From 9a41e29241dbeaf9a06375f26e7301a072979e4a Mon Sep 17 00:00:00 2001 From: Scott Marquis Date: Mon, 10 Feb 2020 18:26:20 +0000 Subject: [PATCH] #729 added electrolyte conductivity --- ...te_electrolyte_reaction_rate_Ecker2015.py} | 11 ++-- .../graphite_entropic_change_Moura2016.py | 33 ------------ ...phite_mcmb2528_diffusivity_Dualfoil1998.py | 35 ------------- .../graphite_mcmb2528_ocp_Dualfoil1998.py | 29 ----------- .../anodes/graphite_Ecker2015/parameters.csv | 4 +- .../LiNiCoO2_Ecker2015/lico2_data_example.csv | 50 ------------------- .../lico2_diffusivity_Dualfoil1998.py | 35 ------------- .../lico2_entropic_change_Moura2016.py | 35 ------------- .../LiNiCoO2_Ecker2015/parameters.csv | 6 +-- .../electrolyte_conductivity_Capiglia1999.py | 43 ---------------- .../electrolyte_conductivity_Ecker2015.py | 48 ++++++++++++++++++ ...y => electrolyte_diffusivity_Ecker2015.py} | 14 +++--- 12 files changed, 69 insertions(+), 274 deletions(-) rename input/parameters/lithium-ion/anodes/graphite_Ecker2015/{graphite_electrolyte_reaction_rate_Dualfoil1998.py => graphite_electrolyte_reaction_rate_Ecker2015.py} (51%) delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_entropic_change_Moura2016.py delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_diffusivity_Dualfoil1998.py delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_ocp_Dualfoil1998.py delete mode 100644 input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_data_example.csv delete mode 100644 input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_diffusivity_Dualfoil1998.py delete mode 100644 input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_entropic_change_Moura2016.py delete mode 100644 input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Capiglia1999.py create mode 100644 input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Ecker2015.py rename input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/{electrolyte_diffusivity_Capiglia1999.py => electrolyte_diffusivity_Ecker2015.py} (63%) diff --git a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Dualfoil1998.py b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Ecker2015.py similarity index 51% rename from input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Dualfoil1998.py rename to input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Ecker2015.py index 062ea36686..25278518b9 100644 --- a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Dualfoil1998.py +++ b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Ecker2015.py @@ -1,13 +1,18 @@ 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 ---------- @@ -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 diff --git a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_entropic_change_Moura2016.py b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_entropic_change_Moura2016.py deleted file mode 100644 index d2f427eb73..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_entropic_change_Moura2016.py +++ /dev/null @@ -1,33 +0,0 @@ -import autograd.numpy as np - - -def graphite_entropic_change_Moura2016(sto, c_n_max): - """ - Graphite entropic change in open circuit potential (OCP) at a temperature of - 298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code - [1]. - - References - ---------- - .. [1] https://github.com/scott-moura/fastDFN - - Parameters - ---------- - sto: double - Stochiometry of material (li-fraction) - - """ - - du_dT = ( - -1.5 * (120.0 / c_n_max) * np.exp(-120 * sto) - + (0.0351 / (0.083 * c_n_max)) * ((np.cosh((sto - 0.286) / 0.083)) ** (-2)) - - (0.0045 / (0.119 * c_n_max)) * ((np.cosh((sto - 0.849) / 0.119)) ** (-2)) - - (0.035 / (0.05 * c_n_max)) * ((np.cosh((sto - 0.9233) / 0.05)) ** (-2)) - - (0.0147 / (0.034 * c_n_max)) * ((np.cosh((sto - 0.5) / 0.034)) ** (-2)) - - (0.102 / (0.142 * c_n_max)) * ((np.cosh((sto - 0.194) / 0.142)) ** (-2)) - - (0.022 / (0.0164 * c_n_max)) * ((np.cosh((sto - 0.9) / 0.0164)) ** (-2)) - - (0.011 / (0.0226 * c_n_max)) * ((np.cosh((sto - 0.124) / 0.0226)) ** (-2)) - + (0.0155 / (0.029 * c_n_max)) * ((np.cosh((sto - 0.105) / 0.029)) ** (-2)) - ) - - return du_dT diff --git a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_diffusivity_Dualfoil1998.py b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_diffusivity_Dualfoil1998.py deleted file mode 100644 index 766ae00082..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_diffusivity_Dualfoil1998.py +++ /dev/null @@ -1,35 +0,0 @@ -import autograd.numpy as np - - -def graphite_mcmb2528_diffusivity_Dualfoil1998(sto, T, T_inf, E_D_s, R_g): - """ - Graphite MCMB 2528 diffusivity as a function of stochiometry, in this case the - diffusivity is taken to be a constant. The value is taken from Dualfoil [1]. - - References - ---------- - .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html - - Parameters - ---------- - sto: :class: `numpy.Array` - Electrode stochiometry - T: :class: `numpy.Array` - Dimensional temperature - T_inf: double - Reference temperature - E_D_s: double - Solid diffusion activation energy - R_g: double - The ideal gas constant - - Returns - ------- - : double - Solid diffusivity - """ - - D_ref = 3.9 * 10 ** (-14) - arrhenius = np.exp(E_D_s / R_g * (1 / T_inf - 1 / T)) - - return D_ref * arrhenius diff --git a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_ocp_Dualfoil1998.py b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_ocp_Dualfoil1998.py deleted file mode 100644 index 57d1989ccc..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_ocp_Dualfoil1998.py +++ /dev/null @@ -1,29 +0,0 @@ -import autograd.numpy as np - - -def graphite_mcmb2528_ocp_Dualfoil1998(sto): - """ - Graphite MCMB 2528 Open Circuit Potential (OCP) as a function of the - stochiometry. The fit is taken from Dualfoil [1]. Dualfoil states that the data - was measured by Chris Bogatu at Telcordia and PolyStor materials, 2000. However, - we could not find any other records of this measurment. - - References - ---------- - .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html - """ - - u_eq = ( - 0.194 - + 1.5 * np.exp(-120.0 * sto) - + 0.0351 * np.tanh((sto - 0.286) / 0.083) - - 0.0045 * np.tanh((sto - 0.849) / 0.119) - - 0.035 * np.tanh((sto - 0.9233) / 0.05) - - 0.0147 * np.tanh((sto - 0.5) / 0.034) - - 0.102 * np.tanh((sto - 0.194) / 0.142) - - 0.022 * np.tanh((sto - 0.9) / 0.0164) - - 0.011 * np.tanh((sto - 0.124) / 0.0226) - + 0.0155 * np.tanh((sto - 0.105) / 0.029) - ) - - return u_eq diff --git a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv index f9d013183e..6a520c125e 100644 --- a/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv +++ b/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv @@ -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,, diff --git a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_data_example.csv b/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_data_example.csv deleted file mode 100644 index 5f2f5fef15..0000000000 --- a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_data_example.csv +++ /dev/null @@ -1,50 +0,0 @@ -0.000000000000000000e+00, 4.714135898019971016e+00 -2.040816326530612082e-02, 4.708899441575220557e+00 -4.081632653061224164e-02, 4.702448345762175741e+00 -6.122448979591836593e-02, 4.694558534379876136e+00 -8.163265306122448328e-02, 4.684994372928071193e+00 -1.020408163265306006e-01, 4.673523893805322516e+00 -1.224489795918367319e-01, 4.659941254449398329e+00 -1.428571428571428492e-01, 4.644096031712390271e+00 -1.632653061224489666e-01, 4.625926611260677390e+00 -1.836734693877550839e-01, 4.605491824833229053e+00 -2.040816326530612013e-01, 4.582992038370575116e+00 -2.244897959183673186e-01, 4.558769704421606228e+00 -2.448979591836734637e-01, 4.533281647154224103e+00 -2.653061224489795533e-01, 4.507041620859735254e+00 -2.857142857142856984e-01, 4.480540404981123714e+00 -3.061224489795917880e-01, 4.454158468368703439e+00 -3.265306122448979331e-01, 4.428089899175588151e+00 -3.469387755102040782e-01, 4.402295604083254155e+00 -3.673469387755101678e-01, 4.376502631465185367e+00 -3.877551020408163129e-01, 4.350272100879827519e+00 -4.081632653061224025e-01, 4.323179536958428493e+00 -4.285714285714285476e-01, 4.295195829713853719e+00 -4.489795918367346372e-01, 4.267407675466301065e+00 -4.693877551020407823e-01, 4.243081968022011985e+00 -4.897959183673469274e-01, 4.220583168834260768e+00 -5.102040816326530726e-01, 4.177032236370062712e+00 -5.306122448979591066e-01, 4.134943568540559333e+00 -5.510204081632652517e-01, 4.075402582839823928e+00 -5.714285714285713969e-01, 4.055407164381796825e+00 -5.918367346938775420e-01, 4.036052896449991323e+00 -6.122448979591835760e-01, 4.012970397550268409e+00 -6.326530612244897211e-01, 3.990385577539371287e+00 -6.530612244897958663e-01, 3.970744780585252709e+00 -6.734693877551020114e-01, 3.954753574690877738e+00 -6.938775510204081565e-01, 3.942237451863396025e+00 -7.142857142857141906e-01, 3.932683425747200534e+00 -7.346938775510203357e-01, 3.925509771581312979e+00 -7.551020408163264808e-01, 3.920182838859009422e+00 -7.755102040816326259e-01, 3.916256861206461881e+00 -7.959183673469386600e-01, 3.913378070528176877e+00 -8.163265306122448051e-01, 3.911274218446639583e+00 -8.367346938775509502e-01, 3.909739285381772067e+00 -8.571428571428570953e-01, 3.908613829807601192e+00 -8.775510204081632404e-01, 3.907726324580658162e+00 -8.979591836734692745e-01, 3.906474088522892796e+00 -9.183673469387754196e-01, 3.900204875423951556e+00 -9.387755102040815647e-01, 3.848912814816038974e+00 -9.591836734693877098e-01, 3.445226042113884724e+00 -9.795918367346938549e-01, 1.687177743081021308e+00 -1.000000000000000000e+00, 6.378908986260003328e-03 diff --git a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_diffusivity_Dualfoil1998.py b/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_diffusivity_Dualfoil1998.py deleted file mode 100644 index b304bcb7b9..0000000000 --- a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_diffusivity_Dualfoil1998.py +++ /dev/null @@ -1,35 +0,0 @@ -import autograd.numpy as np - - -def lico2_diffusivity_Dualfoil1998(sto, T, T_inf, E_D_s, R_g): - """ - LiCo2 diffusivity as a function of stochiometry, in this case the - diffusivity is taken to be a constant. The value is taken from Dualfoil [1]. - - References - ---------- - .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html - - Parameters - ---------- - sto: :class: `numpy.Array` - Electrode stochiometry - T: :class: `numpy.Array` - Dimensional temperature - T_inf: double - Reference temperature - E_D_s: double - Solid diffusion activation energy - R_g: double - The ideal gas constant - - Returns - ------- - : double - Solid diffusivity - """ - - D_ref = 1 * 10 ** (-13) - arrhenius = np.exp(E_D_s / R_g * (1 / T_inf - 1 / T)) - - return D_ref * arrhenius diff --git a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_entropic_change_Moura2016.py b/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_entropic_change_Moura2016.py deleted file mode 100644 index 16b5441298..0000000000 --- a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/lico2_entropic_change_Moura2016.py +++ /dev/null @@ -1,35 +0,0 @@ -import autograd.numpy as np - - -def lico2_entropic_change_Moura2016(sto, c_p_max): - """ - Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at - a temperature of 298.15K as a function of the stochiometry. The fit is taken - from Scott Moura's FastDFN code [1]. - - References - ---------- - .. [1] https://github.com/scott-moura/fastDFN - - Parameters - ---------- - sto: double - Stochiometry of material (li-fraction) - - """ - - # Since the equation for LiCo2 from this ref. has the stretch factor, - # should this too? If not, the "bumps" in the OCV don't line up. - stretch = 1.062 - sto = stretch * sto - - du_dT = ( - 0.07645 * (-54.4806 / c_p_max) * ((1.0 / np.cosh(30.834 - 54.4806 * sto)) ** 2) - + 2.1581 * (-50.294 / c_p_max) * ((np.cosh(52.294 - 50.294 * sto)) ** (-2)) - + 0.14169 * (19.854 / c_p_max) * ((np.cosh(11.0923 - 19.8543 * sto)) ** (-2)) - - 0.2051 * (5.4888 / c_p_max) * ((np.cosh(1.4684 - 5.4888 * sto)) ** (-2)) - - (0.2531 / 0.1316 / c_p_max) * ((np.cosh((-sto + 0.56478) / 0.1316)) ** (-2)) - - (0.02167 / 0.006 / c_p_max) * ((np.cosh((sto - 0.525) / 0.006)) ** (-2)) - ) - - return du_dT diff --git a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv b/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv index ceb25305bb..d4f8990fb3 100644 --- a/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv +++ b/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv @@ -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,,, @@ -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,, diff --git a/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Capiglia1999.py b/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Capiglia1999.py deleted file mode 100644 index f39ad5ab78..0000000000 --- a/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Capiglia1999.py +++ /dev/null @@ -1,43 +0,0 @@ -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. The original - data is from [1]. The fit is from Dualfoil [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 - 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 - """ - - sigma_e = ( - 0.0911 - + 1.9101 * (c_e / 1000) - - 1.052 * (c_e / 1000) ** 2 - + 0.1554 * (c_e / 1000) ** 3 - ) - - arrhenius = np.exp(E_k_e / R_g * (1 / T_inf - 1 / T)) - - return sigma_e * arrhenius diff --git a/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Ecker2015.py b/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Ecker2015.py new file mode 100644 index 0000000000..bf67055141 --- /dev/null +++ b/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_conductivity_Ecker2015.py @@ -0,0 +1,48 @@ +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 diff --git a/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Capiglia1999.py b/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Ecker2015.py similarity index 63% rename from input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Capiglia1999.py rename to input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Ecker2015.py index 579a50b536..17cefa89dd 100644 --- a/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Capiglia1999.py +++ b/input/parameters/lithium-ion/electrolytes/lipf6_Ecker2015/electrolyte_diffusivity_Ecker2015.py @@ -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 ----------