A method of predicting dendrite thermal self-healing temperature for lithium metal batteries

Abstract

The application belongs to the technical field of lithium metal battery, and discloses a method for predicting the dendrite thermal self-healing temperature of a lithium metal battery, which comprises the following steps: constructing the Gibbs free energy functional of a system, obtaining the conserved order parameter control equation describing atomic diffusion and the non-conserved order parameter control equation of dendrite growth according to the energy minimization principle in the phase field method; constructing the concentration field control equation and the electric potential field control equation based on the Nernst-Planck equation and the Poisson equation respectively; constructing the temperature field control equation based on the heat conduction differential equation of the energy conservation equation, and associating the temperature-dependent parameters with the temperature through the Arrhenius formula; inputting the above equations into finite element analysis software to obtain the dendrite growth morphology at different temperatures, and further obtaining the threshold temperature of dendrite thermal self-healing. The application more comprehensively simulates the lithium dendrite growth and evolution process, comprehensively considers the influence of temperature on dendrite growth, and more accurately predicts the threshold temperature of dendrite thermal self-healing.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field related to lithium metal batteries, and more particularly relates to a method for predicting the thermal self-healing temperature of lithium metal battery dendrites. BACKGROUND

[0002] The demand for energy storage and conversion devices with ideal characteristics such as high energy density, high power density, high safety and reliability is increasing day by day. Lithium metal, with an extremely high specific capacity of 3860 mAh / g and a minimum reduction potential of -3.04 V (relative to the standard hydrogen electrode), has attracted widespread attention as an ideal anode material for driving the next generation of secondary batteries. However, the practical application of lithium metal anodes is still challenging. Due to the thermodynamic instability of the electrode / electrolyte interface, non-uniform lithium deposition induces lithium dendrite growth. High specific surface area and high reactivity of lithium dendrites can exacerbate side reactions, causing lithium metal loss and electrolyte degradation. The breakage and shedding of dendrites form electrochemically inactive "dead lithium", further reducing the coulombic efficiency of the battery and shortening the cycle life. Worse still, sharp dendritic dendrites are easy to pierce the porous separator to cause battery short circuit, leading to thermal runaway of the battery and causing fire or even explosion.

[0003] Generally speaking, when the operating conditions are changed by adjusting the temperature or thermodynamic energy to produce regulated lithium deposition, the nucleation and growth behavior of lithium will change significantly. The existing technology uses a phase field model to reveal the inhibitory effect of higher temperature on lithium dendrite growth in order to explain the phenomenon of inhibiting dendrite growth at high temperature (60℃) and reveal the mechanism of dendrite self-heat induced self-healing at high current density, but the mechanism of dendrite self-heat induced self-healing cannot be explained because the effect of lithium atom diffusion on lithium dendrite is ignored. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a method for predicting the thermal self-healing temperature of lithium metal battery dendrites, which more comprehensively simulates the growth and evolution process of lithium dendrites, constructs a multiple temperature-sensitive parameter coupled heat transfer model, and comprehensively considers the effect of temperature on dendrite growth, to more accurately predict the threshold temperature of dendrite thermal self-healing.

[0005] To achieve the above object, according to one aspect of the present application, a method for predicting a lithium metal battery dendrite thermal self-healing temperature is provided, the method comprising: S1: adopting a Cahn-Hilliard equation to describe lithium atom diffusion behavior, and obtaining a conserved order parameter control equation describing lithium atom diffusion; S2: constructing a Gibbs free energy function of a half-cell system composed of lithium metal and electrolyte by using local chemical free energy density, gradient free energy density and electrostatic free energy density of the half-cell system, and substituting the Gibbs free energy function into an Allen-Cahn equation to obtain a non-conserved order parameter control equation describing a solid-liquid diffusion interface in ionic electrolyte; S3: constructing a concentration field control equation of lithium ions in lithium ion electrolyte by using a Nernst-Planck equation, and constructing an electrostatic potential field control equation of lithium ion electrolyte by using a Poisson equation; S4: obtaining a temperature field control equation describing temperature field variation in the lithium dendrite growth process by using a heat conduction differential equation based on an energy conservation equation, and correlating the temperature field with temperature-dependent parameters by using an Arrhenius equation; S5: inputting the conserved order parameter control equation, the non-conserved order parameter control equation, the concentration field control equation, the electrostatic potential field control equation and the temperature field control equation into finite element analysis software to obtain dendrite growth morphology at different temperatures, and further obtaining a threshold temperature of dendrite thermal self-healing.

[0006] Preferably, the conserved order parameter control equation in step S1 is:

[0007]

[0008] wherein ψ is a phase field conserved order parameter, is a chemical potential, is a total free energy function of the system, Wψ 2 (1-ψ) 2 is a chemical free energy density, W is a potential barrier height, is a gradient free energy density, κ0 is a gradient energy coefficient, M(ψ) is an atomic mobility, M(ψ)=D Li ψV m / RT, D Li is an atomic diffusion coefficient, V m is a molar volume of lithium, R is a universal gas constant, and T is a temperature.

[0009] Preferably, the Gibbs free energy function is:

[0010] G=∫ v [f ch (ξ, c i )+f grad (ξ)+f elec (ξ, c i , φ i )]dV

[0011] where f ch (ξ, c i ) is the local chemical free energy density, g(ξ) = Wξ 2 (1 - ξ) 2 is the double-well function, c0is the initial electrolyte concentration, μ i Θ is the reference chemical potential of component i, c Li is the set of lithium atom concentrations, c Li+ is the set of lithium ion concentrations, c i is the set of concentrations of component i; κ0is the gradient energy coefficient, δ is the anisotropy strength, ω is the modulus of anisotropy, θ is the angle between the interface normal direction and the reference axis direction; f elec (ξ, c i , φ i ) = F∑ i z i c i φ i , F is the Faraday constant, z i is the valence of component i, φ i is the local electrostatic potential, and ξ is the non-conservative order parameter.

[0012] Preferably, the non-conservative order parameter governing equation is:

[0013]

[0014] where h'(ξ) is the derivative of the interpolation function h(ξ) = ξ 3 (6ξ 2 - 15ξ + 10), ξ is the non-conservative order parameter, L σ is the interfacial mobility, L η is the interfacial reaction constant, g'(ξ) is the derivative of the double-well function g(ξ) = Wξ 2 (1 - ξ) 2 , a is the charge transfer coefficient, η is the overpotential, η = φ Li - φ e - E Θ , φ Li is the electrode potential, φ e is the electrolyte potential, and E Θ is the standard half-cell potential.

[0015] Preferably, the concentration field governing equation is:

[0016]

[0017] where DLi+ D is the diffusion coefficient of lithium ions in the electrolyte, c Li c is the concentration of lithium atoms, c Li+ F is the Faraday constant, R is the universal gas constant, and T is the temperature.

[0018] Preferably, the electrostatic potential field control equation is:

[0019]

[0020] where σ eff is the effective electrical conductivity, σ eff = σ Li h(ξ) + σ e (1 - h(ξ)), σ Li is the electrode conductivity, σ e is the electrolyte conductivity, is the potential gradient.

[0021] Preferably, the temperature field control equation is:

[0022]

[0023] where C p is the effective specific heat capacity, p is the mass density, and λ is the thermal conductivity, λ eff is the effective electrical conductivity, λ eff = λ Li h(ξ) + λ e (1 - h(ξ)), Q is the heat generation rate, Q ohmic is the Joule heat generated by the solution resistance, Q over is the overpotential heat generation, a s is the specific surface area of the electrode per unit volume, U j is the open-circuit voltage, is the electrolyte potential gradient, φ Li is the electrode potential, φ e is the electrolyte potential, F is the Faraday constant, c Li is the concentration of lithium atoms.

[0024] Preferably, the temperature-dependent parameters include the lithium ion diffusion coefficient, the electrochemical reaction constant, and the lithium atom diffusion coefficient.

[0025] Preferably, the correlation equation relating the temperature field to the temperature-dependent parameters is given by the Arrhenius equation:

[0026]

[0027] where X T is the temperature-sensitive parameter at temperature T, Reference temperature T ref Temperature-sensitive parameter E a，x Let X be the activation barrier corresponding to the physical quantity X.

[0028] In summary, compared with the prior art, the method for predicting the thermal self-healing temperature of lithium metal battery dendrites provided by the present invention has the following beneficial effects:

[0029] 1. This application constructs a conservation order parameter governing equation describing atomic diffusion behavior and combines it with the dendritic phase field model of the coupled thermal model to comprehensively consider the influence of temperature on electrochemical reaction, ion diffusion and atomic diffusion during lithium metal anodic electroplating, thereby accurately predicting the temperature of dendrite thermal self-healing.

[0030] 2. Based on the thermal conductivity differential equation of the energy conservation equation, a temperature field control equation is constructed. The temperature-dependent parameters are correlated with temperature through the Arrhenius formula, and the influence of temperature on the electrodeposition process is examined.

[0031] 3. The temperature field control equations are coupled with physical properties of lithium metal, lithium ions and electrolyte, corresponding parameters of dendrite growth and evolution, and corresponding parameters of lithium atom diffusion, which is more comprehensive and thus makes the predictions more accurate. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of a half-cell system consisting of a lithium metal anode and a lithium iron phosphate electrolyte.

[0033] Figure 2 This is a flowchart illustrating the steps of a method for predicting the thermal self-healing temperature of dendrites in lithium metal batteries.

[0034] Figure 3 This is a schematic diagram illustrating the coupling between atomic diffusion and the dendritic phase field model;

[0035] Figure 4 This is a schematic diagram for predicting the thermal self-healing threshold temperature of dendrites. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0037] Common lithium metal battery systems such as Figure 1 As shown, this application provides a method for predicting the thermal self-healing temperature of dendrites in lithium metal batteries, such as... Figure 2As shown, the method comprises the following steps S1-S5.

[0038] S1: The Cahn-Hilliard equation is used to describe the lithium atom diffusion behavior, and a conserved order parameter control equation describing lithium atom diffusion is obtained.

[0039] The lithium atom diffusion behavior is described by the Cahn-Hilliard equation, because the atom diffusion does not change the total amount of matter in the system, and is described as:

[0040]

[0041] wherein ψ is a phase field conserved order parameter used to describe the phase state of the system, the electrolyte ψ = 0, and the lithium metal electrode ψ = 1, is the chemical potential, is the total free energy function of the system, Wψ 2 (1-ψ) 2 is the chemical free energy density, W is the potential barrier height, is the gradient free energy density, κ0 is the gradient energy coefficient; M(ψ) is the atomic mobility, which depends on the phase field conserved order parameter and is positively correlated with the atomic diffusion coefficient, M(ψ) = D Li ψV m / RT, D Li is the atomic diffusion coefficient, V m is the molar volume of lithium, R is the universal gas constant, and T is the temperature.

[0042] S2: The Gibbs free energy function of the half-cell system composed of lithium metal and electrolyte is constructed by using the local chemical free energy density, gradient free energy density and electrostatic free energy density of the half-cell system, and the non-conserved order parameter control equation describing the solid-liquid diffusion interface in the ionic electrolyte is obtained by substituting the Gibbs free energy function into the Allen-Cahn equation.

[0043] A nonlinear phase field dendrite model is constructed by using the phase field method, which covers the transport of lithium ions in the electrolyte and the electrochemical reaction deposition of the lithium metal anode / electrolyte interface. The non-conserved order parameter is used to describe the diffusion interface, which distinguishes the solid phase lithium (ξ = 1) and the liquid phase electrolyte (ξ = 0). The Gibbs free energy function is:

[0044] G = ∫ v [f ch (ξ(ξ,c i )+f grad (ξ)+f elec (ξ,c i ,φ i )]dV

[0045] where f ch (ξ, c i ) is the local chemical free energy density, 2 a(ξ) = Wξ 2 (1-ξ) Θ is the double well function, which describes the electrode and electrolyte equilibrium state, c0is the initial electrolyte concentration, μi Li is the reference chemical potential of component i, c Li+ is the set of lithium atom concentration, c i is the set of lithium ion concentration, c elec is the set of concentration of component i; κ0is the gradient energy coefficient, δ is the anisotropy strength, ω is the modulus of anisotropy, θ is the angle between the interface normal direction and the reference axis direction; f i (ξ, c i , φ i ) = F∑ i z i c i φ i , F is the Faraday constant, z i is the valence of component i, φ Li is the local electrostatic potential, the electrode electrostatic potential is φ e , the electrolyte electrostatic potential is φ + , and ξ is the non-conservative order parameter.

[0046] The Gibbs free energy functional of the system is the driving force contribution set of the electrochemical reaction (Li - + e p → Li), which is obtained according to the Allen-Cahn equation:

[0047]

[0048] where L 3 is the phase field mobility, based on the dilute solution of the electrolyte, it is assumed that the electrodeposition reaction only occurs at the electrolyte-electrode interface, and the non-conservative order parameter control equation of the solid-liquid diffusion interface in the ionic electrolyte is obtained by substitution:

[0049]

[0050] where h'(ξ(ξ) is the derivative of the interpolation function h(ξ) = ξ 2 (6ξ σ - 15ξ + 10), which limits the electrodeposition reaction to the electrolyte-electrode interface, ξ is the non-conservative order parameter, L η is the interface mobility, L 2 is the interface reaction constant, g'(ξ) is the double well function, g(ξ) = Wξ 2 (1-ξ)The derivative of α, where α is the charge transfer coefficient and η is the overpotential, η = φ Li -φ e -E Θ , φ Li φ is the electrode potential. e E represents the electrolyte potential. Θ This is the standard half-cell potential.

[0051] S3: The concentration field control equation of lithium ions in lithium-ion electrolyte is constructed using the Nernst-Planck equation, and the electrostatic potential field control equation of lithium-ion electrolyte is constructed using the Poisson equation.

[0052] The Nernst-Planck equation describes the transport of lithium ions in the electrolyte, considering lithium ion diffusion and electromigration processes, while neglecting the transport effects of anions and electrons for simplicity. The concentration field governing equation for lithium ions in the electrolyte is:

[0053]

[0054] Among them, D Li+ Let c be the diffusion coefficient of lithium ions in the electrolyte. Li c is the lithium atom concentration. Li+ Let F be the lithium ion concentration, R be the Faraday constant, R be the universal gas constant, and T be the temperature. The first two terms on the right-hand side of the equation describe the concentration diffusion and electromigration of lithium ions, while the last term describes the source term of the phenomenon where electrochemical reactions lead to the consumption of lithium ions on the electrode surface.

[0055] Assuming the system is electrically neutral, and the electrostatic potential distribution is described by the Poisson equation with source terms, then the governing equation for the electrostatic potential field is:

[0056]

[0057] Where, σ eff For effective conductivity, σ eff =σ Li h(ξ)+σ e (1-h(ξ)), σ Li σ is the electrode conductivity. e Electrolyte conductivity, The potential gradient is represented by the source term on the right-hand side of the equation, which indicates the charge transfer caused by the electrochemical reaction during electrodeposition.

[0058] S4: The temperature field control equation describing the temperature field change during lithium dendrite growth is obtained by using the thermal conductivity differential equation based on the energy conservation equation, and the temperature field is correlated with the temperature-dependent parameters by using the Arrhenius equation.

[0059] The heat effect generated by dendrite growth is described by the heat conduction differential equation based on the energy conservation equation, and the temperature field control equation is:

[0060]

[0061] wherein C p is the effective specific heat capacity, p is the mass density, l is the thermal conductivity, l eff is the effective electrical conductivity, l eff = l Li h(ξ) + l e (1-h(ξ)), the reversible heat caused by enthalpy change is ignored, Q is the heat rate composed of the joule heat generated by the solution resistance and the irreversible heat such as overpotential heat, Q ohmic is the joule heat generated by the solution resistance, Q over is the overpotential heat, a s is the specific surface area of the electrode per unit volume, U j is the open circuit voltage, is the electrolyte potential gradient, f Li is the electrode potential, f e is the electrolyte potential, F is the Faraday constant, c Li is the lithium atom concentration set.

[0062] The Arrhenius equation is used to quantify the temperature-sensitive parameters for coupling the heat effect: the lithium ion diffusion coefficient the reaction constant L η and the lithium atom diffusion coefficient D Li , and the expression is:

[0063]

[0064] wherein X T is the temperature-sensitive parameter at temperature T, is the temperature-sensitive parameter at reference temperature T ref , and E a，X is the activation barrier of the physical quantity X.

[0065] S5: input the conservation order parameter control equation, the non-conservation order parameter control equation, the concentration field control equation, the electrostatic potential field control equation and the temperature field control equation into the finite element analysis software to obtain the dendrite growth morphology at different temperatures, and further obtain the threshold temperature of dendrite thermal self-healing.

[0066] The calculation domain is constructed in the finite element analysis software, such as Figure 3 and Figure 4As shown, the conservation order parameter control equation, the non-conservation order parameter control equation, the concentration field control equation, the electrostatic potential field control equation and the temperature field control equation are respectively set in the software, and the dendrite growth morphology, the concentration distribution, the electric potential field distribution and the dendrite morphology after atomic diffusion can be obtained.

[0067] The temperature field equation is set to obtain the thermal effect of dendrite growth and the evolution of the temperature field with time and space, and the temperature and the temperature-sensitive parameters (lithium ion diffusion coefficient, electrochemical reaction constant, lithium atom diffusion coefficient) are associated through the Arrhenius formula, so that the influence of temperature on electrochemical reaction and mass transfer can be reflected.

[0068] The boundary conditions and initial values are set, the appropriate grid type and size are selected to discretize the calculation domain, and the adaptive grid refinement is adopted, which greatly improves the calculation accuracy without significantly increasing the calculation amount.

[0069] The time step and calculation time are set in the transient solver, and the calculation is solved by using the separate solver.

[0070] By comparing the dendrite growth morphology at different temperatures, the threshold temperature of dendrite thermal self-healing can be obtained, and above this temperature, thermal-induced dendrite self-healing can be realized to realize dendrite-free lithium metal anode.

[0071] In the dendrite phase field model, the present application introduces atomic diffusion, which takes the atomic diffusion behavior into the lithium metal electrodeposition kinetics process, and more comprehensively simulates the dendrite growth and evolution. Further, through the coupling of multiple temperature-sensitive parameters (lithium ion diffusion coefficient Reaction constant L η , lithium atom diffusion coefficient D Li ) with the heat transfer model, the influence of temperature on dendrite growth is comprehensively considered, the mechanism of dendrite thermal self-healing is revealed, and the threshold temperature of dendrite thermal self-healing is accurately predicted.

[0072] 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, and 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 of predicting a dendrite thermal self-healing temperature of a lithium metal battery, the method comprising: The method comprises: S1: adopting Cahn-Hilliard equation to describe lithium atom diffusion behavior, and obtaining a conserved order parameter control equation for describing lithium atom diffusion; S2: constructing a Gibbs free energy function of a half-cell system composed of lithium metal and electrolyte by using local chemical free energy density, gradient free energy density and electrostatic free energy density of the half-cell system, and substituting the Gibbs free energy function into Allen-Cahn equation to obtain a non-conserved order parameter control equation for describing solid-liquid diffusion interface in ionic electrolyte; S3: constructing a concentration field control equation of lithium ions in lithium ion electrolyte by using Nernst-Planck equation, and constructing an electrostatic potential field control equation of lithium ion electrolyte by using Poisson equation; S4: obtaining a temperature field control equation for describing temperature field change in lithium dendrite growth process by using heat conduction differential equation based on energy conservation equation, and correlating temperature field and temperature dependent parameters by using Arrhenius equation; S5: inputting the conserved order parameter control equation, the non-conserved order parameter control equation, the concentration field control equation, the electrostatic potential field control equation and the temperature field control equation into finite element analysis software to obtain dendrite growth morphology at different temperatures, and then obtaining threshold temperature of dendrite thermal self-healing.

2. The method of claim 1, wherein, The conserved order parameter control equation in step S1 is: where ψ is a conserved order parameter of phase field, is the chemical potential, is the total free energy function of the system, Wψ 2 (1-ψ) 2 is the chemical free energy density, and W is the potential barrier height, is the gradient free energy density, κ0 is the gradient energy coefficient, and M(ψ) is the atomic mobility, M(ψ) = D Li ψV m / RT, D Li is the atomic diffusion coefficient, V m is the molar volume of lithium, R is the universal gas constant, and T is the temperature.

3. The method of claim 1, wherein, The Gibbs free energy function is: where f ch (ξ, c i ) is the local chemical free energy density, g(ξ) = Wξ 2 (1-ξ) 2 is the double-well function, c0is the initial electrolyte concentration, μ i Θ is the reference chemical potential of component i, c Li is the set of lithium atom concentrations, is the set of lithium ion concentrations, c i is the set of concentrations of component i; κ0is the gradient energy coefficient, δ is the anisotropy strength, ω is the modulus of anisotropy, θ is the angle between the interface normal direction and the reference axis direction; f elec (ξ, c i , φ i ) = F∑ i z i c i φ i , F is the Faraday constant, z i is the valence of component i, φ i is the local electrostatic potential, and ξ is the non-conservative order parameter.

4. The method of claim 3, wherein, The non-conserved order parameter control equation is: where h'(ξ) is the derivative of the interpolation function h(ξ) = ξ 3 (6ξ 2 - 15ξ + 10), ξ is a non-conservative order parameter, L σ is the interfacial mobility, L η is the interfacial reaction constant, g'(ξ) is the derivative of the double-well function g(ξ) = Wξ 2 (1 - ξ) 2 , α is the charge transfer coefficient, and η is the overpotential, η = φ Li - φ e - E Θ , φ Li is the electrode potential, φ e is the electrolyte potential, and E Θ is the standard half-cell potential.

5. The method according to claim 1 or 4, characterized in that, The concentration field control equation is: wherein, D is the diffusion coefficient of lithium ions in the electrolyte, c Li is the lithium atom concentration, is the lithium ion concentration, F is the Faraday constant, R is the universal gas constant, and T is the temperature.

6. The method according to claim 1 or 4, characterized in that, The electrostatic potential field control equation is: where σ eff is the effective conductivity, σ eff = σ Li h(ξ) + σ e (1 - h(ξ)), σ Li is the electrode conductivity, σ e is the electrolyte conductivity, is the potential gradient.

7. The method of claim 1, wherein, The temperature field control equation is: where C is the effective specific heat capacity, p is the mass density, l is the thermal conductivity, l p is the effective electrical conductivity, l eff is the effective electrical conductivity, l eff = l Li h(ξ) + l e (1 - h(ξ)), Q is the heat generation rate, Q ohmic is the Joule heat generated by the solution resistance, Q over is the overpotential heat generation, a s is the specific surface area of the electrode per unit volume, U j is the open circuit voltage, is the electrolyte potential gradient, f Li is the electrode potential, f e is the electrolyte potential, F is the Faraday constant, c Li is the lithium atom concentration set.

8. The method of claim 7, wherein, The temperature dependent parameters include lithium ion diffusion coefficient, electrochemical reaction constant and lithium atom diffusion coefficient.

9. The method of claim 8, wherein, The correlation formula for correlating temperature field and temperature dependent parameters by using Arrhenius equation is: where X T is a temperature sensitive parameter at temperature T, is a temperature sensitive parameter at reference temperature T ref E a，X is the corresponding activation barrier for the physical quantity X.

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