A simulation method for hard carbon negative electrode sodium storage process

Abstract

The application belongs to the technical field of electrochemical energy storage materials, and particularly relates to a simulation method for a hard carbon negative electrode sodium storage process. The core of the method is to construct a numerical model integrating three parallel sodium storage mechanisms of "adsorption-intercalation-pore filling", the adsorption sodium storage is described by pseudo-capacitance characteristics, the intercalation sodium storage is described by a solid-phase diffusion process, and the pore filling sodium storage is described by a quasi-metallic sodium deposition process, and the proportioning coefficients of the sodium storage mechanisms under different voltages are embedded into corresponding electrochemical reaction equations for accurate correction. The simulation method can dynamically analyze the synergistic effect of the mechanisms in the discharge process, accurately predict the voltage platform and slope characteristics, and realize quantitative analysis of the electrochemical performance under different working conditions. The simulation method is suitable for hard carbons derived from different precursors, and provides a reliable method for the analysis and design of hard carbon negative electrodes.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical energy storage materials technology, specifically relating to a simulation method for the sodium storage process of a hard carbon anode. More specifically, this invention establishes an accurate "adsorption-intercalation-pore filling" coupled model by combining quantitative analysis results with multiphysics numerical simulation, which is used to simulate the sodium storage process of sodium-ion batteries and predict the electrochemical performance of hard carbon anodes. Background Technology

[0002] Sodium-ion batteries are considered an important candidate system for next-generation large-scale energy storage and low-temperature power batteries due to their abundant resources, low cost, and similar working principle to lithium-ion batteries. Among them, hard carbon (HC) is currently the most promising anode material for sodium-ion batteries, and has become a research hotspot due to its high specific capacity, low sodium intercalation potential, and good cycle stability. However, unlike the intercalation mechanism of graphite in lithium-ion batteries, the sodium-ion storage mechanism of hard carbon is more complex, and it is generally believed that there are three mechanisms: 1) adsorption sodium storage: sodium ions are adsorbed and stored on the defects, surfaces, and nanopores of hard carbon materials through electrostatic interactions; 2) intercalation sodium storage: sodium ions are intercalated into the graphitized microcrystalline layers of hard carbon materials; 3) pore-filling sodium storage: sodium ions form quasi-metallic sodium clusters in the closed or quasi-closed nanopores inside hard carbon.

[0003] Accurately understanding the contributions of these three mechanisms at different potential stages is crucial for optimizing the structural design of hard carbon materials and improving battery capacity, first-cycle coulombic efficiency, rate performance, and cycle stability. However, traditional electrochemical testing methods, such as cyclic voltammetry (CV) and galvanostatic titration (GITT), struggle to clearly and quantitatively distinguish these three coexisting and partially overlapping mechanisms.

[0004] Finite element analysis (FEM) is a powerful numerical analysis tool capable of solving complex multiphysics coupling problems. However, current FEM-based simulations of hard carbon anodes for sodium-ion batteries face a fundamental challenge: the coupling and overlap of the three sodium storage mechanisms (adsorption, intercalation, and pore filling) in hard carbon materials at the macroscopic electrochemical response level prevent traditional single-mechanism or phenomenological models from accurately reflecting the internal dynamic processes at the physical level. Solid-state nuclear magnetic resonance (NMR) analysis can distinguish different types of sodium species by the chemical shifts of sodium ions. Adsorbed sodium, intercalated sodium, and pore-filled (quasi-metallic) sodium exhibit different chemical shifts in their spectra, allowing for qualitative and quantitative analysis. This provides direct evidence for accurately elucidating the sodium storage mechanism of hard carbon. However, solid-state NMR analysis is a "post-hoc," static material characterization technique; it cannot directly predict how these three mechanisms dynamically evolve under different operating conditions (such as different rate of increase, temperature, and material thickness) and their impact on macroscopic electrochemical performance (such as voltage curves and concentration distribution). By incorporating quantitative mechanistic parameters provided through experimental characterization techniques into the finite element model, a bridge can be built from microscopic mechanisms to macroscopic performance, enabling accurate simulation and prediction of the discharge process of hard carbon anodes.

[0005] Currently, there are no reports of combining quantitative results obtained from experimental characterization techniques with a finite element model that couples adsorption-intercalation-pore filling to simulate the sodium storage process in sodium-ion batteries. Summary of the Invention

[0006] The purpose of this invention is to address the ambiguity in current numerical simulations of sodium storage in hard carbon anodes for sodium-ion batteries. Traditional models simplify hard carbon as a single intercalation material or employ empirical capacity allocation functions. This invention overcomes the shortcomings of existing numerical simulation techniques by providing a simulation method for the sodium storage process of hard carbon anodes. It combines experimental characterization and quantitative analysis with multi-mechanism coupled finite element simulation to achieve accurate and quantitative simulation and prediction of the electrochemical process of hard carbon anodes. This invention aims to achieve precise analysis from microscopic mechanisms to macroscopic performance and is applicable to hard carbon anodes processed from various carbon sources.

[0007] To achieve the above objectives, the present invention provides a simulation method for sodium storage process at a hard carbon anode, comprising the following steps:

[0008] (1) In the finite element software, a three-dimensional geometric model representing hard carbon anode particles is established to decouple the process of sodium storage in hard carbon anode into three separate electrochemical reactions: adsorption sodium storage, intercalation sodium storage, and pore filling sodium storage.

[0009] (2) The proportion coefficients of adsorption sodium storage, intercalation sodium storage and pore filling sodium storage mechanisms are embedded into the corresponding electrochemical reaction equations to obtain the modified electrochemical reaction equations.

[0010] (3) Based on the above three-dimensional geometric model, the sodium storage process of sodium-ion battery is simulated by the modified electrochemical reaction equation.

[0011] Furthermore, in step (1), adsorption sodium storage is described by pseudocapacitive characteristics, intercalation sodium storage is described by solid-phase diffusion process, and pore-filling sodium storage is described by quasi-metallic sodium deposition process.

[0012] Furthermore, in step (2), the revised electrochemical reaction equation is as follows:

[0013] The electrochemical reaction equations at the electrode-electrolyte interface for sodium storage mechanisms involving adsorption, intercalation, or pore filling are as follows:

[0014]

[0015] in ，j m Represents the local current density of m. ε m Let m be the proportion coefficient. i 0,m It is the local current density constant of m. α a,m It is the negative charge transfer coefficient of m. α c,m It is the positive charge transfer coefficient of m. η m It is an overpotential. R It is the ideal gas constant. T It's temperature. F is the Faraday constant, where m is the adsorbed sodium, intercalated sodium, or pore-filled sodium.

[0016] Electrochemical reaction rates under sodium storage mechanisms of adsorption, intercalation, or pore filling:

[0017]

[0018] in, r m The electrochemical reaction rate of m is... s m It is the stoichiometric coefficient of m. n m This indicates the number of electrons transferred to generate m.

[0019] Furthermore, the total current density at the electrode-electrolyte interface is defined as the sum of the local current density of adsorbed sodium, the local current density of intercalated sodium, and the local current density of pore-filling sodium, as follows:

[0020] Total current density at the electrode-electrolyte interface:

[0021]

[0022] in, j tot It is the total current density at the electrode-electrolyte interface. j int , j ads and j fil These are the local current densities of intercalated sodium, adsorbed sodium, and pore-filled sodium, respectively.

[0023] Furthermore, in step (2), the proportion coefficient is obtained by analyzing the experimental data of the hard carbon anode being discharged at different voltages. The analysis is carried out by using solid-state nuclear magnetic resonance analysis technology to distinguish and assign adsorbed sodium, intercalated sodium and pore-filling sodium by characteristic chemical shifts in the spectrum.

[0024] Furthermore, in step (2), the proportion coefficient is obtained through the following steps:

[0025] Electrodes were fabricated using hard carbon materials, and samples were taken and processed at different discharge potential points. 23 Na NMR test;

[0026] For the obtained 23 The Na NMR spectrum was fitted with peaks to obtain the area ratio of each peak. The peak area ratios corresponding to adsorbed sodium, intercalated sodium, and pore-filled sodium were selected to represent the proportion coefficients of adsorption-storage, intercalation-storage, or pore-filling sodium storage mechanisms, respectively.

[0027] Beneficial effects of the present invention

[0028] This invention, for the first time, directly uses the quantitative analysis results of experimental characterization of the sodium storage mechanism as correction terms for the finite element model of the hard carbon anode, enabling the model to be built on a real, experimentally verified microscopic mechanism, thus overcoming the limitations of traditional empirical or semi-empirical models. By correcting model parameters with experimental data, the model's prediction accuracy for the complex discharge behavior of the hard carbon anode is greatly improved, accurately reproducing the discharge curve, especially the plateau and ramp regions. This method can obtain the dynamic spatial distribution of the three mechanisms of "adsorption-intercalation-pore filling" within the electrode during discharge, providing a reliable method for the design of sodium-ion full cells.

[0029] The simulation method of this invention can dynamically analyze the synergistic effects of various mechanisms during discharge, accurately predict voltage plateau and slope characteristics, and achieve quantitative analysis of electrochemical performance under different operating conditions. The simulation method provided by this invention is applicable to hard carbon derived from different precursors, providing a reliable method for the analysis and design of hard carbon anodes. Attached Figure Description

[0030] Figure 1 This is a general flowchart of the method of the present invention;

[0031] Figure 2 This is a schematic diagram of the simulation method of the present invention;

[0032] Figure 3 The hard carbon material prepared in Example 1 under different voltages in a sodium-ion half-cell 23 Na NMR spectrum; where (a) is 23 (a) Na NMR spectrum; (b) Peak fitting diagram;

[0033] Figure 4 Example 1 23 The curves showing the proportion of three sodium storage mechanisms as a function of voltage obtained by Na NMR quantitative analysis.

[0034] Figure 5 This is a comparison graph of the discharge curve obtained by simulation using the simulation method of the present invention and the experimental curve in Example 1;

[0035] Figure 6 A schematic diagram (a) and a schematic diagram (b) of the geometric model of the hard carbon anode constructed for Example 1.

[0036] Figure 7 The image shows the dimensionless concentration distribution cloud map of sodium inside the hard carbon electrode particles under voltages of 0.3V and 0.05V, obtained from the simulation of Example 1. (a) represents a voltage of 0.3V, and (b) represents a voltage of 0.05V. From left to right, the distribution is: total stored sodium, intercalated sodium, adsorbed sodium, and pore-filling sodium. Detailed Implementation

[0037] The present invention will be described in detail below through embodiments, but the present invention is not limited to the embodiments.

[0038] The simulation method for sodium storage in the hard carbon anode of this invention is an iterative process of "model building - numerical solution - experimental verification", the overall flowchart of which is shown below. Figure 1 First, based on electrochemical principles, multiple physical fields are coupled and their governing equations are defined. Then, two-dimensional or three-dimensional geometry is established, material properties are assigned, and boundary conditions are set. In the electrochemical reaction field, the current term of the electrochemical reaction equation distinguishes the proportion coefficients of adsorbed sodium, intercalated sodium, and pore-filling sodium. Subsequently, the core solution and verification loop is entered, that is, numerical iteration is performed in each time step to ensure mathematical convergence. The macroscopic output (such as the discharge curve) is compared with the experimental data to perform accurate simulation analysis (such as sodium ion concentration distribution and overpotential) and performance prediction, thus forming a complete closed-loop process from theoretical model to reliable conclusion.

[0039] Step 1: Construct a finite element model with multiple coupled mechanisms of "adsorption-intercalation-pore filling".

[0040] The core of establishing a two-dimensional or three-dimensional geometric model of hard carbon anode particles in finite element software lies in the dynamic description of the electrode / electrolyte interface.

[0041] 1. Electrolyte liquid phase mass conservation equation and charge conservation equation:

[0042] Sodium ion mass conservation equation:

[0043]

[0044] Where ▽ is the Hamiltonian operator, c e It refers to the sodium ion concentration in the electrolyte. t It is time. D e It is the diffusion coefficient of the electrolyte in the liquid phase. i e It is the current density in the electrolyte. r m It is the electrochemical reaction rate of m (m refers to adsorbed sodium, intercalated sodium, or pore-filled sodium, all of which are hereinafter).

[0045] The equation for the conservation of charge:

[0046]

[0047] in, κ e It is the conductivity of the electrolyte. e It is the electric potential in the electrolyte. κ D It is the diffusion conductivity in the electrolyte. R It is the ideal gas constant. T It's temperature. F It is Faraday's constant. t + It is the sodium ion transference number. f ± It is the mean molar activity coefficient. s It is the electric potential in solid particles. σ s It is the solid-phase diffusion conductivity. j m It is the local current density of m.

[0048] 2. Mass conservation equation and charge conservation equation for the solid phase of hard carbon anode:

[0049] mass conservation equation:

[0050]

[0051] in, c m It is the concentration of m. D m The solid-phase diffusion coefficient is m.

[0052] The equation for the conservation of charge:

[0053]

[0054] in, s It is the electric potential in solid particles. σ s It is the solid-phase diffusion conductivity.

[0055] Sodium ions migrating from the electrolyte undergo electrochemical reactions on the solid surface, which require the fulfillment of the charge conservation equation. The three types of sodium within the solid phase—adsorbed sodium, intercalated sodium, and pore-filling sodium—require the fulfillment of the mass conservation equation, which is used for simulation in finite element analysis software.

[0056] 3. Electrochemical reaction equation on solid particle surface: Mathematically described by the Butler-Volmer equation, this process is the bridge connecting the electrolyte and the electrode active material, and occurs at the interface (particle surface) between the electrolyte and the electrode hard carbon material particles.

[0057] Electrochemical reaction equations at the electrode-electrolyte interface in adsorption-based sodium storage, intercalation-based sodium storage, and pore-filling sodium storage mechanisms:

[0058]

[0059] η m It is an overpotential, satisfying formula (7): where E eq,m These represent the electrochemical reaction equilibrium potentials under each of the three mechanisms.

[0060]

[0061] Electrochemical reaction rates under sodium storage mechanisms of adsorption, intercalation, and pore-filling:

[0062]

[0063] Total electrode current density:

[0064]

[0065] The total current density is substituted into the electrolyte liquid phase charge conservation equation, i.e., formula (2), to calculate the amount of sodium ions consumed in the electrolyte. Then, it is substituted into the hard carbon negative electrode solid phase charge conservation equation, i.e., formula (5), to calculate the total amount of adsorbed sodium, intercalated sodium, and pore-filling sodium generated.

[0066] in, ε m The proportion coefficient of m determined by experimental characterization techniques. i 0,m It is the local current density constant of m. α a,m It is the negative charge transfer coefficient of m. α c,m It is the positive charge transfer coefficient of m. η m It is an overpotential. E eq,m It is the electrochemical equilibrium potential of m. U m 0 It is the characteristic potential of m. c m,max It is the maximum capacity of m. c m It is the concentration of m. c m,0 That is the initial concentration of m. s m It is the stoichiometric coefficient of m. n m This indicates the number of electrons transferred to generate m. j tot It is the total electrode current density. j int , j ads and j fil These are the local current densities of intercalated sodium, adsorbed sodium, and pore-filled sodium, respectively.

[0067] Step Two: Model Validation and Application

[0068] 1. Model verification: Using the modified model, the complete voltage-specific capacity curve of the hard carbon anode under constant current discharge in a sodium-ion half cell was simulated by formulas (1)-(10), and compared with the experimentally measured discharge voltage-specific capacity curve to verify the accuracy of the model.

[0069] 2. Performance Prediction and Application: Using the validated model, by changing the operating conditions or structural conditions, the performance under the corresponding operating conditions or structure can be obtained. For example, changing the discharge rate can obtain the voltage plateau and capacity at the corresponding discharge rate, as well as the spatial distribution of sodium ion concentration inside the electrode, especially the evolution of sodium within the particles over time for the three storage mechanisms; changing the electrode thickness can obtain the effect of different electrode thicknesses on performance, and optimizing material design parameters (such as porosity and particle size) under different electrode thicknesses can maximize the contribution of a specific storage mechanism.

[0070] Example 1

[0071] Hard carbon preparation: 10g of glucose was placed in a muffle furnace and heated to 260℃ at a rate of 10℃ / min under air atmosphere, and held for 3h. Then it was placed in a tube furnace and heated to 800℃ at a rate of 10℃ / min under argon atmosphere, and then heated to 1500℃ at a rate of 3℃ / min, held for 3h, and allowed to cool naturally to room temperature. The mixture was then ball-milled (zirconia, ball milling beads: 50g:1g of raw material) for 5h at 500rpm to obtain a solid powder with a particle size of 5-10μm for the final glucose-based hard carbon material.

[0072] Electrode preparation: Hard carbon HC was used as the negative electrode active material, with carboxymethyl cellulose (CMC) and styrene-butadiene rubber (SBR) added as binders, and conductive carbon black as a conductive agent. The mass ratio of each material was negative electrode material:CMC:SBR:conductive carbon black = 94:2:2:2. Deionized water was used as the solvent to prepare a uniform slurry, which was then coated onto copper foil. After drying, the negative electrode sheet was obtained. The dry matter loading on the aluminum foil was 2 mg / cm³. 2 .

[0073] Sodium metal sheet, glass fiber membrane, and a solution of 1M NaPF6 in 100% DIGLYME (diethylene glycol dimethyl ether) were used as the counter electrode, separator, and electrolyte, respectively. A coin cell (CR-2016 cell) was fabricated using the prepared negative electrode sheet on the sodium metal sheet. The cell was then tested at room temperature (25°C) under the following conditions: discharge at a constant current density of 30 mA / g until the voltage reached 0V, allow to stand for 5 minutes, and then charge at a constant current density of 30 mA / g until the voltage reached 2.5V.

[0074] Testing procedure: A Bruker Avance III 500 MHz solid-state nuclear magnetic resonance spectrometer was used. 23 Na probe. Pulse sequence: single-pulse method, pulse width 1 / 12π, delay time 2 s; chemical shift reference: NaCl (7.2 ppm). Half-cell electrode powders obtained under different discharge conditions (2.5V, 0.5V, 0.3V, 0.15V, 0.1V, 0.05V, 0.03V, 0V) were tested. 23 Na NMR spectrum (see) Figure 3 Peak fitting was performed, and the area ratio of each peak was calculated. The results were summarized in Table 1, showing the peaks at potentials of 0.5V, 0.3V, 0.15V, 0.1V, 0.05V, 0.03V, and 0V. 23 The peak area ratio of the Na NMR spectrum is plotted as follows: Figure 4The percentage-voltage relationship curves shown indicate that in the initial stage of discharge (slope region), adsorbed sodium and intercalated sodium compete, but intercalated sodium dominates; in the final stage of discharge (plateau region), pore-filling sodium becomes the main contributor.

[0075] Table 1 23 The proportions of three sodium storage mechanisms under different voltages obtained from Na NMR quantitative analysis

[0076]

[0077] According to such Figure 1 The process described first involves coupling multiple physical fields based on electrochemical principles and defining their governing equations: the electrochemical physical field of the sodium-ion battery and the rare matter transport physical field; defining the mass conservation equation and charge conservation equation for the electrolyte liquid phase of the sodium-ion battery, the mass conservation equation and charge conservation equation for the solid phase of the hard carbon anode; and defining the electrochemical reaction equations for the electrode-electrolyte interface in adsorption sodium storage, intercalation sodium storage, and pore-filling sodium storage mechanisms. Then, two-dimensional or three-dimensional geometry is established, material properties are assigned, and regions and boundary conditions are defined, including the local current density in the electrochemical reaction equations. j m The proportions of adsorbed sodium, intercalated sodium, and pore-filled sodium are distinguished. Then, the core solution and verification loop is entered, that is, numerical iteration is performed in each time step to ensure mathematical convergence, and the macroscopic output (such as discharge curve) is compared with experimental data to perform accurate simulation analysis (such as sodium ion concentration distribution and overpotential) and performance prediction, thus forming a complete closed loop process from theoretical model to reliable conclusion.

[0078] In finite element software (such as ANSYS or COMSOL Multiphysics), a simplified three-dimensional geometry representing the porous structure of hard carbon anode particles is created using EDEM (Discrete Element Modeling). (See [link to finite element method]) Figure 6 The process of sodium storage on hard carbon is decoupled into three separate electrochemical reactions: adsorption sodium storage, intercalation sodium storage, and pore-filling sodium storage, and their respective mechanisms are considered separately (see [link to relevant documentation]). Figure 2Sodium adsorption is described by a pseudocapacitive adsorption process, sodium intercalation is described by a solid-phase diffusion process (existing technology), and sodium pore filling is described by a quasi-metallic sodium deposition process. Specifically, adsorption is mathematically described by a pseudocapacitive adsorption process, and the Faraday process for generating adsorbed sodium is expressed using the Butler-Volmer equation, with the current term multiplied by the adsorption mechanism proportion coefficient. The pore filling process is mathematically described by a quasi-metallic sodium deposition process, and the Faraday process for generating quasi-metallic sodium is expressed using the Butler-Volmer equation, with the current term multiplied by the pore filling mechanism proportion coefficient. Specifically, the pseudocapacitive adsorption process is capacitive adsorption with a Faraday reaction, described by formula (6) (with a correction for the adsorption proportion coefficient in formula (6)), and then using formula (4)... D m The solid-phase diffusion coefficient of adsorbed sodium represents the adsorption process into the particle interior; similarly, the deposition process of quasi-metallic sodium is described by Equation (6) for the electrochemical process, and the mass conservation equation of Equation (4) contains the inward deposition diffusion coefficient (solid-phase diffusion coefficient of pore-filled sodium).

[0079] After the geometric model is established, input the conductivity of the electrolyte. κ e Electrolyte diffusion coefficient D e Sodium ion transport number t + Mean molar activity coefficient f ± Solid-phase diffusion conductivity σ s Solid diffusion coefficient D m In the electrode reaction interface, the electrode kinetics expression is modified to define the three-mechanism parallel kinetics described in step one. Specifically, the local current density in the Butler-Volmer equation is correlated with the respective proportions of the three sodium storage mechanisms. After completing geometric modeling, equation and parameter settings, mesh generation is performed, transient solver and convergence residuals are set, and the calculation begins.

[0080] The constant current discharge process of a hard carbon anode in a sodium-ion half-cell at 30 mA / g was simulated. The simulated voltage-capacity curves were quantitatively compared with the experimentally measured curves (see [link to simulation]). Figure 5 The results showed that the two methods highly overlapped throughout the entire discharge range, accurately reproducing the slope characteristics of the high-potential region and the plateau characteristics of the low-potential region. This comparison result passed statistical validation (root mean square error RMSE < 0.034V, coefficient of determination R0). 2The result >0.995 fully demonstrates the reliability of this model in predicting macroscopic electrochemical behavior. To reveal the internal sodium storage mechanism of the hard carbon anode, the simulation results were post-processed, and the spatial distribution of the total sodium concentration and its components inside the electrode particles at characteristic voltages of 0.3V and 0.05V were extracted and presented as dimensionless concentration distribution cloud maps (see [link to relevant documentation]). Figure 7 ).

[0081] Cloud plot analysis revealed the following key physical processes: Early discharge phase (0.3V, corresponding to the ramp region): Sodium ions are initially stored near the electrode surface through adsorption and intercalation, mainly concentrated on the surface layer of the electrode particles and in the macropore region, similar to surface-controlled rapid capacitance behavior. The concentration of sodium in the pores is close to zero throughout the entire region, indicating that this mechanism has not yet been activated on a large scale. Late discharge phase (0.05V, corresponding to the plateau region): When the discharge enters the low-potential plateau region, the sodium storage mechanism inside the electrode undergoes a dominant shift. Pore-filled sodium becomes the most important storage form, the concentration distribution of adsorbed sodium tends to saturate, and its incremental contribution decreases significantly. The concentration front of intercalated sodium continues to slowly advance towards the particle core, but its growth rate is much lower than that of the pore-filling process.

Claims

1. A simulation method for sodium storage process at a hard carbon anode, characterized in that, Includes the following steps: (1) In the finite element software, a three-dimensional geometric model representing hard carbon anode particles is established to decouple the process of sodium storage in hard carbon anode into three separate electrochemical reactions: adsorption sodium storage, intercalation sodium storage, and pore filling sodium storage. (2) The proportion coefficients of adsorption sodium storage, intercalation sodium storage and pore filling sodium storage mechanisms are embedded into the corresponding electrochemical reaction equations to obtain the modified electrochemical reaction equations. The aforementioned proportion coefficient was obtained by analyzing experimental data of hard carbon anode discharge at different voltages. The analysis was conducted by using solid-state nuclear magnetic resonance analysis technology to distinguish and assign adsorbed sodium, intercalated sodium, and pore-filling sodium by characteristic chemical shifts in the spectrum. The aforementioned proportion coefficient is obtained through the following steps: Electrodes were fabricated using hard carbon materials, and samples were taken and processed at different discharge potential points. 23 Na NMR test; For the obtained 23 The Na NMR spectrum was fitted by peak segmentation, and the area ratio of each peak was obtained. The peak area ratios corresponding to adsorbed sodium, intercalated sodium, and pore-filled sodium were selected to represent the proportion coefficients of adsorption sodium storage, intercalation sodium storage, or pore-filled sodium storage mechanisms, respectively. (3) Based on the above three-dimensional geometric model, the sodium storage process of sodium-ion battery is simulated by the modified electrochemical reaction equation.

2. The simulation method for sodium storage process at a hard carbon anode according to claim 1, characterized in that: The adsorption sodium storage described in step (1) is described using pseudocapacitive characteristics, the intercalation sodium storage is described using a solid-phase diffusion process, and the pore-filling sodium storage is described using a quasi-metallic sodium deposition process.

3. The simulation method for sodium storage process at a hard carbon anode according to claim 1, characterized in that: The modified electrochemical reaction equation described in step (2) is as follows: The electrochemical reaction equations at the electrode-electrolyte interface for sodium storage mechanisms involving adsorption, intercalation, or pore filling are as follows: ； in ，j m Represents the local current density of m. ε m Let m be the proportion coefficient. i 0,m It is the local current density constant of m. α a,m It is the negative electrode charge transfer coefficient of m. α c,m It is the positive charge transfer coefficient of m. η m It is an overpotential. R It is the ideal gas constant. T It's temperature. F is the Faraday constant, where m is the adsorbed sodium, intercalated sodium, or pore-filled sodium. Electrochemical reaction rates under sodium storage mechanisms of adsorption, intercalation, or pore filling: ； in, r m The electrochemical reaction rate of m is... s m It is the stoichiometric coefficient of m. n m This indicates the number of electrons transferred to generate m.

4. The simulation method for sodium storage process at a hard carbon anode according to claim 3, characterized in that, The total current density at the electrode-electrolyte interface is defined as the sum of the local current density of adsorbed sodium, the local current density of intercalated sodium, and the local current density of pore-filled sodium, as detailed below: Total current density at the electrode-electrolyte interface: ； in, j tot It is the total current density at the electrode-electrolyte interface. j int , j ads and j fil These are the local current densities of intercalated sodium, adsorbed sodium, and pore-filled sodium, respectively.

Images