Mathematical Modeling of Energy-Dense NMC Electrodes: I. Determination of Input Parameters
Authors: Nguyen Tuan-Tu , Delobel Bruno , Berthe Maxime , Fleutot Benoît , Demortière Arnaud , Delacourt Charles 
Published: April 2022

Physics-based models of the Li-ion battery are promising to decipher and quantify the electrode limitations, thereby providing valuable insights for choosing the optimal electrode design for a specific application. However, to obtain relevant results from the models, a reliable set of input parameters is required. This work presents a combined experimental/modeling approach relying on the Newman pseudo-2D model for a complete characterization of a set of LiNi0.5Mn0.3Co0.2O2 electrodes. Intrinsic properties of the active materials are determined and validated using low-loading electrodes having negligible porous-electrode limitations. Then, high-energy-density electrode properties are characterized using appropriate experimental methods, which are widely reported in the literature. In the second part of this series of papers, parameters obtained from this part serve as input parameters in the Newman pseudo-2D model as well as in its extension in order to simulate the rate capability during discharge of the aforementioned set of high-energy-density electrodes.

List of symbols

a

i

m

i

2

/

m

PE

3

interfacial surface area of phase

i

c

s
,

surf

mol

m

−
3

concentration at the surface of the AM particle

c

s
,

max

mol

m

−
3

maximum concentration of intercalated Li in AM particle

c

s

mol

m

−
3

solid-phase Li concentration within the AM particle

c
¯

s

mol

m

−
3

local volume-averaged solid Li concentration of AM phase within the PA

c

mol

m

−
3

salt concentration in a binary electrolyte

d

50

μ
m

median diameter of AM particles

D

m

2

s

−
1

bulk diffusion coefficient of the liquid phase

D

s

m

2

s

−
1

diffusion coefficient of Li in the AM particles

F

C

mol

−
1

Faraday’s constant

i

coexisting phase presented in the PE

i

n

0

A

m

−
2

exchange current density

i

Li

0

A

m

−
2

exchange current density at the Li foil

I

app

A
/

m

CC

2

discharge current density

j

n

mol
/

m

AM

2

·
s

pore-wall flux across the sandwich

k

0

mol

m

2

·
s
·

mol

m

−
3

1.5

−
1

reaction rate constant of the AM

k

0
,

Li

mol

m

2

·
s
·

mol

m

−
3

0.5

−
1

reaction rate constant of Li foil

L

el

μ
m

PE thickness

L

sep

μ
m

separator thickness

Q

th

Ah

kg

−
1

electrode theoretical capacity

R

J

mol
·
K

−
1

ideal gas constant

r

μ
m

radial dimension along the AM particle

T

K

absolute temperature

t

s

time

t

+

0

transference number of Li+ in the electrolyte with respect to the solvent velocity

U

V

equilibrium potential of the AM

Δ
V

V

voltage drop between the two inner contacts in the μ4-probe experiment

x

μ
m

dimension across the sandwich

x

0

initial stoichiometry

Greek Symbols

α

thermodynamic factor

β

charge transfer coefficient

ε

m

elyte

3

/

m

PE

3

PE porosity

ε

sep

m

elyte

3

/

m

sep

3

separator porosity

κ

eff

S

m

−
1

effective ionic conductivity of the liquid phase

ρ

el

g

cm

−
3

electrode density

σ

eff

S

m

−
1

effective electronic conductivity of the solid phase of the electrode

τ

Br

tortuosity factor by Bruggeman

τ

e

electrode tortuosity factor

τ

sep

tortuosity factor of the separator

Φ

1
,

Li

V

electric potential at Li foil

Φ

i

V

electric potential of phase

i