Polarity diaphragm optimization method based on high-fidelity electrochemical-phase field model

Abstract

The invention discloses a polar diaphragm optimization method based on a high-fidelity electrochemical-phase field model, which comprises the following steps: constructing a high-fidelity electrochemical-phase field model considering a diaphragm substrate and a polar coating to describe the growth behavior of lithium dendrites in the electrodeposition process of a lithium battery; collecting physical property parameters of the diaphragm matrix and the polar coating, substituting the physical property parameters into the model, establishing a computational domain and performing grid division; carrying out numerical solution on the model by utilizing a finite difference method to obtain growth morphology data of the lithium dendrites on the surface of the anode; and performing quantitative characterization on dendritic crystal morphology uniformity based on the growth morphology data to obtain dendritic crystal indexes, adjusting diaphragm physical property parameters according to the indexes, and repeating simulation iteration to optimize the diaphragm structure. By introducing multi-phase field sequence parameters and comprehensively describing the influence of the diaphragm matrix and the polar coating on lithium ion transmission, electrochemical reaction and interface characteristics, the high-precision simulation and optimization of the polar diaphragm design are realized, and the growth of lithium dendrites can be effectively inhibited.

Description

Technical Field

[0001] This invention belongs to the fields of lithium battery safety technology and battery modeling technology, specifically involving a polar separator optimization method based on a high-fidelity electrochemical-phase field model. Background Technology

[0002] With the rapid development of electric vehicles, low-altitude aircraft, and intelligent robots, the requirements for battery safety are constantly increasing. In many electric vehicle fires, thermal runaway induced by internal battery short circuits is the primary cause. Lithium batteries (especially lithium metal batteries) are prone to lithium dendrite formation during long-term cycling. Driven by the tip electric field effect, the dendrites continuously extend and eventually pierce the separator, leading to internal short circuits. Therefore, understanding the lithium dendrite growth mechanism and developing effective control strategies are of great significance for improving lithium battery safety.

[0003] Given their unique location and common composition, separators possess unique advantages in regulating lithium-ion flux and lithium deposition behavior. In recent years, the functionalization of polyolefin separators, particularly through the introduction of polar functional groups to modulate the interfacial interaction between the separator and the electrolyte, holds promise as an effective strategy for continuously regulating dendrite growth throughout the deposition process. However, Li... + The evolution of the local electric field induced by the distribution and polar functional groups is difficult to capture experimentally. The underlying mechanisms of dendrite regulation behavior induced by polar functional groups are usually inferred indirectly or qualitatively from SEM images or battery coulombic efficiency, lacking a unified quantitative analysis framework. In addition, traditional phase-field models do not include the separator, making them inadequate for simulating the entire electrodeposition process.

[0004] In the prior art, Chinese patent CN113420472A discloses a method and system for predicting the morphology growth of lithium dendrites based on a nonlinear phase-field model, including: Step 1: deriving the phase-field variable control equation, lithium ion concentration field control equation, and potential field control equation during the lithium dendrite growth process based on the free energy change law and reaction kinetics; Step 2: collecting parameters during the lithium dendrite growth process; Step 3: inputting the parameters and equations into finite element simulation software, determining the size of the electrolyte region to be calculated and performing mesh generation, setting boundary conditions, initial conditions, calculation step size, and calculation time, and performing transient solution of the control equation set; Step 4: outputting the calculation process and the changes in the phase-field variable values ​​of the calculation region as an image to obtain the growth morphology of lithium dendrites on the negative electrode surface of the lithium battery during the charging process.

[0005] However, this method has the following limitations: 1. This method proposes a nonlinear phase-field model to simulate the growth morphology of lithium dendrites. Although it overcomes the limitations of traditional phase-field models in handling non-equilibrium problems, thus enabling a more realistic reproduction of the growth process of lithium dendrites on the negative electrode surface of lithium batteries, the modeling process of lithium batteries is relatively simplified, only including the negative electrode and electrolyte, and not taking into account another key component of the actual lithium battery system—the separator. Therefore, it cannot meet our research needs for polar separator design and optimization. 2. Although the model achieves visualization of the growth morphology of lithium dendrites, it is difficult to identify subtle differences between images with the naked eye, lacking quantitative characterization methods. Especially when fine-tuning a certain parameter, small changes in the morphology of lithium dendrites may lead to subjective misjudgment by the observer.

[0006] Therefore, there is an urgent need for a phase-field simulation method that couples the membrane physical properties with the electrodeposition process in high fidelity, so as to provide systematic design guidance for membrane polarity engineering. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a polar membrane optimization method based on a high-fidelity electrochemical-phase field model.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] This invention provides a method for optimizing polar membranes based on a high-fidelity electrochemical-phase-field model, comprising the following steps:

[0010] Step S1: Construct a high-fidelity electrochemical-phase-field model that considers the separator substrate and polar coating to describe the lithium battery electrodeposition process;

[0011] Step S2: Collect the physical properties of the diaphragm;

[0012] Step S3: Substitute the physical property parameters into the high-fidelity electrochemical-phase field model, establish the computational domain and perform mesh generation, and set the initial conditions, boundary conditions, spatial step size, time step size and simulation duration;

[0013] Step S4: The high-fidelity electrochemical-phase-field model is numerically solved using the finite difference method to obtain the growth morphology data of lithium dendrites on the anode surface;

[0014] Step S5: Based on the growth morphology data, the uniformity of dendrite morphology is quantitatively characterized to obtain dendrite index, and the physical property parameters are adjusted according to the dendrite index. Steps S3-S4 are repeated to optimize the membrane structure.

[0015] Furthermore, the high-fidelity electrochemical-phase-field model introduces three phase field sequence parameters ξ, φ1, and φ2 to describe the phases in the lithium battery system, where ξ, φ1, and φ2 are the first, second, and third phase field sequence parameters, respectively. The phases in the lithium battery system include: lithium metal anode phase (ξ = 1, φ1 = 0, φ2 = 0), electrolyte phase (ξ = 0, φ1 = 0, φ2 = 0), the diffuse interface between the anode and electrolyte is described by a continuous sequence parameter ξ (ξ = (0, 1), φ1 = 0, φ2 = 0), separator substrate phase (ξ = 0, φ1 = 1, φ2 = 0), and separator polar coating phase (ξ = 0, φ1 = 0, φ2 = 1).

[0016] Furthermore, the evolution of the three phase field sequence parameters ξ, φ1, and φ2 follows the following governing equations:

[0017]

[0018] Among them, L ξ , The interface mobilitys are the first-phase field sequence parameter ξ, the second-phase field sequence parameter φ1, and the third-phase field sequence parameter φ2, respectively; L η ξ is the electrochemical reaction kinetic coefficient, α, n, and η are the charge transfer coefficient, the number of electrons transferred, and the overpotential, respectively, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, and h′(ξ) = 30ξ. 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), κ ξ denoted as the gradient energy coefficient at the lithium metal / electrolyte interface, and denoted as the dimensionless positive ion concentration.

[0019] Furthermore, the high-fidelity electrochemical-phase-field model includes phase-field order parameter equations, lithium-ion concentration field control equations, and potential field control equations.

[0020] Furthermore, the phase-field sequence parameter equation describes the total free energy of the lithium battery system, and the formula is:

[0021]

[0022] Where F is the total free energy of the lithium battery system within the computational domain, V is the volume of the computational domain, and f ch (ξ,φ1,φ2,{c i}) represents the energy density associated with the Helmholtz free energy; f represents the energy density associated with the gradient energy. elec (c i ,Φ) represents the energy density related to electrostatic energy; f ns(ξ) represents the energy density associated with noise.

[0023] Furthermore, the energy density f associated with the Helmholtz free energy ch (ξ,φ1,φ2,{c i}) is represented as:

[0024]

[0025] Where W represents the solid-liquid phase barrier, ξ 2 (1-ξ) 2 , It is a double-well function used to describe the phase stability of the lithium metal phase, the membrane substrate phase, and the membrane polar coating phase; These are the interfacial cross-energy terms at the junctions of the lithium metal phase, the separator substrate, and the polar coating, respectively. i This indicates the concentration of species i, which includes lithium ions and anions; Let R be the reference chemical potential of species i, R be the molar gas constant, T be the thermodynamic temperature in Kelvin, and c be the reference chemical potential of species i. + c - These represent the concentrations of positive and negative ions, respectively. These represent the dimensionless concentrations of positive and negative ions, respectively.

[0026] The energy density associated with the gradient energy Represented as:

[0027]

[0028] Among them, κ ξ , These are the gradient energy coefficients at the lithium metal / electrolyte interface, the membrane substrate / electrolyte interface, and the polar coating / electrolyte interface, respectively. Represents the anisotropic interfacial energy at the lithium metal / electrolyte interface; These represent the interfacial energy anisotropy between the membrane substrate and the functional coating, respectively; κ ξ =κ0(1+δcos(ωθ)) 2 κ0 is the reference energy coefficient of the isotropic interface, δ is the anisotropic intensity, ω is the anisotropic modulus, and θ is the angle between the interface normal direction and the reference axis.

[0029] The energy density f related to electrostatic energy elec (c i ,Φ) is represented as:

[0030]

[0031] Where, n iLet F represent the valence of species i, F be the Faraday constant, and Φ be the potential in the electrolyte phase.

[0032] The noise-related energy density f ns (ξ) is represented as:

[0033] f ns =h′(ξ)χψ

[0034] Where h′(ξ)=30ξ 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), χ is a random number in the interval [-1.0, 1.0], and ψ represents the disturbance amplitude.

[0035] Furthermore, the governing equation for the lithium-ion concentration field is described by the Nernst-Planck equation, expressed as:

[0036]

[0037] in, The dimensionless lithium-ion concentration, i.e., the dimensionless positive ion concentration, c + c is the lithium ion concentration in the electrolyte, and c0 is the bulk concentration of the electrolyte solution. Let c represent the spatial gradient operator. s The value represents the site density of lithium metal, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, n represents the number of electrons transferred, and Φ represents the electrolyte potential. The effective diffusion coefficient of lithium ions is used to characterize the lithium ion transport capacity in the electrode, electrolyte, membrane substrate, and membrane polar coating. It is calculated using an interpolation function to obtain values ​​in different regions, and the formula is:

[0038]

[0039] in, These represent the electrolyte region, separator substrate, and functional coating of a lithium battery system, respectively. φ1、 φ2 are both 200x200 matrices, with elements being either 0 or 1. A value of 1 indicates the membrane substrate or functional coating. Subscript 1 indicates the membrane substrate, and 2 indicates the functional coating. If the superscript does not have an asterisk (*), it means it does not include pore channels; if it has an asterisk (*), it includes pore channels in the substrate or coating. D m D m1 D m2 The effective diffusion coefficients of the electrolyte region, the membrane substrate, and the functional coating, respectively, are expressed as:

[0040] Dm =h(ξ)·D e +[1-h(ξ)]·D s

[0041] D ml =h(ξ)·D e +[1-h(ξ)]·D sl

[0042] D m2 =h(ξ)·D e +[1-h(ξ)]·D s2

[0043] Where h(ξ) is the phase field interpolation function, connecting the properties of the lithium metal phase and the electrolyte phase, D e D is the diffusion coefficient of lithium ions in the lithium metal electrode. s D is the diffusion coefficient of lithium ions in the electrolyte. s1 =ε1·D s / τ1、D s2 =ε2·D s / τ2 represents the diffusion coefficients within the pores of the membrane substrate and the functional coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; and τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively, used to describe the complexity of the diffusion path within the pores.

[0044] Furthermore, the governing equation for the potential field in the high-fidelity electrochemical-phase-field model, namely the total potential field Φ within the system during lithium battery charging... total The potential field Φ of the electrode and the potential field of the local polar groups in the polar coating of the diaphragm are determined by the inherent potential field of the electrode. The result of superposition is represented as:

[0045]

[0046] The local polar group potential field distribution of the diaphragm polar coating is described by the Poisson equation, expressed as: in This is the electric potential field generated by polar groups;

[0047] The inherent potential field distribution of the electrode is described by the Poisson equation, which includes the source term of the electrochemical reaction:

[0048]

[0049] in, Let Φ represent the spatial gradient operator, Φ be the potential of the electrolyte phase, n represent the number of electrons transferred during the electrode reaction, F be the Faraday constant, and c be the electrons transferred. s σ represents the site density of lithium metal; effEffective conductivity, representing the different conductivities in different regions within a lithium battery system, is expressed as an interpolation function:

[0050]

[0051] in, These represent the electrolyte region, separator substrate, and polar coating in a lithium battery system, respectively; σ m σ m1 σ m2 The effective conductivity of the electrolyte, membrane substrate, and polar coating regions are respectively represented as follows:

[0052] σ m =h(ξ)·σ e +(1-h(ξ))·σ s

[0053] σ m1 =h(ξ)·σ e +(1-h(ξ))·σ s1

[0054] σ m2 =h(ξ)·σ e +(1-h(ξ))·σ s2

[0055] Where h(ξ) is the phase field interpolation function, σ e σ is the conductivity of the electrode region. s σ is the conductivity of the electrolyte. s1 =ε1·σ s / τ1 and σ s2 =M·ε2·σ s / τ2 represents the electrical conductivity in the pores of the membrane substrate and the polar coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively; and M is the wetting coefficient. The formula is:

[0056] M = P c2 / P cl

[0057] Among them, P cl and P c2 These are the capillary pressures of the diaphragm substrate and the polar coating, respectively, expressed as P. ci =2γ lgi cosθ sli / r i The solid-liquid phase contact angle θ sli It is used to describe the degree of wetting of a liquid on a solid surface.

[0058] Furthermore, the physical properties of the diaphragm include the physical properties of the diaphragm substrate and the physical properties of the polar coating;

[0059] The physical properties of the membrane substrate include: porosity ε s1 tortuosity τ s1 Thickness l1, membrane substrate / electrolyte contact angle cosθ sl1 ;

[0060] The physical properties of the polar coating include: porosity ε s2 tortuosity τ s2 Thickness l2, polar coating / electrolyte contact angle cosθ sl2 .

[0061] Furthermore, the dendrite indicators include: space utilization rate, arc length ratio, root mean square roughness, average deposition height, dendrite growth rate, and electrochemical reaction rate.

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] (1) This invention introduces three phase field order parameters ξ, φ1, and φ2 to jointly describe the various phases inside the lithium battery and their corresponding phase interfaces. An energy density term related to the separator is added to the Helmholtz free energy density and gradient energy density, thereby obtaining the order parameter equations related to ξ, φ1, and φ2. Solving these equations yields the evolution of the separator and lithium dendrite morphology over time during lithium battery charging. This invention addresses the lack of separator modeling in previous phase field models, making the model more closely approximate real-world conditions.

[0064] (2) This invention models the random nucleation behavior of the lithium anode surface during lithium battery charging by introducing a noise term related to the phase field order parameter ξ into the Gibbs free energy density. Considering that the lithium anode surface is often not an ideal smooth interface in actual working conditions, and is affected by factors such as the non-uniformity of the solid electrolyte interphase (SEI) film, lithium nuclei are easily preferentially generated in local areas. By introducing a statistically random perturbation value into the noise term, the non-uniformity of lithium nuclei distribution on the lithium anode surface can be effectively simulated, thereby providing more realistic initial conditions for the subsequent dendrite growth process.

[0065] (3) This invention introduces dynamically variable effective lithium-ion diffusion coefficient and effective conductivity, realizing the adaptive evolution of lithium-ion diffusion capacity and conductivity characteristics during lithium dendrite growth, enabling the model to more realistically reflect local property changes during lithium deposition. The introduced effective lithium-ion diffusion coefficient is coupled with effective conductivity and membrane properties (porosity, pore size, thickness, tortuosity, contact angle), allowing the model to meet our research needs for membrane structure optimization.

[0066] (4) This invention completes the modeling of the total potential field in the lithium battery system by superimposing the inherent potential field between the electrodes with the local potential field of the polar coating of the separator. The zeta(ζ) potential on the surface of the polar coating of the separator is used as the initial value of the local potential field. The positive and negative values ​​of the zeta(ζ) potential represent the positive and negative polarity of the separator surface, respectively, and its absolute value represents the polarity intensity of the separator, so that the model meets our research needs for optimizing the polarity parameters of the separator.

[0067] (5) This invention proposes using lithium dendrite uniformity indices to quantitatively characterize the growth morphology of lithium dendrites. These indices include: space utilization, arc length ratio, root mean square roughness, average deposition height, dendrite growth rate, and maximum deposition height. By plotting curves showing the changes of these indices with the membrane's physical properties, the sensitivity of lithium dendrite morphology to a certain parameter of the membrane can be determined. This allows for the construction of a structure-property relationship map between the membrane and the lithium dendrite morphology, enabling the selection of optimal physical properties and providing theoretical guidance for the rational design of the membrane. Attached Figure Description

[0068] Figure 1 This is a flowchart of the polar diaphragm optimization method according to an embodiment of the present invention;

[0069] Figure 2 This is a flowchart illustrating the method for controlling lithium dendrite morphology in a membrane based on a high-fidelity electrochemical-phase-field model, according to an embodiment of the present invention.

[0070] Figure 3 This is a schematic diagram of the simulated region division and the effective diffusion coefficient within the region, according to an embodiment of the present invention.

[0071] Figure 4 This is a schematic diagram of the simulated region division and the effective conductivity within the region according to an embodiment of the present invention;

[0072] Figure 5 This is a flowchart illustrating the solution of partial differential equations in a high-fidelity electrochemical-phase-field model according to an embodiment of the present invention. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0074] This embodiment provides a polar membrane optimization method based on a high-fidelity electrochemical-phase-field model, such as... Figure 1 , Figure 2 As shown, it includes the following steps:

[0075] Step S1: Construct a high-fidelity electrochemical-phase-field model that considers the separator substrate and polar coating to describe the lithium battery electrodeposition process;

[0076] First, the battery system was determined to be a lithium metal liquid battery, and a high-fidelity electrochemical-phase-field model was constructed:

[0077] The phases in a lithium battery system are described by a combination of three phase field sequence parameters ξ, φ1, and φ2: lithium metal anode phase (ξ = 1, φ1 = 0, φ2 = 0), electrolyte phase (ξ = 0, φ1 = 0, φ2 = 0), the diffuse interface between the anode and electrolyte is described by a continuous sequence parameter ξ (ξ = (0, 1), φ1 = 0, φ2 = 0), separator substrate phase (ξ = 0, φ1 = 1, φ2 = 0), and separator polar coating phase (ξ = 0, φ1 = 0, φ2 = 1).

[0078] The high-fidelity electrochemical-phase-field model includes the phase-field order parameter equation, the lithium-ion concentration field control equation, and the potential field control equation.

[0079] The phase-field sequence parameter equation is used to describe the total free energy of a lithium battery system, and the formula is:

[0080]

[0081] Where F is the total free energy of the lithium battery system within the computational domain, V is the volume of the computational domain, and f ch (ξ,φ1,φ2,{c i}) represents the energy density associated with the Helmholtz free energy; f represents the energy density associated with the gradient energy. elec (c i ,Φ) represents the energy density related to electrostatic energy; f ns (ξ) represents the energy density associated with noise.

[0082] Considering the contributions of the membrane substrate and polar coating to the Helmholtz free energy, the Helmholtz free energy can be expressed as:

[0083]

[0084] Where W represents the solid-liquid phase barrier, ξ 2 (1-ξ) 2 , It is a double-well function used to describe the phase stability of the lithium metal phase, the membrane substrate phase, and the membrane polar coating phase; These are the interfacial cross-energy terms at the junctions of the lithium metal phase, the separator substrate, and the polar coating, respectively. i This indicates the concentration of species i, which includes lithium ions and anions; Let R be the reference chemical potential of species i, R be the molar gas constant, T be the thermodynamic temperature in Kelvin, and c be the reference chemical potential of species i. + c - These represent the concentrations of positive and negative ions, respectively. These represent the dimensionless concentrations of positive and negative ions, respectively.

[0085] Energy density related to gradient energy Represented as:

[0086]

[0087] Where, k ξ , These are the gradient energy coefficients at the lithium metal / electrolyte interface, the membrane substrate / electrolyte interface, and the polar coating / electrolyte interface, respectively. Represents the anisotropic interfacial energy at the lithium metal / electrolyte interface; These represent the interfacial energy anisotropy between the membrane substrate and the functional coating, respectively; κ ξ =κ0(1+δcos(ωθ)) 2 κ0 is the reference energy coefficient of the isotropic interface, δ is the anisotropic intensity, ω is the anisotropic modulus, and θ is the angle between the interface normal direction and the reference axis.

[0088] Energy density fe related to electrostatic energy elec (c i ,Φ) is represented as:

[0089]

[0090] Where, n i Let F represent the valence of species i, F be the Faraday constant, and Φ be the potential in the electrolyte phase.

[0091] Noise-related energy density f ns (ξ) is introduced to simulate the stochastic effect of local non-uniform electrodeposition behavior at the lithium anode / electrolyte interface during actual charging, and is expressed as:

[0092] f ns =h′(ξ)χψ

[0093] Where h′(ξ)=30ξ 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), χ is a random number in the interval [-1.0, 1.0], and ψ represents the disturbance amplitude.

[0094] The evolution of the three phase-field sequence parameters ξ, φ1, and φ2 follows the following governing equations:

[0095]

[0096] Among them, L ξ , The interface mobilitys are the first-phase field sequence parameter ξ, the second-phase field sequence parameter φ1, and the third-phase field sequence parameter φ2, respectively; L η ξ is the electrochemical reaction kinetic coefficient, α, n, and η are the charge transfer coefficient, the number of electrons transferred, and the overpotential, respectively, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, and h′(ξ) = 30ξ. 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), κ ξ denoted as the gradient energy coefficient at the lithium metal / electrolyte interface, and denoted as the dimensionless positive ion concentration.

[0097] During the charging process of lithium metal batteries, the distribution of the lithium-ion concentration field is mainly affected by diffusion, electromigration, and the reduction reaction occurring at the lithium anode. The governing equation for the lithium-ion concentration field is described by the Nernst-Planck equation, expressed as:

[0098]

[0099] in, The dimensionless lithium-ion concentration, i.e., the dimensionless positive ion concentration, c + c is the lithium ion concentration in the electrolyte, and c0 is the bulk concentration of the electrolyte solution. Let c represent the spatial gradient operator. s The value represents the site density of lithium metal, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, n represents the number of electrons transferred, and Φ represents the electrolyte potential. The effective diffusion coefficient (or dynamic diffusion coefficient) of lithium ions represents the different diffusion coefficients in different regions of the lithium battery system (electrode, electrolyte, separator substrate, functional coating), and is expressed as an interpolation function as follows:

[0100]

[0101] in, and They represent Figure 3 Region 1 (electrolyte), Region 2 (membrane substrate), and Region 3 (functional coating); φ1、 φ2 are both 200x200 matrices, with elements of 0 or 1. A "1" indicates the membrane substrate or functional coating (subscript "1" indicates the membrane substrate, "2" indicates the functional coating; if the superscript does not have an asterisk "*", it does not include pore channels; if it has an asterisk "*", it includes the pore channels of the substrate or coating). D m D m1 D m2 Then they respectively represent Figure 3 The effective diffusion coefficients in regions 1, 2, and 3 are expressed as:

[0102] D m =h(ξ)·D e +[1-h(ξ)]·D s

[0103] d ml =h(ξ)·D e +[1-h(ξ)]·D sl

[0104] D m2 =h(ξ)·D e +[1-h(ξ)]·D s2

[0105] Where h(ξ) is the phase field interpolation function, connecting the properties of the lithium metal phase and the electrolyte phase, D e D is the diffusion coefficient of lithium ions in the lithium metal electrode. s D is the diffusion coefficient of lithium ions in the electrolyte. s1 =ε1·D s / τ1、D s2 =ε2·D s / τ2 represents the diffusion coefficients within the pores of the membrane substrate and the functional coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; and τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively, used to describe the complexity of the diffusion path within the pores.

[0106] In a high-fidelity electrochemical-phase-field model, the total potential field Φ within the lithium battery system during charging... total The potential field Φ of the electrode and the potential field of the local polar groups in the polar coating of the diaphragm are determined by the inherent potential field of the electrode. The result of superposition is represented as:

[0107] The inherent potential field distribution of the electrode is described by the Poisson equation, which includes the source term of the electrochemical reaction. The governing equation of the potential field is also described by the Poisson equation, which includes the source term of the electrochemical reaction.

[0108]

[0109] in, Let Φ represent the spatial gradient operator, Φ be the potential of the electrolyte phase, n represent the number of electrons transferred during the electrode reaction, F be the Faraday constant, and c be the electrons transferred. s σ represents the site density of lithium metal; eff Effective conductivity, representing the different conductivities in different regions within a lithium battery system, is expressed as an interpolation function:

[0110]

[0111] in, , , They represent Figure 4 Region 1 (electrolyte), Region 2 (membrane substrate), and Region 3 (polar coating) are defined in the image. , , The effective conductivity of the electrolyte, membrane substrate, and polar coating regions are respectively represented as follows:

[0112] σ m =h(ξ)·σ e +(1-h(ξ))·σ s

[0113] σ m1 =h(ξ)·σ e +(1-h(ξ))·σ s1

[0114] σ m2 =h(ξ)·σ e +(1-h(ξ))·σ s2

[0115] Where h(ξ) is the phase field interpolation function, σ e σ is the conductivity of the electrode region. s σ is the conductivity of the electrolyte. s1 =ε1·σ s / τ1 and σ s2 =M·ε2·σ s / τ2 represents the conductivity in the pores of the membrane substrate and the polar coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively; and the wetting coefficient M is a coefficient proposed in the model that connects the contact angle of the membrane polar coating / electrolyte with the conductivity σ of the polar coating. s2 The parameter is expressed as M = P c2 / P cl , where P c1 and P c2 These are the capillary pressures of the diaphragm substrate and the polar coating, respectively, expressed as P.ci =2γ lgi cosθ sli / r i The solid-liquid phase contact angle θ sli The contact angle is typically used to describe the degree of wettability of a liquid on a solid surface (diaphragm substrate i=1, polar coating i=2). A smaller contact angle generally indicates better wettability of the liquid on the solid surface.

[0116] The local potential field distribution of the polar groups in the polar coating of the diaphragm can be described by the Poisson equation (assuming the polar groups are firmly grafted), expressed as: in It is an electric potential field generated by polar groups.

[0117] Step S2: Collect the physical properties of the diaphragm;

[0118] The physical properties of the diaphragm include the physical properties of the diaphragm substrate and the physical properties of the polar coating;

[0119] The physical properties of the membrane substrate include: porosity ε s1 tortuosity τ s1 Thickness l1, membrane substrate / electrolyte contact angle cosθ sl1 ;

[0120] The physical properties of polar coatings include: porosity ε s2 tortuosity τ s2 Thickness l2, polar coating / electrolyte contact angle cosθ sl2 .

[0121] Step S3: Substitute the physical property parameters into the high-fidelity electrochemical-phase-field model, establish the computational domain and perform mesh generation, and set the initial conditions, boundary conditions, spatial step size, time step size, and simulation duration, specifically including:

[0122] The required simulation region size was determined and meshed, including spatial step size, time step size, and total simulation duration. Initial conditions for the simulation (electrodes, lithium-ion concentration, membrane substrate and polar coating, zeta potential of the polar coating surface) were determined. Boundary conditions for the simulation (lithium-ion concentration field boundary conditions, potential field boundary conditions, phase order parameter boundary conditions) were determined. The model was solved using the finite difference method, and the solution was implemented using MATLAB programming (see flowchart). Figure 5 Those skilled in the art know that the partial differential equations in the model can be solved not only by using algorithms such as the finite difference method and finite element method with MATLAB or C++ programming, but also by using commercial software such as COMSOL.

[0123] Step S4: Numerical solution of the high-fidelity electrochemical-phase-field model is performed using the finite difference method to obtain the growth morphology data of lithium dendrites on the anode surface, specifically including:

[0124] The solution obtained from the phase-field sequence parameter equation is output as an image to obtain the growth morphology of lithium dendrites on the anode surface of the battery.

[0125] Step S5: Quantitatively characterize the uniformity of dendrite morphology based on growth morphology data to obtain dendrite indices, and adjust physical property parameters according to dendrite indices. Repeat steps S3-S4 to optimize the membrane structure, specifically including:

[0126] The dendrite index is calculated using the phase field order parameter ξ, which represents the lithium dendrite morphology, to obtain a structure-property relationship diagram that clearly and quantitatively describes the relationship between dendrite uniformity and membrane properties. The calculation formula for the dendrite index is shown in the table, and the calculation process is preferably implemented using MATLAB programming. Based on the structure-property relationship diagram of polar membrane properties and lithium dendrite morphology, the corresponding polar membrane design scheme can be obtained.

[0127] The uniformity indicators of lithium dendrite morphology include: space utilization, arc length ratio, root mean square roughness, average deposition height, dendrite growth rate, and electrochemical reaction rate. The expressions are shown in the table below.

[0128] Table 1 Uniformity index of lithium dendrite morphology

[0129]

[0130] Where S 沉积 H represents the area occupied by lithium-ion deposition. max The maximum height of lithium dendrites, N x L is the number of grid cells in the x-direction, Δx is the spatial step size, and L is the number of grid cells in the x-direction. 弧长 Let be the arc length of the dendrite.

[0131] This embodiment solves the problem that traditional phase-field models neither consider the influence of the separator during the simulation of dendrite growth nor provide quantitative characterization of lithium dendrite morphology. It also establishes a benign feedback mechanism between separator physical properties and lithium dendrite morphology, providing a reliable method for the rational design of polar separators.

[0132] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing polar diaphragms based on a high-fidelity electrochemical-phase-field model, characterized in that, Includes the following steps: Step S1: Construct a high-fidelity electrochemical-phase-field model that considers the separator substrate and polar coating to describe the lithium battery electrodeposition process; Step S2: Collect the physical properties of the diaphragm; Step S3: Substitute the physical property parameters into the high-fidelity electrochemical-phase field model, establish the computational domain and perform mesh generation, and set the initial conditions, boundary conditions, spatial step size, time step size and simulation duration; Step S4: The high-fidelity electrochemical-phase-field model is numerically solved using the finite difference method to obtain the growth morphology data of lithium dendrites on the anode surface; Step S5: Based on the growth morphology data, the uniformity of dendrite morphology is quantitatively characterized to obtain dendrite index, and the physical property parameters are adjusted according to the dendrite index. Steps S3-S4 are repeated to optimize the polar diaphragm.

2. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 1, characterized in that, The high-fidelity electrochemical-phase-field model introduces three phase field sequence parameters ξ, φ1, and φ2 to describe the phases in the lithium battery system, where ξ, φ1, and φ2 are the first, second, and third phase field sequence parameters, respectively. The phases in the lithium battery system include: lithium metal anode phase (ξ = 1, φ1 = 0, φ2 = 0), electrolyte phase (ξ = 0, φ1 = 0, φ2 = 0), the diffuse interface between the anode and electrolyte is described by a continuous sequence parameter ξ (ξ = (0, 1), φ1 = 0, φ2 = 0), separator substrate phase (ξ = 0, φ1 = 1, φ2 = 0), and separator polar coating phase (ξ = 0, φ1 = 0, φ2 = 1).

3. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 2, characterized in that, The evolution of the three phase field sequence parameters ξ, φ1, and φ2 follows the following governing equations: Among them, L ξ , The interface mobilitys are the first-phase field sequence parameter ξ, the second-phase field sequence parameter φ1, and the third-phase field sequence parameter φ2, respectively; L η ξ is the electrochemical reaction kinetic coefficient, α, n, and η are the charge transfer coefficient, the number of electrons transferred, and the overpotential, respectively, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, and h′(ξ) = 30ξ. 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), κ ξ denoted as the gradient energy coefficient at the lithium metal / electrolyte interface, and denoted as the dimensionless positive ion concentration.

4. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 1, characterized in that, The high-fidelity electrochemical-phase-field model includes phase-field order parameter equations, lithium-ion concentration field control equations, and potential field control equations.

5. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 4, characterized in that, The phase-field sequence parameter equation describes the total free energy of the lithium battery system, and the formula is: Where F is the total free energy of the lithium battery system within the computational domain, V is the volume of the computational domain, and f ch (ξ,φ1,φ2,{c i }) represents the energy density associated with the Helmholtz free energy; f represents the energy density associated with the gradient energy. elec (c i ,Φ) represents the energy density related to electrostatic energy; f ns (ξ) represents the energy density associated with noise.

6. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 5, characterized in that, The energy density f associated with the Helmholtz free energy ch (ξ,φ1,φ2,{c i }) is represented as: Where W represents the solid-liquid phase barrier, ξ 2 (1-ξ) 2 , It is a double-well function used to describe the phase stability of the lithium metal phase, the membrane substrate phase, and the membrane polar coating phase; These are the interfacial cross-energy terms at the junctions of the lithium metal phase and the separator substrate, and the polar coating, respectively. i This indicates the concentration of species i, which includes lithium ions and anions; Let R be the reference chemical potential of species i, R be the molar gas constant, T be the thermodynamic temperature in Kelvin, and c be the reference chemical potential of species i. + c - These represent the concentrations of positive and negative ions, respectively. These represent the dimensionless concentrations of positive and negative ions, respectively. The energy density associated with the gradient energy Represented as: Among them, κ ξ , These are the gradient energy coefficients at the lithium metal / electrolyte interface, the membrane substrate / electrolyte interface, and the polar coating / electrolyte interface, respectively. Represents the anisotropic interfacial energy at the lithium metal / electrolyte interface; These represent the interfacial energy anisotropy between the membrane substrate and the functional coating, respectively; κ ξ =k0(1+δcos(ωθ)) 2 κ0 is the reference energy coefficient of the isotropic interface, δ is the anisotropic intensity, ω is the anisotropic modulus, and θ is the angle between the interface normal direction and the reference axis. The energy density f related to electrostatic energy elec (c i ,Φ) is represented as: Where, n i Let F represent the valence of species i, F be the Faraday constant, and Φ be the potential in the electrolyte phase. The noise-related energy density f ns (ξ) is represented as: f ns =h′(ξ)χψ Where h′(ξ)=30ξ 2 (1-ξ) 2 The interpolation function is h(ξ)=ξ 3 (6ξ 2 The derivative of (-15ξ+10), χ is a random number in the interval [-1.0, 1.0], and ψ represents the disturbance amplitude.

7. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 4, characterized in that, The governing equation for the lithium-ion concentration field is described by the Nernst-Planck equation, expressed as: in, The dimensionless lithium-ion concentration, i.e., the dimensionless positive ion concentration, c + c is the lithium ion concentration in the electrolyte, and c0 is the bulk concentration of the electrolyte solution. Let c represent the spatial gradient operator. s The value represents the site density of lithium metal, F is the Faraday constant, R is the molar gas constant, T is the thermodynamic temperature of the electrolyte, n represents the number of electrons transferred, and Φ represents the electrolyte potential. The effective diffusion coefficient of lithium ions is used to characterize the lithium ion transport capacity in the electrode, electrolyte, membrane substrate, and membrane polar coating. It is calculated using an interpolation function to obtain values ​​in different regions, and the formula is: in, These represent the electrolyte region, separator substrate, and functional coating of a lithium battery system, respectively. φ1、 φ2 are both 200x200 matrices, with elements being either 0 or 1. A value of 1 indicates the membrane substrate or functional coating. Subscript 1 indicates the membrane substrate, and 2 indicates the functional coating. If the superscript does not have an asterisk (*), it means it does not include pore channels; if it has an asterisk (*), it includes pore channels in the substrate or coating. D m D m1 D m2 The effective diffusion coefficients of the electrolyte region, the membrane substrate, and the functional coating, respectively, are expressed as: D m =h(ξ)·D e +[1-h(ξ)]·D s D ml =h(ξ)·D e +[1-h(ξ)]·D sl D m2 =h(ξ)·D e +[1-h(ξ)]·D s2 Where h(ξ) is the phase field interpolation function, connecting the properties of the lithium metal phase and the electrolyte phase, D e D is the diffusion coefficient of lithium ions in the lithium metal electrode. s D is the diffusion coefficient of lithium ions in the electrolyte. s1 =ε1·D s / τ1、D s2 =ε2·D s / τ2 represents the diffusion coefficients within the pores of the membrane substrate and the functional coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; and τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively, used to describe the complexity of the diffusion path within the pores.

8. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 4, characterized in that, The governing equation for the potential field in the high-fidelity electrochemical-phase-field model, namely the total potential field Φ in the system during lithium battery charging. total The potential field Φ of the electrode and the potential field of the local polar groups in the polar coating of the diaphragm are determined by the inherent potential field of the electrode. The result of superposition is represented as: The local polar group potential field distribution of the diaphragm polar coating is described by the Poisson equation, expressed as: in This is the electric potential field generated by polar groups; The inherent potential field distribution of the electrode is described by the Poisson equation, which includes the source term of the electrochemical reaction: in, Let Φ represent the spatial gradient operator, Φ be the potential of the electrolyte phase, n represent the number of electrons transferred during the electrode reaction, F be the Faraday constant, and c be the electrons transferred. s σ represents the site density of lithium metal; eff Effective conductivity, representing the different conductivities in different regions within a lithium battery system, is expressed as an interpolation function: in, These represent the electrolyte region, separator substrate, and polar coating in a lithium battery system, respectively; σ m σ m1 σ m2 The effective conductivity of the electrolyte, membrane substrate, and polar coating regions are respectively represented as follows: s m =h(ξ)·σ e +(1-h(ξ))·σ s s m1 =h(ξ)·σ e +(1-h(ξ))·σ s1 s m2 =h(ξ)·σ e +(1-h(ξ))·σ s2 Where h(ξ) is the phase field interpolation function, σ e σ is the conductivity of the electrode region. s σ is the conductivity of the electrolyte. s1 =ε1·σ s / τ1 and σ s2 =M·ε2·σ s / τ2 represents the electrical conductivity in the pores of the membrane substrate and the polar coating, respectively; ε1 and ε2 represent the porosity of the membrane substrate and the functional coating, respectively; τ1 and τ2 represent the tortuosity of the membrane substrate and the functional coating, respectively; and M is the wetting coefficient. The formula is: M=P c2 / P c1 Among them, P cl and P c2 These are the capillary pressures of the diaphragm substrate and the polar coating, respectively, expressed as P. ci =2γ lgi cosθ sli / r i The solid-liquid phase contact angle θ sli It is used to describe the degree of wetting of a liquid on a solid surface.

9. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 1, characterized in that, The physical properties of the diaphragm include the physical properties of the diaphragm substrate and the physical properties of the polar coating. The physical properties of the membrane substrate include: porosity ε s1 tortuosity τ s1 Thickness l1, membrane substrate / electrolyte contact angle cosθ sl1 ; The physical properties of the polar coating include: porosity ε s2 tortuosity τ s2 Thickness l2, polar coating / electrolyte contact angle cosθ sl2 .

10. The polar membrane optimization method based on a high-fidelity electrochemical-phase-field model according to claim 1, characterized in that, The dendrite parameters include: space utilization, arc length ratio, root mean square roughness, average deposition height, dendrite growth rate, and electrochemical reaction rate.

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