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Electrochemistry Cell Model 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-ion 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 electrode 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 electrolyte 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 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 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 Electrochemical Cell Model Comprised of Dynamic Coupled One-Dimensional Multi-Scale Subsystems Transport through Cell Sandwich Bulk Solid-State Phase ∂c ε ∂ ∂c 1 ∂[()1 −cV() 1 − to i ] Transition & Diffusion ε = D + e + 2 ∂tτ ∂ x ∂x z+ν + F ∂x ∂(εSSSSSS1c 1 + ε 2 c 2 + ε 3 c 3 ) ∂ ε SS1D 1 ∂ cSSS1ε 2D 2 ∂ cSSS2ε 3D 3 ∂ cS 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 Fτn νz ν ∂ ln c c ∂x ∂ε + + + S 2 =KKKKε − ε + ε − ε ∂t SSSSSSSS12 1 21 2 32 3 23 2 ∂i2 ∂Φ1 = Fz+ a j i1 = −σ eff ∂ε ∑ k kn I= i1 + i 2 S 3 ∂x k ∂x =KKε − ε ∂t SSSS23 2 32 3 . 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 ∂t∂ z ∂z 2 ∂Φ ∂ ∂c f y ∂L f∂c f D f ∂ c f z+ v + F 2, f c f − = −i2, f = ()z+ u +− z − u − Fc f +()DD+ − − 2 2 L ∂Y ∂Y ∂t L ∂t ∂Y ()L ∂Y f f f Positive SEI Reaction/Transport ∂ i2, f dL f − j n2 i= F z j 2 = =v = n ∑ i n, i inδ f RTs c+ electrolyte 0 f ∂c+ ∂ c+ + dt c = D η f = + ln ∂y SEI ∂ + ∂ 2 κ t y f nF c+ active material α1F ()Φ 1 −Φ f −α1F () Φ 1 −Φ f α F ()Φ −Φ −α F () Φ −Φ 2 2 1 f 2 1 f ∂c ∂ c 0 RT RT 0 RT RT Si Si jn1= k 1 cs, k e − K1 c+ , f() c T− c s, k e j= k c e − K e = DSi n2 2 f 2 ∂ ∂ 2 t y α α α α F ()Φ −Φ −α F () Φ −Φ A A C αF η αF η 1 f 2 1 f 2 AK − CK 0 c c− c c RT RT −α2F ( Φf −Φ2 −U 2 ) + Ti Si Si RT RT j= k c+ e − K ce i= i e− e n1 1 , f 1 0 n 0 RT c+ c− c c jn2= − k 2 c−,,f c + f e ,ref Ti Si,ref Si,ref Vehicle Technologies Program ηR= σ Pz+ Fj n 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 concentration (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 electron 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) ohm-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 .
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