KR101672812B1 - A method of predicting performance of a lithium-ion secondary battery by two-dimensional modeling - Google Patents

Abstract

The present invention relates to a method for predicting battery performance by two-dimensional modeling of a lithium ion secondary battery.
For the application of the developed model, the effects of particle coating and conductive agent on electrode conductivity and efficiency were studied. Both particle coatings and conductive agents appeared to be effective in improving the conductivity, while uniformly distributed conductive agents were found to significantly improve electrode conductivity as well as electrical conductivity.
In addition, further studies have been conducted on the effect of particle size on the electrode conductivity, and it has been found that electrodes made of particles having small particle diameters have higher contact resistance than electrodes having particles having a large particle diameter, Respectively.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a method for predicting battery performance by a two-dimensional modeling of a lithium ion secondary battery,

The present invention relates to a method for predicting battery performance by two-dimensional modeling of a lithium ion secondary battery.

It is important to improve the charge-transfer ability of the electrode in the production of a lithium ion secondary battery having a high output and a high energy density. Generally, an electrode of a lithium ion secondary battery is composed of a complex porous microstructure including active material particles, a binder and a conductive agent. This microstructure is intended to facilitate the charge transfer at the electrode, and the pore space formed by the solid material in the electrode is filled with the electrolyte.

The electrons move along the electrical path formed by the conductive solid material connected to each other, while the lithium ions move through the gap between the solids. In general, an electrode having a high degree of porosity and a low tortuosity is preferable for improving ion movement, but an electrode having a low degree of porosity is preferred in terms of electron transport in a closely packed state. Further, since the charge transfer on the electrode is greatly influenced not only by the porosity and the bending degree but also by the electrode parent polymer, it is not sufficient to express the charge transfer only by the porosity and the bending degree.

On the other hand, it is very difficult to experimentally investigate the influence of electrode morphology on cell performance. For this reason, in recent years, attempts have been made to numerically model a lithium ion secondary battery to understand the phenomenon of migration in a lithium ion secondary battery in a quantitative and theoretical manner. Physics-based models have been used to predict the performance of lithium ion secondary cells and to analyze migration phenomena. In addition, modeling of blended electrodes having a plurality of active materials is also being developed.

Basically, these physics-based models employ a volume-averaging method based on porous electrode theory that uses porosity and curvature as electrode morphology parameters. However, it is not easy to measure these parameters and to show the correlation of these parameters with the transport parameters used in the physics-based model. Thus, when modeling a lithium ion secondary battery with the porous electrode theory, the parameter is generally treated as an adjustable parameter.

As a way to overcome the limitations of this physics-based model, direct numerical simulation (DNS) can be used to reflect the complex morphology of the electrode. The DNS morphology itself has model parameter information, such as porosity and bend, which is advantageous in reducing model parameters. However, when using the DNS model, there is a disadvantage that it requires a large computational cost which depends on the size of the simulation case.

Studies on DNS modeling can be classified into three types according to the problem category to be solved: a) a method for numerically reconstructing three-dimensional morphology of electrodes, b) a method for extracting movement parameters of electrodes by DNS method , And c) a method for predicting electrode performance in electrochemical device modeling having a reconstituted electrode parent. A common feature of the DNS studies listed above is that the 3D simulation is performed on a very small scale because the amount of computation increases greatly with geometric size.

It is an object of the present invention to provide a two-dimensional DNS model including a lithium ion secondary battery electrode parameter that affects cell performance instead of a full three-dimensional model of the electrode.

Another object of the present invention is to predict cell performance such as solid particle packing and electrical conductivity approximation at an electrode using a two-dimensional DNS model.

In one aspect of the present invention, a method for predicting battery performance by two-dimensional modeling of a lithium ion secondary battery is provided.

The cell performance may be electrical conductivity, electrode efficiency or both.

The method also includes determining component and component parameters of the electrode morphology; Generating a two-dimensional electrode morphology using the component; And obtaining electrical conductivity, electrode efficiency, or both from the two-dimensional electrode morphology.

The component may be one or more selected from the group consisting of active material particles and a conductive agent.

The parameters of the above components may be one or two or more selected from the group consisting of particle coating, particle size and presence of a conductive agent.

In addition, two-dimensional electrode morphology can be generated by disposing the active material particles and the conductive material in a two-dimensional quadratic cell in order of particles having a large particle size.

The electric conductivity can be obtained by calculating the reciprocal of the electric resistance obtained from the following equation (2): < EMI ID =

&Quot; (2) "

In this formula,

? represents a resistance,? represents a potential (V), L represents a length (cm), and I represents a current (A).

The above electrode efficiency can be obtained by the following equation (3): < EMI ID =

&Quot; (3) "

는 활성화된 활물질 체적(cm³)을 나타내고,

는 전체 활물질 체적(cm³)을 나타낸다.
In the above equation,? Represents the electrode efficiency,

(Cm < ³ >) of the active material,

Represents the total active material volume (cm < ³ >).

According to the present invention, the performance of the lithium ion secondary battery can be predicted from the electrode morphology generated by the two-dimensional stochastic method.

Therefore, in the present invention, simulation results can be obtained more quickly with less computational cost than the three-dimensional model.

In one aspect of the present invention, various cases were simulated to study the effect of the active material particle coating, the conductive agent distribution, and / or the active material particle size on the electrical conductivity and the electrode efficiency. As a result, it was confirmed that uniform distribution of the conductive agent by filling the gaps is effective in improving both the electric conductivity and the efficiency of the active material.

1 shows an SEM image (left image) of an actual electrode section and an electrode section image (right image) simplified to a specific particle type, respectively.
FIG. 2 is a diagram schematically showing a method of generating a two-dimensional electrode morphology by disposing the particles in a particle size order.
3 is a diagram schematically showing the active material particles shown in the calculation domain.
4 schematically shows an embodiment in which the left and right ends of the electrode model are covered with aluminum foil.
Fig. 5 shows the electrical conductivity distributions of the simulation cases 1 to 6. Fig.
Fig. 6 shows the potential distributions of the simulation cases 1 to 6.
Fig. 7 shows the current density distributions of the simulation cases 1 to 6.
Fig. 8 shows the electric conductivity of the case containing the conductive agent (left side) and the electric conductivity of the case containing no conductive agent (right side).
Fig. 9 schematically shows an electrode morphology according to particle size.
10 is a graph showing an electric conductivity of the electrode according to particle diameters of the active material particles.

Hereinafter, the present invention will be described in detail. The terms and words used in the present specification and claims should not be construed as limited to ordinary or dictionary terms and the inventor may appropriately define the concept of the term in order to best describe its invention It should be construed as meaning and concept consistent with the technical idea of the present invention.

As shown in the SEM image shown on the left side of FIG. 1, the actual electrode of the lithium ion secondary battery has a complex cross-sectional morphology including various sizes of active material particles and a conductive agent. Thus, it is difficult to completely reconstruct the actual electrode morphology to perform the simulation. Instead, the electrode morphology can be simplified to have a selected particle type (in this case three diameters), as shown on the right hand side of FIG.

In one aspect of the present invention, it is assumed that one or more members selected from the group consisting of the active material and the conductive agent are considered as constituent elements of the electrode morphology for generating the two-dimensional electrode morphology, and these particles are all spherical.

The parameters of the component may include particle coating, presence of a conductive agent, or both. The particle coating means a coating layer applied to the surface of the active material particles.

Further, the particle morphology may be included as a parameter of the electrode morphology component. 9 shows the difference between the electrode parent particles generated according to the particle size, and the particle size of the active material particle also corresponds to the parameter affecting the electric conductivity. It is predicted that, when the same boundary condition is applied, the electrode conductivity decreases as the size of the active material particles decreases (see FIG. 10). This is because the number of contact points increases in particles having a small size, and as a result, the contact resistance of the electrode increases. Although electrodes with large size particles have high electrical conductivity due to their low contact resistance, they have a longer solid-diffusion path and a smaller reaction surface area than electrodes made of small size particles, rate.

The kind of the active material, conductive agent and particle coating layer applicable to the present invention is not particularly limited as long as it is used in the art. Particularly preferable are active materials and conductive materials which can be assumed to be spherical for two-dimensional modeling.

Next, a two-dimensional electrode morphology having the above components is generated.

In order to create a two-dimensional electrode parent, first, particles having a large particle size are randomly arranged in an empty space. Subsequently, the particles having a smaller particle diameter are arranged in a void space between particles having a larger particle diameter. In Figure 2, a method of arranging particles of three different particle diameters is schematically illustrated, and generally the conductive agent with the smallest particle size can be placed last.

FIG. 3 shows an embodiment in which solid particles are arranged in a calculation domain composed of a two-dimensional quadratic cell.

Referring to FIG. 3, the computation domain is composed of a two-dimensional quadratic cell, where solid particles are denoted by '1' and empty space domains are denoted by '0'. Each solid particle has a spherical shape consisting of a plurality of quadratic cells. When a new solid particle is added to the electrode domain, the x-y coordinate corresponding to the new particle center is selected from the node labeled '0'. Then, '1' is filled from the particle core to the outer shell until the particles are spherical with the desired radius. At this time, when the new solid particles penetrate into the interior of the existing solid particles, the particle generation at the selected position is stopped and other coordinates are found. For example, in Figure 3 the second layer of new solid particles (the dark gray color domain) should not penetrate the other particle region (the area marked '1'). Particle-to-particle contact can be made if the outermost shell layer of the new particle shares a node with the outermost shell layer of the existing particle. The outermost shell layer of the particles may be referred to as a 'solid' or 'coated'. Although the electrode morphology is constituted by " randomly " arranged solid particles, this 'randomness' is produced by the seed value in the present invention. Therefore, the same morphology can be obtained when the same seed value is used in the procedure of constructing the morphology.

From the two-dimensional electrode morphology generated above, the electrical conductivity, the electrode efficiency or both are obtained.

Therefore, it is necessary to determine the electrical conductivity of the electrode morphology generated by using the experimentally obtained or estimated electrical conductivity from each of the particles of the electrode to be considered for modeling the electrode morphology, the distribution method of the coating agent, do. For example, in the case of active material particles having particle diameters of 6 탆, 5 탆 and 4 탆, the electric conductivity is 0.10 S · cm ^-1 , 0.05 S · cm ^-1 and 0.02 S · cm ^-1 , respectively, cm ^-1 electric conductivity, assuming that the conductivity is 1.00 S · cm ^-1 from the conductive agent, the electric conductivity of the electrode can be obtained.

That is, the electrical conductivity of the electrode component is known. When the potential of one side of the electrode is fixed (Vref = 0) and the current value (I) is flowed on the opposite side after generating the electrode using these components, a voltage difference (? V) , The resistance value at this time can be obtained by R =? V / I, and the reciprocal of the resistance value becomes the electric conductivity.

More specifically, a two-dimensional electrical potential field is obtained by calculating the following equation (1) together with a boundary condition. Reference numerals and subscripts used throughout the present specification refer to the detailed description of the present invention and the subscripts.

[Equation 1]

The electrical resistance is defined by the following equation:

&Quot; (2) "

The electrode efficiency is used in the same sense as the 'active material efficiency' in the present specification, and the active material efficiency is defined as a fraction of the activated active material through which the electric current flows, as follows:

&Quot; (3) "

The local current density at position (i, j) can be obtained from the charge flux as shown in Equation (4) using an electrical potential field.

&Quot; (4) "

As shown in Fig. 4, it is assumed that the left and right ends of the electrode model are covered with aluminum foil to set boundary conditions.

In addition to the electrical conductivity through the solid material described above, there may also be a charge-transfer resistance due to an electrochemical reaction occurring at the interface between the active material particles and the electrolyte.

The charge-transfer resistance can be simplified by: < RTI ID = 0.0 >

&Quot; (5) "

Equation 5 shows that the charge-transfer resistance can be reduced by increasing the reaction surface, which means that the case with the highest efficiency from the simulation results can have the lowest charge-transfer resistance.

The two-dimensional electrode morphology model is input to FORTRAN 90 together with a finite volume method. When the remainder reaches 10 ^-12 , it is assumed that the numerical solution converges.

Example

Six cases were selected to investigate the effects of presence of particles, presence of conductive agent, and distribution of conductive agent on electrical resistance and active material efficiency. Specific simulation cases are listed in Table 1 below.

Particle coating Conductive agent Conductor distribution profile Case 1 NO NO - Case 2 NO YES Uniformity Case 3 NO YES Horizontal (horizontal) Case 4 NO YES Vertical (vertical) Case 5 YES NO - Case 6 YES YES Uniformity

In each case, active material particles having three particle diameters of large, medium, and small are randomly distributed in the electrode domain. It was assumed that all cases had the same active particle distribution in order to properly evaluate the effects of particle coating and conductive agent.

Fig. 5 shows the electrical conductivity distributions of the simulation cases 1 to 6. Case 1 is a reference model without an active material particle coating and without a conductive agent. Cases 2 to 4 are for studying the influence of the conductive agent distribution. Case 5 is a configuration with a particle coating without a conductive agent, while Case 6 is a configuration with a uniformly distributed conductive agent and particle coating.

Electrical conductivity of each component is shown in Table 2 below.

Electrical conductivity (S cm ^-1 ) Remarks Active material 1 0.10 Estimate Active material 2 0.05 Estimate Active material 3 0.02 Estimate Particle Coating 4 0.50 Estimate Conductive agent 1.00 Estimate

6 shows the potential distributions of the simulation cases 1 to 6. Case 1 shows the highest voltage drop at the electrode, while Case 6 with both the particle coating and the conductive agent exhibits the lowest voltage drop. The other cases (2, 3, 4, 5) having a particle coating and a conductive agent show intermediate values between case 1 and case 6.

FIG. 7 shows the current density distributions of the simulation cases 1 to 6.

Referring to FIG. 7, the solid domain has a positive current density value because current flows through the solid domain in which the active material particles and the conductive material are present. Cases 1, 3, 4, and 5 have regions marked with black, and no current flows there. This is because some particles are electrically disconnected when they are packed in the electrode. When the active material particles are electrically disconnected, these regions remain dead space and lithium can not be intercalated. As a result, these regions reduce the capacity or efficiency of the entire electrode.

It was observed that the inactive regions in the cases 1, 3, 4 and 5 were not present in the cases 2 and 6 in which the conductive agent was distributed in the active material particles.

Fig. 8 compares the electrical conductivity of a case containing a conductive agent with the electrical conductivity of a case not containing a conductive agent. The connectivity of the blocked or isolated active material particles (left-hand diagram) was clearly shown to be improved by the addition of a conductive agent to the electrode.

In summary, cases 1 through 6 can be summarized in Table 3 as follows.

Particle coating Conductor (%) Conductor distribution Porosity (%) Conductivity (S cm ^-1 ) Active material efficiency (%) Case 1 NO 0.0 - 28.2 9.00 E-3 84.5 Case 2 NO 5.5 Uniformity 23.8 2.13 E-2 99.7 Case 3 NO 5.5 Horizontal direction 23.7 2.43 E-2 85.2 Case 4 NO 5.5 Vertical direction 24.1 1.52 E-2 91.1 Case 5 YES 0.0 - 28.2 3.00 E-2 84.5 Case 6 YES 5.5 Uniformity 23.8 5.92 E-2 99.7

From the above it can be seen that the particle coating and the conductive agent improve the electrical conductivity of the electrode. When the distributions of the conductive agents in Cases 2 to 4 are compared, in Case 3 in which the conductive agent is arranged in the horizontal direction, the electric conductivity is the highest. In contrast, in Case 4 in which the conductive material is arranged in the vertical direction, the electric conductivity is the lowest. The highest efficiency of the electrodes is expected in cases 2 and 6 with a uniform distribution, while Case 2 represents the conductivity value between cases 3 and 4.

<Explanation of symbols>

Area A (cm ² )

α _s Specific surface area (cm ² cm ^-3 )

i Current density (A cm ^-2 )

i ₀ exchange residual density (A cm ^-2 )

I Current (A)

j Volumetric current density (A cm ^-3 )

L Length (cm)

R Resistance (ohm)

체적(cm³)

Volume (cm ³ )

sigma electrical conductivity (S cm ^-1 )

Φ potential (V)

ω resistance

<Subscript explanation>

cell battery

eff valid

i x direction node number

j y direction node number

ref reference

s surface

Claims (8)

Forming a two-dimensional electrode morphology by disposing active material particles and a conductive material in a two-dimensional quadratic cell in order of particles having a large particle size; And
Characterized in that it comprises the step of obtaining electrical conductivity, electrode efficiency or both from the two-dimensional electrode morphology
A method for estimating battery performance by two-dimensional modeling of a lithium ion secondary battery.
delete delete delete delete delete The method according to claim 1,
Wherein the electric conductivity is obtained by obtaining an inverse number of an electric resistance value obtained from the following formula:
&Quot; (2) &quot;

In this formula,
? represents a resistance,? represents a potential (V), L represents a length (cm), and I represents a current (A).
The method according to claim 1,
Characterized in that the electrode efficiency is obtained by the following equation (3): &lt; EMI ID =
&Quot; (3) &quot;

In the above equation,? Represents the electrode efficiency,

(Cm &lt; ³ &gt;) of the active material,

Represents the total active material volume (cm &lt; ³ &gt;).

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