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Electrochemistry Cell Model

Dennis Dees and Kevin Gallagher Chemical Sciences and Engineering Division

May 9-13, 2011

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 . ~43% Complete that meets or exceeds all performance goals – Interpreting complex cell electrochemical phenomena – Identification of cell degradation mechanisms Budget Partners (Collaborators) . Total project funding . Daniel Abraham, Argonne – 100% DOE . Sun-Ho Kang, Argonne . FY2010: $400K . Andrew Jansen, Argonne . FY2011: $400K . 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- battery technologies for PHEV applications – Link experimental efforts through electrochemical modeling studies – Identify performance limitations and aging mechanisms . Milestones for this year: – Initiate development of AC impedance two phase model (completed) – Integrate SEI growth model into full cell model (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

. Adopted new differential equation solver software (PSE gPROMS) to address several long term issues limiting model advancement – Integrating complex dynamic interfaces into full cell Li-ion models to examine factors limiting performance and life – Streamlining parameter estimation for new cell chemistries – Implementing the AC impedance version of model with increasingly more intricate interfacial and bulk active particle phenomena . Implemented SEI growth model on the negative to analyze capacity fade mechanisms including cross-interactions with positive electrode . Developed 3D electrochemical model to examine primary-secondary active particle microstructure and properties affecting impedance (e.g. porosity, surface area, electronic conductivity, electronic contacts, and wetting) . Utilized electrochemical model to further examine electrode thickness limitations 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 – 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 and possible phase change in active particles included, along with multiple particle fractions . The system of coupled 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 Increasingly Complex Model Comprised of Dynamic Coupled One-Dimensional Multi-Scale Subsystems

Transport through Cell Sandwich Bulk Solid-State Phase ∂c ε ∂  ∂c  1 [()()11 −−∂ o itVc ] Transition & Diffusion ε =  D  + e + 2   ∂ τ ∂xt  ∂  ν ++ Fzx ∂x ( ++∂ εεε ccc SSSSSS 332211 ) ∂ ε SS 11 ∂cD ε SSS 221 ∂cD ε SSS 332 ∂cD S 3 =  + +  o ∂t ∂y τ ∂y τ ∂y τ ∂y κε Φ∂ κε  s t  ∂ ln f  1 ∂c  S1 S 2 S 3  −= 2 −ν  + + +  + ± i2 RT  1  τ ∂x F n z νντ  ∂ ln  cc ∂x ∂ε  + ++  S 2 −+−= KKKK εεεε ∂t 112 221 332 SSSSSSSS 223 ∂i2 Φ∂ 1 = Fz+ ja i1 −= σ eff ∂ε ∑ k kn += iiI 21 S 3 ∂x k ∂x −= KK εε ∂t 223 SSSS 332 . Adopted new differential algebraic equation solver package (PSE gPROMS®) that will solve a wide variety Bulk Solid-State of cell studies at the required level of complexity Diffusion ∂cSb ∂  ∂cSb  =  DSb  Negative SEI Reaction/Transport ∂ ∂zt  ∂z  2  Φ∂ ∂  ∂c f y ∂L ∂c ff D f ∂ c f ++ Fvz ,2 f c f − = i ,2 f =− ()− uzuz −−++ Fc f ()−+ DD −+  2 2 L ∂Y ∂Y ∂t L ∂t ∂Y ()L ∂Y f   f f Positive SEI Reaction/Transport ∂ i ,2 f dL f − j n2 = jzFi 2 = v == n ∑ ,ini   i δ fn RTs c+ electrolyte 0 f ∂c+ ∂ c+ + dt c = D   η f += ln ∂y SEI ∂ +  ∂ 2  κ t  y  f nF c+ active material

α F ()11 Φ−Φ f α F ()11 Φ−Φ− f α F ()Φ−Φ α F ()Φ−Φ− 2    12 f 12 f  ∂c  ∂ c  0 RT RT 0  RT RT  Si  Si  n = 11  ,ks eckj − +,1 ()− ,ksTf ecccK  = eckj − eK = DSi   n 22  f 2  ∂  ∂ 2      t  y  α α α α F ()Φ−Φ α F ()Φ−Φ− A A C  Fηα   Fηα   1 f 2 1 f 2   KA − KC  0    c   − cc   c        RT RT α2F ( f −Φ−Φ− U 22 )  +   Ti Si   Si   RT   RT  =  + eckj − K ce  = ii  − ee  n 11 , f 1 0 n 0         RT c+ − cc c     n −= 22 +− ,, ff ecckj  ,ref   Ti Si,ref   Si,ref   

Vehicle Technologies Program = ση z+ FjnPR 6 Advantages & Current Status of Software Implementation . Previously treated coupled multi-scale problems using a multi-dimensional solver . New approach explicitly treats each length scale to allow for greater stability and increased dynamic complexity . Successfully recreated past DC modeling work with increased complexity capable of examining short time scales – Dynamic multi-layered interfaces on particles in porous electrode – Figures for a 15C/11.25C HPPC test with current relaxation at end

1.3 31 1.2

1.1 30 1.0

0.9

0.8 29

0.7 Electrolyte in pore

(mol/L) concentration +

Li 0.6

Lithium concentration (mol/L) concentration Lithium 28

0.50.0 0.0 Distance to0.2 surface (z/ Electrolyte film Distance 0.2to surface (z/ 60 0.4 60 0.4 40 0.6 Particle surface 40 0.6

20 0.8 Time (s) 20 δ 0.8 film Time (s) ) 0 δ 1.0 surf 0 Vehicle Technologies Program Bulk particle (NCA) ) 1.0 7 SEI Growth Model Implementation . Implementing SEI growth model necessary to understand power and energy fade of future cell builds . Differing negative electrode aging behavior from Gen 2 to Gen 3 – Graphite changed from MAG10 to MCMB – Positive electrode changed from NCA to NCM – Gen 2 negative impedance stabilized; Gen 3 continuously increased

+ - - 2- 2- 2- Li PF6 EC SRP F ,O ,C2O4 ,CO3 Li+ insertion into Electrolyte in equilibrium Li+ interc. solid electrolyte. with outer layer w/ e- tx

LixC6 Inner layer: Outer layer: Electrolyte Disordered solvent reduction products e- into graphite inorganic solids swollen w/ electrolyte conduction band 2-50 nm 5-100 nm Vehicle Technologies Program 8 SEI Growth Model Status . Single phase SEI growth model completed for single particle and implemented in porous electrode – Coupled Li interstitial and transport through insulating film1 . Parameter estimation in progress for film transport properties

0.40 0.1 6.0 -11 DLi 5x10

) 0.35 U c & c

-11 + LixC6 Li e- 5.5 D 2x10 Li U -11 0.30 LixC6 / film D 1x10 0.01 5.0 Li U -12 film / sol'n D 5x10 0.25 4.5 Li -12 DLi 2x10 0.20 4.0 -12 1E-3

D 1x10 Li 0.15 3.5

3.0 0.10

SEI Thickness (nm) 1E-4 2.5 0.05

0.00 Charge carriers in film (mol/L) 2.0 Equilibrium potential (V vs Li/Li

1.5 -0.05 1E-5 0 200 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 1.0

Time (min) xLi in LixC6

1. J. Christensen and J. Newman, J. Electrochem. Soc. 151 (11) A1977 (2004) Vehicle Technologies Program 9 Primary-Secondary Positive Active Particle Microstructure

45

. Electron microscopy images of many positive active 40 Experimental 1 mHz

2 3 Particle materials indicate the secondary particles have 35

1 Particle some degree of porosity 30

1 Particle & . NCA positive electrode low frequency Warburg EIS 25 0.5*Dsb data could only be fit using multiple active material 20 particle fractions 15

-Z" (Imaginary) -cm (Imaginary) -Z" 10 . Characteristic diffusion lengths from EIS studies 10 mHz 5 100 mHz indicate electrochemical reactions penetrate 0 secondary oxide particles 0 5 10 15 20 25 30 35 40 45 Z' (Real) ohm-cm2

. TEM images of aged BF NCA particles show films on the surface Surface Film

of the secondary Oxide particles and in TEM pores between Oxide primary particles 50 nm Vehicle Technologies Program 200 nm DF 10 3D Electrochemical Model Developed for Positive Active Material Spherical Secondary Particle Ionic Current Distribution in Secondary Particle . Electrochemical model with simplified Electronic SEI relation applied to Particle Contacts particle scale . Secondary particle assumed to be made Model Outer of primary particles Perimeter with independent core and outer layer characteristics Bulk . Particle porosity Electrolyte allows access of Particle Outer electrolyte and ionic Core Layer current to reach into the particle core

Vehicle Technologies Program 11 Particle Properties Established and Impedance Terms Defined to Assess Particle Performance Estimated Change in Particle Characteristics . Wealth of diagnostic studies and 5 3.0 associated model development for NCA

4 2.5 3 /g

active material with Gen 2 electrolyte 2

utilized to create baseline parameter 3 2.0 Surface Area set and particle characteristics Tap density 2 1.5 . Simple relations developed for active Surface Area, m Area, Surface Tap g/cm Density, material surface area and tap density 1 1.0

with changes in particle porosity 0 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Particle Impedance, 10s Discharge Pulse Particle Porosity 380 0.100

Area Specific Impedance (ASI) . Two specific impedance terms are used to 360 0.095

2 Specific Impedance (MSI) describe particle performance: area (ASI), 340 0.090 based on particle active area (i.e. not the

320 0.085 electrode area), and particle mass (MSI) MSI, ohm g ASI, ohm cm ASI,

300 0.080 . When the ratio of active area to mass is fixed then both impedance effects behave 280 0.075 0 100 200 300 400 similarly, as is the case for the change in Applied Overvoltage, mV particle impedance with applied Vehicle Technologies Program 12 Impact of Electronic Conductivity on Particle

Performance Particle Impedance, 10s Discharge Pulse . At effective electronic conductivities 1000 0.300 Area Specific Impedance -5 -1 -1 less than about 10 Ω cm the 800 Mass Specific Impedance 0.250 particle impedance is a strong function 2 of conductivity 600 0.200 The impedance is governed by other 400 0.150 . MSI, ohm g ASI, ohm cm ASI,

phenomena at greater conductivities 200 0.100 Particle Impedance, 10s Discharge Pulse 0.5 micron Contact Diameter 10000 0 0.050 -1 -1 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 Effective Electronic Conductivity, ohm cm -1 -1 1.E-04 Effective Electronic Conductivity, ohm cm 1.E-05 1.E-06 2 . The particle impedance is relatively

1000 independent of the number of contacts

ASI, ohm cm ASI, for effective electronic conductivities greater than 10-4 Ω-1 cm-1 . Varying the diameter of the particle

100 0 10 20 30 40 50 60 70 80 contacts can have a similar impact on Number of Contact Points impedance Vehicle Technologies Program 13 Electrolyte Soaking into Particle Significantly

Improves Performance Particle Performance, 10s Discharge Pulse . It is much easier for Li ions to 700 100 Area Specific Impedance (ASI) diffuse through the liquid Outer Layer/Core Reaction electrolyte than the the solid– 600 2

state oxide active material by a 500 4 factor of about 10 10 . Therefore, even a small amount 400 of electrolyte in the oxide particle ohm cm ASI, 300 pores can enhance the overall Reaction layer/Core Outer electrochemical reaction in the 200 1 core of the particle and reduce its 0.0001 0.001 0.01 0.1 impedance Bulk Particle Electrolyte Wetted Volume Fraction . The impedance levels out at higher volume fractions because the electrochemical reaction in the core is not limited by Li ion transport in the electrolyte . At lower volume fractions the amount of electrochemical reaction in the core goes to zero and the impedance is governed by the reaction in the outer layer Vehicle Technologies Program 14 Impact of Particle Porosity on Particle Performance

Particle Impedance, 10s Discharge Pulse . As the particle 1600 0.160 Area Specific porosity increases, its 1400 Impedance (ASI) 0.140 active surface area 1200 Mass Specific 0.120

rises dramatically 2 Impedance (MSI) reducing the particle 1000 0.100

impedance on a 800 0.080 gravimetric basis

600 0.060 MSI, ohm g . For a fixed applied ohm cm ASI, polarization, the 400 0.040 particle impedance on 200 0.020

an active area basis 0 0.000 rises significantly with 0.0 0.1 0.2 0.3 0.4 0.5 0.6 increasing porosity Particle Porosity . As the porosity increases, there is less active material available for the lithium to diffuse into, resulting in increasingly higher concentration polarization and ASI Vehicle Technologies Program 15 Electrochemical Model Utilized to Examine Electrode Thickness Limitations

Discharge Capacity for NCA/Graphite Cell . The cell discharge capacity effectively 10

reaches a limiting capacity with 2 3- Discharge Capacity increasing electrode thickness 8 1-Hour Discharge Capacity

. During discharge, salt concentration 6 in positive approaches zero

Salt Concentration Distribution 4 NCA/Graphite Cell at End-of-Discharge 245 micron 2.5 2 Discharge Capacity, mAh/cm Capacity, Discharge

2.0 0 1C Discharge 0 50 100 150 200 250 300 350 C/3 Discharge 1.5 Electrode Thickness, microns

Negative avg

c/c . Lowering the discharge current 1.0 allows a greater fraction of the Positive 0.5 electrode capacity to be utilized . As electrode thickness increases 0.0 0 100 200 300 400 500 transport of salt in electrolyte limits Cell Coordinate, microns Vehicle Technologies Program constant C-rate discharge capacity 16 Increasing Electrode Thickness Affects the Current Distribution in Electrodes Current Distribution in Positive Electrode . Because of a relatively large 1C Discharge of NCA/Graphite Cell One Hour into Discharge interfacial impedance, thinner 2.0 electrodes (i.e. ~≤ 150 µm for 1C 245 micron Positive discharge) have a relatively uniform 35 micron Positive 1.5 current distribution Current Collector Current

Current Distribution in Positive Electrode avg 1C Discharge of NCA/Graphite Cell 1.0

245 micron Electrodes jn/jn 2.0 10 min into Discharge 0.5 1 hour into Discharge Separator 1.5

0.0 0.0 0.2 0.4 0.6 0.8 1.0 avg 1.0 Cell Coordinate, microns Current Collector Current jn/jn Separator . Electrolyte transport limitations in 0.5 thick electrodes shifts the current towards the separator that changes 0.0 0.0 0.2 0.4 0.6 0.8 1.0 continuously during discharge Cell Coordinate, microns Vehicle Technologies Program 17 Electrode Impedance Relatively Constant Over a Wide Thickness Range

10 s 5C Discharge Pulse ASI . Impedance of thin electrodes NCA/Graphite Cell at 60%SOC increase as the active area decreases 50 . Thick electrode cell impedance 40 Full Cell

increases result from electrolyte 2 Positive Electrode Negative Electrode transport limitations 30

5C Charge Pulse , ohm cm

NCA/Graphite Cell at 60%SOC 10s 20 0.1 ASI

10 0.0

, 0 -0.1 0 100 200 300 400 500 Lithium Electrode Thickness, microns 1s Pulse Time

vs. V vs. -0.2 10s Pulse Time . Primary performance limitation for

Negative -0.3 thick electrodes is that thicker V graphite negatives can dip below the -0.4 0 50 100 150 200 250 300 350 lithium deposition voltage during Electrode Thickness, microns Vehicle Technologies Program regen charging pulses 18 Future Plans . Advance development of PHEV focused electrochemical models using new differential algebraic equation solver package (PSE gPROMS) – Continue conversion of existing models – Develop full numerical AC impedance version – Utilize parameter fitting routines in new software to examine advanced PHEV couples . Continue development electrochemical models directed towards examining capacity fade phenomena – Implement cation accelerated growth of SEI (e.g. Mn2+, Li+, etc) – Implement dual layer SEI growth – Address cycle and calendar aging tests (large time scales) . Continue support of other ABR projects . Milestones for next year – Complete conversion of existing models – Complete implementation and initial testing of full SEI growth model – Initiate parameter estimation of high-energy NMC/graphite system Vehicle Technologies Program 19 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 – Adopted new differential equation solver software – Implemented SEI growth model on the negative electrode to analyze capacity fade mechanisms – Developed 3D electrochemical model to examine primary- secondary active particle microstructure – Utilized electrochemical model to further examine electrode thickness limitations . Future plans include the continued development of PHEV focused electrochemical models, further development of models examining capacity fade phenomena, and support of other ABR projects

Vehicle Technologies Program 20 Acknowledgment

Support for this work from DOE-EERE, Office of Vehicle Technologies is gratefully acknowledged - David Howell - Peter Faguy

Vehicle Technologies Program 21