Method for calculating lithium ion diffusion rate in lithium ion battery

Abstract

The application discloses a kind of lithium ion diffusion rate calculation method in lithium ion battery, including based on constant current intermittent titration method when considering electrode porosity and electrode material specific surface area in solving diffusion coefficient, deduce the improved calculation formula of diffusion coefficient calculation;Parameter in the improved calculation formula is collected and obtained;Based on the parameter of acquisition is brought into the improved calculation formula, the diffusion coefficient corresponding to the ion diffusion rate in lithium ion battery is calculated.This application has the advantages that: GITT model is optimized again, and the specific surface area of material and the porosity in electrode are introduced into formula, the calculation method of diffusion coefficient is more in line with the actual situation of electrode, with very high universality and engineering significance;Compared with the calculation result of prior art diffusion coefficient is more accurate and reliable.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery parameter calculation, and in particular to a method for calculating the lithium-ion diffusion rate in a lithium-ion battery. Background Technology

[0002] In recent years, various types of energy storage systems have attracted significant attention in the field of electrochemical energy storage, including increasingly mature lithium, sodium, and potassium-ion batteries, as well as alkali metal-ion capacitors. In particular, with the rapid popularization of electric vehicles, the demand for batteries with fast-charging capabilities has become increasingly prominent, making the exploration of electrode materials with high rate performance a hot topic. The rate performance of an electrode depends not only on its inherent electronic conductivity but also on the diffusion rate of electroactive ions in the electrode material. To purposefully select suitable electrode materials, it is necessary to evaluate the chemical diffusion coefficient (D value) related to ion insertion and extraction in the material beforehand. The lithium-ion diffusion rate in lithium-ion batteries is evaluated based on the different diffusion coefficients.

[0003] In electrochemistry, various methods for analyzing D values ​​have emerged, each with its own advantages, such as cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), galvanostatic titration (GITT), and potentiostatic titration (PITT). Among these, GITT, as a test method combining transient and steady-state measurements, was first proposed by W. Weppnerand and R.A. Huggins in 1997 and has stood out among many test methods. To date, GITT has been widely used in various secondary batteries.

[0004] Typically, the specific testing process of GITT can be described as follows: First, the battery is charged and discharged at a constant current; second, the current is interrupted to allow the battery system to enter a relaxation state. During this step, the ions within the system diffuse, gradually making the compounds within the system more uniform; finally, the above two steps are repeated until the battery is fully charged or discharged (e.g., ...). Figure 1 As shown). GITT is a semi-infinite diffusion model based on Fick's second diffusion law. By limiting the boundary conditions in the battery system, the expression for D is calculated (as shown in formula (1)):

[0005]

[0006] Where, m B and M B These are the mass and molar mass of the electrode material, respectively; V m The molar volume of the electrode material is represented by S; the electrolyte-electrode contact area is represented by τ; the constant current charging time is represented by ΔE. s ΔE represents the change in system voltage during relaxation. tThis represents the voltage change caused by current during charging / discharging, such as... Figure 1 As shown.

[0007] However, in actual practice, the V of the material m Parameters such as S are difficult to measure and collect. To facilitate application, researchers usually simplify the electrode active material into a steel ball model and use mathematical geometry to represent the volume and contact area in the formula. Therefore, formula (1) is further derived as follows:

[0008]

[0009] r is the radius of the electrode material, usually expressed as D. 50 / 2 represents.

[0010] However, for electrode active materials with relatively rough surfaces, the actual surface area is much larger than the geometric surface area. For example, in ternary cathode materials for lithium-ion batteries, the secondary spherical surface is composed of many nanoscale primary particles. These primary particles increase the surface roughness of the material, and its actual surface area is larger than the geometric surface area. This will cause a large error in the final calculated diffusion coefficient, resulting in an inaccurate calculated diffusion coefficient. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the diffusion rate of lithium ions in lithium-ion batteries. This method solves the problem of inaccurate calculation of diffusion coefficient in the prior art. By re-optimizing the GITT model and incorporating the specific surface area of ​​the material and the porosity in the electrode into the formula, the method for calculating the diffusion coefficient in this invention is more in line with the actual situation of the electrode and has extremely high universality and engineering significance.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for calculating the diffusion rate of lithium ions in a lithium-ion battery, comprising deriving an improved calculation formula for the diffusion coefficient based on the constant current intermittent titration method, considering the porosity of the electrode sheet and the specific surface area of ​​the electrode material when solving for the diffusion coefficient; and collecting and acquiring the parameters in the improved calculation formula;

[0013] The diffusion coefficient corresponding to the ion diffusion rate in the lithium-ion battery is calculated by substituting the acquired parameters into the improved calculation formula.

[0014] The improved formula for calculating the diffusion coefficient is derived as follows:

[0015]

[0016] Where D is the diffusion coefficient, V 总 S represents the volume of the electrode coating, ε is the porosity of the electrode, and S BETThe specific surface area of ​​the electrode material is m. B This refers to the mass of the electrode material.

[0017] The parameters in the improved calculation formula were collected, including the volume V of the electrode coating. 总 The porosity ε of the electrode sheet and the specific surface area S of the electrode material. BET The mass m of the electrode material B And the changes in system voltage ΔE during constant current charging / discharging time τ and relaxation during constant current intermittent titration. s and the voltage change ΔE caused by current during charging / discharging. t .

[0018] The porosity ε of the electrode is calculated using the following formula:

[0019]

[0020] Where L is the coating thickness after cold pressing of the electrode, and S 面 ρ1 represents the coating surface density of the cold-pressed electrode sheet, w1, w2, and w3 represent the weight percentages of the electrode material, conductive agent, and binder in the slurry, respectively, and ρ1, ρ2, and ρ3 represent the true densities of the electrode material, conductive agent, and binder, respectively.

[0021] The specific surface area S of the electrode material was measured using a specific surface area tester. BET .

[0022] Based on the preparation process of the electrode slurry, the weight percentages of electrode materials, binders, and conductive agents during the slurry preparation process are collected, and the true density of each component is confirmed based on its composition.

[0023] Based on the electrode preparation process, the compaction density ρ and coating surface density S of the electrode after cold pressing were collected. 面 Coating thickness L and electrode coating area S 涂 ;

[0024] The porosity of the electrode after cold pressing is calculated and denoted as ε.

[0025] The prepared electrode sheet was assembled with a pure lithium metal sheet into a coin cell, with LiPF6 as the electrolyte, and encapsulated in a coin cell case.

[0026] The assembled coin half-cell was tested using a constant current intermittent titration method; voltage parameters were recorded during the test, and the change in system voltage ΔE during relaxation was collected. s And the voltage change ΔE caused by current during charging / discharging. t .

[0027] The test of the assembled coin half-cell by galvanostatic intermittent titration method includes: on an electrochemical workstation, the assembled coin half-cell is tested by galvanostatic intermittent titration method. The test procedure parameters are: current density is a1C, galvanostatic time is τs, followed by rest relaxation a2s, and the galvanostatic and rest relaxation procedures are repeated until the cell voltage reaches the upper or lower limit of the test range; where a1 and a2 are the set procedure parameters.

[0028] The advantages of this invention are: the GITT model is re-optimized, and the specific surface area of ​​the material and the porosity in the electrode are introduced into the formula. The method for calculating the diffusion coefficient is more in line with the actual situation of the electrode, and has extremely high universality and engineering significance. Compared with the calculation results of the diffusion coefficient in the prior art, it is more accurate and reliable. Attached Figure Description

[0029] The following is a brief explanation of the contents of each of the accompanying drawings and the markings in the drawings:

[0030] Figure 1 This is a schematic diagram of relevant parameters in the GITT test of this invention;

[0031] Figure 2 The lithium-ion diffusion coefficient diagram of the NCM523-1 sample of this invention.

[0032] Figure 3 The lithium-ion diffusion coefficient diagram of the NCM523-2 sample of this invention.

[0033] Figure 4 This is a graph showing the lithium-ion diffusion coefficient of the sample from this invention. Detailed Implementation

[0034] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and the description of the preferred embodiments.

[0035] This invention aims to describe the change of the diffusion coefficient of lithium ions within a material as a function of time and diffusion distance during the charging and discharging process of a lithium-ion battery, using Fick's second law and a semi-infinite diffusion model. The method for calculating the diffusion coefficient in this invention is more closely aligned with the actual conditions of electrode sheets, possessing high universality and engineering significance.

[0036] Based on formula (1), this invention re-optimizes the GITT model and incorporates the specific surface area of ​​the material and the porosity of the electrode into the formula. The method for calculating the diffusion coefficient in this invention is more consistent with the actual situation of the electrode and has high universality and engineering significance. The specific solution is as follows:

[0037] A method for calculating the lithium-ion diffusion rate based on constant current intermittent titration technology, comprising:

[0038] Step 1: Establish a lithium-ion diffusion rate model that considers electrode porosity and electrode material specific surface area, and derive the calculation formula.

[0039] Step 2: Measure the specific surface area of ​​the electrode material using a specific surface area meter, and record it as S. BET ;

[0040] Step 3: According to the preparation process of the electrode slurry, collect the weight percentage of electrode materials, binders and conductive agents during the preparation of the slurry, and confirm the true density of each component based on its composition.

[0041] Step 4: According to the electrode preparation process, collect the compaction density ρ and coating surface density S of the cold-pressed electrode. 面 Coating thickness L and electrode coating area S 涂 ;

[0042] Step 5: Calculate the porosity of the cold-pressed electrode sheet, denoted as ε;

[0043] Step 6: Calculate the volume of electrode material in the electrode sheet based on the calculated porosity ε;

[0044] Step 7: Assemble the prepared electrode sheet and pure lithium metal sheet into a coin cell, using LiPF6 as the electrolyte, and encapsulate it in a CR2032 stainless steel coin cell case.

[0045] Step 8: On the electrochemical workstation, perform GITT testing on the assembled coin half-cell. The test parameters are: current density of 0.1C, voltage range of 3.0-4.3V, constant current time of 60s, followed by resting relaxation for 30s. Repeat the constant current and resting relaxation program until the cell voltage reaches the upper or lower limit of the test range.

[0046] Step 9: Based on the voltage-capacity curve during the test, collect the change in system voltage ΔE during relaxation. s And the voltage change ΔE caused by current during charging or discharging. t ;

[0047] Step 10: Substitute the collected data into the lithium-ion diffusion rate calculation formula to obtain the lithium-ion diffusion coefficient during the charging or discharging process.

[0048] The formula for calculating the lithium-ion diffusion rate is as follows:

[0049]

[0050] Among them, V 总 S represents the volume of the electrode coating, ε is the porosity of the electrode, and S BET The specific surface area of ​​the electrode material is m. B This refers to the mass of the electrode material.

[0051] The theoretical basis of the calculation formula is as follows:

[0052] In formula (1), from the chemical definition, we can derive that m B *V m / M B The practical meaning of is expressed as the volume of the electrode material, that is:

[0053]

[0054] Where V B This indicates the volume of the electrode material.

[0055] In the electrode sheet, the volume of the electrode material is difficult to measure because the electrode sheet also contains conductive agents, binders, and pore structures, as shown in formula (5):

[0056] V 总 =V B +V 导 +V 粘 +V 孔 (5)

[0057] Where V 导 V 粘 V 孔 The volumes of the conductive agent, binder, and pore structure are represented respectively.

[0058] In an electrode, as the weight ratio of the electrode material increases, the proportion of conductive agent and binder decreases, and their volume can be ignored; while the volume of the pore structure can be expressed by the porosity of the electrode, i.e.:

[0059] V 孔 =V 总 ε (6)

[0060] Therefore, the volume of the electrode material can be expressed as:

[0061] V B =V 总 (1-ε) (7)

[0062] In lithium-ion batteries, the electrolyte is typically in a liquid state and exhibits good wettability within the electrodes, completely filling the surface of the electrode materials. Therefore, the contact area between the electrolyte and the electrode materials can be expressed as the specific surface area of ​​the electrode materials:

[0063] S = S BET m B (8)

[0064] Combining formulas (1) and (4-8) above, we can derive the formula for calculating the lithium-ion diffusion rate considering the electrode porosity and the specific surface area of ​​the electrode material:

[0065]

[0066] The porosity ε in step 5 is calculated as follows:

[0067]

[0068] Where L is the coating thickness after cold pressing of the electrode, and S 面 ρ1 represents the areal density of the electrode sheet after cold pressing, w1, w2, and w3 represent the weight percentages of the electrode material, conductive agent, and binder in the slurry, respectively, and ρ1, ρ2, and ρ3 represent the true densities of the electrode material, conductive agent, and binder, respectively, with the following values:

[0069] Components <![CDATA[LiNi 0.5 What 0.2 Mn 0.3 O2]]> Conductive carbon PVDF <![CDATA[True density / (g / cm -3 )]]> 4.8 2.25 1.78

[0070] To verify the difference between the calculation method of this application and the prior art, this application conducts comparative experiments, specifically including:

[0071] Example: Step 1, three different cathode materials from different manufacturers, their composition is LiNi 0.5 Co 0.2 Mn 0.3 O2, labeled NCM523-1, NCM523-2, and NCM523-3 respectively, was uniformly dispersed in NMP at a mass ratio of positive electrode material: conductive carbon: PVDF = 9:0.5:0.5 to obtain a positive electrode slurry, which was then coated on one side of an aluminum foil with a coating density of 13.9 mg / cm³. -2 And dry in a vacuum drying oven at 110℃ for 12 hours;

[0072] Step 2: The obtained positive electrode sheet is cold-pressed and then cut into 14mm diameter prototypes. In a glove box filled with high-purity argon, button-type half-cells are assembled. The water and oxygen content in the glove box is controlled below 0.1ppm. Pure lithium metal sheets are used as the counter electrode, LiPF6 as the electrolyte, and the cells are encapsulated in a CR2032 stainless steel button-type battery casing.

[0073] The process parameter data collected during steps 1 and 2 are shown in Table 1.

[0074] Table 1. Data on the preparation process of three NCM523 materials.

[0075]

[0076] Step 3: On the electrochemical workstation, perform GITT testing on the assembled coin half-cell. The test parameters are: current density of 0.1C, voltage range of 3.0-4.3V, constant current time of 60s, followed by rest relaxation of 30s. Repeat the constant current and rest relaxation program until the cell voltage reaches the upper or lower limit of the test range.

[0077] Step 4: Based on the voltage-capacity curve during the test, collect the change in system voltage ΔE during relaxation. s And the voltage change ΔE caused by current during charging or discharging. t ;

[0078] Step 5: Substitute the collected data into the lithium-ion diffusion rate calculation formula (Formula (3)) to obtain the lithium-ion diffusion coefficient during charging or discharging. The test results are as follows: Figure 2-4 As shown.

[0079] Comparative example:

[0080] Simultaneously, Formula 2 is used to process the GITT test results in the embodiments, and the results are compared with the experimental data of this application on a single graph, such as... Figure 2-4 As shown.

[0081] pass Figure 2-4 A comparison of the data revealed that the lithium-ion diffusion coefficients of the examples and comparative examples of the same material exhibited the same trend. When the specific surface area of ​​the material was small, the data differences between the examples and comparative examples were not significant. Figure 2 (NCM523-1) and Figure 4 (NCM523-3); however, for NCM523-2 sample ( Figure 3 The material has a relatively large specific surface area of ​​1.40 cm². 2 The geometric surface area of ​​a surface area of ​​g is smaller than its actual surface area. Therefore, using the geometric surface area for calculations will result in an overestimation of the actual surface area. Figure 3 As can be seen, the comparative sample is one order of magnitude larger than the example sample. Therefore, this application has more accurate test results compared to the GITT test results of the prior art.

[0082] Obviously, the specific implementation of this invention is not limited to the above-described methods. Any non-substantial improvements made using the inventive concept and technical solution of this invention are within the protection scope of this invention.

Claims

1. A method for calculating the lithium-ion diffusion rate in a lithium-ion battery, characterized in that: An improved calculation formula for the diffusion coefficient is derived based on the constant current intermittent titration method, taking into account the porosity of the electrode sheet and the specific surface area of ​​the electrode material when solving for the diffusion coefficient. The parameters in the improved calculation formula were collected and acquired. The diffusion coefficient corresponding to the ion diffusion rate in the lithium-ion battery is calculated by substituting the collected parameters into the improved calculation formula. The improved formula for calculating the diffusion coefficient is derived as follows: Where D is the diffusion coefficient, V 总 S represents the volume of the electrode coating, ε is the porosity of the electrode, and S BET The specific surface area of ​​the electrode material is m. B Let τ be the mass of the electrode material, τ be the constant current charging / discharging time during the constant current intermittent titration test, and ΔE be the constant current charging / discharging time. s The change in system voltage during relaxation, ΔE t This refers to the voltage change caused by the current during charging / discharging.

2. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 1, characterized in that: The porosity ε of the electrode is calculated using the following formula: Where L is the coating thickness after cold pressing of the electrode, and S 面 ρ1 represents the coating surface density of the cold-pressed electrode sheet, w1, w2, and w3 represent the weight percentages of the electrode material, conductive agent, and binder in the slurry, respectively, and ρ1, ρ2, and ρ3 represent the true densities of the electrode material, conductive agent, and binder, respectively.

3. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 1, characterized in that: The specific surface area S of the electrode material was measured using a specific surface area tester. BET .

4. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 1, characterized in that: Based on the preparation process of the electrode slurry, the weight percentages of electrode materials, binders, and conductive agents during the slurry preparation process are collected, and the true density of each component is confirmed based on its composition.

5. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 2, characterized in that: Based on the electrode preparation process, the compaction density ρ and coating surface density S of the electrode after cold pressing were collected. 面 Coating thickness L and electrode coating area S 涂 ; The porosity of the electrode after cold pressing is calculated and denoted as ε.

6. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 1, characterized in that: The prepared electrode sheet was assembled with a pure lithium metal sheet into a coin cell, with LiPF6 as the electrolyte, and encapsulated in a coin cell case. The assembled coin half-cell was tested using a constant current intermittent titration method; voltage parameters were recorded during the test, and the change in system voltage ΔE during relaxation was collected. s And the voltage change ΔE caused by current during charging / discharging. t .

7. The method for calculating the lithium-ion diffusion rate in a lithium-ion battery as described in claim 1, characterized in that: The galvanostatic intermittent titration test of the assembled coin half-cell includes: performing the galvanostatic intermittent titration test on the assembled coin half-cell on an electrochemical workstation. The test procedure parameters are: current density a1 C, galvanostatic time a2 s, followed by resting relaxation a3 s, and repeating the galvanostatic and resting relaxation procedure until the cell voltage reaches the upper or lower limit of the test range; where a1, a2, and a3 are the set procedure parameters.

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