sum_k X_k \ln(X_k)
     * @f]
     * The reference-state pure-species entropies
     * @f$ \hat s^0_k(T,p_{ref}) @f$ are computed by the species thermodynamic
     * property manager. The pure species entropies are independent of
     * pressure since the volume expansivities are equal to zero.
     * @see MultiSpeciesThermo
     */
    double entropy_mole() const override;
 
    /**
     * Molar Gibbs free energy of the solution. Units: J/kmol. For an ideal,
     * constant partial molar volume solution mixture with pure species phases
     * which exhibit zero volume expansivity:
     * @f[
     * \hat g(T, P) = \sum_k X_k \hat g^0_k(T,P) + \hat R T \sum_k X_k \ln(X_k)
     * @f]
     * The reference-state pure-species Gibbs free energies
     * @f$ \hat g^0_k(T) @f$ are computed by the species thermodynamic
     * property manager, while the standard state Gibbs free energies
     * @f$ \hat g^0_k(T,P) @f$ are computed by the member function, gibbs_RT().
     * @see MultiSpeciesThermo
     */
    double gibbs_mole() const override;
 
    /**
     * Molar heat capacity of the solution at at constant pressure and composition
     * [J/kmol/K].
     *
     * For an ideal, constant partial molar volume solution mixture with
     * pure species phases which exhibit zero volume expansivity:
     * @f[
     * \hat c_p(T,P) = \sum_k X_k \hat c^0_{p,k}(T) .
     * @f]
     * The heat capacity is independent of pressure. The reference-state pure-
     * species heat capacities @f$ \hat c^0_{p,k}(T) @f$ are computed by the
     * species thermodynamic property manager.
     * @see MultiSpeciesThermo
     */
    double cp_mole() const override;
 
    /**
     * Molar heat capacity of the solution at constant volume and composition
     * [J/kmol/K].
     *
     * For an ideal, constant partial molar volume solution mixture with pure
     * species phases which exhibit zero volume expansivity:
     * @f[ \hat c_v(T,P) = \hat c_p(T,P) @f]
     * The two heat capacities are equal.
     */
    double cv_mole() const override {
        return cp_mole();
    }
 
    //! @}
    //! @name Mechanical Equation of State Properties
    //!
    //! In this equation of state implementation, the density is a function only
    //! of the mole fractions. Therefore, it can't be an independent variable.
    //! Instead, the pressure is used as the independent variable. Functions
    //! which try to set the thermodynamic state by calling setDensity() will
    //! cause an exception to be thrown.
    //! @{
 
    /**
     * Pressure. Units: Pa. For this incompressible system, we return the
     * internally stored independent value of the pressure.
     */
    double pressure() const override {
        return m_Pcurrent;
    }
 
    /**
     * Set the pressure at constant temperature. Units: Pa. This method sets a
     * constant within the object. The mass density is not a function of
     * pressure.
     *
     * @param p   Input Pressure (Pa)
     */
    void setPressure(double p) override;
 
    /**
     * Calculate the density of the mixture using the partial molar volumes and
     * mole fractions as input
     *
     * The formula for this is
     *
     * @f[
     * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
     * @f]
     *
     * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
     * weights, and @f$ V_k @f$ are the pure species molar volumes.
     *
     * Note, the basis behind this formula is that in an ideal solution the
     * partial molar volumes are equal to the pure species molar volumes. We
     * have additionally specified in this class that the pure species molar
     * volumes are independent of temperature and pressure.
     */
    virtual void calcDensity();
 
    //! @}
    //! @name Chemical Potentials and Activities
    //!
    //! The activity @f$ a_k @f$ of a species in solution is related to the
    //! chemical potential by
    //! @f[
    //!   \mu_k(T,P,X_k) = \mu_k^0(T,P) + \hat R T \ln a_k.
    //!  @f]
    //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential
    //! at unit activity. It may depend on the pressure and the temperature.
    //! However, it may not depend on the mole fractions of the species in the
    //! solid solution.
    //!
    //! The activities are related to the generalized concentrations, @f$ \tilde
    //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following
    //! formula:
    //!
    //!  @f[
    //!  a_k = \frac{\tilde C_k}{C^0_k}
    //!  @f]
    //! The generalized concentrations are used in the kinetics classes to
    //! describe the rates of progress of reactions involving the species. Their
    //! formulation depends upon the specification of the rate constants for
    //! reaction, especially the units used in specifying the rate constants. The
    //! bridge between the thermodynamic equilibrium expressions that use a_k and
    //! the kinetics expressions which use the generalized concentrations is
    //! provided by the multiplicative factor of the standard concentrations.
    //! @{
 
    Units standardConcentrationUnits() const override;
 
    /**
     * This method returns the array of generalized concentrations. The
     * generalized concentrations are used in the evaluation of the rates of
     * progress for reactions involving species in this phase. The generalized
     * concentration divided by the standard concentration is also equal to the
     * activity of species.
     *
     * For this implementation the activity is defined to be the mole fraction
     * of the species. The generalized concentration is defined to be equal to
     * the mole fraction divided by the partial molar volume. The generalized
     * concentrations for species in this phase therefore have units of
     * kmol/m^3. Rate constants must reflect this fact.
     *
     * On a general note, the following must be true. For an ideal solution, the
     * generalized concentration must consist of the mole fraction multiplied by
     * a constant. The constant may be fairly arbitrarily chosen, with
     * differences adsorbed into the reaction rate expression. 1/V_N, 1/V_k, or
     * 1 are equally good, as long as the standard concentration is adjusted
     * accordingly. However, it must be a constant (and not the concentration,
     * btw, which is a function of the mole fractions) in order for the ideal
     * solution properties to hold at the same time having the standard
     * concentration to be independent of the mole fractions.
     *
     * In this implementation the form of the generalized concentrations
     * depend upon the member attribute, #m_formGC.
     *
     * HKM Note: We have absorbed the pressure dependence of the pure species
     *        state into the thermodynamics functions. Therefore the standard
     *        state on which the activities are based depend on both temperature
     *        and pressure. If we hadn't, it would have appeared in this
     *        function in a very awkward exp[] format.
     *
     * @param c  Pointer to array of doubles of length m_kk, which on exit
     *           will contain the generalized concentrations.
     */
    void getActivityConcentrations(span<double> c) const override;
 
    /**
     * The standard concentration @f$ C^0_k @f$ used to normalize the
     * generalized concentration. In many cases, this quantity will be the
     * same for all species in a phase. However, for this case, we will return
     * a distinct concentration for each species. This is the inverse of the
     * species molar volume. Units for the standard concentration are kmol/m^3.
     *
     * @param k Species number: this is a require parameter, a change from the
     *     ThermoPhase base class, where it was an optional parameter.
     */
    double standardConcentration(size_t k) const override;
 
    //! Get the array of species activity coefficients
    /*!
     * @param ac output vector of activity coefficients. Length: m_kk
     */
    void getActivityCoefficients(span<double> ac) const override;
 
    /**
     * Get the species chemical potentials. Units: J/kmol.
     *
     * This function returns a vector of chemical potentials of the
     * species in solution.
     * @f[
     *    \mu_k = \mu^{ref}_k(T) + V_k * (p - p_o) + R T \ln(X_k)
     * @f]
     *  or another way to phrase this is
     * @f[
     *    \mu_k = \mu^o_k(T,p) + R T \ln(X_k)
     * @f]
     *  where @f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o) @f$
     *
     * @param mu  Output vector of chemical potentials.
     */
    void getChemPotentials(span<double> mu) const override;
 
    //! @}
    //! @name  Partial Molar Properties of the Solution
    //! @{
 
    //! Returns an array of partial molar enthalpies for the species in the
    //! mixture.
    /*!
     * Units (J/kmol). For this phase, the partial molar enthalpies are equal to
     * the pure species enthalpies
     *  @f[
     * \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
     * @f]
     * The reference-state pure-species enthalpies, @f$ \hat h^{ref}_k(T) @f$,
     * at the reference pressure,@f$ P_{ref} @f$, are computed by the species
     * thermodynamic property manager. They are polynomial functions of
     * temperature.
     * @see MultiSpeciesThermo
     *
     * @param hbar Output vector containing partial molar enthalpies.
     *             Length: m_kk.
     */
    void getPartialMolarEnthalpies(span<double> hbar) const override;
 
    /**
     * Returns an array of partial molar entropies of the species in the
     * solution. Units: J/kmol/K. For this phase, the partial molar entropies
     * are equal to the pure species entropies plus the ideal solution
     * contribution.
     * @f[
     *  \bar s_k(T,P) =  \hat s^0_k(T) - R \ln(X_k)
     * @f]
     * The reference-state pure-species entropies,@f$ \hat s^{ref}_k(T) @f$, at
     * the reference pressure, @f$ P_{ref} @f$, are computed by the species
     * thermodynamic property manager. They are polynomial functions of
     * temperature.
     * @see MultiSpeciesThermo
     *
     * @param sbar Output vector containing partial molar entropies.
     *             Length: m_kk.
     */
    void getPartialMolarEntropies(span<double> sbar) const override;
 
    /**
     * Returns an array of partial molar Heat Capacities at constant pressure of
     * the species in the solution. Units: J/kmol/K. For this phase, the partial
     * molar heat capacities are equal to the standard state heat capacities.
     *
     * @param cpbar  Output vector of partial heat capacities. Length: m_kk.
     */
    void getPartialMolarCp(span<double> cpbar) const override;
 
    /**
     * returns an array of partial molar volumes of the species
     * in the solution. Units: m^3 kmol-1.
     *
     * For this solution, the partial molar volumes are equal to the
     * constant species molar volumes.
     *
     * @param vbar  Output vector of partial molar volumes. Length: m_kk.
     */
    void getPartialMolarVolumes(span<double> vbar) const override;
 
    //! @}
    //! @name  Properties of the Standard State of the Species in the Solution
    //! @{
 
    /**
     * Get the standard state chemical potentials of the species. This is the
     * array of chemical potentials at unit activity @f$ \mu^0_k(T,P) @f$. We
     * define these here as the chemical potentials of the pure species at the
     * temperature and pressure of the solution. This function is used in the
     * evaluation of the equilibrium constant Kc. Therefore, Kc will also depend
     * on T and P. This is the norm for liquid and solid systems.
     *
     *  units = J / kmol
     *
     * @param mu0   Output vector of standard state chemical potentials.
     *              Length: m_kk.
     */
    void getStandardChemPotentials(span<double> mu0) const override;
 
    //! Get the array of nondimensional Enthalpy functions for the standard
    //! state species at the current *T* and *P* of the solution.
    /*!
     * We assume an incompressible constant partial molar volume here:
     * @f[
     *  h^0_k(T,P) = h^{ref}_k(T) + (P - P_{ref}) * V_k
     * @f]
     * where @f$ V_k @f$ is the molar volume of pure species *k*.
     * @f$ h^{ref}_k(T) @f$ is the enthalpy of the pure species *k* at the
     * reference pressure, @f$ P_{ref} @f$.
     *
     * @param hrt Vector of length m_kk, which on return hrt[k] will contain the
     *            nondimensional standard state enthalpy of species k.
     */
    void getEnthalpy_RT(span<double> hrt) const override;
 
    //! Get the nondimensional Entropies for the species standard states at the
    //! current T and P of the solution.
    /*!
     * Note, this is equal to the reference state entropies due to the zero
     * volume expansivity: that is, (dS/dP)_T = (dV/dT)_P = 0.0
     *
     * @param sr Vector of length m_kk, which on return sr[k] will contain the
     *           nondimensional standard state entropy for species k.
     */
    void getEntropy_R(span<double> sr) const override;
 
    /**
     * Get the nondimensional Gibbs function for the species standard states at
     * the current T and P of the solution.
     *
     * @f[
     *  \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k
     * @f]
     * where @f$ V_k @f$ is the molar volume of pure species *k*.
     * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure species *k*
     * at the reference pressure, @f$ P_{ref} @f$.
     *
     * @param grt Vector of length m_kk, which on return sr[k] will contain the
     *           nondimensional standard state Gibbs function for species k.
     */
    void getGibbs_RT(span<double> grt) const override;
 
    void getIntEnergy_RT(span<double> urt) const override;
 
    /**
     * Get the nondimensional heat capacity at constant pressure function for
     * the species standard states at the current T and P of the solution.
     * @f[
     *  Cp^0_k(T,P) = Cp^{ref}_k(T)
     * @f]
     * where @f$ V_k @f$ is the molar volume of pure species *k*.
     * @f$ Cp^{ref}_k(T) @f$ is the constant pressure heat capacity of species
     * *k* at the reference pressure, @f$ p_{ref} @f$.
     *
     * @param cpr Vector of length m_kk, which on return cpr[k] will contain the
     *           nondimensional constant pressure heat capacity for species k.
     */
    void getCp_R(span<double> cpr) const override;
 
    void getStandardVolumes(span<double> vol) const override;
 
    //! @}
    //! @name Thermodynamic Values for the Species Reference States
    //! @{
 
    void getEnthalpy_RT_ref(span<double> hrt) const override;
    void getGibbs_RT_ref(span<double> grt) const override;
    void getGibbs_ref(span<double> g) const override;
    void getEntropy_R_ref(span<double> er) const override;
    void getIntEnergy_RT_ref(span<double> urt) const override;
    void getCp_R_ref(span<double> cprt) const override;
 
    //! @}
    //! @name Utility Functions
    //! @{
 
    bool addSpecies(shared_ptr<Species> spec) override;
    void initThermo() override;
    void getParameters(AnyMap& phaseNode) const override;
    void getSpeciesParameters(const string& name, AnyMap& speciesNode) const override;
    void setToEquilState(span<const double> mu_RT) override;
 
    //! Set the form for the standard and generalized concentrations
    /*!
     * Must be one of 'unity', 'species-molar-volume', or
     * 'solvent-molar-volume'. The default is 'unity'.
     *
     *  | m_formGC             | GeneralizedConc | StandardConc |
     *  | -------------------- | --------------- | ------------ |
     *  | unity                | X_k             | 1.0          |
     *  | species-molar-volume | X_k / V_k       | 1.0 / V_k    |
     *  | solvent-molar-volume | X_k / V_N       | 1.0 / V_N    |
     *
     *  The value and form of the generalized concentration will affect
     *  reaction rate constants involving species in this phase.
     */
    void setStandardConcentrationModel(const string& model);
 
    /**
     * Report the molar volume of species k
     *
     * units - @f$ m^3 kmol^-1 @f$
     *
     * @param  k species index
     */
    double speciesMolarVolume(int k) const;
 
    /**
     * Fill in a return vector containing the species molar volumes.
     *
     * units - @f$ m^3 kmol^-1 @f$
     *
     * @param smv  output vector containing species molar volumes.
     *             Length: m_kk.
     */
    void getSpeciesMolarVolumes(span<double> smv) const;
 
    //! @}
 
protected:
    void compositionChanged() override;
 
    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    span<const double> enthalpy_RT_ref() const;
 
    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    span<const double> gibbs_RT_ref() const {
        _updateThermo();
        return m_g0_RT;
    }
 
    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    span<const double> entropy_R_ref() const;
 
    /**
     * Returns a reference to the vector of nondimensional enthalpies of the
     * reference state at the current temperature. Real reason for its existence
     * is that it also checks to see if a recalculation of the reference
     * thermodynamics functions needs to be done.
     */
    span<const double> cp_R_ref() const {
        _updateThermo();
        return m_cp0_R;
    }
 
    /**
     * The standard concentrations can have one of three different forms:
     * 0 = 'unity', 1 = 'species-molar-volume', 2 = 'solvent-molar-volume'. See
     * setStandardConcentrationModel().
     */
    int m_formGC = 0;
 
    /**
     * Value of the reference pressure for all species in this phase. The T
     * dependent polynomials are evaluated at the reference pressure. Note,
     * because this is a single value, all species are required to have the same
     * reference pressure.
     */
    double m_Pref = OneAtm;
 
    /**
     * m_Pcurrent = The current pressure
     * Since the density isn't a function of pressure, but only of the
     * mole fractions, we need to independently specify the pressure.
     * The density variable which is inherited as part of the State class,
     * m_dens, is always kept current whenever T, P, or X[] change.
     */
    double m_Pcurrent = OneAtm;
 
    //! Vector of molar volumes for each species in the solution
    /**
     * Species molar volumes (@f$ m^3 kmol^-1 @f$) at the current mixture state.
     * For the IdealSolidSolnPhase class, these are constant.
     */
    mutable vector<double> m_speciesMolarVolume;
 
    //! Vector containing the species reference enthalpies at T = m_tlast
    mutable vector<double> m_h0_RT;
 
    //! Vector containing the species reference constant pressure heat
    //! capacities at T = m_tlast
    mutable vector<double> m_cp0_R;
 
    //! Vector containing the species reference Gibbs functions at T = m_tlast
    mutable vector<double> m_g0_RT;
 
    //! Vector containing the species reference entropies at T = m_tlast
    mutable vector<double> m_s0_R;
 
    //! Vector containing the species reference exp(-G/RT) functions at
    //! T = m_tlast
    mutable vector<double> m_expg0_RT;
 
    //! Temporary array used in equilibrium calculations
    mutable vector<double> m_pp;
 
private:
    //! @name Utility Functions
    //! @{
    /**
     * This function gets called for every call to functions in this class. It
     * checks to see whether the temperature has changed and thus the reference
     * thermodynamics functions for all of the species must be recalculated. If
     * the temperature has changed, the species thermo manager is called to
     * recalculate G, Cp, H, and S at the current temperature.
     */
    virtual void _updateThermo() const;
 
    //! @}
};
}
 
#endif