A method for modeling overpotential of liquid metal battery molten salt electrolyte considering material transport

Abstract

The application belongs to the technical field of liquid metal battery application, and specifically discloses a modeling method of overpotential of molten salt electrolyte of liquid metal battery considering material migration, which comprises the following steps: obtaining a potential gradient based on a current density equation and an ion concentration change rate equation in the molten salt electrolyte; simplifying a material electric migration process caused by the potential gradient by using a lumped negative ion parameter based on an electric neutrality condition equation to obtain a simplified material electric migration equation; establishing an equation for describing lithium ion concentration change, determining a boundary condition of the equation, solving the equation combined with the boundary condition to obtain a spatiotemporal distribution of lithium ion concentration in the molten salt electrolyte; solving the spatiotemporal distribution of lithium ion concentration to obtain a potential distribution inside the molten salt electrolyte; and calculating the overpotential of the molten salt electrolyte according to the potential distribution. The application can accurately analyze the material migration process in the molten salt electrolyte of the liquid metal battery and effectively calculate the overpotential.

Description

Technical Field

[0001] This application belongs to the field of liquid metal battery application technology, and more specifically, relates to a method for modeling the overpotential of molten salt electrolyte in liquid metal batteries that takes into account mass migration. Background Technology

[0002] As a novel grid-scale energy storage technology, liquid metal batteries exhibit superior performance compared to traditional solid-state batteries due to their unique thermodynamic and kinetic characteristics. At operating temperatures, the metal anode, molten salt electrolyte, and alloy cathode are all in a molten state, forming a stable three-layer liquid structure based on density differences. This electrodeless design effectively avoids common aging mechanisms in solid-state batteries, such as dendrite growth and electrode material pulverization, resulting in superior cycle life and stability, while also offering significant cost-effectiveness and scalability potential.

[0003] However, liquid metal batteries operate at high temperatures (300℃-700℃) and undergo complex alloying processes. In particular, the molten salt electrolyte is a mixture of multiple salts, leading to more complex ion transport pathways. Therefore, a model needs to be constructed specifically for the mass transfer characteristics of the molten salt electrolyte in this battery. Currently, the most commonly used simulation methods for the molten salt electrochemical processes in liquid metal batteries are finite element method (FEM) and finite volume method (FCV). These methods require complex calculations and are heavily reliant on simulation software such as OpenFOAM or COMSOL, making them difficult to apply in practice. Chinese invention patent CN115376619B discloses a method for modeling molten salt mass migration in liquid metal batteries based on a counter electrode battery. However, this counter electrode design is cumbersome and struggles to characterize the mass migration patterns in the molten salt electrolyte under real-world operating conditions, lacking precise analysis of mass migration within the molten salt electrolyte. This method is deficient in both accuracy and practicality.

[0004] Therefore, accurately analyzing the mass migration process in the molten salt electrolyte of liquid metal batteries and effectively calculating the overpotential is a problem that urgently needs to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this application is to provide a method for modeling the overpotential of molten salt electrolyte in liquid metal batteries that considers mass migration, which can accurately analyze the mass migration process in the molten salt electrolyte of liquid metal batteries and achieve effective calculation of overpotential.

[0006] To achieve the above objectives, in a first aspect, this application provides a method for modeling the overpotential of molten salt electrolyte in liquid metal batteries that considers mass migration, comprising the following steps: S10. Based on the equations describing the ion flux, the mass conservation equation, and the electroneutrality condition equation in the molten salt electrolyte, the current density equation and the ion concentration change rate equation in the molten salt electrolyte are derived; the potential gradient is obtained by combining the current density equation and the ion concentration change rate equation. S20, the diffusion coefficient, concentration, and electromobility parameters of all negatively charged ions in the molten salt electrolyte are lumped together to obtain lumped negative ion parameters; based on the electroneutrality condition equation, the electromigration process of matter caused by the potential gradient is simplified using the lumped negative ion parameters to obtain a simplified electromigration equation. S30. Based on the simplified mass electromigration equation and the ion concentration change rate equation, an equation describing the change in lithium ion concentration is established; based on the fact that only lithium ions undergo electrochemical reactions at the electrode-molten salt electrolyte interface, the boundary conditions of the equation are determined; the equation is solved in combination with the boundary conditions to obtain the spatiotemporal distribution of lithium ion concentration in the molten salt electrolyte. S40, Based on the spatiotemporal distribution of the lithium ion concentration, the potential distribution inside the molten salt electrolyte is obtained by integral calculation based on the current density equation; S50, calculate the overpotential of the molten salt electrolyte based on the potential distribution.

[0007] As a further preferred embodiment, in step S10, the equation describing the ion flux in the molten salt electrolyte is:

[0008] The mass conservation equation is:

[0009] The equation for the condition of electrical neutrality is:

[0010] In the formula, D i , c i , z i and m i Let represent the diffusion coefficient, concentration, charge, and electromobility of ion i, respectively. The potential of the molten salt electrolyte; u For flow rate; F is Faraday's constant.

[0011] As a further preferred embodiment, in step S10, the current density equation is:

[0012] The equation for the rate of change of ion concentration is:

[0013] In the formula, R Represents the molar gas constant; T Indicates temperature; t Indicates time; J el Current density; It is the potential difference; This represents the potential difference in the molten salt layer.

[0014] As a further preferred embodiment, in step S20, the aggregated negative ion parameter includes the aggregated negative ion diffusion coefficient. D - Total negative ion concentration C - and total negative ion electromobility m - ; The simplified mass electromigration equation is as follows:

[0015] in, D + , C + , m + These represent the diffusion coefficient, concentration, and electromobility of lithium ions, respectively.

[0016] As a further preferred embodiment, in step S30, the equation describing the change in lithium ion concentration is:

[0017] The boundary conditions are as follows:

[0018] in, x Indicates the length in the x-direction; D Indicates the diffusion coefficient; J This represents the current density.

[0019] As a further preferred embodiment, in step S30, the spatiotemporal distribution of lithium ion concentration in the molten salt electrolyte is expressed as follows:

[0020] in, s Represents the complex frequency domain; γ represents the time constant of mass migration within the electrolyte; L Ls represents the thickness of the positive electrode; Ls represents the thickness of the molten salt. represents the initial lithium concentration; cosh represents a trigonometric function.

[0021] As a further preferred embodiment, the mass migration time constant γ is used to describe the mass transfer characteristics in the molten salt electrolyte, and is expressed by the following formula: .

[0022] As a further preferred embodiment, the molten salt electrolyte is a mixture of LiF, LiCl and LiBr, and the liquid metal battery is a Li||SbSn battery.

[0023] As a further preferred embodiment, in step S40, the analytical expression for the spatiotemporal distribution of the potential inside the molten salt electrolyte is:

[0024] In the formula, .

[0025] Secondly, this application provides a liquid metal battery management system, including a processing unit and a storage unit, wherein the storage unit stores a computer program, and the processing unit executes the computer program to implement the steps of the liquid metal battery molten salt electrolyte overpotential modeling method considering mass migration as described above.

[0026] This application has the following advantages: First, by establishing governing equations based on ion flux, mass conservation, and electroneutrality, and deriving current density equations and ion concentration change rate equations, a complete physical and mathematical model foundation is provided for describing the complex multi-ion migration and reaction processes within molten salt electrolytes, thus enabling the mechanistic analysis of the mass migration process. Furthermore, by lumping the parameters of all negatively charged ions in the molten salt electrolyte and simplifying the electromigration process caused by the potential gradient using electroneutrality conditions, the challenge of complex migration paths and direct solution difficulties caused by the coexistence of multiple ion components is effectively overcome. This method significantly reduces the complexity and computational requirements of the model, freeing it from heavy reliance on dedicated simulation software. Based on this, an equation describing the change in lithium-ion concentration is established and solved according to the interface conditions where only lithium ions undergo electrochemical reactions. This yields an analytical solution for the spatiotemporal distribution of the concentration of key reactive ions (lithium ions) in the molten salt electrolyte, enabling precise analysis of the mass migration process. Finally, based on this precise concentration distribution, the analytical expression for the potential distribution inside the molten salt electrolyte can be directly obtained through the integral operation of the current density equation. This allows for the effective calculation of overpotentials, providing crucial internal state parameters for battery management. By organically combining and synergistically integrating the above steps, this method transforms the complex physics of multi-ion migration into a model that can be handled through mathematical analysis, improving computational efficiency and practicality while maintaining model accuracy. Attached Figure Description

[0027] Figure 1 This is a flowchart of the method for modeling the overpotential of molten salt electrolyte in liquid metal batteries that takes into account mass migration, provided in the embodiments of this application. Figure 2 Here are structural diagrams of the liquid metal battery provided in the embodiments of this application; wherein, (a) is a physical structure diagram; and (b) is a quasi-two-dimensional battery model diagram. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] The purpose of this application is to provide a method for modeling the overpotential of molten salt electrolyte in liquid metal batteries that considers mass migration. The method provided in this application can practically calculate the overpotential of the molten salt electrolyte during the charging and discharging process of the battery, ensuring the accuracy and reliability of the liquid metal battery management process and providing a foundation for its large-scale application.

[0030] According to this application, Figure 1 As shown, the mass transfer process in the molten salt electrolyte of a liquid metal battery is first analyzed. Specifically, the ion flux in the molten salt electrolyte is described by the following equation: (1) In the formula, D i , c i , z i and m i These represent the diffusion coefficient, concentration, charge, and electromobility of the corresponding ions, respectively. F el This represents the potential of the molten salt electrolyte. u For flow rate, F Let be the Faraday constant. The relationship between the diffusion coefficient and electromobility of ions is calculated by the following equation: (2) in, R Represents the molar gas constant. T The temperature is represented by . Meanwhile, all ions in the molten salt electrolyte satisfy the law of conservation of mass, that is, the sum of the rate of change of ion concentration and the divergence of the ion flux is always zero, as shown in equation (3): (3) in t Indicates time. There is no localized charge accumulation in molten salt electrolytes: (4) Combining equations (1) to (4) above, the current density in the molten salt electrolyte... J el It can be represented as: (5) Molten salt electrolytes contain various ions, and the transport of these ions is complex. The concentration of the substance is influenced by multiple factors, including potential and concentration gradient. The determination of the corresponding ions is crucial. i rate of concentration change: (6) The ionic composition and migration process in molten salts are complex. Preferably, this embodiment uses a Li||SbSn battery with a molten salt of LiF|LiCl|LiBr mixture as an example. The molten salt electrolyte contains positively charged ions (Li... + ) and negatively charged ions (F - Cl - ,Br - The conductivity of molten salt electrolytes is determined by the concentration of all ions, including those involved in diffusion and electromigration. This complex composition presents a significant challenge in determining the concentration and diffusion coefficient of each ion. Therefore, numerical analysis is required to construct a molten salt overpotential model.

[0031] In one embodiment, the technical solution for achieving the above objective can be specifically as follows: Figure 2 As shown, liquid metal batteries exhibit a typical three-layer structure based on automatic separation due to density differences: the bottom layer is a high-density positive electrode metal alloy (Sb-Sn alloy), the top layer is a low-density negative electrode metal (Li), and the middle layer is a LiF-LiCl-LiBr molten salt electrolyte. Based on this physical structure, this application constructs a liquid metal battery as shown in the figure. Figure 2 The quasi-two-dimensional battery model shown in (b) is illustrated. In this model, the cross-sectional area of ​​the battery is set to A, and the electron exchange reaction mainly occurs at two interfaces: the positive electrode / electrolyte interface at x=L, and... x = L + L s The negative electrode / electrolyte interface at that location. Furthermore, x=0 and... x = L + L s + L n These correspond to the current collector boundaries of the positive and negative electrodes, respectively.

[0032] Equation (6) describes the specific laws governing the influence of electromigration and diffusion on the concentration of substances in molten salt electrolytes. Equation (5) describes the relationship between battery current density and concentration. Combining equations (5) and (6), the potential gradient can be obtained: (7) in s Indicates the conductivity of molten salt: (8) To simplify calculations, in this study, the parameters of all negatively charged ions are uniformly processed using lumped parameters, and the symbols are... D - , C - , m - These represent the total diffusion coefficient, concentration, and electromobility of negatively charged ions in the molten salt, respectively. Conversely, the symbols... D + , C + , m + Li + The diffusion coefficient, concentration, and electromobility of the electrolyte. Simultaneously, since all ions in the electrolyte are single-charged, the total negative charge is also a single charge, i.e., ionic charge. z It can be represented as: (9) Based on the above analysis and simplifying assumptions, the electromigration of matter caused by the potential gradient can be derived as follows: (10) Considering that molten salt electrolytes always remain electrically neutral, as shown in equation (4), the electromigration process can be further simplified by combining equations (9) to (10): (11) Equation (6) describes how the concentration changes of substances in molten salt electrolytes are affected by electromigration and diffusion. Furthermore, the concentration of Li in the electrolyte can be calculated. + concentration: (12) parameter This is a lumped parameter composed of the electromobility and diffusion coefficient of positive and negative ions in the molten salt electrolyte, describing the mass transfer characteristics of the electrolyte. In this embodiment, the mass transfer time constant within the electrolyte is defined as [symbol missing]. c To reflect this characteristic: (13) Molten salt electrolytes facilitate the transport of multiple substances, but only Li is present at the electrode / molten salt boundary. + An electrochemical reaction occurs, therefore the boundary conditions only consider Li. + : (14) By performing a Laplace transform on equations (12) to (14), Li can be calculated. + Changes in concentration: (15) Equation (15) describes Li at any position and at any time. + Concentration divergence. Since only the concentration of substances in molten salt electrolytes is considered... x The propagation in direction, the divergence of concentration can be understood as the concentration formula's effect on... x The derivative of . In order to obtain the specific analytical expression for the substance concentration, it is necessary to take the derivative of equation (15). x The spatiotemporal distribution of the concentration can be calculated by integrating the integral: (16) in c e 0 Indicates Li in molten salt + The initial concentration. When the battery is in a stable state, the concentration of substances in the molten salt electrolyte is equal everywhere, and because the overall Li in the electrolyte is... + The concentration remains constant, therefore c e 0 It remains unchanged.

[0033] The mass transfer process not only alters the concentration distribution of substances in the molten salt electrolyte but also changes its potential distribution. Using equation (5), the potential distribution in the molten salt electrolyte can be calculated: (17) Furthermore, by combining equations (15) to (17), the specific expression for the potential distribution can be obtained: (18) Equation (18) consists of two terms. For ease of description, they are represented by symbols. f 1 and f 2 represents the first and second terms, that is, using f =-( f 1+ f 2) indicates.

[0034] For equation (18) f 1: (19) Integrating equation (19), we get: (20) For ease of calculation, letx Therefore, the integral term in equation (20) can be transformed into: (twenty one) Furthermore, define Therefore, it can be deduced that: Therefore, equation (21) can be calculated as: (twenty two) Therefore, it can be deduced that f The value of 1: (twenty three) For equation (18) f 2: (twenty four) Integrating this formula yields: (25) Furthermore, the distribution of electric potential in the molten salt at any time and any location can therefore be determined: (26) in, .

[0035] Based on this formula, the overpotential in molten salt can be determined by calculating the potential at different locations.

[0036] Overall, the above-described technical solutions conceived in this application present, for the first time, a method for modeling the overpotential of molten salt electrolyte in liquid metal batteries. This method can help with the further management and control of the batteries, paving the way for their large-scale application.

[0037] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration, characterized in that, Includes the following steps: S10. Based on the equations describing the ion flux, the mass conservation equation, and the electroneutrality condition equation in the molten salt electrolyte, the current density equation and the ion concentration change rate equation in the molten salt electrolyte are derived; the potential gradient is obtained by combining the current density equation and the ion concentration change rate equation. S20, the diffusion coefficient, concentration, and electromobility parameters of all negatively charged ions in the molten salt electrolyte are lumped together to obtain lumped negative ion parameters; based on the electroneutrality condition equation, the electromigration process of matter caused by the potential gradient is simplified using the lumped negative ion parameters to obtain a simplified electromigration equation. S30. Based on the simplified mass electromigration equation and the ion concentration change rate equation, an equation describing the change in lithium ion concentration is established; based on the fact that only lithium ions undergo electrochemical reactions at the electrode-molten salt electrolyte interface, the boundary conditions of the equation are determined; the equation is solved in combination with the boundary conditions to obtain the spatiotemporal distribution of lithium ion concentration in the molten salt electrolyte. S40, Based on the spatiotemporal distribution of the lithium ion concentration, the potential distribution inside the molten salt electrolyte is obtained by integral calculation based on the current density equation; S50, calculate the overpotential of the molten salt electrolyte based on the potential distribution.

2. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S10, the equation describing the ion flux in the molten salt electrolyte is: The mass conservation equation is: The equation for the condition of electrical neutrality is: In the formula, D i , c i , z i and μ i Let represent the diffusion coefficient, concentration, charge, and electromobility of ion i, respectively. This represents the potential of the molten salt electrolyte. u For flow rate; F is Faraday's constant.

3. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S10, the current density equation is: The equation for the rate of change of ion concentration is: In the formula, R Represents the molar gas constant; T Indicates temperature; t Indicates time; J el Current density; It is the potential difference; This represents the potential difference in the molten salt layer.

4. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S20, the aggregated negative ion parameters include the aggregated negative ion diffusion coefficient. D - Total negative ion concentration C - and total negative ion electromobility μ - ; The simplified mass electromigration equation is as follows: in, D + , C + , μ + These represent the diffusion coefficient, concentration, and electromobility of lithium ions, respectively.

5. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S30, the equation describing the change in lithium ion concentration is: The boundary conditions are as follows: in, x Indicates the length in the x-direction; D Indicates the diffusion coefficient; J This represents the current density.

6. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S30, the spatiotemporal distribution of lithium ion concentration in the molten salt electrolyte is expressed as follows: in, s Represents the complex frequency domain; γ represents the time constant of mass migration within the electrolyte; L Ls represents the thickness of the positive electrode; Ls represents the thickness of the molten salt. represents the initial lithium concentration; cosh represents a trigonometric function.

7. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 6, characterized in that, The mass migration time constant γ is used to describe the mass transfer characteristics in the molten salt electrolyte, and is expressed by the following formula: 。 8. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, The molten salt electrolyte is a mixture of LiF, LiCl and LiBr, and the liquid metal battery is a Li||SbSn battery.

9. The method for modeling the overpotential of molten salt electrolyte in liquid metal batteries considering mass migration as described in claim 1, characterized in that, In step S40, the analytical expression for the spatiotemporal distribution of potential inside the molten salt electrolyte is: In the formula, .

10. A liquid metal battery management system, characterized in that, It includes a processing unit and a storage unit, wherein the storage unit stores a computer program, and the processing unit executes the computer program to implement the steps of the liquid metal battery molten salt electrolyte overpotential modeling method considering mass migration as described in any one of claims 1 to 9.

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