Electrolyte Models · Clapeyron.jl

Index

Clapeyron.Born
Clapeyron.ConstRSP
Clapeyron.DH
Clapeyron.DHBorn
Clapeyron.ESElectrolyte
Clapeyron.GCMSABorn
Clapeyron.LinMixRSP
Clapeyron.MSA
Clapeyron.MSABorn
Clapeyron.Schreckenberg
Clapeyron.ZuoFurst
Clapeyron.ePCSAFT
Clapeyron.eSAFTVRMie
Clapeyron.SAFTVREMie
Clapeyron.SAFTgammaEMie

Main model

Clapeyron.ESElectrolyte — Type

ESElectrolyte(solvents::Array{String,1}, 
    ions::Array{String,1}; 
    idealmodel::IdealModel = BasicIdeal,
    neutralmodel::EoSModel = pharmaPCSAFT,
    ionmodel::IonModel = DH,
    RSPmodel::RSPModel = ConstRSP,
    userlocations::Vector{String}=[],
    ideal_userlocations::Vector{String}=[],
    verbose::Bool=false)

Description

This function provides the necessary framework to create an electrolyte model by combining ideal, neutral and ion models:

model = ESElectrolyte(["water"],["sodium","chloride"];
            idealmodel = BasicIdeal,
            neutralmodel = pharmaPCSAFT,
            ionmodel = DH,
            RSPmodel = ConstRSP)

Any of the available models in Clapeyron can be combined in the above. Note that neutral (solvent) species and ions are defined separately. Within Clapeyron, we will only support ion-based electrolyte models; as such, any salt-based approach (i.e. where the salt is treated as a separate species) will not be supported.

Ion Models

Clapeyron.Born — Type

Born(solvents::Array{String,1}, 
     salts::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a Born model. The Born term gives the excess Helmholtz energy to account for the electrostatic interactions between ions in solution.

References

Born, M. (1920). Z. Phys. 1, 45.

Clapeyron.DH — Type

DH(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a Debye-Hückel model. The Debye-Hückel term gives the excess Helmholtz energy to account for the electrostatic interactions between ions in solution.

References

Debye, P., Huckel, E. (1923). Phys. Z. 24, 185.

Clapeyron.MSA — Type

MSA(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma: Single Parameter (Float64) - Hard-sphere diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a Mean Spherical Approximation model. The MSA term gives the excess Helmholtz energy to account for the electrostatic interactions between ions in solution.

References

Blum, L. (1974). Solution of a model for the solvent‐electrolyte interactions in the mean spherical approximation, 61, 2129–2133.

Clapeyron.DHBorn — Type

DHBorn(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a Debye-Hückel-Born model. The Debye-Hückel-Born term gives the excess Helmholtz energy to account for the electrostatic interactions between ions in solution.

References

Debye, P., Huckel, E. (1923). Phys. Z. 24, 185.
Born, M. (1920). Z. Phys. 1, 45.

Clapeyron.MSABorn — Type

MSABorn(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma: Single Parameter (Float64) - Hard-sphere diameter [m]
sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a Mean Spherical Approximation-Born model. The MSA-Born term gives the excess Helmholtz energy to account for the electrostatic interactions between ions in solution.

References

Blum, L. (1974). Solution of a model for the solvent‐electrolyte interactions in the mean spherical approximation, 61, 2129–2133.
Born, M. (1920). Z. Phys. 1, 45.

Clapeyron.GCMSABorn — Type

GCMSABorn(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     RSPmodel=ConstW, 
     SAFTlocations=String[], 
     userlocations=String[], 
     verbose=false)

Input parameters

sigma: Single Parameter (Float64) - Hard-sphere diameter [m]
sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

RSPmodel: Relative Static Permittivity Model

Description

This function is used to create a group-contribution Mean Spherical Approximation-Born model used in SAFT-gamma E Mie

Electrolyte Models

Clapeyron.ePCSAFT — Type

ePCSAFT(solvents::Array{String,1}, 
    ions::Array{String,1}; 
    idealmodel::IdealModel = BasicIdeal,
    neutralmodel::EoSModel = pharmaPCSAFT,
    ionmodel::IonModel = DH,
    RSPmodel::RSPModel = ConstRSP,
    userlocations::Vector{String}=[],
    ideal_userlocations::Vector{String}=[],
    assoc_options::AssocOptions = AssocOptions(),
    verbose::Bool=false)

Description

This function is used to create an ePCSAFT model which is a combination of the PC-SAFT and Debye-Hückel model. It is based on the ePC-SAFT Revised variant.

Input parameters

PC-SAFT Parameters

Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
segment: Single Parameter (Float64) - Number of segments (no units)
sigma: Single Parameter (Float64) - Segment Diameter [A°]
epsilon: Single Parameter (Float64) - Reduced dispersion energy [K]
k: Pair Parameter (Float64) (optional) - Binary Interaction Paramater (no units)
epsilon_assoc: Association Parameter (Float64) - Reduced association energy [K]
bondvol: Association Parameter (Float64) - Association Volume [m^3]

Debye-Hückel Parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

idealmodel: Ideal Model
neutralmodel: Neutral EoS Model
ionmodel: Ion Model

References

Held, C., Reschke, T., Mohammad, S., Luza, A., Sadowski, G. (2014). ePC-SAFT Revised. Chemical Engineering Research and Design, 92(12), 2884-2897.

Clapeyron.eSAFTVRMie — Type

eSAFTVRMie(solvents::Array{String,1}, 
    ions::Array{String,1}; 
    idealmodel::IdealModel = BasicIdeal,
    neutralmodel::EoSModel = SAFTVRMie15,
    ionmodel::IonModel = DHBorn,
    RSPmodel::RSPModel = ZuoFurst,
    userlocations::Vector{String}=[],
    ideal_userlocations::Vector{String}=[],
    assoc_options::AssocOptions = AssocOptions(),
    verbose::Bool=false)

Description

This function is used to create an eSAFTVRMie model which is a combination of the SAFTVR-Mie, Debye-Hückel and Born models.

Input parameters

SAFT-VR Mie Parameters

Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
segment: Single Parameter (Float64) - Number of segments (no units)
sigma: Single Parameter (Float64) - Segment Diameter [A°]
epsilon: Single Parameter (Float64) - Reduced dispersion energy [K]
lambda_a: Pair Parameter (Float64) - Atractive range parameter (no units)
lambda_r: Pair Parameter (Float64) - Repulsive range parameter (no units)
k: Pair Parameter (Float64) (optional) - Binary Interaction Paramater (no units)
epsilon_assoc: Association Parameter (Float64) - Reduced association energy [K]
bondvol: Association Parameter (Float64) - Association Volume [m^3]

Debye-Hückel Parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
charge: Single Parameter (Float64) - Charge [-]

Born Parameters

sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

idealmodel: Ideal Model
neutralmodel: Neutral EoS Model
ionmodel: Ion Model

References

Selam, M., Economou, I., Castier, M. (2018). A thermodynamic model for strong aqueous electrolytes based on the eSAFT-VR Mie equation of state. Fluid Phase Equilibria, 464, 47-63.

Clapeyron.SAFTVREMie — Function

SAFTVREMie(solvents::Array{String,1}, 
    ions::Array{String,1}; 
    idealmodel::IdealModel = BasicIdeal,
    neutralmodel::EoSModel = SAFTVRMie,
    ionmodel::IonModel = MSABorn,
    RSPmodel::RSPModel = Schreckenberg,
    userlocations::Vector{String}=[],
    ideal_userlocations::Vector{String}=[],
    assoc_options::AssocOptions = AssocOptions(),
    verbose::Bool=false)

Description

This function is used to create an SAFT-VRE Mie model which is a combination of the SAFT-VR Mie, MSA and Born models.

Input parameters

SAFT-VR Mie Parameters

Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
segment: Single Parameter (Float64) - Number of segments (no units)
sigma: Single Parameter (Float64) - Segment Diameter [A°]
epsilon: Single Parameter (Float64) - Reduced dispersion energy [K]
lambda_a: Pair Parameter (Float64) - Atractive range parameter (no units)
lambda_r: Pair Parameter (Float64) - Repulsive range parameter (no units)
k: Pair Parameter (Float64) (optional) - Binary Interaction Paramater (no units)
epsilon_assoc: Association Parameter (Float64) - Reduced association energy [K]
bondvol: Association Parameter (Float64) - Association Volume [m^3]

MSA Parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
charge: Single Parameter (Float64) - Charge [-]

Born Parameters

sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

idealmodel: Ideal Model
neutralmodel: Neutral EoS Model
ionmodel: Ion Model

References

Eriksen, D.K., Lazarou, G., Galindo, A., Jackson, G., Adjiman, C.S., & Haslam, A.J. (2016). Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state. Molecular Physics, 114(18), 2724-2749.

Clapeyron.SAFTgammaEMie — Function

SAFTgammaEMie(solvents::Array{String,1}, 
    ions::Array{String,1}; 
    idealmodel::IdealModel = BasicIdeal,
    neutralmodel::EoSModel = SAFTgammaMie,
    ionmodel::IonModel = GCMSABorn,
    RSPmodel::RSPModel = Schreckenberg,
    userlocations::Vector{String}=[],
    ideal_userlocations::Vector{String}=[],
    assoc_options::AssocOptions = AssocOptions(),
    verbose::Bool=false)

Description

This function is used to create an SAFT-gammaE Mie model which is a combination of the SAFT-gamma Mie, MSA and Born models.

Input parameters

SAFT-VR Mie Parameters

Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
vst: Single Parameter (Float64) - Number of segments (no units)
S: Single Parameter (Float64) - Shape factor for segment (no units)
sigma: Single Parameter (Float64) - Segment Diameter [A°]
epsilon: Single Parameter (Float64) - Reduced dispersion energy [K]
lambda_a: Pair Parameter (Float64) - Atractive range parameter (no units)
lambda_r: Pair Parameter (Float64) - Repulsive range parameter (no units)
epsilon_assoc: Association Parameter (Float64) - Reduced association energy [K]
bondvol: Association Parameter (Float64) - Association Volume

MSA Parameters

sigma: Single Parameter (Float64) - Diameter of closest approach [m]
charge: Single Parameter (Float64) - Charge [-]

Born Parameters

sigma_born: Single Parameter (Float64) - Born Diameter [m]
charge: Single Parameter (Float64) - Charge [-]

Input models

idealmodel: Ideal Model
neutralmodel: Neutral EoS Model
ionmodel: Ion Model

References

Haslam, A.J., González-Pérez, A., Di Lecce, S., Khalit, S.H., Perdomo, F.A., Kournopoulos, S., Kohns, M., Lindeboom, T., Wehbe, M., Febra, S., Jackson, G., Adjiman, C.S. & Galind, A. (2020). Expanding the Applications of the SAFT-γ Mie Group-Contribution Equation of State: Prediction of Thermodynamic Properties and Phase Behavior of Mixtures. Journal of Chemical Engineering Data, 65(12), 5862–5890

Relative Static Permittivity Models

Clapeyron.ConstRSP — Type

ConstRSP(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     userlocations::Vector{String}=[], 
     value::Float64 = 78.38484961, 
     verbose::Bool=false)

Input parameters

value::Float64: Constant Relative Static Permittivity [-]

Description

This function is used to create a constant Relative Static Permittivity model, given by value.

Clapeyron.LinMixRSP — Type

LinMixRSP(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     userlocations::Vector{String}=[], 
     verbose::Bool=false)

Input parameters

dielectric_constant::Float64: Constant Relative Static Permittivity [-]

Description

This function is used to create a Linear Mixing-Rule Relative Static Permittivity model, for a mixture of solvents, where each solvent has a dielectric_constant.

Clapeyron.Schreckenberg — Type

Schreckenberg(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     userlocations::Vector{String}=[], 
     verbose::Bool=false)

Input parameters

d_T::Float64: Single Parameter - Temperature dependent dielectric constant [-]
d_V::Float64: Single Parameter - Volume dependent dielectric constant [-]
charge::Float64: Single Parameter - Charge [-]

Description

This function is used to create a Schreckenberg model. The Schreckenberg term estimates the dielectric constant for a mixture of solvents.

References

Schreckenberg, J., Dufal, S., Haslam, A.J., Adjiman, C.S., Jackson, G., Galindo, A. (2014). Modelling of the thermodynamic and solvation properties of electrolyte solutions with the statistical associating fluid theory for potentials of variable range. Molecular Physics, 112(17), 2339-2364.

Clapeyron.ZuoFurst — Type

ZuoFurst(solvents::Array{String,1}, 
     ions::Array{String,1}; 
     userlocations::Vector{String}=[], 
     verbose::Bool=false)

Description

This function is used to create a Zuo-First model. The Zuo-First expression estimates the dielectric constant of water for a range of temperatures.

References

Zuo, Y-X., Fürst, W. (1997). Prediction of vapor pressure for nonaqueous electrolyte solutions using an electrolyte equation of state, Fluid Phase Equilibria, 138(1-2), 87-104.