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Chen2020_params.py
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from pybamm import exp, tanh, constants, Parameter, ParameterValues
def electrolyte_diffusivity_Nyman2008(c_e, T):
"""
Diffusivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
comes from [1]
References
----------
.. [1] A. Nyman, M. Behm, and G. Lindbergh, "Electrochemical characterisation and
modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte,"
Electrochim. Acta, vol. 53, no. 22, pp. 6356–6365, 2008.
Parameters
----------
c_e: :class:`pybamm.Symbol`
Dimensional electrolyte concentration
T: :class:`pybamm.Symbol`
Dimensional temperature
Returns
-------
:class:`pybamm.Symbol`
Solid diffusivity
"""
D_c_e = 8.794e-11 * (c_e / 1000) ** 2 - 3.972e-10 * (c_e / 1000) + 4.862e-10
# Nyman et al. (2008) does not provide temperature dependence
return D_c_e
def electrolyte_conductivity_Nyman2008(c_e, T):
"""
Conductivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
comes from [1].
References
----------
.. [1] A. Nyman, M. Behm, and G. Lindbergh, "Electrochemical characterisation and
modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte,"
Electrochim. Acta, vol. 53, no. 22, pp. 6356–6365, 2008.
Parameters
----------
c_e: :class:`pybamm.Symbol`
Dimensional electrolyte concentration
T: :class:`pybamm.Symbol`
Dimensional temperature
Returns
-------
:class:`pybamm.Symbol`
Solid diffusivity
"""
sigma_e = (
0.1297 * (c_e / 1000) ** 3 - 2.51 * (c_e / 1000) ** 1.5 + 3.329 * (c_e / 1000)
)
# Nyman et al. (2008) does not provide temperature dependence
return sigma_e
def graphite_LGM50_electrolyte_exchange_current_density_Chen2020(c_e, c_s_surf, T):
"""
Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in
EC:DMC.
References
----------
.. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
Electrochemical Society 167 (2020): 080534.
Parameters
----------
c_e : :class:`pybamm.Symbol`
Electrolyte concentration [mol.m-3]
c_s_surf : :class:`pybamm.Symbol`
Particle concentration [mol.m-3]
T : :class:`pybamm.Symbol`
Temperature [K]
Returns
-------
:class:`pybamm.Symbol`
Exchange-current density [A.m-2]
"""
m_ref = 6.48e-7 # (A/m2)(mol/m3)**1.5 - includes ref concentrations
E_r = 35000
arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
c_n_max = Parameter("Maximum concentration in negative electrode [mol.m-3]")
return (
m_ref * arrhenius * c_e**0.5 * c_s_surf**0.5 * (c_n_max - c_s_surf) ** 0.5
)
def nmc_LGM50_electrolyte_exchange_current_density_Chen2020(c_e, c_s_surf, T):
"""
Exchange-current density for Butler-Volmer reactions between NMC and LiPF6 in
EC:DMC.
References
----------
.. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
Electrochemical Society 167 (2020): 080534.
Parameters
----------
c_e : :class:`pybamm.Symbol`
Electrolyte concentration [mol.m-3]
c_s_surf : :class:`pybamm.Symbol`
Particle concentration [mol.m-3]
T : :class:`pybamm.Symbol`
Temperature [K]
Returns
-------
:class:`pybamm.Symbol`
Exchange-current density [A.m-2]
"""
m_ref = 3.42e-6 # (A/m2)(mol/m3)**1.5 - includes ref concentrations
E_r = 17800
arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
c_p_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")
return (
m_ref * arrhenius * c_e**0.5 * c_s_surf**0.5 * (c_p_max - c_s_surf) ** 0.5
)
def graphite_LGM50_ocp_Chen2020(sto):
"""
LG M50 graphite open circuit potential as a function of stochiometry, fit taken
from [1].
References
----------
.. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
Electrochemical Society 167 (2020): 080534.
Parameters
----------
sto: :class:`pybamm.Symbol`
Electrode stochiometry
Returns
-------
:class:`pybamm.Symbol`
Open circuit potential
"""
u_eq = (
1.9793 * exp(-39.3631 * sto)
+ 0.2482
- 0.0909 * tanh(29.8538 * (sto - 0.1234))
- 0.04478 * tanh(14.9159 * (sto - 0.2769))
- 0.0205 * tanh(30.4444 * (sto - 0.6103))
)
return u_eq
def nmc_LGM50_ocp_Chen2020(sto):
"""
LG M50 NMC open circuit potential as a function of stochiometry, fit taken
from [1].
References
----------
.. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
Electrochemical Society 167 (2020): 080534.
Parameters
----------
sto: :class:`pybamm.Symbol`
Electrode stochiometry
Returns
-------
:class:`pybamm.Symbol`
Open circuit potential
"""
u_eq = (
-0.8090 * sto
+ 4.4875
- 0.0428 * tanh(18.5138 * (sto - 0.5542))
- 17.7326 * tanh(15.7890 * (sto - 0.3117))
+ 17.5842 * tanh(15.9308 * (sto - 0.3120))
)
return u_eq
parameter_values = ParameterValues(
{
"1 + dlnf/dlnc": 1.0,
"Ambient temperature [K]": 298.15,
"Cation transference number": 0.2594,
"Cell cooling surface area [m2]": 0.00531,
"Cell volume [m3]": 2.42e-05,
"Current function [A]": 5.0,
"Electrode height [m]": 0.065,
"Electrode width [m]": 1.58,
"Electrolyte conductivity [S.m-1]": electrolyte_conductivity_Nyman2008,
"Electrolyte diffusivity [m2.s-1]": electrolyte_diffusivity_Nyman2008,
"Initial concentration in electrolyte [mol.m-3]": 1000.0,
"Initial concentration in negative electrode [mol.m-3]": 29866.0,
"Initial concentration in positive electrode [mol.m-3]": 17038.0,
"Initial temperature [K]": 298.15,
"Lower voltage cut-off [V]": 2.5,
"Maximum concentration in negative electrode [mol.m-3]": 33133.0,
"Maximum concentration in positive electrode [mol.m-3]": 63104.0,
"Negative current collector conductivity [S.m-1]": 58411000.0,
"Negative current collector density [kg.m-3]": 8960.0,
"Negative current collector specific heat capacity [J.kg-1.K-1]": 620.7659832284165,
"Negative current collector thermal conductivity [W.m-1.K-1]": 401.0,
"Negative current collector thickness [m]": 1.2e-05,
"Negative electrode Bruggeman coefficient (electrode)": 1.5,
"Negative electrode Bruggeman coefficient (electrolyte)": 1.5,
"Negative electrode OCP [V]": graphite_LGM50_ocp_Chen2020,
"Negative electrode OCP entropic change [V.K-1]": 0.0,
"Negative electrode active material volume fraction": 0.75,
"Negative electrode conductivity [S.m-1]": 215.0,
"Negative electrode density [kg.m-3]": 1657.0,
"Negative electrode diffusivity [m2.s-1]": 3.3e-14,
"Negative electrode electrons in reaction": 1.0,
"Negative electrode exchange-current density [A.m-2]": graphite_LGM50_electrolyte_exchange_current_density_Chen2020,
"Negative electrode porosity": 0.25,
"Negative electrode specific heat capacity [J.kg-1.K-1]": 1128.6654240516666,
"Negative electrode thermal conductivity [W.m-1.K-1]": 1.7,
"Negative electrode thickness [m]": 8.52e-05,
"Negative particle radius [m]": 5.86e-06,
"Nominal cell capacity [A.h]": 5.0,
"Number of cells connected in series to make a battery": 1.0,
"Number of electrodes connected in parallel to make a cell": 1.0,
"Positive current collector conductivity [S.m-1]": 36914000.0,
"Positive current collector density [kg.m-3]": 2700.0,
"Positive current collector specific heat capacity [J.kg-1.K-1]": 1446.3041219633499,
"Positive current collector thermal conductivity [W.m-1.K-1]": 237.0,
"Positive current collector thickness [m]": 1.6e-05,
"Positive electrode Bruggeman coefficient (electrode)": 1.5,
"Positive electrode Bruggeman coefficient (electrolyte)": 1.5,
"Positive electrode OCP [V]": nmc_LGM50_ocp_Chen2020,
"Positive electrode OCP entropic change [V.K-1]": 0.0,
"Positive electrode active material volume fraction": 0.665,
"Positive electrode conductivity [S.m-1]": 0.18,
"Positive electrode density [kg.m-3]": 3262.0,
"Positive electrode diffusivity [m2.s-1]": 4e-15,
"Positive electrode electrons in reaction": 1.0,
"Positive electrode exchange-current density [A.m-2]": nmc_LGM50_electrolyte_exchange_current_density_Chen2020,
"Positive electrode porosity": 0.335,
"Positive electrode specific heat capacity [J.kg-1.K-1]": 1128.6654240516666,
"Positive electrode thermal conductivity [W.m-1.K-1]": 2.1,
"Positive electrode thickness [m]": 7.56e-05,
"Positive particle radius [m]": 5.22e-06,
"Reference temperature [K]": 298.15,
"Separator Bruggeman coefficient (electrolyte)": 1.5,
"Separator density [kg.m-3]": 397.0,
"Separator porosity": 0.47,
"Separator specific heat capacity [J.kg-1.K-1]": 1128.6654240516666,
"Separator thermal conductivity [W.m-1.K-1]": 0.16,
"Separator thickness [m]": 1.2e-05,
"Total heat transfer coefficient [W.m-2.K-1]": 20.0,
"Typical current [A]": 5.0,
"Typical electrolyte concentration [mol.m-3]": 1000.0,
"Upper voltage cut-off [V]": 4.2,
},
)