Electrochemistry Cell Model
Presented by Dennis Dees Chemical Sciences and Engineering Division
June 7-11, 2010
Vehicle Technologies Program Annual Merit Review and Peer Evaluation Meeting Washington, D.C. Project ID: ES031 This presentation does not contain any proprietary, confidential, or otherwise restricted information. Overview
Timeline Barriers . Start: October 2008 . Development of a safe cost-effective PHEV . Finish: September 2014 battery with a 40 mile all electric range . ~25% Complete that meets or exceeds all performance goals – Interpreting complex cell electrochemical phenomena – Identification of cell degradation mechanisms Budget Partners (Collaborators) . Total project funding . Kevin Gallagher, Argonne – 100% DOE . Daniel Abraham, Argonne . FY2009: $400K . Sun-Ho Kang, Argonne . FY2010: $400K . Andrew Jansen, Argonne . Wenquan Lu, Argonne . Kevin Gering, INL
Vehicle Technologies Program 2 Objectives, Milestones, and Approach . The objective of this work is to correlate analytical diagnostic results with the electrochemical performance of advanced lithium-ion battery technologies for PHEV applications – Link experimental efforts through electrochemical modeling studies – Identify performance limitations and aging mechanisms . Milestones for this year: – Complete development of two phase active material model (completed) – Initiate development of capacity loss model (completed) – Complete development of an efficient parameter fitting method (mostly completed) . Approach for electrochemical modeling activities is to build on earlier successful characterization and modeling studies in extending efforts to new PHEV technologies – Expand and improve data base and modeling capabilities
Vehicle Technologies Program 3 Major Accomplishments and Technical Progress
. Further development and evaluation of phase transition lithium diffusion transport
model for two phase electrode active materials (e.g. LiC6, LiFePO4, LiMn2O4, Li4Ti5O12) – Model simulations indicate the coexistence of three phases (i.e. Stage 1, Stage 2, and Stage 3) in graphitic negative electrode (MCMB, Gen 3) during normal cell operation – Model was modified to account for coexistence of three phases and changes were integrated into full cell model – Initiated study of second graphite negative electrode (Mag 10, PHEV baseline) . Initiated development of capacity loss degradation model – Conducted literature review and considered possible phenomena – SEI model developed to examine growth mechanisms . Supported other development efforts in program – Integrated improved electrode impedance and limiting current estimates into Paul Nelson’s Battery Design Model – Developed spherical geometry four probe conductivity model for single particle conductivity measurements – Initiated modeling studies on binder-carbon-free electrodes to examine primary- secondary active particle microstructure and interactions
Vehicle Technologies Program 4 Description of Electrochemical Model . Phenomenological model developed for AC impedance and DC studies using same constituent equations and parameters . Combines thermodynamic, kinetic, and interfacial effects with continuum based transport equations . Complex active material / electrolyte interfacial structure – Film on active particles acts as an electrolyte layer with restricted diffusion and migration of lithium ions – Surface layer of active particle inhibits the diffusion of lithium into the bulk active material – Electrochemical reaction and double layer capacitance at film/layer interface – Particle contact resistance and film capacitance . Volume averaged transport equations account for the composite electrode geometry . Lithium diffusion in active particles and multiple particle fractions . The system of partial differential equations are solved numerically . Model parameters determined independently (e.g. electrolyte parameters are supplied by Kevin Gering’s Advanced Electrolyte Model) Vehicle Technologies Program 5 Electrochemical Model Effectively Used to Examine Interfacial and Diffusional Phenomena in Intercalation 45 Positive Electrode Active Materials 40 2 35 Experimental 30 Theory
25
20
15
Lithium-Ion Electrochemical Model ohm-cm (Imaginary) -Z" 10 5 o ∂c ε ∂ ∂c 1 ∂[(1 − cVe )(1 − t + )i2 ] 0 ε = D + AC 0 5 10 15 20 25 30 35 40 45 ∂t τ ∂x ∂x z+ν + F ∂x Z' (Real) ohm-cm2 Model -9 o κε ∂Φ κε s t ∂ ln f 1 ∂c DC model = − 2 −ν + + + + ± i2 RT 1 AC model τ ∂x Fτ nν + z+ν + ∂ ln c c ∂x -10 /s 2 ∂i2 ∂Φ1 = i = −σ ), cm -11 Fz+ ∑ ak jkn I = i + i 1 eff s 1 2 D ∂x k ∂x log( 2 i δ c+ ∂c+ ∂ c+ n f RTs+ electrolyte -12 = D η f = + ln ∂ + ∂ 2 κ t y f nF c+ active material 2 -13 ∂cSi ∂ cSi ∂ ∂ ∂ = cSb cSb 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 DSi 2 = D DC ∂t ∂y ∂t ∂z Sb ∂z Positive elctrode potential, V vs. Li Model 60 α A α A αC α AFηK αC FηK 40 − − c+ cTi cSi cSi RT RT i = i e − e 20 n 0 c c − c c +,ref Ti Si,ref Si,ref , mV 0 initial -20 ηR = σ P z+ Fjn - V -40 3.1C Experimental positive V -60 3.1C Theory 5.0C Experimental -80 . Diffusion coefficient obtained from GITT studies using DC 5.0C Theory -100 0 10 20 30 40 50 60 70 model shows strong correlation with AC modeling studies Time, seconds
Vehicle Technologies Program 6 Parallel Development for Graphitic Negative Electrode was not Near as Productive HPPC Studies
20 150 Experimental
EIS Studies 100 Theoretical 2 15 . Initially, no correlation was Experimental , mV 50 Theoretical initial 10 obtained between AC and DC - V models using established 0 Negative
-Z"(Imaginary) ohm cm -Z"(Imaginary) 5 V electrochemical intercalation -50
0 0 5 10 15 20 electrode model. -100 2 Z'(Real) ohm cm 0 10 20 30 40 50 60 70 Time, seconds . Correlation between AC and DC models HPPC Studies 150 obtained through empirically based model and Experimental parameter modifications 100 Theoretical Theoretical, Adjusted , mV Parameters 50
. Analysis indicated that potential effects initial - V associated with diffusion of lithium in the 0 Negative V
graphite was not being accurately described -50 (i.e. treating the lithium diffusion in graphite as -100 0 10 20 30 40 50 60 70 a single phase process was not adequate) Time, seconds
Vehicle Technologies Program 7 Electrochemical Model Development Darker Blue Shade Indicates More Mature Effort
Examine Full Cell Develop Model Integrate Phase Integrated Phase for Phase Change Change Model Into Change Model Active Materials Full Cell DC Model
Full Cell AC and DC Models with Intercalation Develop General Single Phase Active Electrode Materials and Full Cell AC and DC Complex SEI Microstructure Models
Develop SEI Model Integrate SEI Examine Full Cell To Account for Model Into Integrated SEI Degradation Full Cell DC Model Mechanisms Model
Vehicle Technologies Program 8 Galvanic Intermittent Titration Technique (GITT) Studies on Graphite Negative Electrode Used to Examine Phase Transition and Lithium Diffusion 0.40 Room Temperature GITT Experiments Gen 3 Graphite Negative Electrode (0.2 mA/cm2 for 10 min) 0.30 35 OCV (~C/180) vs Li
30 0.20
25
0.10 20 Negative Electrode Voltage, V Voltage, Negative Electrode
15 0.00 Two Phase Region 0 0.2 0.4 0.6 0.8 1 10 X in LixC6 Single Phase Region
5 Electrode Voltage Change, mV Change, Voltage Electrode
0 -50 0 50 100 150 200 250 Time, minutes . Staged lithium intercalation into graphite well established in literature with open circuit voltage (OCV) curve showing single and two phase regions . Polarization diffusional potential rise similar in both single and two phase regions despite significant differences in slope of OCV curve . Very slow relaxation of potential apparent in two phase region Vehicle Technologies Program 9 Phase Growth Model Based on Avrami Equation Adopted after Alternative Phase Transition Models Examined Active Material Particle LiC12 / LiC32 Two Phase Region Room Temperature GITT Experiment (0.2 mA/cm2 for 10 min)
Cross-Section 0.165
Active Material 0.160 Surface 0.155 Experiment 0.150 Theory
C 0.145 Li Li+ 0.140 Second Phase 0.135 0.130
Growth Following volts Voltage, Electrode 0.125
Avrami Equation 0.120 n 2200 2250 2300 2350 2400 2450 2500 −(kt ) Time, minute ε S 2 =1− e . Lithium diffusion in both phases of active material and equilibrium at interfaces – Volume averaged transport equations . Well known Avrami phase growth equation with a lithium concentration dependent rate constant is used to describe the phase transition . Avrami, equilibrium, and diffusion equations integrated into full electrochemical cell model Vehicle Technologies Program 10 Phase Growth Model Modified to Allow for Coexistence of Three Phases and Changes Integrated into Full Cell
Electrochemical Model Li Concentration Distribution in Graphite Particle Gen 3 Graphite Negative Electrode OCV (~C/180) vs Li 1000s into C/1 Discharge 0.40 1.0
Stable Single Phase Regions 0.8 Stage 3 0.30 Shown in Color Stage 2 Particle
Stage 1 Surface Stage 0.6
1 for Stage
0.20 6 C
Stage x 0.4 2 x in Li 0.10 Stage 0.2 Negative Electrode Voltage, V Voltage, Negative Electrode 3
0.0 0.00 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 X in LixC6 Dimensionless Particle Coordinate . OCV curve used to establish stable single phase regions. For simplicity, Stages greater than Stage 2 treated as Stage 3. . As the cell is discharged, the lithium concentration in each phase drops . When the lithium concentrations in each phase falls below its stability limit the lower concentration phase begins to form following the Avrami equation . Early modeling studies with two phase model on the graphite negative electrode indicated that the lithium concentration in both phases could drop below their stability limit Vehicle Technologies Program 11 Impact of Slow Phase Transition Rate Constant on Stage Formation During Discharge: Simulation of Graphite Negative Active Material Graphite Particle during C/50 Discharge Graphite Particle during C/20 Discharge Graphite Particle during C/10 Discharge 1.0 1.0 1.0
0.8 0.8 0.8
0.6 0.6 0.6
Stage 1 Stage 1 Stage 1 Stage 2 0.4 0.4 Stage 2 0.4 Stage 2 Stage 3 Stage 3 Stage 3 Volume Fraction of Stage of Volume Fraction Volume Fraction of Stage of Volume Fraction
0.2 Stage of Volume Fraction 0.2 0.2
0.0 0.0 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 x in LixC6 x in LixC6 x in LixC6 Graphite Particle during C/5 Discharge Graphite Particle during C/1 Discharge 1.0 1.0
0.8 0.8
0.6 0.6
Stage 1 Stage 1 0.4 Stage 2 0.4 Stage 2 Stage 3 Stage 3 Volume Fraction of Stage of Volume Fraction Volume Fraction of Stage of Volume Fraction 0.2 0.2
0.0 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 x in LixC6 x in LixC6 . Coexistence of all three stages indicates that equilibrium is not attained even at a C/50 rate . Three phase width increases with discharge rate and Stage 2 maximum decreases
Vehicle Technologies Program 12 Negative Electrode Current and Phase Distributions Relatively Uniform During a C/1 Discharge
Negative Electrode Phase Change Negative Electrode Current Distribution During C/1 Discharge 2000s into C/1 Discharge 1.0 1.10 Stage 3 Stage 2 0.8 Stage 1 1.05 2000s into Discharge 0.6 Current Collector average
) 1.00 n
0.4 /(j n j
0.95 Separator 0.2 Volume Fraction of Stage of Volume Fraction
0.0 0.90 1.0 0.8 0.6 0.4 0.2 0.0 0 5 10 15 20 25 30 35 x in LixC6 Cell Coordinate, microns Li Concentration Distribution in Graphite Particle Stage Distribution in Graphite Particle from Indicated Side of Negative Electrode: from Indicated Side of Negative Electrode: 2000s into C/1 Discharge 2000s into C/1 Discharge 1.0 1.0 Current Collector Separator 0.8 0.8 Stage 3 Stage 3 Current Stage 2 Stage 2 Separator Collector Stage 1 Stage 1 0.6 Stage 3 Stage 3 0.6 for Stage 6 Particle Stage 2 Stage 2 Surface C x 0.4 Stage 1 Stage 1 0.4 Particle Surface x in Li 0.2 0.2 Volume Fraction of Stage of Volume Fraction
0.0 0 0.2 0.4 0.6 0.8 1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless Particle Coordinate Vehicle Technologies Program Dimensionless Particle Coordinate 13 Graphite Negative Electrode Phase Transition Diffusion Model Accounts for Observed Hysteresis Mag-10 Graphite (Gen 2) Electrode vs Li MCMB Graphite (Gen 3) Electrode Room Temperature C/50 Discharge with 0.5h Interrupts 0.20 0.20
0.15
0.10 0.15 C/180 Discharge
C/50 Half Cell Cycle Simulation 0.05 Negative Electrode Voltage, volts Voltage, Negative Electrode
0.10 0.00 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Capacity, mah/cm2 . Slow cycling hysteresis 0.05 may be useful technique
Negative Electrode Voltage, volts Voltage, Negative Electrode to estimate phase 0.00 transition rate constant 0 0.2 0.4 0.6 0.8 1 1.2 x in LixC6 . Faster lithium diffusion allows for high lithium transport rates (i.e. electrode able to support high currents) . The slow phase transition rate constant accounts for the electrode’s apparent sluggishness to reach equilibrium
Vehicle Technologies Program 14 Future Plans
. Advance development of electrochemical model for two phase active materials focusing on impedance effects – Develop AC impedance two phase model and integrate SEI model – Continue examination of baseline PHEV negative electrode . Continue development of PHEV focused electrochemical models – Advance SEI growth model to examine capacity loss degradation mechanisms – Alternative materials, higher electrode loadings, and different testing protocols . Continue support of other ABR projects . Milestones for next year – Initiate development of AC impedance two phase model – Integrate SEI growth model into full cell model
Vehicle Technologies Program 15 Summary . The objective of this work is to correlate analytical diagnostic results with the electrochemical performance of advanced lithium-ion battery technologies for PHEV applications . Approach for electrochemical modeling activities is to build on earlier successful characterization and modeling studies in extending efforts to new PHEV technologies . Technical Accomplishments – Further development and evaluation of phase transition lithium diffusion transport model for two phase electrode active materials – Initiated development of capacity loss degradation model – Supported other development efforts in program . Future plans include development of a full cell AC impedance two phase active material model and advance an SEI growth model to examine capacity loss degradation mechanisms, as well as continued support of other ABR projects
Vehicle Technologies Program 16 Acknowledgment
Support for this work from DOE-EERE, Office of Vehicle Technologies is gratefully acknowledged - David Howell
Vehicle Technologies Program 17