Added documentation for the class
This commit is contained in:
Harry Moffat
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30d59b8c49
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1 changed files with 325 additions and 6 deletions
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/**
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* @file
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* @file PhaseCombo_Interaction.h
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* Header for intermediate ThermoPhase object for phases which
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* employ the Margules gibbs free energy formulation and eliminates the ideal mixing term.
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* (see \ref thermoprops
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* and class \link Cantera::PhaseCombo_Interaction PhaseCombo_Interaction\endlink).
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*/
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/*
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* Copywrite (2006) Sandia Corporation. Under the terms of
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* Copywrite (2011) Sandia Corporation. Under the terms of
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* Contract DE-AC04-94AL85000 with Sandia Corporation, the
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* U.S. Government retains certain rights in this software.
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*/
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/*
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* $Id: MargulesVPSSTP.h 641 2010-11-12 21:37:41Z hkmoffa $
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* $Author: hkmoffa $
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* $Date: 2009-11-09 16:36:49 -0700 (Mon, 09 Nov 2009) $
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* $Revision: 255 $
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*/
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#ifndef CT_LIFES_X_ONEPHASE_VPSSTP_H
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#define CT_LIFES_X_ONEPHASE_VPSSTP_H
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#include "PseudoBinaryVPSSTP.h"
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#include "GibbsExcessVPSSTP.h"
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namespace Cantera {
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@ -23,9 +30,321 @@ namespace Cantera {
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*/
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//! MargulesVPSSTP is a derived class of GibbsExcessVPSSTP that employs
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//! the Margules approximation for the excess gibbs free energy
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//! PhaseCombo_Interaction is a derived class of GibbsExcessVPSSTP that employs
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//! the Margules approximation for the excess gibbs free energy while eliminating
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//! the entropy of mixing term.
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/*!
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*
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* %PhaseCombo_Interaction derives from class GibbsExcessVPSSTP which is derived from VPStandardStateTP,
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* and overloads the virtual methods defined there with ones that
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* use expressions appropriate for the Margules Excess gibbs free energy approximation.
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* The reader should refer to the MargulesVPSSTP class for information on that class.
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* This class in addition adds a term to the activity coefficient that eliminates the
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* ideal solution mixing term within the chemical potential. This is a very radical thing
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* to do, but it is supported by experimental evidence under some conditions.
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*
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* The independent unknowns are pressure, temperature, and mass fraction.
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*
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* Several concepts are introduced. The first concept is that there are temporary
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* variables for holding the species standard state values of Cp, H, S, G, and V at the
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* last temperature and pressure called. These functions are not recalculated
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* if a new call is made using the previous temperature and pressure. Currently,
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* these variables and the calculation method are handled by the VPSSMgr class,
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* for which VPStandardStateTP owns a pointer to.
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*
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* To support the above functionality, pressure and temperature variables,
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* m_plast_ss and m_tlast_ss, are kept which store the last pressure and temperature
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* used in the evaluation of standard state properties.
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*
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* This class is introduced to represent specific conditions observed in thermal batteries.
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* HOwever, it may be physically motivated to represent conditions where there may
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* be a mixture of componds that are not "mixed" at the molecular level. Therefore, there
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* is no mixing term.
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*
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* The lack of a mixing term has profound effects. First, the mole fraction of a species
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* can now be identically zero due to thermodynamic considerations. The phase behaves more
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* like a series of phases. That's why we named it PhaseCombo.
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*
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*
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*
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* <HR>
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* <H2> Specification of Species Standard %State Properties </H2>
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* <HR>
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*
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* All species are defined to have standard states that depend upon both
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* the temperature and the pressure. The Margules approximation assumes
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* symmetric standard states, where all of the standard state assume
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* that the species are in pure component states at the temperatue
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* and pressure of the solution. I don't think it prevents, however,
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* some species from being dilute in the solution.
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*
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*
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* <HR>
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* <H2> Specification of Solution Thermodynamic Properties </H2>
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* <HR>
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*
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* The molar excess Gibbs free energy is given by the following formula which is a sum over interactions <I>i</I>.
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* Each of the interactions are binary interactions involving two of the species in the phase, denoted, <I>Ai</I>
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* and <I>Bi</I>.
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* This is the generalization of the Margules formulation for a phase
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* that has more than 2 species. The second term in the excess gibbs free energy is a negation of the
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* ideal solution's mixing term.
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*
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* \f[
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* G^E = \sum_i \left( H_{Ei} - T S_{Ei} \right) - \sum_i \left( n_i R T \ln{X_i} \right)
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* \f]
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* \f[
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* H^E_i = n X_{Ai} X_{Bi} \left( h_{o,i} + h_{1,i} X_{Bi} \right)
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* \f]
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* \f[
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* S^E_i = n X_{Ai} X_{Bi} \left( s_{o,i} + s_{1,i} X_{Bi} \right)
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* \f]
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*
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* where n is the total moles in the solution.
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*
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* The activity of a species defined in the phase is given by an excess Gibbs free energy formulation.
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*
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* \f[
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* a_k = \gamma_k X_k
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* \f]
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*
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* where
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*
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* \f[
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* R T \ln( \gamma_k )= \frac{d(n G^E)}{d(n_k)}\Bigg|_{n_i}
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* \f]
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*
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* Taking the derivatives results in the following expression
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*
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* \f[
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* R T \ln( \gamma_k )= \sum_i \left( \left( \delta_{Ai,k} X_{Bi} + \delta_{Bi,k} X_{Ai} - X_{Ai} X_{Bi} \right)
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* \left( g^E_{o,i} + g^E_{1,i} X_{Bi} \right) +
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* \left( \delta_{Bi,k} - X_{Bi} \right) X_{Ai} X_{Bi} g^E_{1,i} \right) - RT \ln{X_k}
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* \f]
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*
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* where
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* \f$ g^E_{o,i} = h_{o,i} - T s_{o,i} \f$ and \f$ g^E_{1,i} = h_{1,i} - T s_{1,i} \f$
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* and where \f$ X_k \f$ is the mole fraction of species <I>k</I>.
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*
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* This object inherits from the class VPStandardStateTP. Therefore, the specification and
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* calculation of all standard state and reference state values are handled at that level. Various functional
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* forms for the standard state are permissible.
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* The chemical potential for species <I>k</I> is equal to
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*
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* \f[
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* \mu_k(T,P) = \mu^o_k(T, P) + R T \ln(\gamma_k X_k)
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* \f]
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*
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* The partial molar entropy for species <I>k</I> is given by the following relation,
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*
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* \f[
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* \tilde{s}_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k )
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* - R T \frac{d \ln(\gamma_k) }{dT}
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* \f]
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*
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* The partial molar enthalpy for species <I>k</I> is given by
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*
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* \f[
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* \tilde{h}_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
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* \f]
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*
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* The partial molar volume for species <I>k</I> is
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*
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* \f[
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* \tilde V_k(T,P) = V^o_k(T,P) + R T \frac{d \ln(\gamma_k) }{dP}
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* \f]
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*
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* The partial molar Heat Capacity for species <I>k</I> is
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*
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* \f[
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* \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma_k )}{dT}
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* - R T^2 \frac{d^2 \ln(\gamma_k) }{{dT}^2}
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* \f]
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*
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*
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* <HR>
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* <H2> %Application within %Kinetics Managers </H2>
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* <HR>
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*
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* \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k /
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* C^s_k, \f$ where \f$ C^s_k \f$ is a standard concentration
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* defined below and \f$ a_k \f$ are activities used in the
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* thermodynamic functions. These activity (or generalized) concentrations are used
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* by kinetics manager classes to compute the forward and reverse rates of elementary reactions.
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* The activity concentration,\f$ C^a_k \f$,is given by the following expression.
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*
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* \f[
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* C^a_k = C^s_k X_k = \frac{P}{R T} X_k
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* \f]
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*
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* The standard concentration for species <I>k</I> is independent of <I>k</I> and equal to
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*
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* \f[
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* C^s_k = C^s = \frac{P}{R T}
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* \f]
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*
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* For example, a bulk-phase binary gas reaction between species j and k, producing
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* a new gas species l would have the
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* following equation for its rate of progress variable, \f$ R^1 \f$, which has
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* units of kmol m-3 s-1.
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*
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* \f[
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* R^1 = k^1 C_j^a C_k^a = k^1 (C^s a_j) (C^s a_k)
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* \f]
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*
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* where
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*
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* \f[
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* C_j^a = C^s a_j \mbox{\quad and \quad} C_k^a = C^s a_k
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* \f]
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*
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* \f$ C_j^a \f$ is the activity concentration of species j, and
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* \f$ C_k^a \f$ is the activity concentration of species k. \f$ C^s \f$
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* is the standard concentration. \f$ a_j \f$ is
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* the activity of species j which is equal to the mole fraction of j.
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*
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* The reverse rate constant can then be obtained from the law of microscopic reversibility
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* and the equilibrium expression for the system.
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*
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* \f[
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* \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
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* \f]
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*
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* \f$ K_a^{o,1} \f$ is the dimensionless form of the equilibrium constant, associated with
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* the pressure dependent standard states \f$ \mu^o_l(T,P) \f$ and their associated activities,
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* \f$ a_l \f$, repeated here:
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*
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* \f[
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* \mu_l(T,P) = \mu^o_l(T, P) + R T \log(a_l)
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* \f]
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*
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* We can switch over to expressing the equilibrium constant in terms of the reference
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* state chemical potentials
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*
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* \f[
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* K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P}
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* \f]
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*
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* The concentration equilibrium constant, \f$ K_c \f$, may be obtained by changing over
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* to activity concentrations. When this is done:
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*
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* \f[
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* \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
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* \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT}
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* \f]
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*
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* %Kinetics managers will calculate the concentration equilibrium constant, \f$ K_c \f$,
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* using the second and third part of the above expression as a definition for the concentration
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* equilibrium constant.
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*
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* For completeness, the pressure equilibrium constant may be obtained as well
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*
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* \f[
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* \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} )
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* \f]
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*
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* \f$ K_p \f$ is the simplest form of the equilibrium constant for ideal gases. However, it isn't
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* necessarily the simplest form of the equilibrium constant for other types of phases; \f$ K_c \f$ is
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* used instead because it is completely general.
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*
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* The reverse rate of progress may be written down as
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* \f[
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* R^{-1} = k^{-1} C_l^a = k^{-1} (C^o a_l)
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* \f]
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*
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* where we can use the concept of microscopic reversibility to
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* write the reverse rate constant in terms of the
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* forward reate constant and the concentration equilibrium
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* constant, \f$ K_c \f$.
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*
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* \f[
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* k^{-1} = k^1 K^1_c
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* \f]
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*
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* \f$k^{-1} \f$ has units of s-1.
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*
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*
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* <HR>
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* <H2> Instantiation of the Class </H2>
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* <HR>
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*
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*
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* The constructor for this phase is located in the default ThermoFactory
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* for %Cantera. A new %PhaseCombo_Interaction object may be created by the following code
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* snippet:
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*
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* @code
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* XML_Node *xc = get_XML_File("LiFeS_X_combo.xml");
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* XML_Node * const xs = xc->findNameID("phase", "LiFeS_X");
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* ThermoPhase *l_tp = newPhase(*xs);
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* PhaseCombo_Interaction *LiFeS_X_solid = dynamic_cast <PhaseCombo_Interaction *>(l_tp);
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* @endcode
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*
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* or by the following code
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*
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* @code
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* std::string id = "LiFeS_X";
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* Cantera::ThermoPhase *LiFeS_X_Phase = Cantera::newPhase("LiFeS_X_combo.xml", id);
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* PhaseCombo_Interaction *LiFeS_X_solid = dynamic_cast <PhaseCombo_Interaction *>(l_tp);
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* @endcode
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*
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*
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* or by the following constructor:
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*
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* @code
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* XML_Node *xc = get_XML_File("LiFeS_X_combo.xml");
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* XML_Node * const xs = xc->findNameID("phase", "LiFeS_X");
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* PhaseCombo_Interaction *LiFeS_X_solid = new PhaseCombo_Interaction(*xs);
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* @endcode
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*
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*
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* <HR>
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* <H2> XML Example </H2>
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* <HR>
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* An example of an XML Element named phase setting up a PhaseCombo_Interaction
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* object named LiFeS_X is given below.
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*
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*
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* @verbatim
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<phase dim="3" id="LiFeS_X">
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<elementArray datasrc="elements.xml">
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Li Fe S
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</elementArray>
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<speciesArray datasrc="#species_LiFeS">
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LiTFe1S2(S) Li2Fe1S2(S)
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</speciesArray>
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<thermo model="PhaseCombo_Interaction">
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<activityCoefficients model="Margules" TempModel="constant">
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<binaryNeutralSpeciesParameters speciesA="LiTFe1S2(S)" speciesB="Li2Fe1S2(S)">
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<excessEnthalpy model="poly_Xb" terms="2" units="kJ/mol">
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84.67069219, -269.1959421
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</excessEnthalpy>
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<excessEntropy model="poly_Xb" terms="2" units="J/mol/K">
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100.7511565, -361.4222659
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</excessEntropy>
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<excessVolume_Enthalpy model="poly_Xb" terms="2" units="ml/mol">
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0, 0
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</excessVolume_Enthalpy>
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<excessVolume_Entropy model="poly_Xb" terms="2" units="ml/mol/K">
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0, 0
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</excessVolume_Entropy>
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</binaryNeutralSpeciesParameters>
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</activityCoefficients>
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</thermo>
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<transport model="none"/>
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<kinetics model="none"/>
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</phase>
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@endverbatim
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*
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* The model attribute "PhaseCombo_Interaction" of the thermo XML element identifies the phase as
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* being of the type handled by the PhaseCombo_Interaction object.
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*
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* @ingroup thermoprops
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*
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*/
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class PhaseCombo_Interaction : public GibbsExcessVPSSTP {
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public:
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