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#729 added electrolyte conductivity
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Scottmar93 committed Feb 10, 2020
1 parent e096a23 commit 9a41e29
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import autograd.numpy as np


def graphite_electrolyte_reaction_rate_Dualfoil1998(T, T_inf, E_r, R_g):
def graphite_electrolyte_reaction_rate_Ecker2015(T, T_inf, E_r, R_g):
"""
Reaction rate for Butler-Volmer reactions between graphite and LiPF6 in EC:DMC.
References
----------
.. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
.. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery i. determination of parameters." Journal of the
Electrochemical Society 162.9 (2015): A1836-A1848.
.. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery ii. model validation." Journal of The Electrochemical
Society 162.9 (2015): A1849-A1857.
Parameters
----------
Expand All @@ -25,7 +30,7 @@ def graphite_electrolyte_reaction_rate_Dualfoil1998(T, T_inf, E_r, R_g):
:`numpy.Array`
Reaction rate
"""
m_ref = 2 * 10 ** (-5)
m_ref = 2.79 * 10 ** (-6)
arrhenius = np.exp(E_r / R_g * (1 / T_inf - 1 / T))

return m_ref * arrhenius

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Expand Up @@ -30,7 +30,7 @@ Negative electrode thermal conductivity [W.m-1.K-1],N/A,,
Negative electrode OCP entropic change [V.K-1],N/A,,
,,,
# Activation energies,,,
Reference temperature [K],298.15,25C,
Negative electrode reaction rate,ADD,,
Reference temperature [K],296.15,23C,
Negative electrode reaction rate,[function]graphite_electrolyte_reaction_rate_Ecker2015,,
Negative reaction rate activation energy [J.mol-1],53400,,
Negative solid diffusion activation energy [J.mol-1],3.03E+04,,

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Expand Up @@ -10,7 +10,7 @@ Positive electrode OCP [V],[data]nco_ocp_Ecker2015,,
# Microstructure,,,
Positive electrode porosity,0.296,,
Positive particle radius [m],1E-05,,
Positive electrode surface area density [m-1],ADD,,
Positive electrode surface area density [m-1],188455,,
Positive electrode Bruggeman coefficient,N/A,,
,,,
# Interfacial reactions,,,
Expand All @@ -30,7 +30,7 @@ Positive electrode thermal conductivity [W.m-1.K-1],N/A,,
Positive electrode OCP entropic change [V.K-1],N/A,,
,,,
# Activation energies,,,
Reference temperature [K],298.15,25C,
Positive electrode reaction rate,ADD,,
Reference temperature [K],296.15,25C,
Positive electrode reaction rate,[function]nco_electrolyte_reaction_rate_Ecker2015,,
Positive reaction rate activation energy [J.mol-1],4.36E+04,,
Positive solid diffusion activation energy [J.mol-1],8.06E+04,,

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import autograd.numpy as np


def electrolyte_conductivity_Capiglia1999(c_e, T, T_inf, E_k_e, R_g):
"""
Conductivity of LiPF6 in EC:DMC as a function of ion concentration [1, 2].
References
----------
.. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery i. determination of parameters." Journal of the
Electrochemical Society 162.9 (2015): A1836-A1848.
.. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery ii. model validation." Journal of The Electrochemical
Society 162.9 (2015): A1849-A1857.
Parameters
----------
c_e: :class: `numpy.Array`
Dimensional electrolyte concentration
T: :class: `numpy.Array`
Dimensional temperature
T_inf: double
Reference temperature
E_k_e: double
Electrolyte conductivity activation energy
R_g: double
The ideal gas constant
Returns
-------
:`numpy.Array`
Solid diffusivity
"""

x = c_e / 1000

# in mS / cm
sigma_e = 2.667 * x ** 3 - 12.983 * x ** 2 + 17.919 * x + 1.726

# convert to S / m
sigma_e = sigma_e / 10

# In Ecker paper there is factor of 1/T out the front but this doesn't
# make much sense so just going to leave it out for now
arrhenius = np.exp(E_k_e / R_g * (1 / T_inf - 1 / T))

return sigma_e * arrhenius
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Expand Up @@ -3,15 +3,17 @@

def electrolyte_diffusivity_Capiglia1999(c_e, T, T_inf, E_D_e, R_g):
"""
Diffusivity of LiPF6 in EC:DMC as a function of ion concentration. The original data
is from [1]. The fit from Dualfoil [2].
Diffusivity of LiPF6 in EC:DMC as a function of ion concentration [1, 2].
References
----------
.. [1] C Capiglia et al. 7Li and 19F diffusion coefficients and thermal
properties of non-aqueous electrolyte solutions for rechargeable lithium batteries.
Journal of power sources 81 (1999): 859-862.
.. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
.. [1] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery i. determination of parameters." Journal of the
Electrochemical Society 162.9 (2015): A1836-A1848.
.. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
a lithium-ion battery ii. model validation." Journal of The Electrochemical
Society 162.9 (2015): A1849-A1857.
l
Parameters
----------
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