Method for measuring diffusion coefficient of lithium ions
By decoupling the diffusion overpotential through a single-layer particle electrode structure and analytical solution of Fick's law equations, the accuracy and applicability issues of lithium-ion diffusion coefficient measurement are resolved, enabling accurate measurement of different electrode materials and supporting battery performance optimization.
Patent Information
- Application Number
- CN202511724989.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-24
- Publication Date
- 2026-02-27
AI Technical Summary
Existing methods for measuring lithium-ion diffusion coefficients suffer from low accuracy and limited applicability, making it difficult to accurately reflect the lithium-ion transport characteristics of electrode materials with different morphologies and diffusion modes, thus affecting battery design and optimization.
Employing a single-layer particle electrode structure, the solid-phase diffusion overpotential of the active material is decoupled through continuous pulse-relaxation measurements and analytical solution of Fick's law equations. The lithium-ion diffusion coefficient is calculated by combining the interface lithium-ion concentration and flux, making it suitable for electrode materials with various morphologies and diffusion modes.
It improves the accuracy and stability of lithium-ion diffusion coefficient measurement, has wide applicability, can accurately reflect the lithium-ion transport characteristics of different electrode materials, and supports battery performance optimization.
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Figure CN121577490A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the technical field related to electrochemical test, and more particularly relates to a measurement method of lithium ion diffusion coefficient. BACKGROUND
[0002] Lithium ion batteries are widely used in portable electronic devices, electric vehicles, energy storage systems, aerospace, etc. due to their high energy density, long cycle life and low storage cost. From material properties to simulation applications, the lithium ion diffusion coefficient in the electrode solid phase is a key parameter that directly affects the charge-discharge performance and cycle life of the battery. For active materials in electrode materials, the diffusion coefficient directly determines the kinetic transport process of lithium ions inside the particles. Incorrect diffusion coefficient will lead researchers to make incorrect judgments about the kinetic performance of electrode materials, hindering the development of high-rate performance electrodes and affecting the progress of various energy storage systems.
[0003] The most widely used method for measuring lithium ion diffusion coefficient in existing methods is the constant current intermittent titration technique (GITT). Due to the dependence of the diffusion coefficient itself on lithium ion concentration, the traditional method must comply with various complex condition assumptions and test requirements, resulting in insufficient accuracy and poor stability in actual measurement. In addition, due to the great diversity of the morphology of electrode active materials, the traditional method is only suitable for materials that meet the linear diffusion of lithium ions, and it is difficult to meet the diffusion of electrode materials in various forms such as spherical, fibrous, etc. The data obtained cannot accurately reflect the lithium ion transport characteristics of the electrode material. This poses a challenge to the design and optimization of the battery, especially when pursuing high-rate performance and long-life cycles, the limitations of traditional measurement methods become more apparent. SUMMARY
[0004] In view of the above defects or improvement needs of the prior art, the present application provides a measurement method of lithium ion diffusion coefficient, which aims to solve the problem of low measurement accuracy of existing lithium ion diffusion coefficient.
[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a measurement method of lithium ion diffusion coefficient is provided, comprising the following steps: (1) After the obtained single-layer particle structure battery is formed, continuous pulse-relaxation measurement is performed on a time high-resolution measuring instrument to obtain a pulse-relaxation curve; wherein the active material to be measured is prepared into a single-layer particle electrode sheet, and the single-layer particle electrode sheet is made into the single-layer particle structure battery; (2) The solid-phase diffusion overpotential is extracted from the extracted pulse-relaxation curve, and the lithium ion concentration of the surface layer of the active material is calculated, and the interface lithium ion flux is calculated according to the size of the applied pulse current; (3) The calculated interfacial lithium ion flux and the lithium ion concentration of the active material surface layer are substituted into the analytical solution equation of Fick's law corresponding to the diffusion mode to calculate the lithium ion diffusion coefficient.
[0006] Further, according to the inverse function of the open circuit potential curve, the decoupled solid phase diffusion overpotential is substituted to solve the lithium ion concentration of the active material surface layer during the pulse, and the corresponding formula is:
[0007] In the formula, is the lithium ion concentration on the surface of the particle after diffusion for a certain time; is the inverse function of the thermodynamic potential curve of the electrode particle material; is the overpotential caused by diffusion; is the electrode potential measured after the test is static; is the maximum embedded lithium ion concentration of the electrode particle; is time; is the duration of the test current.
[0008] Further, the analytical solution equation of Fick's law is selected according to the specific particle morphology and diffusion mode. Linear diffusion equation can be selected for flaky particles, and spherical diffusion equation can be selected for spherical particles.
[0009] Further, the linear diffusion equation is:
[0010] In the formula, is the lithium ion concentration at position R after diffusion for a certain time; is the gas constant; is the test current; is the initial lithium ion concentration of the electrode particle; is the Faraday constant; is the surface area of the electrode particle; is the lithium ion diffusion coefficient.
[0011] Further, the spherical diffusion equation is:
[0012] In the formula, is the lithium ion concentration at position R after diffusion for a certain time; is the gas constant; is the test current; is the initial lithium ion concentration of the electrode particle; is the Faraday constant; is the surface area of the electrode particle; is the solution of the equation x-tanx=0, This is one of the solutions; It is a complementary error function; is the lithium-ion diffusion coefficient.
[0013] Furthermore, after the obtained monolayer particle structure battery was divided three times at a current of 0.1C, continuous pulse-relaxation measurements were performed on a time-resolution measuring instrument until the battery state of charge reached 0 or 1. High-frequency sampling at 1kHz was started from the moment the pulse current was applied to obtain the pulse-relaxation curve.
[0014] Furthermore, the particle size distribution of the active material powder to be measured is tested to obtain the average particle size and specific surface area. Then, based on the mass of the active material of the monolayer particle electrode sheet, the mass of the active material and the total interfacial area are calculated, and the interfacial lithium-ion flux is calculated by applying a pulse current.
[0015] Furthermore, the pulse-relaxation curve of the single-layer particle structure battery was analyzed. The interfacial reaction overpotential in the total overpotential was identified based on the response time. After excluding the thermodynamic potential change caused by the change in lithium-ion concentration, the overpotential generated by the diffusion of solid-phase lithium ions was calculated. The thermodynamic potential change is determined by the static potential difference before and after the pulse.
[0016] In summary, compared with the prior art, the method for measuring the lithium-ion diffusion coefficient provided by this invention has the following advantages: 1. This invention decouples the solid-phase lithium-ion diffusion overpotential of the active material and measures the lithium-ion concentration on the surface of the active material using this overpotential. Then, it combines this overpotential with the Fick equation to directly calculate the lithium-ion diffusion coefficient, which can effectively improve the accuracy of diffusion coefficient measurement for different electrode materials.
[0017] 2. The present invention uses a single-layer particle electrode structure to eliminate the influence of uneven current distribution in the thickness direction and liquid phase ion diffusion, thereby reducing the error of decoupling of interfacial lithium ion flux and solid phase diffusion overpotential, and thus improving measurement accuracy and stability.
[0018] 3. This invention takes into account the differences in the morphology and diffusion mode of active particles. The extracted solid-phase diffusion overpotential method is applicable to electrode materials with various morphologies and diffusion modes. Combined with the Fick equation for the corresponding diffusion mode, it can effectively improve the accuracy of diffusion coefficient measurement for different electrode materials and has a wider range of applications.
[0019] 4. The obtained electrode sheets are used to make batteries. Lithium sheets are selected as the counter electrode, and the lithium ion concentration of the electrolyte is greater than 1 mol / L to ensure the elimination of liquid phase ion diffusion overpotential at different rates. Attached Figure Description
[0020] Figure 1 is a schematic diagram of the principle of a lithium ion diffusion coefficient measurement method provided by an embodiment of the present application; Figure 2 is an open-circuit potential curve of an electrode related to an embodiment of the present application; Figure 3 is a scanning electron microscope image of a single-layer NCM523 electrode related to an embodiment of the present application; Figure 4 is a scanning electron microscope image of a single NCM523 particle related to an embodiment of the present application; Figure 5 is a NCM523 lithium ion diffusion coefficient result graph obtained by an embodiment of the present application; Figure 6 is a comparison diagram of the results of measuring the diffusion coefficient by using the measurement method (i.e. the new method) provided by the present application and the traditional method; Figure 7 (a), (b) and (c) in are comparison diagrams of the simulated results of the measured values against the voltage and the experimental values obtained by using different methods. DETAILED DESCRIPTION
[0021] In order to make the object, technical scheme and advantages of the present application clearer, further detailed description will be made to the present application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.
[0022] Please refer to Figure 1 The present application provides a lithium ion diffusion coefficient measurement method, which is used to solve the lithium ion diffusion coefficient according to Fick's second diffusion law, the ion concentration on the surface layer of the particle is simplified according to Fick equation, the solid phase overpotential is obtained by combining the overpotential decomposition of the single-layer electrode, and the correct lithium ion diffusion coefficient of the material can be solved by combining the ion concentration on the surface layer with Fick equation. The structure of the single-layer particle electrode eliminates the difference of the applied test current in the thickness direction, and the lithium ion flux at the active material interface can be directly calculated according to the test current; the half-cell structure composed of the single-layer particle electrode and lithium metal is applied with pulse current and high-frequency sampling to decouple the interface reaction overpotential of the active material under different lithium ion concentrations and the overpotential generated by the solid phase lithium ion diffusion; the lithium ion concentration on the surface layer of the active material is calculated according to the open-circuit potential curve of the active material and the decoupled solid phase diffusion overpotential; and the correct lithium ion diffusion coefficient is calculated by substituting the measurement results of the interface lithium ion flux and the surface layer lithium ion concentration into the Fick equation under the corresponding diffusion mode.
[0023] The measurement method comprises the following steps: Step one, the active material to be measured is prepared into a single-layer particle electrode tab.
[0024] The active material to be measured is prepared into a single-layer particle electrode tab with good conductivity. To reduce the ohmic impedance between the current collector and the active material, the content of the conductive agent in the slurry should be more than 10wt% of the total solid material, and the coating pitch should be as small as possible to ensure that the coated tab contains only single-layer active particles and the particles are as dispersed as possible.
[0025] The particle distribution density of the single-layer particle electrode tab should not be higher than 10 5 cm -2 . The drying method after coating is selected as infrared heating, the temperature is 100℃~120℃, and the time is 3h~5h.
[0026] Step two, the single-layer particle electrode tab is prepared into a single-layer particle structure battery, the counter electrode of the single-layer particle structure battery is selected as lithium sheet, and the lithium ion concentration of the electrolyte is greater than 1mol / L.
[0027] The tab obtained in step one is prepared into a battery, the counter electrode is selected as lithium sheet, and the lithium ion concentration of the electrolyte is greater than 1mol / L to ensure the elimination of liquid phase ion diffusion overpotential under different rates.
[0028] Step three, after the obtained single-layer particle structure battery is formed, continuous pulse-relaxation measurement is carried out on the time high-resolution measuring instrument to obtain the pulse-relaxation curve.
[0029] After the obtained single-layer particle structure battery is formed for 3 times under a current of 0.1C, continuous pulse-relaxation measurement is carried out on the time high-resolution measuring instrument until the state of charge of the battery reaches 0 or 1, and high-frequency sampling of 1kHz is started at the same time as the pulse current is applied to obtain the pulse-relaxation curve. The test current is not greater than 0.1C, the single current pulse time is 15min, and the relaxation time is 1h.
[0030] The pulse current should not be greater than 0.1C, the sampling frequency should not be less than 1kHz, the single discharge time should be as long as possible within 15min~30min to ensure that the battery potential changes significantly, and the relaxation time should be at least 1h.
[0031] In an embodiment, the higher the sampling frequency at the pulse moment, the higher the requirement, 1kHz can meet the requirement, and 1ms is sufficient to distinguish the interface reaction overpotential and the solid phase diffusion overpotential. The rapid response potential jump at the pulse moment is the interface reaction overpotential and a small part of the ohmic overpotential of the electronic components (which can be ignored), and the slowly changing overpotential after the pulse is the solid phase lithium ion diffusion overpotential and the thermodynamic overpotential corresponding to the change of solid phase lithium ion concentration.
[0032] Step four, extract the solid-state diffusion overpotential from the extracted pulse-relaxation curve, and calculate the lithium ion concentration at the active material surface layer, while calculating the interfacial lithium ion flux according to the applied pulse current size.
[0033] Wherein, the thermodynamic potential change due to the change of lithium ion concentration should be excluded when decoupling the solid-state diffusion overpotential.
[0034] In one embodiment, the active material powder to be measured is subjected to particle size distribution test to obtain the average particle size and specific surface area, and then the active material mass and total interfacial area are calculated according to the active material mass of the single-layer particle electrode tab, and the interfacial lithium ion flux is calculated by the applied pulse current, as formula (1):
[0035] The pulse-relaxation curve of the single-layer particle structure battery is analyzed, the interfacial reaction overpotential in the total overpotential is distinguished according to the response time, the thermodynamic potential change due to the change of lithium ion concentration is excluded, and the overpotential generated by the solid-state lithium ion diffusion is calculated, as formula (2). The thermodynamic potential change can be determined according to the difference between the open-circuit potential before and after the pulse, as formula (3):
[0036]
[0037] According to the inverse function of the open-circuit potential curve, the decoupled solid-state diffusion overpotential is substituted to solve the lithium ion concentration at the active material surface layer during the pulse, as formula (4):
[0038] In one embodiment, the particle count is counted according to the SEM scanned image to confirm whether the electrode structure is qualified. The active material mass should be confirmed according to the theoretical discharge capacity and the actual discharge capacity to confirm the effective active material mass. The open-circuit voltage curve is obtained from the continuous pulse-relaxation test according to the theoretical charge capacity.
[0039] Step five, substitute the calculated interfacial lithium ion flux and lithium ion concentration at the active material surface layer into the analytical solution equation of Fick's law corresponding to the diffusion mode to calculate the lithium ion diffusion coefficient.
[0040] Substitute the calculated interfacial lithium ion flux and lithium ion concentration at the active material surface layer into the analytical solution equation of Fick's law corresponding to the diffusion mode to calculate the lithium ion diffusion coefficient. Generally, there are linear, spherical and other diffusion modes: Linear:
[0041] Spherical: (6) Calculating lithium ion diffusion coefficient .
[0042] Wherein, Fick diffusion equation should be selected according to the specific particle morphology and diffusion mode. Linear diffusion equation can be selected for flaky particles, and spherical diffusion equation can be selected for spherical particles.
[0043] The application will be further described in detail below with specific examples.
[0044] This embodiment takes the lithium ion diffusion coefficient measurement process of ternary (NCM523) material as an example to describe the technical solutions of the application in detail.
[0045] In this embodiment, the positive and negative active materials of the single-layer particle electrode lithium ion battery are NCM523 and lithium sheet respectively, the positive current collector material is aluminum, the separator material is polyethylene, and the electrolyte material is LiPF6 dissolved in EC, DMC and EMC mixed in a ratio of 1:1:1 to form a solvent. The specific steps are as follows: Step one: use NCM523 active particles to prepare a single-layer particle electrode, the binder is polyvinylidene fluoride (PVDF), the conductive agent is conductive carbon black (SuperP), and the solvent is N-methyl pyrrolidone (NMP), the mass ratio of NMP, PVDF, SuperP and NCM523 is 20:1:0.5:3, and the total amount is 2.45g. First, 100mg of PCVDF is added to 2000mg of NMP solvent and stirred for 30min to form a uniform gel solution at a rate of 500r / min, then SuperP is added to the gel solution and stirred at 500r / min for 5min, and finally NCM523 active particles are added to the gel solution and stirred at 650r / min for 6.5h to obtain an electrode slurry. Then use an infrared drying flat bed coater to coat the electrode slurry on an aluminum foil, adjust the coating gap to 40um. Finally, dry the electrode sheet at 100℃ by infrared drying for 3h to obtain a single-layer NCM523 particle structure electrode.
[0046] Step two: cut the prepared single-layer NCM523 particle structure electrode into small round pieces (diameter 12mm) by a slicing machine, and assemble it into a 2032 type button cell (NCM523||Li) in an argon atmosphere glove box. The lithium sheet, with a diameter of 15.4mm, is used as the counter electrode, and the separator uses Celgard 2400 (diameter 18mm) and adds 80μl of electrolyte (1MLiPF.EC / EMC / DMC 1:1:1 1.0%VC).
[0047] Step three: the schematic diagram of measuring the lithium ion diffusion coefficient is as followsFigure 1 The single-layer NCM523 particle structure battery is clamped to a LANHE test system (LANHE M340A) after 3 cycles at 0.1C for testing, with an ambient temperature of 25°C, a pulse current of 0.1C applied for 15 min, and a high-frequency sampling test of 1 kHz performed simultaneously, followed by 1 h of relaxation after the pulse, and the above pulse-relaxation cycle repeated 20 times. First, the ohmic overpotential and the interface reaction overpotential of the electronic components are distinguished according to different response times , and the remaining overpotential is the thermodynamic overpotential including the solid-phase diffusion overpotential and the thermodynamic overpotential generated by the change in lithium ion concentration , wherein the thermodynamic overpotential is determined by the difference between the relaxation potentials before and after the pulse , the potential points sampled from the pulse-relaxation test can be used to calculate , and formula (4) can be obtained by substituting formula (5) into formula (4)
[0048] The lithium ion concentration at the interface is solved as , wherein the open-circuit potential curve of the electrode is as shown in Figure 2 .
[0049] Step five: Calculate the lithium ion flux at the interface. After the NCM523 powder is fully dried in an electric drum air drying oven at 70°C for 12 h, the particle size distribution is tested, the experimental equipment is Mastersizer 3000, the average particle size is calculated by volume fraction weighting, D50 is 12 um, and the specific surface area is 0.5 um -1 ; whether the correct single-layer electrode structure is obtained is confirmed by obtaining the SEM image of the surface of the NCM523 single-layer ultra-thin electrode sheet, as shown in Figure 3 , it can be considered that the correct single-layer isolated particle structure is obtained. The total mass is obtained by dividing the actual discharge capacity of the battery by the theoretical discharge capacity, the total volume is obtained by dividing the total mass by the density of NCM523, the total interface area is obtained by multiplying the total volume by the specific surface area, and the lithium ion flux is obtained by substituting formula (1) into formula (1).
[0050] Step six: Calculate the lithium ion diffusion coefficient. As shown in Figure 4 , the SEM image of a single NCM523 particle shows that it is a spherical particle, and NCM523 also conforms to the spherical diffusion mode, so and are substituted into formula (6) to solve , and the above method is substituted into the continuous pulse-relaxation curve to obtain multiple values plotted into the NCM523 diffusion coefficient graph, as shown in Figure 5 .
[0051] Please refer to Figure 6 and Figure 7 Based on the comparison of the measurement results and experimental values of the present application and other different existing methods, it can be seen that the results obtained by the method provided by the present application are basically consistent with the experimental values, indicating that the measurement accuracy of the present application is higher, and is much higher than other existing methods in Figure 6 and Figure 7 .
[0052] Those skilled in the art will readily understand that the above description is only the preferred embodiment of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims
1. A method for measuring the lithium-ion diffusion coefficient, characterized in that, The steps are as follows: (1) After the obtained monolayer particle structure battery is formed, continuous pulse-relaxation measurement is performed on a time high-resolution measuring instrument to obtain the pulse-relaxation curve; wherein, the active material to be tested is prepared into a monolayer particle electrode sheet, and the monolayer particle electrode sheet is made into the monolayer particle structure battery. (2) Extract the solid-phase diffusion overpotential from the extracted pulse-relaxation curve and calculate the lithium ion concentration on the surface of the active material. At the same time, calculate the interfacial lithium ion flux based on the magnitude of the applied pulse current. (3) Substitute the calculated interfacial lithium ion flux and the lithium ion concentration on the surface of the active material into the analytical solution equation of Fick's law for the corresponding diffusion mode to calculate the lithium ion diffusion coefficient.
2. The method for measuring the lithium-ion diffusion coefficient as described in claim 1, characterized in that: Based on the inverse function of the open-circuit potential curve, substituting the decoupled solid-phase diffusion overpotential, the lithium-ion concentration on the surface of the active material during the pulse can be calculated. The corresponding formula is: In the formula, The concentration of lithium ions on the particle surface after a certain diffusion time; It is the inverse function of the thermodynamic potential curve of the electrode particle material; This is the overpotential caused by diffusion; To test the electrode potential measured after resting; This represents the maximum lithium-ion concentration that can be intercalated into the electrode particles. For time; The duration of the test current.
3. The method for measuring the lithium-ion diffusion coefficient as described in claim 2, characterized in that: The analytical solution equation for Fick's law is selected based on the specific particle morphology and diffusion mode. For plate-shaped particles, a linear diffusion equation can be used, while for spherical particles, a spherical diffusion equation can be used.
4. The method for measuring the lithium-ion diffusion coefficient as described in claim 3, characterized in that: The linear diffusion equation is: In the formula, The lithium ion concentration at position R after a period of diffusion; It is the gas constant; For testing current; The initial lithium-ion concentration of the electrode particles; It is Faraday's constant; The surface area of the electrode particles; is the lithium-ion diffusion coefficient.
5. The method for measuring the lithium-ion diffusion coefficient as described in claim 3, characterized in that: The equation for spherical diffusion is: In the formula, The lithium ion concentration at position R after a period of diffusion; Let be the gas separation constant; For testing current; The initial lithium-ion concentration of the electrode particles; It is Faraday's constant; The surface area of the electrode particles; Let x be a solution to the equation x - tanx = 0. This is one of the solutions; It is a complementary error function; is the lithium-ion diffusion coefficient.
6. The method for measuring the lithium-ion diffusion coefficient as described in any one of claims 1-5, characterized in that: After the obtained monolayer particle structure battery was divided three times at a current of 0.1C, continuous pulse-relaxation measurements were performed on a time-resolution measuring instrument until the battery state of charge reached 0 or 1. High-frequency sampling at 1kHz was started from the moment the pulse current was applied to obtain the pulse-relaxation curve.
7. The method for measuring the lithium-ion diffusion coefficient as described in any one of claims 1-5, characterized in that: The particle size distribution of the active material powder to be measured is tested to obtain the average particle size and specific surface area. Then, based on the mass of the active material of the monolayer particle electrode sheet, the mass of the active material and the total interfacial area are calculated, and the interfacial lithium-ion flux is calculated by applying a pulse current.
8. The method for measuring the lithium-ion diffusion coefficient as described in claim 7, characterized in that: The pulse-relaxation curve of a single-layer granular battery was analyzed. The interfacial reaction overpotential in the total overpotential was identified based on the response time. The overpotential generated by solid-phase lithium ion diffusion was calculated after excluding the thermodynamic potential change caused by the change in lithium ion concentration. The thermodynamic potential change was determined by the static potential difference before and after the pulse.