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Journal of The Electrochemical Society,161 (8) E3021-E3027 (2014) E3021
0013-4651/2014/161(8)/E3021/7/$31.00 ©The Electrochemical Society
JES FOCUS ISSUE ON MATHEMATICAL MODELING OF ELECTROCHEMICAL SYSTEMS AT MULTIPLE SCALES
Numerical Analysis of Distribution and Evolution
of Reaction Current Density in Discharge Process
of Lithium-Ion Power Battery
Yiwei Tang, Ming Jia,zJie Li, Yanqing Lai, Yun Cheng, and Yexiang Liu
School of Metallurgy and Environment, Central South University, Changsha 410083, China
The reaction current density is an important process parameter of lithium-ion battery, significantly influencing its electrochemical
performance. In this study, aimed at the discharge process of lithium-ion power battery, an electrochemical-thermal model was
established to analyze the distribution of the reaction current density at various parts of the cathode and its evolution with the time
of discharge, and to probe into the causes of distribution and evolution. The investigation revealed that the electrochemical-thermal
coupled model showed more accurate compared to the single electrochemical model, which was more obvious in high rate discharge.
The results demonstrated that the conductivity of solid and liquid-phases was an important factor affecting the distribution of the
reaction current density. Moreover, the uniformity of the distribution of the current density was related to the rate of utilization of the
active materials in the electrodes. By optimizing the porosity and thickness of the electrode, not only the distribution of the current
density was improved, but also the rate of utilization of the active materials in the electrodes and the energy density of batteries were
significantly enhanced.
© 2014 The Electrochemical Society. [DOI: 10.1149/2.004408jes] All rights reserved.
Manuscript submitted January 21, 2014; revised manuscript received February 19, 2014. Published March 4, 2014. This paper is
part of the JES Focus Issue on Mathematical Modeling of Electrochemical Systems at Multiple Scales.
Lithium-ion battery is low maintenance with a series of advantages
such as high voltage, high energy density, long cycle life, and no
“memory effect”1–3; therefore, it has been extensively employed in
portable electronic products and become a preferred battery of choice
for electric vehicles and hybrid electric vehicles.4The study of Li-ion
battery is of significant scientific and technological interest. In recent
years, the new energy vehicle market has developed rapidly; thus, to
satisfy the needs for the Li-ion battery with higher single capacity and
specific energy, the battery manufacturers are encouraged to improve
their electrode design. Therefore, it is extremely important and urgent
to analyze in depth the dynamics of Li-ion power battery because it is
inevitably necessary to increase the battery power.
The research conducted on the Li-ion batteries is based on the ex-
perimental approach; thus, to gain insight into the characteristics of the
battery and to examine its performance, different experiments would
have to be performed. Operating mechanism of the battery can be well
understood by the visual data obtained from the experiments and by
summarizing the related criterion for electrode design by comparing
the effect of different electrode designs on the battery performance.
However, the Li-ion battery is a closed chemical system with complex
internal structure and components; therefore, it is difficult to acquire
directly the distribution of its internal physical quantities from the
experiments in real time, which significantly affects the understand-
ing for the battery operation. Instead, real time management of the
electrochemical process can be effectively studied by applying the
computer numerical simulation technology to establish mathematical
models on the basis of a strict electrode dynamics theory framework
and enormous amount of accumulated battery data. The mathematical
models across multiple scales were widely used in understanding and
describing behaviors of Li-ion battery,5–8it forms the core of sys-
tems engineering approach for the optimal design of Li-ion battery.9
Newman et al.10–17 applied Butler–Volmer equation to describe the
electrochemical process occurring between the interface of electrode
and electrolyte based on the porous electrode theory. Fick’s law was
used to describe the intercalation and deintercalation of the Li-ions
inside the active-material particles, and the mass transfer process of
the Li-ion in electrolyte was described using concentrated solution
theory. Moreover, the changes in the concentration distribution, elec-
trochemical potential, and exchange current density of the battery at
various parts with time of discharge were obtained from the calcu-
lation. Wang18 et al. applied the abovementioned model to study the
zE-mail: jiamingsunmoon@aliyun.com
distribution and changes in local reaction current density during the
discharge process and to probe into the relationship between the reac-
tion current density and electrode design. However, this study ignored
the effect of temperature on the electrochemical process revealing that
a large error could be produced by the increase in temperature due to
a high-powered discharge of the battery.9Incorporation of the energy
conservation in the electrochemical process would be helpful to im-
prove the accuracy of model.19 Smith20 et al. and Ye21 et al. utilized
the electrochemical-thermal coupled model to study the relationships
of the temperature with the electrochemical reaction, as well as with
the key parameters such as the diffusion coefficients of the solid and
liquid-phases, indicating that the influence of temperature change on
the electrochemical parameters could not be neglected; and verify-
ing the accuracy of the model via experimental method. The reaction
current density is an important parameter in the operating process
of the Li-ion battery and significantly influencing its electrochemical
performance. To analyze the dynamics during operation and to ac-
quire a deeper understanding of the battery, real-time and quantitive
analysis should be conducted to study the parameters and the factors
influencing them.
In allusion to the Li-ion power battery; this study established a
one-dimensional electrochemical-thermal coupled model capable of
investigating the distributionand evolution of the local reaction current
density during discharge process by considering anode as an example.
The model was useful in analyzing the causes of distribution and
evolution; thus, further providing guidance for the design of Li-ion
power battery.
Model Development and Experimental
Taking into account the coupling relationship between electro-
chemical reaction and heat, an electrochemical thermal coupling
model was established to investigate the electrochemical process of
lithium ion battery. The schematic of the battery modeled in this study
is shown in Fig. 1. The complete electrochemical system is composed
of five media, namely negative current collector, negative electrode,
separator, positive electrode and positive current collector. The active
materials of solid electrodes are treated as homogenous media, and
are comprised with spherical particles.
Electrochemical model.— The model developed in this paper con-
siders porous electrode theory, Ohm’s law, concentrated solution the-
ory, intercalation /deintercalation kinetics and transport in solid phase
and electrolyte phase. The main governing equations and boundary
conditions required in this model are as follows:
