V. Focused Fundamental Research - EERE - U.S. Department of ...

V.E.4 Mathematical Modeling of Next-generation Li-ion Chemistries (LBNL)
Srinivasan – LBNL
Particle size study on LiFePO 4 cathodes. For studying
the effect of particle size distribution in the LiFePO 4
system, a porous electrode model that incorporates
transport in both the solid and electrolyte phases along
with two particles sizes was developed. The LiFePO 4
system is characterized by its flat equilibrium potential.
The equilibrium potential was obtained by measuring the
open-circuit potential after discharging the electrode at a
slow rate to a certain SOC. The measured equilibrium
potential was applied in the porous electrode model to 4.2
calculate the electrode potentials during charge and
discharge.
4.0
Stress studies on graphite anodes. A single particle
with a layer of binder was used to study the mechanical
degradation of battery anodes. Equations were developed
for stress generation in the particle and the interaction of
stress in the active material with that in the binder. The
model also considers the volume changes in the active
increasing SOC also explains the asymmetry of electrode
utilization between charge and discharge as seen in Figure
2. The strong dependency of Li diffusion coefficient on its
concentration suggests that the use of a varying diffusion
coefficient is necessary for studying the transport
processes in insertion materials and for further application
to the macroscopic porous electrode.
Potential (V) vs. Li
4.4
3.8
3.6
3.4
3.2
3.0
2.8
material and pressure diffusion. Simulations were
2.6
conducted to evaluate the stress in the particle and in the
2.4
binder during delithiation to understand the cause of
failure of the battery electrode.
Results
Transport studies on NMC cathodes. The change of
electrode potential during passage of current provides an
overview of the electrode behavior, such as electrode
capacity and rate, and cycle performances. Figure V - 197
shows the charge and discharge curves on a thin NMC
electrode measured at various rates. The charge and
discharge curves were obtained in separate experiments
and plotted together to compare the differences. The
electrode capacity measured at the end of charge/discharge
at C/25 is ca. 160 mAh/g. More than 50% of the capacity
was still retained when discharged at rates up to 100C.
This capacity retention observed on the thin NMC
electrodes is much higher than that reported on the thicker
electrodes made of the same material. An even higher rate
capability was seen for charge cycles and a clear
asymmetry between the charge and discharge was
observed.
The high rate capability of the NMC electrode was
explored by examining the transport properties of the
material at the particle scale. Since the electrodes were made
to have approximately one to two layers of NMC particles on
the current collector, porous electrode effects are minimized.
The NMC particle is assumed to be a nonporous sphere
and to be representative of the whole electrode. The
diffusion of Li inside the NMC particle is assumed to be
the limiting process of the intercalation reaction and is
described by Fick’s second law. Figure V - 198 shows the
estimated Li diffusion coefficients at various states of
charge. The diffusion coefficient is strongly dependent on
Li concentration. The increasing diffusion coefficient with
100C
100C
Thickness = 6m
Loading = 0.49 mg/cm 2
50C
10C
1C
C/25
C/25
1C
10C
50C
0 20 40 60 80 100 120 140 160 180
Capacity (mAh/g)
Figure V - 197: Experimental charge and discharge curves on a NMC thin
electrode (~6 µm) at various rates. The charge and discharge curves,
obtained in separate experiments, are plotted together to compare the
differences.
D (m 2 /sec)
Li
1E-13
1E-14
1E-15
1E-16
Discharge
Charge
0.0 0.2 0.4 0.6 0.8 1.0
SOC
Figure V - 198: Estimated lithium diffusion coefficient as a function of state
of charge (SOC). The charge data (•) was obtained by charging the
electrode with several current interruptions, and the discharge data () was
obtained by discharging the electrode with several current interruptions to
estimate the diffusion coefficients at various SOC.
Particle size study on LiFePO 4 cathodes. During
discharge, the smaller particles lithiate at a higher rate than
the larger particles. The self-regulating mechanism does
not exist in the flat-potential system, and therefore there is
a disparity in the level of lithiation between the small and
large particles. During charge, on the other hand, the
smaller particles delithiate at a higher rate and have
smaller Li content. The path dependency on the amount of
Energy Storage R &D 642 FY 2011 Annual Progress Report