Things that only depend on the components themselves, but not on composition, temperature, or density. More...

#include <saftvrmie.hpp>

Public Member Functions
	SAFTVRMieChainContributionTerms (const Eigen::ArrayXd &m, const Eigen::ArrayXd &epsilon_over_k, const Eigen::ArrayXd &sigma_m, const Eigen::ArrayXd &lambda_r, const Eigen::ArrayXd &lambda_a, const Eigen::ArrayXXd &kmat, const std::optional< nlohmann::json > &flags=std::nullopt)

auto	get_EPSKIJ_K_matrix () const
	Get the matrix of \(\varepsilon_{ij}/k_B\) with the entries in K.

auto	get_SIGMAIJ_m_matrix () const
	Get the matrix of \(\sigma_{ij}\) with the entries in m.

template<typename RType >
auto	get_uii_over_kB (std::size_t i, const RType &r) const
	Eq. A2 from Lafitte.

template<typename TType >
auto	get_j_cutoff_dii (std::size_t i, const TType &T) const
	Solve for the value of \(j=\sigma/r\) for which the integrand in \(d_{ii}\) becomes equal to 1 to numerical precision.

template<typename TType >
TType	get_dii (std::size_t i, const TType &T) const

template<typename TType >
auto	get_dmat (const TType &T) const

template<typename TType , typename RhoType , typename VecType >
auto	get_core_calcs (const TType &T, const RhoType &rhomolar, const VecType &molefracs) const

template<typename RhoType >
auto	get_KHS (const RhoType &pf) const
	Eq. A21 from Lafitte.

template<typename RhoType >
auto	get_rhos_dK_HS_drhos (const RhoType &zeta_x) const

template<typename RhoType , typename ZetaType , typename DType >
auto	get_a_HS (const RhoType &rhos, const Eigen::Array< ZetaType, 4, 1 > &zeta, const Eigen::Array< DType, 4, 1 > &D) const
	Eq. A6 from Lafitte, accounting for the case of rho_s=0, for which the limit is zero.

template<typename ZetaType , typename IJ >
auto	get_Bhatij (const ZetaType &zeta_x, const ZetaType &one_minus_zeta_x3, const IJ &I, const IJ &J) const

template<typename ZetaType , typename IJ >
auto	get_rhodBijdrho (const ZetaType &zeta_x, const ZetaType &, const IJ &I, const IJ &J, const ZetaType &Bhatij) const

template<typename ZetaType >
auto	get_a1Shatij (const ZetaType &zeta_x_eff, double lambda_ij) const

template<typename ZetaType >
auto	get_rhoda1Shatijdrho (const ZetaType &zeta_x, const ZetaType &zeta_x_eff, const ZetaType &dzetaxeffdzetax, double lambda_ij) const

Public Attributes
const Eigen::ArrayXd	m

const Eigen::ArrayXd	epsilon_over_k

const Eigen::ArrayXd	sigma_A

const Eigen::ArrayXd	lambda_a

const Eigen::ArrayXd	lambda_r

const Eigen::ArrayXXd	kmat

const Eigen::Index	N

const EpsilonijFlags	epsilon_ij_flag = EpsilonijFlags::kLafitte

const Eigen::ArrayXXd	lambda_r_ij

const Eigen::ArrayXXd	lambda_a_ij

const Eigen::ArrayXXd	C_ij

const Eigen::ArrayXXd	alpha_ij

const Eigen::ArrayXXd	sigma_ij

const Eigen::ArrayXXd	epsilon_ij

const std::vector< Eigen::ArrayXXd >	crnij

const std::vector< Eigen::ArrayXXd >	canij

const std::vector< Eigen::ArrayXXd >	c2rnij

const std::vector< Eigen::ArrayXXd >	c2anij

const std::vector< Eigen::ArrayXXd >	carnij

const std::vector< Eigen::ArrayXXd >	fkij

Detailed Description

Things that only depend on the components themselves, but not on composition, temperature, or density.

Definition at line 85 of file saftvrmie.hpp.

Constructor & Destructor Documentation

◆ SAFTVRMieChainContributionTerms()

teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::SAFTVRMieChainContributionTerms	(	const Eigen::ArrayXd &	m,
		const Eigen::ArrayXd &	epsilon_over_k,
		const Eigen::ArrayXd &	sigma_m,
		const Eigen::ArrayXd &	lambda_r,
		const Eigen::ArrayXd &	lambda_a,
		const Eigen::ArrayXXd &	kmat,
		const std::optional< nlohmann::json > &	flags = std::nullopt )

inline

Definition at line 264 of file saftvrmie.hpp.

Member Function Documentation

◆ get_a1Shatij()

template<typename ZetaType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_a1Shatij	(	const ZetaType &	zeta_x_eff,
		double	lambda_ij ) const

inline

Note: Starting from Eq. A16 from Lafitte

\[ \hat a^S_{1,ii} = \frac{a^S_{1,ii}}{2\pi\epsilon_{ij}d^3_{ij}\rho_s} \]

so

\[ a^S_{1,ii} = \kappa\rho_s\hat a^S_{1,ii} \]

Definition at line 749 of file saftvrmie.hpp.

◆ get_a_HS()

template<typename RhoType , typename ZetaType , typename DType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_a_HS	(	const RhoType &	rhos,
		const Eigen::Array< ZetaType, 4, 1 > &	zeta,
		const Eigen::Array< DType, 4, 1 > &	D ) const

inline

Eq. A6 from Lafitte, accounting for the case of rho_s=0, for which the limit is zero.

Definition at line 661 of file saftvrmie.hpp.

◆ get_Bhatij()

template<typename ZetaType , typename IJ >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_Bhatij	(	const ZetaType &	zeta_x,
		const ZetaType &	one_minus_zeta_x3,
		const IJ &	I,
		const IJ &	J ) const

inline

Note: Starting from Eq. A12 from Lafitte

Defining:

\[ \hat B_{ij} \equiv \frac{B_{ij}}{2\pi\epsilon_{ij}d^3_{ij}\rho_s} = \frac{1-\zeta_x/2}{(1-\zeta_x)^3}I-\frac{9\zeta_x(1+\zeta_x)}{2(1-\zeta_x)^3}J \]

Definition at line 713 of file saftvrmie.hpp.

◆ get_core_calcs()

template<typename TType , typename RhoType , typename VecType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_core_calcs	(	const TType &	T,
		const RhoType &	rhomolar,
		const VecType &	molefracs ) const

inline

Definition at line 396 of file saftvrmie.hpp.

◆ get_dii()

template<typename TType >

TType teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_dii	(	std::size_t	i,
		const TType &	T ) const

inline

Note: Eq. A9 from Lafitte

The calculation of the diameter is based upon

\[ d_{ii} = \int_0^{\sigma_{ii}}(1-\exp(-\beta u_{ii}^{\rm Mie}(r)){\rm d}r \]

which is broken up into two parts:

\[ d = \int_0^{r_{\rm cut}} 1 {\rm d} r + \int_{r_{\rm cut}}^{\sigma_{ii}} [1-\exp(-\beta u_{ii}^{\rm Mie}(r))] {\rm d}r \]

but the integrand is basically constant (to numerical precision) from 0 to some cutoff value of \(r\), which we'll call \(r_{\rm cut}\). So first we need to find the value of \(r_{\rm cut}\) that makes the integrand take its constant value, which is explained well in the paper from Aasen (https://github.com/ClapeyronThermo/Clapeyron.jl/issues/152#issuecomment-1480324192). Finding the cutoff value is obtained when

\[ \exp(-\beta u_{ii}^{\rm Mie}(r)) = EPS \]

where EPS is the numerical precision of the floating point type. Taking the logs of both sides,

\[ -\beta u_{ii}^{\rm Mie} = \ln(EPS) \]

To get a starting value, it is first assumed that only the repulsive contribution contributes to the potential, yielding \(u^{\rm rep} = C\epsilon(\sigma/r)^{\lambda_r}\) (with \(C\) the same as the full potential with attraction) which yields

\[ -\beta C\epsilon(\sigma/r)^{\lambda_r} = \ln(EPS) \]

and

\[ (\sigma/r)_{\rm guess} = (-\ln(EPS)/(\beta C \epsilon))^{1/\lambda_r} \]

Then we solve for the residual \(R(r)=0\), where \(R_0=\exp(-u/T)-EPS\). Equivalently we can write the residual in logarithmic terms as \(R=-u/T-\ln(EPS)\). This simplifies the rootfinding as you need \(R\), \(R'\) and \(R''\) to apply Halley's method, which are themselves quite straightforward to obtain because \(R'=-u'/T\), \(R''=-u''/T\), where the primes are derivatives taken with respect to \(\sigma/r\).

Definition at line 362 of file saftvrmie.hpp.

◆ get_dmat()

template<typename TType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_dmat ( const TType & T ) const

inline

Definition at line 379 of file saftvrmie.hpp.

◆ get_EPSKIJ_K_matrix()

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_EPSKIJ_K_matrix ( ) const

inline

Get the matrix of \(\varepsilon_{ij}/k_B\) with the entries in K.

Definition at line 284 of file saftvrmie.hpp.

◆ get_j_cutoff_dii()

template<typename TType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_j_cutoff_dii	(	std::size_t	i,
		const TType &	T ) const

inline

Solve for the value of \(j=\sigma/r\) for which the integrand in \(d_{ii}\) becomes equal to 1 to numerical precision.

Definition at line 297 of file saftvrmie.hpp.

◆ get_KHS()

template<typename RhoType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_KHS ( const RhoType & pf ) const

inline

Eq. A21 from Lafitte.

Definition at line 643 of file saftvrmie.hpp.

◆ get_rhoda1Shatijdrho()

template<typename ZetaType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_rhoda1Shatijdrho	(	const ZetaType &	zeta_x,
		const ZetaType &	zeta_x_eff,
		const ZetaType &	dzetaxeffdzetax,
		double	lambda_ij ) const

inline

\[ \left(\frac{\partial a^S_{1,ii}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat a^S_{1,ii} + \rho_s\frac{\partial \hat a^S_{1,ii}}{\partial \rho_s} \right) \]

\[ \left(\frac{\partial a^S_{1,ii}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat a^S_{1,ii} + \rho_s\frac{\partial \hat a^S_{1,ii}}{\partial \zeta_{x,eff}}\frac{\partial \zeta_{x,eff}}{\partial \zeta_x}\frac{\partial \zeta_x}{\partial \rho_s} \right) \]

since \(\rho_s\frac{\partial \zeta_x}{\partial \rho_s} = \zeta_x\)

Definition at line 767 of file saftvrmie.hpp.

◆ get_rhodBijdrho()

template<typename ZetaType , typename IJ >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_rhodBijdrho	(	const ZetaType &	zeta_x,
		const ZetaType &	,
		const IJ &	I,
		const IJ &	J,
		const ZetaType &	Bhatij ) const

inline

\[ B = \hat B_{ij}\kappa \rho_s \]

\[ \left(\frac{\partial B_{ij}}{\partial \rho_s}\right)_{T,\vec{z}} = \kappa\left(\hat B + \zeta_x \frac{\partial \hat B}{\partial \zeta_x}\right) \]

and thus

\[ \rho_s \left(\frac{\partial B_{ij}}{\partial \rho_s}\right)_{T,\vec{z}} = \hat B + \zeta_x \frac{\partial \hat B}{\partial \zeta_x} \]

Definition at line 732 of file saftvrmie.hpp.

◆ get_rhos_dK_HS_drhos()

template<typename RhoType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_rhos_dK_HS_drhos ( const RhoType & zeta_x ) const

inline

\[ \rho_s\frac{\partial K_{HS}}{\partial \rho_s} = \zeta\frac{\partial K_{HS}}{\partial \zeta} \]

Definition at line 653 of file saftvrmie.hpp.

◆ get_SIGMAIJ_m_matrix()

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_SIGMAIJ_m_matrix ( ) const

inline

Get the matrix of \(\sigma_{ij}\) with the entries in m.

Definition at line 286 of file saftvrmie.hpp.

◆ get_uii_over_kB()

template<typename RType >

auto teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::get_uii_over_kB	(	std::size_t	i,
		const RType &	r ) const

inline

Eq. A2 from Lafitte.

Definition at line 290 of file saftvrmie.hpp.

Member Data Documentation

◆ alpha_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::alpha_ij

Definition at line 259 of file saftvrmie.hpp.

◆ c2anij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::c2anij

Definition at line 261 of file saftvrmie.hpp.

◆ c2rnij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::c2rnij

Definition at line 261 of file saftvrmie.hpp.

◆ C_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::C_ij

Definition at line 259 of file saftvrmie.hpp.

◆ canij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::canij

Definition at line 261 of file saftvrmie.hpp.

◆ carnij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::carnij

Definition at line 261 of file saftvrmie.hpp.

◆ crnij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::crnij

Definition at line 261 of file saftvrmie.hpp.

◆ epsilon_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::epsilon_ij

Definition at line 259 of file saftvrmie.hpp.

◆ epsilon_ij_flag

const EpsilonijFlags teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::epsilon_ij_flag = EpsilonijFlags::kLafitte

Definition at line 256 of file saftvrmie.hpp.

◆ epsilon_over_k

const Eigen::ArrayXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::epsilon_over_k

Definition at line 252 of file saftvrmie.hpp.

◆ fkij

const std::vector<Eigen::ArrayXXd> teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::fkij

Definition at line 262 of file saftvrmie.hpp.

◆ kmat

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::kmat

Definition at line 253 of file saftvrmie.hpp.

◆ lambda_a

const Eigen::ArrayXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::lambda_a

Definition at line 252 of file saftvrmie.hpp.

◆ lambda_a_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::lambda_a_ij

Definition at line 259 of file saftvrmie.hpp.

◆ lambda_r

const Eigen::ArrayXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::lambda_r

Definition at line 252 of file saftvrmie.hpp.

◆ lambda_r_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::lambda_r_ij

Definition at line 259 of file saftvrmie.hpp.

◆ m

const Eigen::ArrayXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::m

Definition at line 252 of file saftvrmie.hpp.

◆ N

const Eigen::Index teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::N

Definition at line 255 of file saftvrmie.hpp.

◆ sigma_A

const Eigen::ArrayXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::sigma_A

Definition at line 252 of file saftvrmie.hpp.

◆ sigma_ij

const Eigen::ArrayXXd teqp::SAFTVRMie::SAFTVRMieChainContributionTerms::sigma_ij

Definition at line 259 of file saftvrmie.hpp.

The documentation for this struct was generated from the following file:

include/teqp/models/saftvrmie.hpp

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SAFTVRMieChainContributionTerms()

Member Function Documentation

◆ get_a1Shatij()

◆ get_a_HS()

◆ get_Bhatij()

◆ get_core_calcs()

◆ get_dii()

◆ get_dmat()

◆ get_EPSKIJ_K_matrix()

◆ get_j_cutoff_dii()

◆ get_KHS()

◆ get_rhoda1Shatijdrho()

◆ get_rhodBijdrho()

◆ get_rhos_dK_HS_drhos()

◆ get_SIGMAIJ_m_matrix()

◆ get_uii_over_kB()

Member Data Documentation

◆ alpha_ij

◆ c2anij

◆ c2rnij

◆ C_ij

◆ canij

◆ carnij

◆ crnij

◆ epsilon_ij

◆ epsilon_ij_flag

◆ epsilon_over_k

◆ fkij

◆ kmat

◆ lambda_a

◆ lambda_a_ij

◆ lambda_r

◆ lambda_r_ij

◆ m

◆ N

◆ sigma_A

◆ sigma_ij