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LMO Decomposition
Introduction
Some positive electrode materials are known to deteriorate in overcharged lithium-ion battery cells. Predominantly, manganese-containing electrode materials such as LMO and NMC can lose capacity due to manganese dissolution when overcharged. This decomposition is a chemical reaction driven by protons that originate from solvent oxidation and water. The reaction decreases the electrode volume fraction.
This example models the capacity fade of an LMO vs. Li(s) cell. An abusive cycling condition, with repeated C/3 charge-discharge cycling between 3.6 V and 4.5 V at elevated temperature, is investigated.
Model Definition
general
The model is set up in 1D for a Li(s)/LMO cell with a 1.0 M LiPF6 in EC:EMC (3:7 by weight) electrolyte. The lithium foil is defined at a boundary and the LMO porous electrode at a domain. The two electrodes are parted by a separator (Figure 1).
Figure 1: Model geometry.
The Lithium-Ion Battery interface is used, accounting for:
•
Electronic conduction in the LMO electrode
•
Ionic charge transport in the electrode and electrolyte/separator
•
Material transport in the electrolyte, allowing for including the effects of concentration on ionic conductivity and concentration overpotentials
•
Material transport within solid spherical particles in the LMO electrode
•
Butler–Volmer electrode intercalation kinetics using experimentally measured equilibrium potentials
•
Electrode surface with Butler–Volmer kinetics for lithium foil
Most material properties are taken from the Battery material library. More information about how to use the Lithium-Ion Battery interface can be found in the 1D Isothermal Lithium-Ion Battery example.
Additional features are used in the Lithium-Ion Battery interface to account for the detrimental electrochemical and chemical reactions. The Transport of Diluted Species interface is used to define the reactions and transport of foreign species in the cell.
Detrimental reactions
Several reactions are involved in the LMO decomposition and are accounted for in the model. In short, solvent oxidation is the triggering reaction as the presence of protons in the electrolyte maintains the decomposition. The detrimental reaction details are described below (Ref. 1).
Solvent Oxidation
At 4.2 V cell voltage, the solvent is electrochemically decomposed at the electronically conductive material of the LMO electrode:
The reaction is assumed to be irreversible and the loss of solvent is neglected, that is, exhausted and fresh solvent is assumed to behave in the same manner. Anodic Tafel kinetics are set, giving the following volumetric reaction source, rv,oxid (mol/(m3·s)):
(1)
LMO Decomposition by Protons
Manganese dissolves as LMO (LiMn2O4) decomposes in an irreversible chemical reaction driven by protons:
The volumetric reaction source, rv,proton, is defined as:
(2)
Electrolyte Salt Loss by Water
Electrolyte salt decomposes irreversibly with water. The model assumes that one Li+ is lost as LiF and that HF is fully ionized:
The volumetric reaction source, rv,water, depends on the water and electrolyte salt concentrations:
(3)
Additional Electrochemical Reactions at Lithium Foil
The concentrations of protons and manganese ions in the electrolyte are counteracted by reduction reactions at the lithium foil surface. For simplicity, only reductions are considered and the products are said to be inert:
The reduction reactions are defined using cathodic Tafel kinetics, giving the following reaction rate fluxes, Ni (mol/(m2·s)):
(4)
(5)
In the expressions in the sections above:
•
 acs is the specific surface area at the electronically conductive material set to 106 m−1.
•
 as, is the specific surface area of the electrode material defined by the electrode material volume fraction, εs, and the radius of the LMO particles, rLMO:
(6)
•
 ci is the concentration of species i.
•
  ci,ref is the reference concentration of i.
•
 i0, oxid is the exchange current density of the solvent oxidation.
•
 i0, i, ref is the exchange current density of i at the reference concentration.
•
 kproton (m/s) is the rate constant of the LMO decomposition by protons reaction.
•
 kwater (m6/(mol·s)) is the rate constant for the electrolyte salt loss by water reaction.
•
 Eeq, oxid is the equilibrium potential of the solvent oxidation.
•
 Eeq, i, ref is the reference equilibrium potential of the reduction of i.
•
 νi is the stoichiometric coefficient of i in the electrochemical reaction.
•
 The electrochemical reactions are dependent on the solid phase potential, ϕs, and the pseudo-potentiostatic electrolyte potential, ϕl,ps. The latter is used instead of the electrolyte phase potential variable, ϕl, and includes an ideal electrolyte concentration dependence for single charged ions (that is, the dominating charge of ions in this example). For more information, see the Copper Current-Collector Dissolution example.
Detrimental Reactions in the Lithium-Ion Battery Interface
Foreign Species
Since the Lithium-Ion Battery interface is primarily intended for a binary electrolyte (Li+/PF6- with solvent), the addition of foreign species requires some assumptions to be made. In this example, all cations are treated as Li+ and any unreacted water is considered to constitute a negligible part of the solvent. This approach means that electroneutrality can be ensured at all times and that the salt transport is affected by the total concentration of species in the electrolyte.
Electrochemical Reactions
At the LMO, the solvent oxidation reaction is defined as an additional reaction to the main lithium intercalation reaction. This is done using an additional Porous Electrode Reaction in the Porous Electrode node.
At the lithium foil boundary, the proton and manganese ion reductions are defined as additional reactions to the lithium reaction. This is done by adding an Electrode Reaction subnode for each reduction in the Electrode Surface node.
The reactions give a net change of cations. The stoichiometric coefficients for each cation, νi, will be represented by the stoichiometric coefficient of Li+, νLi+, (Equation 1-Equation 5) following the assumption above. Therefore, for the proton reduction and solvent oxidation reactions, the coefficient will be set to −1 and for the manganese deposition −2 (two Li+ for each Mn2+).
Chemical Reactions
The net change of cations from the chemical reactions need to be accounted for as well. The LMO decomposition gives no net change in cations. However, the electrolyte salt loss gives a net increase of ions, as two H+ and two F-are formed on the expense of one Li+ and one LF6-. Assuming that both anions behave in a similar way, the cation volumetric reaction source, rv, cation, is defined as:
(7)
The cation source is defined using a Reaction Source node that can be added when the Advanced Physics Options is enabled.
Loss of Electrode Volume Fraction
The LMO decomposition results in a loss in electrode (LMO) volume fraction, εs. The Dissolving–Depositing Species section of the Porous Electrode node is used to solve for an additional degree of freedom to keep track of the concentration of exhausted LMO, cLMOdead (mol/m3), according to:
(8)
The reaction rate is defined using a Nonfaraidaic Reactions subnode. With the Add volume change to electrode volume fraction enabled in the Porous Electrode node, the change in electrode volume fraction, Δεs, is computed with the molar volume of LMO, Vm, as follows:
(9)
Furthermore, the electrolyte volume fraction is set as constant in the model, assuming that the molar volume of LMO is unchanged.
Inhibited Transport in LMO Material
Lithium transport in the remaining LMO material is, in accordance with Ref. 1, inhibited from forming an inactive film consisting of precipitated decomposition products. This example incorporates the relationship between the diffusion coefficient, DLMO, and the electrode volume fraction, given by:
(10)
In the equation, the subscript 0 indicates the state at the beginning of cycling and ns is an adjust factor typically fitted to experimental results.
Detrimental Reactions in the Transport of Diluted Species Interface
The foreign species concentrations are assumed to be low in comparison to the Li+/PF6- (+ solvent) electrolyte, and therefore a dilute approximation of the transport and electrochemical reactions is valid. It follows that the electrolyte phase potential field is governed by the lithium-ion transport, and that the contribution to the electrolyte potential field from the foreign species transport may be neglected.
The Transport of Diluted Species interface solves for the transport of foreign species by diffusion and migration. For the migration term, the pseudopotentiostatic electrolyte potential, ϕl ps, is used. On the lithium foil boundary, the fluxes due to proton reduction and manganese deposition are computed using the Electrode Surface Coupling node. At the LMO porous electrode, the Porous Electrode Coupling node is used to account for the solvent oxidation reaction. All chemical reactions are defined using Reactions nodes.
Electrolyte salt concentration
In accordance to the definitions and assumptions above, the LiPF6 concentration, cl,net, is given by the difference in electrolyte salt concentration, cl, as computed by the Lithium-Ion Battery interface (in other words the total concentration of cations) and the foreign cation concentrations:
(11)
Results and Discussion
The difference between the first and last C/3 discharge cycle can be seen in Figure 2. Results indicate considerable capacity fade.
Figure 2: 1st and 50th discharge curves taken from continuous C/3 charge-discharge cycling of the LMO versus Li(s) cell at 328 K.
In Figure 3, the loss in electrode (LMO) volume fraction in the porous electrode after 50 cycles is shown to be about 4%.
Figure 3: Electrode volume fraction in the porous electrode with cycling.
Figure 4 displays the decrease in the diffusion coefficient of lithium within the LMO particles with cycling. The decrease declines with the number of cycles.
Figure 4: Diffusion coefficient of lithium within the LMO particles with cycling.
The relative capacity of the cell decreases over time as shown in Figure 5. The capacity based on cyclable lithium and host capacity follows the electrode volume fraction. The nominal C/3 discharge capacity declines more with time since this capacity captures the increased polarization caused by the lowered diffusion coefficient of lithium in LMO.
Figure 5: Change in relative capacity with cycling.
In Figure 6, the change in electrolyte salt concentration shows the LMO decomposition reaction to be dominant after about 12 cycles increasing the salt concentration considerably.
Figure 6: Electrolyte salt concentration in cell with cycling.
References
1. Y. Dai, L. Cai, and R. E. White, “Capacity Fade Model For Spinel LiMn2O4,” J. Elec. Soc., vol. 160, no. 1, p. A182, 2013.
Application Library path: Battery_Design_Module/Lithium-Ion_Batteries,_Aging_and_Abuse/lmo_decomposition
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  1D.
2
In the Select Physics tree, select Electrochemistry > Batteries > Lithium-Ion Battery (liion).
3
Click Add.
4
In the Select Physics tree, select Chemical Species Transport > Transport of Diluted Species (tds).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select Preset Studies for Selected Physics Interfaces > Lithium-Ion Battery > Time Dependent with Initialization.
8
Click  Done.
Global Definitions
Parameters 1
Load the parameters from a text file.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file lmo_decomposition_parameters.txt.
Draw 1D geometry of the half cell and make selections.
Geometry 1
Interval 1 (i1)
1
In the Model Builder window, under Component 1 (comp1) right-click Geometry 1 and choose Interval.
2
In the Settings window for Interval, locate the Interval section.
3
In the table, enter the following settings:
Coordinates (m)
0
L_sep
L_sep+L_pos
4
Click  Build All Objects.
5
Right-click Interval 1 (i1) and choose Plot.
Definitions
Separator
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Separator in the Label text field.
3
Select Domain 1 only.
LMO
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type LMO in the Label text field.
3
Select Domain 2 only.
Lithium Metal
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Lithium Metal in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 1 only.
Add material data for the electrolyte and the electrodes from the material library.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Battery > Electrolytes > LiPF6 in 1:1 EC:DMC (Liquid, Li-ion Battery).
4
Click the Add to Component button in the window toolbar.
5
In the tree, select Battery > Electrodes > LMO, LiMn2O4 Spinel (Positive, Li-ion Battery).
6
Click the Add to Component button in the window toolbar.
7
In the tree, select Battery > Electrodes > Lithium Metal, Li (Negative, Li-ion Battery).
8
Click the Add to Component button in the window toolbar.
9
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
LiPF6 in 1:1 EC:DMC (Liquid, Li-ion Battery) (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Separator.
LMO, LiMn2O4 Spinel (Positive, Li-ion Battery) (mat2)
1
In the Model Builder window, click LMO, LiMn2O4 Spinel (Positive, Li-ion Battery) (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose LMO.
Lithium Metal, Li (Negative, Li-ion Battery) (mat3)
1
In the Model Builder window, click Lithium Metal, Li (Negative, Li-ion Battery) (mat3).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Lithium Metal.
Definitions
Add model variables. Unknown variables warnings will be resolved as soon as the physics have been set up.
Variables - All Domains
1
In the Definitions toolbar, click  Local Variables.
2
In the Settings window for Variables, type Variables - All Domains in the Label text field.
3
Locate the Variables section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file lmo_decomposition_variables.txt.
Variables - LMO
1
In the Definitions toolbar, click  Local Variables.
2
In the Settings window for Variables, type Variables - LMO in the Label text field.
3
Locate the Geometric Entity Selection section. From the Geometric entity level list, choose Domain.
4
From the Selection list, choose LMO.
5
Locate the Variables section. Click  Load from File.
6
Browse to the model’s Application Libraries folder and double-click the file lmo_decomposition_variables_lmo.txt.
Integration LMO
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type Integration LMO in the Label text field.
3
In the Operator name text field, type intop_lmo.
4
Locate the Source Selection section. From the Selection list, choose LMO.
Integration Separator
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type Integration Separator in the Label text field.
3
In the Operator name text field, type intop_sep.
4
Locate the Source Selection section. From the Selection list, choose Separator.
Now begin defining the physics. Start with the Lithium-Ion Battery interface.
Lithium-Ion Battery (liion)
Use the SOC and Initial Charge Distribution node to compute initial concentration, battery cell capacity, and C-rate. The selection of the LMO electrode will be applicable once a Porous Electrode node is defined on the domain.
1
In the Model Builder window, under Component 1 (comp1) click Lithium-Ion Battery (liion).
2
In the Settings window for Lithium-Ion Battery, locate the Cell Settings section.
3
Select the Define cell state of charge (SOC) and initial charge inventory checkbox.
SOC and Initial Charge Distribution 1
1
In the Model Builder window, under Component 1 (comp1) > Lithium-Ion Battery (liion) click SOC and Initial Charge Distribution 1.
2
In the Settings window for SOC and Initial Charge Distribution, locate the Cell Type section.
3
From the list, choose Half cell.
4
Locate the State-of-Charge Definition section. From the list, choose User defined. In the Ecell0%SOC text field, type Vlow.
5
In the Ecell100%SOC text field, type Vhigh.
6
Locate the Initial Cell Charge Distribution section. In the SOC0 text field, type 0.
Positive Electrode Domain Selection 1
1
In the Model Builder window, click Positive Electrode Domain Selection 1.
2
In the Settings window for Positive Electrode Domain Selection, locate the Domain Selection section.
3
From the Selection list, choose LMO.
Separator 1
1
In the Model Builder window, under Component 1 (comp1) > Lithium-Ion Battery (liion) click Separator 1.
2
In the Settings window for Separator, locate the Porous Matrix Properties section.
3
In the εl text field, type epsl_sep.
Porous Electrode - LMO
1
In the Physics toolbar, click  Domains and choose Porous Electrode.
2
In the Settings window for Porous Electrode, type Porous Electrode - LMO in the Label text field.
3
Select Domain 2 only.
4
Locate the Electrolyte Properties section. From the Electrolyte material list, choose LiPF6 in 1:1 EC:DMC (Liquid, Li-ion Battery) (mat1).
5
Locate the Electrode Properties section. In the σs text field, type sigmas_pos.
6
Locate the Porous Matrix Properties section. In the εs text field, type epss_pos0.
7
In the εl text field, type epsl_pos.
Add a Dissolving/Depositing Species variable named LMO_dead. The variable represents the amount of exhausted LMO from the LMO decomposition by protons reaction.
8
Click to expand the Dissolving–Depositing Species section. Click  Add.
9
In the table, enter the following settings:
Species
Density (kg/m^3)
Molar mass (kg/mol)
LMO_dead
rho_LMO
M_LMO
The electrolyte volume fraction is set as constant, that is, the molar volume of LMO is constant.
10
Clear the Subtract volume change from electrolyte volume fraction checkbox.
Particle Intercalation 1
1
In the Model Builder window, click Particle Intercalation 1.
2
In the Settings window for Particle Intercalation, locate the Particle Transport Properties section.
3
From the Ds list, choose User defined. In the associated text field, type D_LMO.
4
In the rp text field, type rp_lmo.
Porous Electrode Reaction - Intercalation
1
In the Model Builder window, under Component 1 (comp1) > Lithium-Ion Battery (liion) > Porous Electrode - LMO click Porous Electrode Reaction 1.
2
In the Settings window for Porous Electrode Reaction, type Porous Electrode Reaction - Intercalation in the Label text field.
3
Locate the Electrode Kinetics section. In the i0,ref(T) text field, type i0_ref_lmo.
Add the additional reactions taking place in the porous LMO electrode domain. Treat all cations (protons) in terms of lithium ions as an assumption.
Porous Electrode - LMO
In the Model Builder window, click Porous Electrode - LMO.
Porous Electrode Reaction - Solvent Oxidation
1
In the Physics toolbar, click  Attributes and choose Porous Electrode Reaction.
2
In the Settings window for Porous Electrode Reaction, type Porous Electrode Reaction - Solvent Oxidation in the Label text field.
3
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Eeq_oxid+delta_phil.
4
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Anodic Tafel equation.
5
In the i0 text field, type i0_oxid*(cl/cl_ref)^0.5.
6
In the Aa text field, type Aa_oxid.
7
Locate the Active Specific Surface Area section. From the Active specific surface area list, choose User defined. In the av text field, type av_oxid.
8
Locate the Stoichiometric Coefficients section. In the νLiθ text field, type 0.
Porous Electrode - LMO
In the Model Builder window, click Porous Electrode - LMO.
Nonfaradaic Reactions - LMO Decomposition
1
In the Physics toolbar, click  Attributes and choose Nonfaradaic Reactions.
2
In the Settings window for Nonfaradaic Reactions, type Nonfaradaic Reactions - LMO Decomposition in the Label text field.
3
Locate the Reaction Rate section. In the Reaction rate for dissolving–depositing species table, enter the following settings:
Species
Reaction rate (mol/(m^3*s))
LMO_dead
-Rproton
Use the Electrode Surfacenode to add all electrochemical reactions taking place on the lithium metal. Treat all cations (manganese ions and protons) in terms of lithium ions as an assumption..
Electrode Surface - Lithium Metal
1
In the Physics toolbar, click  Boundaries and choose Electrode Surface.
2
Select Boundary 1 only.
3
In the Settings window for Electrode Surface, type Electrode Surface - Lithium Metal in the Label text field.
Electrode Reaction - Lithium
1
In the Model Builder window, under Component 1 (comp1) > Lithium-Ion Battery (liion) > Electrode Surface - Lithium Metal click Electrode Reaction 1.
2
In the Settings window for Electrode Reaction, type Electrode Reaction - Lithium in the Label text field.
Electrode Surface - Lithium Metal
In the Model Builder window, click Electrode Surface - Lithium Metal.
Electrode Reaction - Manganese Deposition
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
In the Settings window for Electrode Reaction, type Electrode Reaction - Manganese Deposition in the Label text field.
3
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Eeq_Mn+delta_phil.
4
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.
5
In the i0 text field, type i0_ref_Mn*cMn/cMn_ref.
6
In the Ac text field, type Ac_Mndep.
7
Locate the Stoichiometric Coefficients section. In the n text field, type 2.
8
In the νLi+ text field, type -2.
Electrode Surface - Lithium Metal
In the Model Builder window, click Electrode Surface - Lithium Metal.
Electrode Reaction - Proton Reduction
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
In the Settings window for Electrode Reaction, type Electrode Reaction - Proton Reduction in the Label text field.
3
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Eeq_H+delta_phil.
4
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.
5
In the i0 text field, type i0_ref_H*cH/cH_ref.
6
In the Ac text field, type Ac_Hred.
Define the net cation change from the chemical reactions using a Reaction Source node. To do this enable Advanced Physics Options.
7
Click the  Show More Options button in the Model Builder toolbar.
8
In the Show More Options dialog, in the tree, select the checkbox for the node Physics > Advanced Physics Options.
9
Click OK.
Reaction Source - Cation Net Chemical Reactions
1
In the Physics toolbar, click  Domains and choose Reaction Source.
2
In the Settings window for Reaction Source, type Reaction Source - Cation Net Chemical Reactions in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose All domains.
4
Locate the Reaction Source section. In the Rl,src text field, type Rwater.
Set the cell to cycle between 3.5 V and 4.5 V at C/3 with a Charge-Discharge Cycling node.
Charge-Discharge Cycling - Galvanic Cycling C/3
1
In the Physics toolbar, click  Boundaries and choose Charge-Discharge Cycling.
2
In the Settings window for Charge-Discharge Cycling, type Charge-Discharge Cycling - Galvanic Cycling C/3 in the Label text field.
3
Select Boundary 3 only.
4
Locate the Discharge Settings section. From the list, choose C-rate multiple.
5
In the Crate,dch text field, type -Crate.
6
In the Vmin text field, type Vlow.
7
Locate the Charge Settings section. From the list, choose C-rate multiple.
8
In the Crate,ch text field, type Crate.
9
In the Vmax text field, type Vhigh.
10
Locate the Start Mode section. From the Start with list, choose Charge first.
Continue by defining the Transport of Diluted Species interface that is used to model the proton, manganese ion, and water transport and reaction in the electrolyte. All fluxes related to electrochemical reactions need to be coupled to the Lithium-Ion Battery interface.
Transport of Diluted Species (tds)
1
In the Model Builder window, under Component 1 (comp1) click Transport of Diluted Species (tds).
2
In the Settings window for Transport of Diluted Species, locate the Transport Mechanisms section.
3
Clear the Convection checkbox.
4
Select the Migration in electric field checkbox.
5
Select the Mass transfer in porous media checkbox.
6
Click to expand the Dependent Variables section. In the Concentrations (mol/m³) table, enter the following settings:
cH
7
Click  Add Concentration.
8
In the Concentrations (mol/m³) table, enter the following settings:
cH
cMn
9
Click  Add Concentration.
10
In the Concentrations (mol/m³) table, enter the following settings:
cH
cMn
cH2O
Species Charges
1
In the Model Builder window, under Component 1 (comp1) > Transport of Diluted Species (tds) click Species Charges.
2
In the Settings window for Species Properties, locate the Charge section.
3
In the zcH text field, type zH.
4
In the zcMn text field, type zMn.
Porous Electrode - LMO
1
In the Physics toolbar, click  Domains and choose Porous Medium.
2
In the Settings window for Porous Medium, type Porous Electrode - LMO in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose LMO.
Fluid 1
1
In the Model Builder window, click Fluid 1.
2
In the Settings window for Fluid, locate the Diffusion section.
3
In the DF,cH text field, type D_H.
4
In the DF,cMn text field, type D_Mn.
5
In the DF,cH2O text field, type D_H2O.
6
From the Effective diffusivity model list, choose Bruggeman model.
7
Locate the Migration in Electric Field section. In the V text field, type phil_ps.
Porous Matrix 1
1
In the Model Builder window, click Porous Matrix 1.
2
In the Settings window for Porous Matrix, locate the Matrix Properties section.
3
From the εp list, choose User defined. In the associated text field, type epsl_pos.
Porous Electrode Coupling 1
1
In the Physics toolbar, click  Domains and choose Porous Electrode Coupling.
2
In the Settings window for Porous Electrode Coupling, locate the Domain Selection section.
3
From the Selection list, choose LMO.
Reaction Coefficients 1
1
In the Model Builder window, click Reaction Coefficients 1.
2
In the Settings window for Reaction Coefficients, locate the Reaction Current Source section.
3
From the iv list, choose Local current source, Porous Electrode Reaction - Solvent Oxidation (liion/pce1/per2).
4
Locate the Stoichiometric Coefficients section. In the νcH text field, type -1.
Porous Medium - Separator
1
In the Physics toolbar, click  Domains and choose Porous Medium.
2
In the Settings window for Porous Medium, type Porous Medium - Separator in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Separator.
Fluid 1
1
In the Model Builder window, click Fluid 1.
2
In the Settings window for Fluid, locate the Diffusion section.
3
In the DF,cH text field, type D_H.
4
In the DF,cMn text field, type D_Mn.
5
In the DF,cH2O text field, type D_H2O.
6
From the Effective diffusivity model list, choose Bruggeman model.
7
Locate the Migration in Electric Field section. In the V text field, type phil_ps.
Porous Matrix 1
1
In the Model Builder window, click Porous Matrix 1.
2
In the Settings window for Porous Matrix, locate the Matrix Properties section.
3
From the εp list, choose User defined. In the associated text field, type epsl_sep.
Electrode Surface Coupling - Lithium Metal
1
In the Physics toolbar, click  Boundaries and choose Electrode Surface Coupling.
2
In the Settings window for Electrode Surface Coupling, type Electrode Surface Coupling - Lithium Metal in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Lithium Metal.
Reaction Coefficients - Manganese deposition
1
In the Model Builder window, expand the Electrode Surface Coupling - Lithium Metal node, then click Reaction Coefficients 1.
2
In the Settings window for Reaction Coefficients, type Reaction Coefficients - Manganese deposition in the Label text field.
3
Locate the Reaction Current Density section. From the iloc list, choose Local current density, Electrode Reaction - Manganese Deposition (liion/es1/er2).
4
Locate the Stoichiometric Coefficients section. In the n text field, type 2.
5
In the νcMn text field, type -1.
Electrode Surface Coupling - Lithium Metal
In the Model Builder window, click Electrode Surface Coupling - Lithium Metal.
Reaction Coefficients - Proton Reduction
1
In the Physics toolbar, click  Attributes and choose Reaction Coefficients.
2
In the Settings window for Reaction Coefficients, type Reaction Coefficients - Proton Reduction in the Label text field.
3
Locate the Reaction Current Density section. From the iloc list, choose Local current density, Electrode Reaction - Proton Reduction (liion/es1/er3).
4
Locate the Stoichiometric Coefficients section. In the νcH text field, type -1.
The last step is to define the chemical reactions in Reaction nodes.
Reactions - LMO
1
In the Physics toolbar, click  Domains and choose Reactions.
2
In the Settings window for Reactions, type Reactions - LMO in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose LMO.
4
Locate the Reaction Rates section. In the RcH text field, type -4*Rproton+2*Rwater.
5
In the RcMn text field, type Rproton.
6
In the RcH2O text field, type 2*Rproton-Rwater.
Reactions - Separator
1
In the Physics toolbar, click  Domains and choose Reactions.
2
In the Settings window for Reactions, type Reactions - Separator in the Label text field.
3
Locate the Domain Selection section. From the Selection list, choose Separator.
4
Locate the Reaction Rates section. In the RcH text field, type 2*Rwater.
5
In the RcH2O text field, type -Rwater.
Add multiple time-dependent study steps to refine the results of the first and last cycle.
Study 1
Step 3: Time Dependent 1
In the Model Builder window, under Study 1 right-click Step 2: Time Dependent and choose Duplicate.
Step 4: Time Dependent 2
In the Model Builder window, right-click Step 3: Time Dependent 1 and choose Duplicate.
Time Dependent - First Cycle
1
In the Settings window for Time Dependent, type Time Dependent - First Cycle in the Label text field.
2
Locate the Study Settings section. From the Time unit list, choose h.
3
In the Output times text field, type 0 7.
Time Dependent - Cycling
1
In the Model Builder window, under Study 1 click Step 3: Time Dependent 1.
2
In the Settings window for Time Dependent, type Time Dependent - Cycling in the Label text field.
3
Locate the Study Settings section. From the Time unit list, choose h.
4
In the Output times text field, type range(0,0.5,300).
Time Dependent - Last Cycle
1
In the Model Builder window, under Study 1 click Step 4: Time Dependent 2.
2
In the Settings window for Time Dependent, type Time Dependent - Last Cycle in the Label text field.
3
Locate the Study Settings section. From the Time unit list, choose h.
4
In the Output times text field, type 0 7.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node, then click Time-Dependent Solver 1.
3
In the Settings window for Time-Dependent Solver, locate the General section.
4
From the Times to store list, choose Steps taken by solver.
5
Right-click Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 and choose Stop Condition.
6
In the Settings window for Stop Condition, locate the Stop Expressions section.
7
Click  Add.
8
In the table, enter the following settings:
Stop expression
Stop if
Active
Description
comp1.cycle_no>0
True (>=1)
√
Stop expression 1
9
Locate the Output at Stop section. Clear the Add information checkbox.
10
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) right-click Time-Dependent Solver 2 and choose Stop Condition.
11
In the Settings window for Stop Condition, locate the Stop Expressions section.
12
Click  Add.
13
In the table, enter the following settings:
Stop expression
Stop if
Active
Description
comp1.cycle_no>48
True (>=1)
√
Stop expression 1
14
Locate the Output at Stop section. Clear the Add information checkbox.
15
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) click Time-Dependent Solver 3.
16
In the Settings window for Time-Dependent Solver, locate the General section.
17
From the Times to store list, choose Steps taken by solver.
18
Right-click Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 3 and choose Stop Condition.
19
In the Settings window for Stop Condition, locate the Stop Expressions section.
20
Click  Add.
21
In the table, enter the following settings:
Stop expression
Stop if
Active
Description
comp1.cycle_no>49
True (>=1)
√
Stop expression 1
22
Locate the Output at Stop section. Clear the Add information checkbox.
23
In the Study toolbar, click  Compute.
Results
Cell Voltage
The following steps produce the plot groups and images in the model documentation.
1
In the Settings window for 1D Plot Group, type Cell Voltage in the Label text field.
2
Locate the Data section. From the Dataset list, choose Study 1/Solution Store 3 (sol4).
3
Click to expand the Title section. From the Title type list, choose None.
4
Locate the Plot Settings section. Select the x-axis label checkbox.
5
Select the y-axis label checkbox. In the associated text field, type Cell voltage (V).
6
Locate the Legend section. Clear the Show legends checkbox.
Global 1
1
In the Model Builder window, expand the Cell Voltage node, then click Global 1.
2
In the Settings window for Global, locate the x-Axis Data section.
3
From the Parameter list, choose Expression.
4
In the Expression text field, type t+t_cycle_first.
5
From the Unit list, choose h.
6
In the Cell Voltage toolbar, click  Plot.
Cell and Average Electrode Cell State of Charge (liion)
1
In the Model Builder window, under Results click Cell and Average Electrode Cell State of Charge (liion).
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 1/Solution Store 3 (sol4).
4
Locate the Plot Settings section. Select the x-axis label checkbox.
Global 1
1
In the Model Builder window, expand the Cell and Average Electrode Cell State of Charge (liion) node, then click Global 1.
2
In the Settings window for Global, locate the x-Axis Data section.
3
From the Parameter list, choose Expression.
4
In the Expression text field, type t+t_cycle_first.
5
From the Unit list, choose h.
Global 2
1
In the Model Builder window, click Global 2.
2
In the Settings window for Global, locate the x-Axis Data section.
3
From the Parameter list, choose Expression.
4
In the Expression text field, type t+t_cycle_first.
5
From the Unit list, choose h.
6
In the Cell and Average Electrode Cell State of Charge (liion) toolbar, click  Plot.
Some of the default plots are redundant for the scope of this example and can be removed.
Concentration, H (tds), Concentration, H2O (tds), Concentration, Mn (tds), Concentrations, All Species (tds), Electrode Potential with Respect to Adjacent Reference (liion), Electrolyte Salt Concentration (liion), Particle Surface State of Charge (liion), Volumetric Current Density (liion)
1
In the Model Builder window, under Results, Ctrl-click to select Electrode Potential with Respect to Adjacent Reference (liion), Electrolyte Salt Concentration (liion), Volumetric Current Density (liion), Particle Surface State of Charge (liion), Concentrations, All Species (tds), Concentration, H (tds), Concentration, Mn (tds), and Concentration, H2O (tds).
2
Right-click and choose Delete.
Cell Capacity
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Cell Capacity in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Solution Store 3 (sol4).
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Plot Settings section. Select the x-axis label checkbox.
6
Locate the Legend section. Clear the Show legends checkbox.
Global 1
1
Right-click Cell Capacity and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Lithium-Ion Battery > liion.Q_cell - Battery cell capacity - C.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
liion.Q_cell
Ah
Battery cell capacity
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
In the Expression text field, type t+t_cycle_first.
6
From the Unit list, choose h.
7
In the Cell Capacity toolbar, click  Plot.
Electrode Volume Fraction
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Electrode Volume Fraction in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Solution Store 3 (sol4).
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Legend section. Clear the Show legends checkbox.
Global 1
1
In the Electrode Volume Fraction toolbar, click  Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
epss_LMO_pos
1
Electrode volume fraction in the positive electrode
4
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1) > Lithium-Ion Battery > Charge-Discharge Cycling - Galvanic Cycling C/3 > liion.cdc1.cycle_counter - Number of cycles.
5
In the Electrode Volume Fraction toolbar, click  Plot.
Diffusion Coefficient in LMO Particles
1
In the Model Builder window, right-click Electrode Volume Fraction and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Diffusion Coefficient in LMO Particles in the Label text field.
3
Locate the Plot Settings section.
4
Select the y-axis label checkbox. In the associated text field, type Diffusion coefficient LMO (m<sup>2</sup>/s).
Global 1
1
In the Model Builder window, expand the Diffusion Coefficient in LMO Particles node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
D_LMO_pos
m^2/s
Diffusion coefficient of lithium within LMO particles in the positive electrode
4
In the Diffusion Coefficient in LMO Particles toolbar, click  Plot.
Discharge Curve Comparison
1
In the Model Builder window, right-click Diffusion Coefficient in LMO Particles and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Discharge Curve Comparison in the Label text field.
3
Locate the Data section. From the Dataset list, choose None.
4
Locate the Plot Settings section.
5
Select the x-axis label checkbox. In the associated text field, type Discharge time (s).
6
In the y-axis label text field, type Cell voltage (V).
7
Locate the Legend section. Select the Show legends checkbox.
Global 1
1
In the Model Builder window, expand the Discharge Curve Comparison node, then click Global 1.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 1/Solution Store 2 (sol3).
4
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Lithium-Ion Battery > Charge-Discharge Cycling - Galvanic Cycling C/3 > liion.cdc1.phis0 - Cell potential - V.
5
Locate the x-Axis Data section. In the Expression text field, type t_cycle_dch_first.
6
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
7
Click to expand the Legends section. From the Legends list, choose Manual.
8
In the table, enter the following settings:
Legends
1st cycle
Filter 1
1
Right-click Global 1 and choose Filter.
2
In the Settings window for Filter, locate the Line Segment Selection section.
3
Clear the Decreasing x checkbox.
4
Clear the Increasing y checkbox.
Global 2
1
Right-click Global 1 and choose Duplicate.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (sol1).
4
Locate the x-Axis Data section. In the Expression text field, type t_cycle_dch_last.
5
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Solid.
6
Locate the Legends section. In the table, enter the following settings:
Legends
50th cycle
7
In the Discharge Curve Comparison toolbar, click  Plot.
Capacity vs. Cycle Number
1
In the Model Builder window, right-click Diffusion Coefficient in LMO Particles and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Capacity vs. Cycle Number in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Relative capacity (-).
4
Locate the Legend section. Select the Show legends checkbox.
5
From the Position list, choose Lower left.
Global 1
1
In the Model Builder window, expand the Capacity vs. Cycle Number node, then click Global 1.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Lithium-Ion Battery > liion.SOH_cell - Cell state of health - 1.
3
Locate the Legends section. From the Legends list, choose Manual.
4
In the table, enter the following settings:
Legends
Based on cyclable lithium and host capacity
Global 2
1
Right-click Results > Capacity vs. Cycle Number > Global 1 and choose Duplicate.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
(t-liion.cdc1.t_dch_start)/t_cycle_first
1
 
4
Locate the Legends section. In the table, enter the following settings:
Legends
Nominal C/3 discharge capacity
Filter 1
1
Right-click Global 2 and choose Filter.
2
In the Settings window for Filter, locate the Line Segment Selection section.
3
Clear the Decreasing x checkbox.
4
In the Capacity vs. Cycle Number toolbar, click  Plot.
Electrolyte Salt Concentration in Battery
1
In the Model Builder window, right-click Diffusion Coefficient in LMO Particles and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Electrolyte Salt Concentration in Battery in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Electrolyte salt concentration (mol/m<sup>2</sup>).
Global 1
1
In the Model Builder window, expand the Electrolyte Salt Concentration in Battery node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
cl_battery
mol/m^3
Net lithium ion concentration in battery
4
In the Electrolyte Salt Concentration in Battery toolbar, click  Plot.