Modelling of the Mass Transport Modelling of the Mass Transport Phenomena in LiPhenomena in Li--ion Battery ion Battery ElectrolytesElectrolytes

Andreas Nyman, Mårten Behm and Göran LindberghApplied Electrochemistry School of Chemical Science and Engineering Royal Institute of Technology, KTHStockholm, Sweden

Presented at the COMSOL Conference 2008 Hannover

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LithiumLithium--Ion BatteriesIon Batteries

Two types of commercial batteries:• Conventional lithium-ion batteries, commercialised 1991 (80% of the

market)

• Lithium-ion polymer batteries, commercialised around 1996 (20% of the market)

Introduction - Experimental Methods - Results - Conclusions

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The LithiumThe Lithium--Ion BatteryIon Battery

vLi+ ≈250 nm/s

Introduction - Experimental Methods - Results - Conclusions

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ElectrolyteElectrolyte

• LiPF6 dissolved in ethylene carbonate (EC), propylene carbonate (PC) and poly(vinylidene fluoride-co-hexafluoropropylene) (PVdF-HFP)

EC:PC (6:4)Random P(VdF-HFP)

Introduction - Experimental Methods - Results - Conclusions

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ModelModel

Introduction - Experimental Methods - Results - Conclusions

iF = F NLi+

− NPF6

−( )c

Li+= c

PF6− = cLiPF6

ciVim

i∑ = 1

μLi+

= FΦ

i = Li+ ,PF6− ,EC / PC & P(VdF − HFP)

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ModelModel

Introduction - Experimental Methods - Results - Conclusions

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ModelModel

• Galvanostatic polarization modelUniform concentration at t=0Fluxes at the boundaries are known: NPF6-=NEC:PC=0

• Solvent and salt diffusion modelUniform concentration at t=0Concentrations at the boundaries are known

• PDE-mode in Comsol MultiphysicsOne-dimensionalTime dependent solver

• The models were compared to experimental data

Introduction - Experimental Methods - Results - Conclusions

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Techniques used in this study:

• Density measurements

• Conductivity measurements

• Concentration Cells

• Galvanostatic Polarisation

• Solvent and salt diffusion measurements

Experimental TechniquesExperimental Techniques

Other Techniques:

• Hittorf’s methodtransport numbers referenced to the Hittorf frame

• Electrophoretic NMRvelocities of species

• PFG-NMRself-diffusion coefficient

• Raman Spectroscopytime dependent concentration profiles

Introduction - Experimental Methods - Results - Conclusions

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Concentration Cells and EISConcentration Cells and EIS

Introduction - Experimental Methods - Results - Conclusions

Electrochemical Impedance Spectroscopy

Concentration Cell

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OptimizationOptimization

Introduction - Experimental Methods - Results - Conclusions

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Galvanostatic Polarisation Galvanostatic Polarisation ExperimentsExperiments

Information about the transport phenomena

Introduction - Experimental Methods - Results - Conclusions

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Diffusion ExperimentsDiffusion Experiments

Introduction - Experimental Methods - Results - Conclusions

Information about the transport phenomena

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ResultsResults

Introduction - Experimental Methods - Results - Conclusions

Galvanostatic polarization experiments

Solvent diffusion experiments

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ResultsResults

Introduction - Experimental Methods - Results - Conclusions

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ResultsResults

Introduction - Experimental Methods - Results - Conclusions

Polarization with 50 µA during 1 h

Polarization with 2.4 mA during 60 s

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SummarySummary

• The mass transport phenomena of a LiPF6-EC-PC-P(VdF-HFP) gel was characterized and modeled at 298 K.

• Two types of models were implemented in Comsol. A galvanostatic polarization model (constant fluxes at the boundaries) and a salt and solvent diffusion model (constant concentrations at the boundaries).

• Two diffusion coefficients, two transport numbers and two drag coefficients were all calculated by fitting the models to experimental data.

• The conductivity was obtained from electrochemical impedance measurements while the two diffusion potential coefficients were directly calculated from concentration cell data.

• The solvent diffusion potential was relative small compared to the ohmic potential drop and the salt diffusion potential.

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AcknowledgementsAcknowledgements

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Transport Properties and Transport Properties and Thermodynamic PropertiesThermodynamic Properties

ΔΦ =RT

cLiPF6F

2 1− t+0( ) 1+

∂ ln f±∂ ln cLiPF6

⎛

⎝⎜

⎞

⎠⎟ − tEC−PC

0 ∂ ln fEC−PC

∂ ln cLiPF6

⎛

⎝⎜

⎞

⎠⎟ dcLiPF6∫ +

RT

cEC−PCF2 1− t+

0( ) ∂ ln f±∂ ln cEC−PC

− tEC−PC0 1+

∂ ln fEC−PC

∂ ln cEC−PC

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎞

⎠⎟dcEC−PC∫

∂cLiPF6

∂t= −

∂∂x

− 1−VmLiPF6 cLiPF6

( )D̂11 − VmEC−PCcLiPF6

( )D̂21( )∂cLiPF6

∂x

− 1−VmLiPF6 cLiPF6

( )D̂12 − VmEC−PCcLiPF6

( )D̂22( )∂cEC−PC

∂x

− 1−VmLiPF6 cLiPF6

( )1− t+0( )+ Vm

EC−PCcLiPF6( )tEC−PC

0( )i

F

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

∂cEC−PC

∂t= −

∂∂x

− 1−VmEC−PCcEC−PC( )D̂21 − Vm

LiPF6 cEC−PC( )D̂11( )∂cLiPF6

∂x

− 1−VmEC−PCcEC−PC( )D̂22 − Vm

LiPF6 cEC−PC( )D̂12( )∂cEC−PC

∂x

+ 1−VmEC−PCcEC−PC( )tEC−PC

0 + VmLiPF6 cEC−PC( ) 1− t+

0( )( ) i

F

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

VmLiPF6

VmEC−PC

1+∂ ln f±∂ ln cLiPF6

⎛

⎝⎜

⎞

⎠⎟

∂ ln f±∂ ln cEC−PC

∂ ln fEC−PC

∂ ln cLiPF6

1+∂ ln fEC−PC

∂ ln cEC−PC

⎛⎝⎜

⎞⎠⎟

D̂11

D̂12

D̂21

D̂22

t+0

tEC−PC0

κ

Introduction - Experimental Methods - Results - Conclusions