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Improve documentation in CoverageDependentSurfPhase.h

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Jongyoon Bae 2023-03-17 16:45:49 -04:00 committed by Ray Speth
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include/cantera/thermo/CoverageDependentSurfPhase.h
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@ -19,23 +19,24 @@
namespace Cantera
{
//! A thermodynamic model for a coverage-dependent surface phase, applying adsorbate
//! lateral interaction correction factors to the ideal surface phase properties.
//! A thermodynamic model for a coverage-dependent surface phase, applying surface
//! species lateral interaction correction factors to the ideal surface phase
//! properties.
/*!
* The ideal surface phase assumes no lateral interaction among adsorbates.
* The ideal surface phase assumes no lateral interaction among surface species.
* This coverage-dependent surface phase allows adding lateral interaction
* correction terms to the ideal surface phase (SurfPhase) thermodynamic properties
* so that more accurate adsorbate thermochemistry can be achieved.
* so that more accurate surface species thermochemistry can be achieved.
*
* ## Coverage-dependent Thermodynamic Properties Formulations
*
* At a low-coverage limit, an adsorbate thermochemistry is the same as
* that of ideal species since there are no adsorbates in the vicinity to cause
* lateral interaction. Therefore, it is logical to set ideal species properties
* as the low-coverage limit properties and add lateral interaction terms, i.e.
* lateral interaction correction terms, to them as excess properties.
* Accordingly, standard state coverage-dependent enthalpy, entropy,
* and heat capacity of a species \f$ k \f$ can be formulated as follows.
* At a low-coverage limit, a surface species thermochemistry is the same as
* that of ideal surface species since there are no adsorbates in the vicinity
* to cause lateral interaction. Therefore, it is logical to set ideal surface
* species properties as the low-coverage limit and add lateral interaction terms
* to them as excess properties. Accordingly, standard state coverage-dependent
* enthalpy, entropy, and heat capacity of a surface species \f$ k \f$ can be
* formulated as follows.
*
* \f[
* h_k^o(T,\theta)
@ -57,20 +58,22 @@ namespace Cantera
*
* \f[
* c_{p,k}^o(T,\theta)
* = c_{p,k}^{o,ideal}(T) + c_{p,k}^{o,cov}(T,\theta)
* = \underbrace{c_{p,k}^{o,ideal}(T)}_{\text{low-coverage limit}}
* + \underbrace{c_{p,k}^{o,cov}(T,\theta)}_{\text{coverage dependence}}
* \f]
*
* ## Mathematical Models for Coverage-dependent Correction Terms
*
* Coverage-dependent correction terms for enthalpy and entropy can be calculated
* with one of the four algebraic models: linear dependecy model, piecewise-linear
* dependency model, polynomial dependency model, and interpolative dependency model.
* with one of the four algebraic models: linear dependecy model, polynomial
* dependency model, piecewise-linear, and interpolative dependency model.
* In the dependency model equations, a coverage-dependent correction term is denoted
* by \f$ f^{cov} \f$ where \f$ f \f$ can be either enthalpy or entropy. Because
* lateral interaction can compose of both self- and cross- interactions, the total
* correction term of species \f$ k \f$ is a sum of all interacting species \f$ j \f$
* which can include itself. Coefficients \f$ c^{(1)}_{k,j}-c^{(6)}_{k,j} \f$
* are user-provided parameters that can be given in input mechanism.
* by \f$ f^{cov} \f$ where \f$ f \f$ can be either enthalpy (\f$ h^{cov} \f$) or
* entropy (\f$ s^{cov} \f$). Because lateral interaction can compose of both
* self- and cross- interactions, the total correction term of species \f$ k \f$
* is a sum of all interacting species \f$ j \f$ which can include itself.
* Coefficients \f$ c^{(1)}_{k,j}-c^{(6)}_{k,j} \f$ are user-provided parameters
* that can be given in a input yaml.
*
* Linear dependency model:
* \f[
@ -101,8 +104,8 @@ namespace Cantera
* f^{cov}_k(\theta) =
* \sum_j \left[\frac{f^{cov}_k(\theta^{higher}_j) - f^{cov}_k(\theta^{lower}_j)}
* {\theta^{higher}_j - \theta^{lower}_j}(\theta_j - \theta^{lower}_j)
* + f^{cov}_k (\theta^{lower}_j)\right] \text{, }
* \theta^{lower}_j \leq \theta_j < \theta^{higher}_j
* + f^{cov}_k (\theta^{lower}_j)\right] \\
* \text{where } \theta^{lower}_j \leq \theta_j < \theta^{higher}_j
* \f]
*
* Coverage-dependent heat capacity is calculated using an equation with a
@ -111,7 +114,7 @@ namespace Cantera
* The coverage-dependent heat capacity of species \f$ k \f$ is a sum of
* all quantities dependent on coverage of species \f$ j \f$. Coefficients
* \f$ c^{(a)}_{k,j} \text{ and } c^{(b)}_{k,j} \f$ are user-provided parameters
* that can be given in input mechanism.
* that can be given in an input yaml.
*
* Coverage-dependent heat capacity model:
* \f[