Method for fitting chemical capacitance of solid oxide battery and measuring electrode current

Abstract

The invention discloses a method for fitting chemical capacitance of a solid oxide battery and measuring electrode current, and belongs to the technical field of battery numerical simulation. According to the method disclosed by the invention, the influence of electrochemical reaction factors and non-electrochemical reaction factors on the chemical capacitance is accurately described by constructing a model, describing an electrode process by using a differential equation, generating a current-voltage curve and measuring a real chemical capacitance value by comparing the current-voltage curves generated at different scanning voltage rates; the measurement and calculation accuracy of the chemical capacitance value is effectively improved; and the real electrode current is calculated by using the measured and calculated real chemical capacitance value, so that the chemical capacitance current and the reaction current of the electrode can be accurately separated, and the dynamic characteristics of the electrode process can be accurately captured.

Description

Technical Field

[0001] The invention belongs to the technical field of battery numerical simulation, and more specifically, relates to a method for fitting the chemical capacitance of a solid oxide battery and measuring electrode current. Background Art

[0002] Solid oxide cells (SOC) have the advantages of high efficiency and pollution-free products. As an efficient and clean energy conversion device, they have attracted widespread attention in recent years. Chemical capacitance, as an important parameter, can characterize the charging and discharging of solid oxide cells. The factor that has the greatest impact on the chemical capacitance value is the change in current when the perturbation voltage changes. The change in current is the sum of the reaction current (electrochemical reaction part) and the chemical capacitance current (non-electrochemical reaction part). The reaction current is also called the Faraday current. Therefore, the accurate determination of chemical capacitance is of great significance for measuring the electrode current of the battery.

[0003] However, in actual experiments, the changes in chemical capacitance current are difficult to distinguish from changes in reaction current. In addition, the chemical capacitance value measured during electrochemical testing will be mixed with other capacitances, such as the double-layer capacitance of each interface, making it difficult to accurately measure the chemical capacitance value.

[0004] The most widely used method at present is electrochemical impedance spectroscopy. For example, patent CN107526881A discloses a lithium battery electrode impedance modeling method based on continuity derivation, which includes the following steps: Step 1, battery voltage and current calculation based on electrochemical principles; Step 2, electrode impedance model establishment; Step 3, single lithium battery electrochemical equivalent model establishment based on electrode impedance model; Step 4, electrode impedance model verification based on SOC value. The invention starts with the study of the reaction rate of the insertion layer and the extraction layer to establish an equivalent impedance model for solid thin film lithium battery electrodes; the electrode equivalent impedance model includes an RC parallel circuit to represent the charge transfer characteristics, a finite length Warburg model to represent the electrolyte diffusion characteristics, and a finite space Warburg model to represent the solid diffusion characteristics; the finite space Warburg model is used to establish an equivalent capacitor, which simulates the differential capacitance value of the cathode and anode of the lithium battery. However, the data analysis and calculation accuracy of the electrochemical impedance spectrum are limited.

[0005] Using simulation methods to measure chemical capacitance is an effective method. The current simulation method used for solid oxide batteries is the Butler-Volmer equation. However, the Butler-Volmer equation is not accurate in describing the electrode mass transfer and reaction process when describing electrode kinetics. The mass transfer coefficient deviates significantly from the classical value usually assumed, so it cannot describe the capacitance effect of the electrode. In addition, since the reaction current is generally measured using the capacitance effect, the inaccurate capacitance effect not only cannot accurately separate the chemical capacitance current and reaction current of the electrode, but also cannot accurately separate the cathode current and anode current of the battery.

[0006] Patent CN111625929A discloses a numerical simulation method for SOFC under multi-physical field coupling, including: establishing a multi-physical field coupling model of a single solid oxide fuel cell; defining the physical parameters required for simulating solid oxide fuel cells and the boundary conditions of the multi-physical field model; coupling the various physical fields involved in the actual operation of the battery; performing steady-state and transient calculations on the gridded solid oxide fuel cell multi-physical field model to obtain the calculation results of the battery internal temperature field, stress field, gas flow field, material concentration distribution field, and current density distribution under different working conditions. However, this patent does not involve how to fit the chemical capacitance of the SOFC battery, and the chemical capacitance involves the changes in material concentration in both the electrochemical reaction and non-electrochemical reaction areas. This patent only considers the influence of electrochemical reaction factors on chemical capacitance, but does not introduce non-electrochemical reaction factors, so it is impossible to obtain accurate chemical capacitance.

[0007] Patent CN103544339A discloses a modeling method for distributed capacitance between transmission lines of an underwater XCTD profiler. ProE is used for 3D modeling and the AC / DC module in Comsol Multiphysics (multi-physics field) is used to calculate the capacitance value of the model, thereby obtaining the distributed capacitance value between the two metal wires and the capacitance value between each metal wire and the seawater. Finally, the two capacitance values ​​obtained are compared with the theoretical calculated values ​​to verify the correctness of the simulation results. However, this patent is aimed at metal wires with uniform capacitance distribution. For solid oxide batteries, the capacitance values ​​will be different at different battery locations, so it is impossible to obtain accurate chemical capacitance.

[0008] Based on the above problems, how to improve the measurement accuracy of the chemical capacitance of solid oxide fuel cells is an issue that needs to be solved urgently. Summary of the invention

[0009] 1. Problem to be solved

[0010] In view of the problem of poor measurement accuracy of chemical capacitance in the prior art, the present invention provides a method for fitting the chemical capacitance of a solid oxide battery. The chemical capacitance measured by this method accurately describes the influence of electrochemical reaction factors and non-electrochemical reaction factors on the chemical capacitance, thereby effectively improving the measurement accuracy of the chemical capacitance of the solid oxide fuel cell.

[0011] Another object of the present invention is to accurately separate the chemical capacitance current and the reaction current of the solid oxide fuel cell by using the calculated chemical capacitance to measure the reaction current.

[0012] 2. Technical solution

[0013] In order to solve the above problems, the technical solution adopted by the present invention is as follows:

[0014] A method for fitting the chemical capacitance of a solid oxide battery and measuring the electrode current comprises the steps of:

[0015] S1. Modeling: Input the geometric parameters of the battery into the multi-physics model for geometric modeling, and input the initial chemical capacitance value C chem ;

[0016] S2, fitting generated current I total :According to the geometric model fitting, the current in the current-voltage curve is the current I generated by the fitting. total , the fitting generates a current I total is the fitting reaction current I reac With the fitted chemical capacitance current I c The sum of the fitting reaction current I reac According to the calculation of chemical reaction rate, the fitted chemical capacitance current I c is the ratio of potential difference to resistance;

[0017] S3. Get the real chemical capacitance value C chem,real :Compare the fitted generated current I under the same voltage total and experimental current, the experimental current is measured under the same conditions, when the fitting generated current I at different scanning voltage rates total If the current is consistent or close to the experimental current, then input the initial chemical capacitance value C of the model. chem That is the actual chemical capacitance value C chem,real .

[0018] If the fitting generated current I total If the current is not consistent or close to the experimental current, enter a new chemical capacitance value C chem , until the fitting current I is generated at different scanning voltage rates total The current is consistent with the experiment.

[0019] The consistency or similarity described in step S3 is the fitting generated current I total The maximum error value of the experimental current is less than 10%, and the average error value is less than 3%.

[0020] Furthermore, the geometric parameters of the battery in step S1 include the diameter and thickness of the electrolyte and the working electrode. To improve the accuracy of the measurement, the geometric parameters of the battery can be obtained by measurement, such as performing a scanning electron microscope test on the battery.

[0021] The experimental conditions set in this application include temperature, gas concentration, flow rate and scanning voltage rate, which are consistent with the actual experimental conditions.

[0022] In this application, the fitting generated current I total Satisfy the formula:

[0023]

[0024] In formula (7), F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(e - ) is the electrode electron concentration, c reac is the reactant concentration, E is the applied overvoltage, is the lattice oxygen concentration, C chem is the initial chemical capacitance value; R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

[0025] Furthermore, in step S3, the fitted current I is compared with the current I generated under the same voltage. total and experimental current, when the fitting generated current I total When the current is consistent or close to the experimental current, it can be considered that the initial chemical capacitance value C of the input multi-physics model chem is the actual chemical capacitance value C chem,real , where the fitting generates the current I total It refers to the current obtained by fitting according to the above formula, and the experimental current refers to the actual current obtained through actual experimental testing.

[0026] In this application, the fitting generated current I total is the fitting reaction current (Faraday current) I reac and fitting chemical capacitor current (charging current) I c The sum of I total =I reac +I c ; where the fitted reaction current I reac Satisfy the formula:

[0027] I reac =F*k*c(e - ) 4 *c reac Formula (1)

[0028] In formula (1), F is the Faraday constant; k is the material heterogeneous reaction rate constant; c(e - ) is the electrode electron concentration; c reac is the concentration of the reactant.

[0029] In this application, the fitted chemical capacitance current I c for:

[0030]

[0031] In formula (6), F is the Faraday constant, E is the magnitude of the applied overvoltage, is the lattice oxygen concentration, C chem is the initial chemical capacitance value, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

[0032] The solid oxide cell includes an anode and a cathode. In some specific embodiments of the present application, the method provided in the present application can fit both the cathode chemical capacitance of the solid oxide cell and the anode chemical capacitance of the solid oxide cell. Among them, CO2 reduction and lattice oxygen generation occur at the cathode, and lattice oxygen consumption occurs at the anode. Therefore, the electrode electron concentration, surface adsorbed carbon dioxide concentration and electrode oxygen vacancy concentration are introduced into the reaction current of the cathode, and the electrode electron concentration and lattice oxygen concentration are introduced into the reaction current of the anode.

[0033] When fitting the cathode chemical capacitance of solid oxides, the reactant concentration c reac Satisfies the following formula:

[0034]

[0035] That is, the fitted cathode reaction current I reac,cath for:

[0036]

[0037] Total cathode current I total,cath for:

[0038]

[0039] Where F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(CO 2(ad) ) is the surface adsorbed carbon dioxide concentration, c(e - ) is the electrode electron concentration, is the electrode oxygen vacancy concentration, E cath is the external voltage, is the lattice oxygen concentration, C chem is the initial chemical capacitance value, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

[0040] When fitting the anodic current of the solid oxide,

[0041] That is, the fitted anode reaction current I reac,ano Satisfies the following formula:

[0042]

[0043] Total anode current I reac,ano for:

[0044]

[0045] Where F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(e - ) is the electrode electron concentration, E ano is the anode applied voltage, is the lattice oxygen concentration, C chem is the initial chemical capacitance value, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

[0046] The change in current is the sum of the reaction current and the chemical capacitance current. However, in actual experiments, the reaction current and the chemical capacitance current are generally difficult to separate. The present invention uses differential equations to describe the electrode process, adopts multi-physics field simulation, and uses the finite element method to solve the differential equations.

[0047] The derivation process of the differential equation is as follows, taking the cathode current as an example:

[0048] During the experiment, CO2 was introduced into the cathode region. CO2 molecules penetrated the porous electrode structure by diffusion and were adsorbed in the process. CO2 molecules adsorbed on the cathode surface dissociated with oxygen vacancies on the surface of the electrode material to generate CO and lattice oxygen. Subsequently, the lattice oxygen was transferred to the anode by diffusion and further oxidized at the anode. Since the electrode material is a mixed ion and electron conductor, this dissociation reaction occurs not only at the three-phase interface, but also at the two-phase interface.

[0049] The cathode is provided with an inlet at the bottom, and the experiment assumes that the incoming gas flow is uniform and the gas composition is consistent over the entire electrode surface. Based on these assumptions, a constant concentration boundary condition is set to simulate the actual gas supply situation:

[0050] c i =c0 Formula (11)

[0051] where c i is the concentration of the reactants. Different subscripts correspond to gases CO and CO2, respectively. c0 is the gas concentration in the incoming flow. According to the experimental airflow of the actual SOC, the concentration of CO is set to 0 and the concentration of CO2 is set to 44.24 mol / L, respectively.

[0052] Volume rate of material∈ SOC and porosity ε SOC The relationship is:

[0053] ∈ SDC =1-ε SDC Formula (12)

[0054] The mechanism of SOC as cathode electrolysis of CO2 is as follows:

[0055] (Adsorption step)

[0056] (Dissociation Step)

[0057] Among them, dissociation is the rate-determining step. Assuming that CO does not accumulate on the surface of the gas diffusion electrode and the reverse process of the reaction can be ignored, the cathode reaction rate can be determined by the following formula:

[0058]

[0059] Where k is the surface exchange coefficient, that is, the material heterogeneous reaction rate constant. According to the results in the reference, considering the concentration of electrons and oxygen vacancies, the k value is determined to be 7*10 -18 m 16 / (mol 5 *s). With the 2(ad) Lattice oxygen is generated at the same rate as it is consumed in the dissociation step.

[0060] In this step, electrons are provided by cations in the cathode material. Taking samarium-doped cerium oxide SDC as an example, in a CO2 / CO mixed atmosphere, trivalent cerium ions (Ce 4+ ) can be oxidized to tetravalent cerium ions (Ce 3+ ), thereby reducing the electronic resistance R eon The electron concentration c(e - ) concentration was determined by the Nernst-Einstein equation:

[0061]

[0062] Among them, n is used to characterize c(e - ), K is the Boltzmann constant, T is the absolute temperature, D is the diffusion coefficient of the electron, q is the charge of the electron, σ eff is the effective conductivity of the electrode, which is 5.88*10 at 750°C. -2 S / cm, this value is used to calculate c(e at 0V overpotential - ), c(e - ) will increase with the increase of overpotential.

[0063] In the process of deeply exploring the intrinsic kinetic parameters of porous MIEC electrode materials (mixed electron ion conductors), when the Butler-Volmer equation is applied to describe the electrode process, the transfer coefficient may significantly deviate from the classical value of 0.5 usually assumed. In addition, the traditional Tafel method may also deviate from its intrinsic value when calculating the transfer coefficient. In order to seek a more universal and accurate method, the present invention chooses to use the Nernst equation to describe the electrode reaction process in detail. This method not only improves the accuracy of the analysis, but also provides a solid theoretical basis for subsequent research.

[0064] The method of the present invention further comprises step S4: calculating and obtaining a real electrode current, wherein the real electrode current I total,real is the real reaction current I reac,real The real chemical capacitance current I c,real The sum of the actual chemical capacitance C chem,real Calculate the real electrode current I reac,real .

[0065] It is worth noting that the fitted current obtained in step S2 is based on the initial chemical capacitance value C chem If the initial chemical capacitance value C is obtained by fitting, chem Not the actual chemical capacitance value C chem,real , then according to the initialization value of the chemical capacitance C chem The calculated fitting generated current I total It is not the real electrode current of the electrode and cannot reflect the real situation of the electrode. Therefore, this application first fits the real chemical capacitance value C chem,real , and then use the actual chemical capacitance value C chem,real The real electrode current I is calculated total,real , which in turn reflects the actual current situation of the electrode.

[0066] Among them, the cathode real reaction current (Faraday current) I reac,cath,real Determined by the following formula:

[0067]

[0068] Real chemical capacitor current (charging current) I c,real Determined by the following formula:

[0069]

[0070] Where F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(CO 2(ad) ) is the surface adsorbed carbon dioxide concentration, c(e - ) is the electrode electron concentration, is the electrode oxygen vacancy concentration, E is the applied overvoltage, and E is defined as E = E0 + v scan *t, where E0 is the initial overpotential on the three-electrode system (usually 0 V), v scan is the speed of potential scanning, t represents time, is the lattice oxygen concentration, C chem,real is the actual chemical capacitance value, obtained by the method of fitting the chemical capacitance of the solid oxide battery in steps S1 to S3, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode; where vol eff Determined by the following formula:

[0071] vol eff =∈ SOC *vol total Formula (17)

[0072] In formula (17), vol total is the total volume of the electrode, ∈ SOC is the volume fraction of the electrode material.

[0073] Therefore, the charge transport process inside the electrode is associated with the porosity of the electrode. The total capture current (real cathode current I total,cath , real ) is determined by the sum of the reaction current and the chemical capacitance current.

[0074]

[0075] It is worth noting that during the negative scan, the electrode is in a charging state and the chemical capacitance current I c is a negative value, so the capture current (real cathode current) is smaller than the reaction current; while in the forward scan, the opposite is true.

[0076] Similarly, the real anode electrode current I can be derived total,ano,real The calculation formula is as follows:

[0077]

[0078] In summary, in this application, the electrode current Itotal,real is the reaction current I reac,real and chemical capacitance current I c,real The sum of the reaction current I reac According to the chemical reaction rate, the influence of the reaction species on the electrode material is comprehensively considered. The reaction species at the cathode are electrode electrons, surface adsorbed carbon dioxide and oxygen vacancies, and the reaction species at the anode are electrons and lattice oxygen. The chemical capacitance current I c It is the ratio of potential difference to resistance. The potential difference is the difference between the applied overpotential and the overpotential formed by the capacitor. When the SOC is in electrolysis mode, since an electrolysis reaction occurs on the cathode, the applied overvoltage is negative, and the chemical capacitor current is negative; an electrolysis reaction occurs on the anode, and the applied overvoltage is positive. When the SOC is in power generation mode, there is no need to apply an external voltage to the battery, so there is no need to consider the applied overvoltage.

[0079] The present application introduces lattice oxygen concentration to add an examination of non-electrochemical reaction factors, and the non-electrochemical reaction factors include gases introduced during the experiment. This is because the velocity and concentration distribution of the gas will affect the reaction rate of reactants in different parts of the battery, thereby affecting the chemical capacitance and electrode current; in addition, since the present application measures the body capacitance, the generation of chemical capacitance is closely related to the uneven distribution of ions inside the electrode. The difference in non-stoichiometric coefficients at different positions inside the electrode leads to the formation of an ion concentration gradient, which in turn stores ions in the electrode and forms a capacitive effect. The present application introduces lattice oxygen concentration to characterize the chemical capacitance at different positions, so as to more accurately describe the electrode mass transfer and reaction process.

[0080] Comparison fitting generates current I total When the generated current I is fitted with the experimental current total When the experimental current is the same or similar at different scan rates, the chemical capacitance value input into the multi-physics model is the true chemical capacitance value of the electrode.

[0081] Among them, when determining the chemical capacitance value, the present invention first assigns an initial chemical capacitance value C chem , bring it into the model for verification. If the fitted current generated by the chemical capacitance value is consistent with the experimental current result under different scanning voltage rate conditions, it means that the chemical capacitance value is the real chemical capacitance value. If not, adjust the chemical capacitance value until it meets the requirements. Depending on the electrode material, the real chemical capacitance value C chem,real Follow the Arrhenius equation.

[0082] The method of the present invention is applicable to the capacitance measurement of all solid oxide batteries, and can be used for measuring the air electrode capacitance of SOC batteries, wherein the air electrode includes but is not limited to a samarium-doped cerium oxide (SDC) electrode, a lanthanum strontium cobalt iron (LSCF) electrode, a gadolinium-doped cerium oxide (GDC) electrode, a LSM (lanthanum strontium manganese) electrode, and a LSC (lanthanum strontium cobalt) electrode; and can also be used for measuring the capacitance of an SOC fuel electrode, wherein the composition of the fuel electrode includes an electronic conductive phase and an ion conductive phase; wherein the electronic conductive phase includes but is not limited to at least one of NiO, Co3O4, CuO, Ag2O and ZnO; and the ion conductive phase includes but is not limited to one of doped or undoped zirconium oxide and doped or undoped cerium oxide.

[0083] The solid oxide battery of the present invention includes a solid oxide fuel cell (SOFC) and a solid oxide electrolyzer (SOEC). When used as a solid oxide fuel cell (SOFC), the aforementioned air pole is the cathode of the SOFC; when used as a solid oxide electrolyzer (SOEC), the aforementioned air pole is the anode of the SOEC.

[0084] 3. Beneficial effects

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] (1) The present invention constructs a multi-physics field model to generate a current-voltage curve, and compares the fitted current and the experimental current at different scanning voltage rates. When the fitted current and the experimental current are the same or similar at different scanning rates, the chemical capacitance value input into the multi-physics field model is the true chemical capacitance value of the electrode. This method accurately describes the influence of electrochemical reaction factors and non-electrochemical reaction factors on chemical capacitance, and effectively improves the accuracy of chemical capacitance value calculation;

[0087] (2) The present invention uses the obtained real chemical capacitance value to measure the real reaction current, which can accurately measure the cathode current and anode current of the solid oxide fuel cell, and accurately separate the chemical capacitance current and reaction current of the electrode;

[0088] (3) The fitting method constructed by the present invention can accurately capture the dynamic characteristics of the electrode process. After changing the scanning direction, the change of current density can still be observed, which is consistent with the actual measured current density trend. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but it should be understood that these drawings are designed only for explanation purposes and are not intended to limit the scope of the present invention. In addition, unless otherwise specified, these drawings are intended only to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.

[0090] Figure 1 The electrode model constructed for Example 1;

[0091] Figure 2 The grid structure and grid quality distribution of the electrode model of Example 1;

[0092] Figure 3 The current-voltage curves obtained by experiment and the current-voltage curves obtained by fitting in Examples 1 and 2;

[0093] Figure 4 The current-voltage curves of the fitted reaction current and the fitted chemical capacitance current separated when the scanning voltage rate is 20 mV / s in Example 1;

[0094] Figure 5 The current-voltage curves of the fitted reaction current and the fitted chemical capacitance current separated when the scanning voltage rate is 50 mV / s in Example 2;

[0095] Figure 6 The current-voltage curves obtained by experiment and the current-voltage curves obtained by fitting are respectively shown in Examples 1 and 2 when the positive scan and the negative scan are performed. DETAILED DESCRIPTION

[0096] The following detailed description of exemplary embodiments of the present invention refers to the accompanying drawings, which form a part of the description, and in which exemplary embodiments of the present invention that can be implemented are shown as examples. Although these exemplary embodiments are described in sufficient detail to enable those skilled in the art to implement the present invention, it should be understood that other embodiments can be implemented and various changes can be made to the present invention without departing from the spirit and scope of the present invention. The following more detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but is only for the purpose of illustrating and not limiting the description of the characteristics and features of the present invention, so as to propose the best mode for performing the present invention and to enable those skilled in the art to implement the present invention. Therefore, the scope of the present invention is limited only by the appended claims.

[0097] The present invention uses differential equations to describe the electrode process, uses multi-physics field simulation, and uses the finite element method to solve the differential equations. By generating voltage-current curves at different scanning voltage rates, the fitted generated current and the experimental current are compared. When the fitted generated current and the experimental current are the same at different scanning voltage rates, the chemical capacitance value of the input model is the true chemical capacitance value of the electrode. The fitted generated current has a one-to-one correspondence with the input parameters. When the input parameters are consistent with the actual values, the fitted generated current can be consistent with the actual experimental values. This method can be used to fit the electrode intrinsic parameters.

[0098] The reagents in the examples are all Chinese medicine reagents with a purity greater than 99%.

[0099] The SOC solid oxide battery includes a working electrode and an electrolyte. The working electrode in the embodiment is samarium-doped cerium oxide (Sm 0.2 Ce 0.8 O 2.8 ,SDC); the electrolyte is yttria stabilized zirconia (YSZ). The preparation steps of SOC solid oxide battery include:

[0100] A spraying liquid containing an electrode material and an electrolyte sheet are prepared; and the spraying liquid is sprayed onto the electrolyte sheet.

[0101] Samarium-doped cerium oxide SDC is synthesized by a citrate-glycine combustion method, which specifically includes the following steps:

[0102] Step a, ingredients: weigh cerium nitrate (Ce(NO3)3·6H2O), samarium nitrate (Sm(NO3)3·6H2O) and glycine respectively, wherein the molar ratio of cerium nitrate to samarium nitrate is 1:4, the molar ratio of glycine to metal ion is 2.5:1, and the metal ion is Ce. 3+ and Sm 3+ The sum of the molar amounts of .

[0103] Step b, preparing a precursor: adding the raw material obtained in step a to distilled water at 60° C. and dissolving it under stirring, and continuing stirring for 2 hours to ensure that the metal cations and glycine are fully complexed to obtain a clear precursor solution; heating the precursor solution to 60° C. to fully evaporate the water in the solution to obtain a light yellow precursor powder, which is collected in a crucible.

[0104] Step c, placing the collected precursor powder in a muffle furnace, heating it to 600°C in air at a heating rate of 200°C / h, keeping it warm for 2h, annealing, cooling it to room temperature in the furnace at a rate of 200°C / h, and mixing the calcined precursor powder with a coating liquid (85% ethanol, the rest is polyvinyl butyraldehyde) to prepare a spray liquid, wherein the amount of the precursor powder added is 10wt% of the coating liquid.

[0105] The electrolyte used is yttria stabilized zirconia (YSZ). The preparation method of the electrolyte is: YSZ powder is pressed into sheets, and the pressed YSZ is sintered at high temperature according to the following process: first, the temperature is raised from room temperature to 200°C over 1 hour, and kept warm for 30 minutes; then the temperature is raised to 1450°C at a rate of 300°C / h, and kept warm for 5 hours for sintering; then the temperature is lowered to 200°C at a rate of 300°C / h, and cooled with the furnace to obtain a sintered YSZ electrolyte sheet.

[0106] Electrode preparation: The spraying liquid is sprayed onto the YSZ electrolyte by ultrasonic spraying, and then placed in a furnace for sintering. Sintering process: The temperature is raised from room temperature to 1000℃ at a rate of 200℃ / h and kept at this temperature for 2h. 0.2 Ce 0.8 O 2.8 Sintered on the electrolyte as the working electrode.

[0107] Platinum was applied to the symmetrical position on the opposite side, and the temperature was raised from room temperature to 900°C at a rate of 200°C / h and kept at this temperature for 30 minutes to serve as an anode.

[0108] Electrochemical test: Use silver to point a tiny reference electrode on the side of the electrode for the measurement characterization of the three-electrode system. When pointing the silver electrode, ensure that the distance between the reference electrode and the working electrode exceeds three times the electrode thickness so that the overpotential of the reference electrode is consistent with the overpotential on the working electrode.

[0109] In this study, electrochemical impedance spectroscopy (EIS) and linear sweep voltammetry (LSV) tests were performed on the constructed three-electrode system. The EIS test was carried out at 700°C, using an electrochemical workstation Solatron-1260, and an overpotential of 0 to -1V was applied relative to the reference electrode. The test used perturbation voltages of 10mV and 20mV, and data was collected in the frequency range of 1MHz to 0.01Hz. The obtained AC impedance spectrum was fitted and analyzed in detail using Z-view software.

[0110] In addition, LSV experiments were performed in the same overpotential range with scanning voltage rates of 20mV / s and 50mV / s to explore the effect of different scanning voltage rates on electrode performance. In all electrochemical tests, the gas introduced was a mixture of CO2 and CO with a molar ratio of 1:1, and the gas flow rate was 30mL / min.

[0111] The experimental conditions for obtaining the chemical capacitance value by model fitting in the embodiment are consistent with the actual experiment.

[0112] Example 1

[0113] A method for fitting the chemical capacitance of a solid oxide battery and measuring the cathode current comprises the steps of:

[0114] S1. Modeling: Input the geometric parameters of the battery into the multi-physics model for geometric modeling, and input the initial chemical capacitance value C chem .

[0115] The geometric parameters of the battery in step S1 include the diameter and thickness of the electrolyte and the working electrode, and the geometric parameters of the above electrodes are obtained by performing a scanning electron microscope test on the battery.

[0116] The geometric parameters of the battery in this embodiment are:

[0117] The electrolyte has a diameter of 1.3 cm and a thickness of 500 μm;

[0118] The diameter of the working electrode is 0.55 cm and the thickness is 20 μm, wherein SDC serves as the cathode.

[0119] The model constructed using the geometric parameters of the battery is as follows Figure 1 As shown, the experimental conditions are loaded for simulation.

[0120] The parameters introduced to affect the mass transfer process include: physical parameters: materials, density, conductivity of anode, cathode, electrolyte, permeability and porosity of porous materials; gas parameters: dynamic viscosity and molar mass of gas.

[0121] The boundary conditions include: setting the pressure outlet boundary at the flow field outlet, and there is no slip between the fluid and the wall; using thermal insulation boundaries for the rest of the battery fluid inlet and outlet; applying rigid body motion suppression boundaries to the solid part of the entire battery model when solving the internal thermal stress of the battery. During the experiment, the CO2 / CO mixture was introduced into the cathode area. There is an air inlet at the bottom of the cathode. The experiment assumes that the incoming airflow is uniform and the gas composition remains consistent over the entire electrode surface.

[0122] The domain selection and parameter setting of the physical fields involved in SOFC are carried out, and the multi-physical field coupling is set in parallel, so that the results obtained through coupling are used when setting the parameters of the physical fields.

[0123] The mesh of the entire model uses a structured mesh. In the cathode and anode regions, the concentration gradient is high due to the presence of surface electrochemical reactions. Therefore, in order to improve the calculation accuracy, the mesh division of these areas is finer to ensure that the concentration changes and electrochemical activities in these key areas can be captured. On the contrary, inside the electrolyte, since there is no electrochemical reaction, only the transfer of lattice oxygen occurs, and the concentration gradient is relatively small. In order to balance the calculation accuracy and efficiency, a larger grid size is selected. This strategy aims to reduce the amount of calculation and save calculation time while maintaining a high-precision simulation of key reaction areas. In this embodiment, the grid structure and grid quality distribution are as follows: Figure 2 shown.

[0124] The number and quality of the overall mesh in the multi-physics model of this embodiment are shown in Table 1. The mesh quality is good, providing a solid foundation for subsequent numerical simulations. This meshing strategy that comprehensively considers accuracy and efficiency can improve the reliability of simulation results while optimizing the use of computing resources.

[0125] Table 1. Grid distribution in multi-physics model

[0126] Mesh parameter type Numeric Mesh Vertex Count 923683 Tetrahedral mesh number 5383441 Number of triangle meshes 621010 Minimum mesh quality 0.2156 Average mesh quality 0.6685 Finite element volume ratio <![CDATA[4.108*10 -4 ]]> Mesh Volume <![CDATA[3.24*10 10 μm]]>

[0127] S2. Fitting to generate current: The current-voltage curve is obtained by fitting. The current in the current-voltage curve is the current generated by fitting I total , the fitting generates a current I total Satisfy the formula:

[0128]

[0129] Wherein, F is the Faraday constant, which is 96500C / mol; k is the cathode material heterogeneous reaction rate constant, and the k value in this embodiment is 7*10 -18 m 16 / (mol 5 *s);c(CO 2(ad) ) is the surface adsorbed carbon dioxide concentration, the value varies according to the reaction; c(e - ) is the electrode electron concentration, and its value varies according to the reaction; is the oxygen vacancy concentration of the electrode, and its value varies according to the reaction; E is the applied overvoltage, and its value is E=E0+v*t, where E0 is the initial overpotential on the three-electrode system, v is the scanning voltage rate, and t is the time. In this embodiment, the initial overpotential E0 is 0, and v is 20 mV / s; is the lattice oxygen concentration, the value varies according to the reaction; C chem is the initial chemical capacitance value of the input model; R ohm is the ohm impedance, the value is 5.39Ω, vol effis the effective volume of the electrode, through the formula vol eff =∈ SDC *vol total Determine, where ∈ SDC is the volume ratio of the electrode, vol total is the total volume of the electrode, where ∈ SDC =1-ε SDC , ε SDC is the porosity of the electrode, in this embodiment, vol eff The value is 0.00038cm 3 .

[0130] The set experimental conditions include temperature, gas concentration and flow rate, which are consistent with the actual experimental conditions.

[0131] In this embodiment, the reactant introduced is set to be a CO2 / CO mixed gas, the flow ratio is 1:1, and the total flow rate is 30mL / min; the temperature is 923K, and the scanning voltage rate is 20mV / s. The battery is subjected to an LSV experiment to obtain a CV curve. First, scan in the negative voltage direction to obtain a CV curve until it reaches -1V relative to the reference electrode, and then immediately scan forward at the same scanning voltage rate. The IV curve obtained from the experiment is then compared and analyzed with the simulation results. The SDC battery prepared above is measured as the negative electrode.

[0132] Among them, the surface adsorbed carbon dioxide concentration c(CO 2(ad) ), electrode electron concentration c(e - ), electrode oxygen vacancy concentration and the lattice oxygen concentration The value of is calculated according to the following formula:

[0133] (1) Surface adsorbed carbon dioxide concentration c(CO 2(ad) ):

[0134] The mechanism of SDC as cathode electrolysis of CO2 is as follows:

[0135] (Adsorption step)

[0136] (Dissociation Step)

[0137] In the electrolysis of CO2 using SDC as cathode, dissociation is the rate-determining step. Assuming that CO does not accumulate on the surface of the SDC electrode as a gas diffusion electrode and the reverse process of the reaction can be ignored, the generated CO 2(ad) The rate can be determined by the following formula:

[0138] r ad =k ad *c(CO2(gas) )-k de *c(CO 2(ad) ) Formula (20)

[0139] Among them, k ad is the adsorption rate constant, c(CO 2(gas) ) is the concentration of carbon dioxide in the airway, the initial concentration is 44.24 mol / L, k de is the desorption rate constant, c(CO 2(ad) ) is the adsorbed carbon dioxide concentration. Since the adsorption step is not a rate-determining step, k is set ad Very large, k de In this embodiment, k is set ad is 10000, k de is 0.1 (negligible), and the initial r is calculated ad It is 442400.

[0140] (2) Electron concentration c(e - ):

[0141] c(e - ) is the electrode electron concentration, as CO 2(ad) The lattice oxygen is generated at the same rate as the consumption in the dissociation step. In this step, the electrons are provided by metallic cerium. In a CO2 / CO mixed atmosphere, trivalent cerium ions (Ce 4+ ) is oxidized to tetravalent cerium ions (Ce 3+ ), thereby reducing the electronic resistance. Electron concentration c(e - ) is determined by the Nernst-Einstein equation:

[0142]

[0143] In the formula, n is used to characterize c(e - ), K is the Boltzmann constant, T is the absolute temperature, σ eff It is Sm 0.2 Ce 0.8 O 2-δ The effective conductivity is 5.88*10 at 750℃. -2 S / cm, this value is used to calculate c(e at 0V overpotential - ), n is the number of electrons per unit volume, i.e., the electron concentration, and D is the diffusion coefficient of the electrons, which is set to 3.2*10 in this embodiment. -14 m 2 / s, q is the charge of the electron, which is 1.6*10 -19 C.

[0144] (3) Electrode oxygen vacancy concentration

[0145] Nonstoichiometric δ and vacancy concentration satisfy:

[0146]

[0147] Wherein, V is the unit cell volume of the crystal, which is set as N A is Avogadro's constant, which is 6.022*10 23 mol -1 , the initial non-stoichiometric coefficient δ is set to 0.00007322.

[0148] (4) Lattice oxygen concentration

[0149] Lattice oxygen and oxygen vacancies together constitute all possible locations of oxygen in the unit cell. The stoichiometric number is 3 when there is no doping, that is:

[0150]

[0151] The initial lattice oxygen concentration is thus:

[0152]

[0153] Wherein, V is the unit cell volume of the crystal, which is set to N A is Avogadro's constant, which is 6.022*10 23 mol -1 .

[0154] S3. Calculate the chemical capacitance C chem :Compare the fitted generated current I under the same voltage total And the experimental current I real , when the fitting generated current I at different scanning voltage rates total With the experimental current I real When they are consistent, the initial chemical capacitance value C of the input multi-physics model can be considered chem is the actual chemical capacitance of the electrode, C chem,real .

[0155] The generated current-voltage curve is as follows Figure 3 As shown, the fitting generates current I totalThe results are consistent with the experimental current results under the condition of scanning voltage rate of 20mV / s, which reveals the consistency of the current contributed by chemical reaction under the same overpotential conditions during the positive and negative scanning processes. The maximum error between the simulation value and the experimental value is 7.88%, and the average error is less than 3%. Therefore, the chemical capacitance value input into the multi-physics model is the real chemical capacitance value, and the real chemical capacitance value C chem,real for:

[0156]

[0157] When determining the chemical capacitance, the present invention first assigns an initial chemical capacitance value C chem , bring it into the model for verification, if the fitting of the chemical capacitance value is brought into the generated current I total If the chemical capacitance value is consistent with the experimental current result under different scanning voltage rate conditions, it means that the chemical capacitance value is the real chemical capacitance value. If it is inconsistent, the chemical capacitance value is adjusted until it meets the requirements. The prediction form of the chemical capacitance value follows the Arrhenius equation. Finally, the inventor found that the formula for the real chemical capacitance value that meets the requirements is:

[0158] Among them, the initial chemical capacitance value C is given first chem It can be obtained by the transmission line circuit impedance formula in the paper by Bisquert et al. (Anomalous transport effects in the impedance of porous film electrodes [J]. Electrochemistry Communications, 1999, 1 (9): 429-435.).

[0159] S4. Calculate the real reaction current I reac,real :Based on the actual chemical capacitance value C chem,real Get the real reaction current I reac,real .

[0160] The real reaction current I is calculated reac,real for:

[0161]

[0162] Real chemical capacitance current I c,real for:

[0163]

[0164] The experimental and simulated IV results of the separated fitted reaction current and fitted chemical capacitance current at a scan rate of 20 mV / s are shown in Figure 4 As shown, the separated fitted reaction current and fitted chemical capacitance current were obtained when the scanning voltage rate was 20 mV / s.

[0165] Example 2

[0166] The steps of the method for calculating the chemical capacitance and determining the electrode current of a solid oxide battery in this embodiment are basically the same as those in Example 1, except that the scanning voltage rate is 50 mV / s, and the electrode current-voltage curve is generated at this scanning voltage rate.

[0167] The fitted reaction current I separated at a scanning voltage rate of 50 mV / s reac,cath and the fitted chemical capacitance current I c The experimental and simulated current-voltage curves are shown in Figure 5 shown.

[0168] In both experiments, the intrinsic physical quantities of the material were not changed, only the scanning voltage rate was changed, and the fitted current was consistent with the experimental current, indicating that the calculated reaction current and chemical capacitance current were both true values.

[0169] In summary, the generated current at different scanning voltage rates in the present invention is consistent with the experimental current results, that is, the chemical capacitance value of the input multi-physical field is the true chemical capacitance value of the electrode, and the calculated fitting reaction current and fitting chemical capacitance current are also true values, which verifies the validity of the equivalent circuit model theory adopted.

[0170] To further verify the rationality of the model, Figure 6 As shown in the figure, after changing the scanning direction, the current density was observed to increase slightly and then decrease. This phenomenon occurred at both 20mV / s and 50mV / s scanning voltage rates, and the simulation results can well reproduce this experimental observation, indicating that the model can accurately capture the dynamic characteristics of the electrode process.

[0171] The reason for the above phenomenon is that chemical capacitance has a significant effect on current density. During the negative scan direction, the charging effect of the chemical capacitance causes the observed current density to be lower than the expected value when there is no capacitance effect. Conversely, during the forward scan direction, the discharge effect of the chemical capacitance causes the current density to increase relatively. When the overpotential deviates significantly from the equilibrium voltage, the charge accumulation in the electrode body leads to a large amount of discharge current, sometimes even exceeding the reduction in the reaction current, so that the current density exceeds the peak of the negative scan in the forward scan. This phenomenon is the reason for the inconsistent current density of the metal oxide single-phase MIEC cathode in the positive and negative IV scan experiments, and it is also the explanation for the phenomenon of a brief increase in current during the reverse scan. However, this phenomenon cannot be sustained, and the current decreases as the overpotential is scanned in the forward direction.

[0172] During the experiment, the EIS test was limited to the range of -0.1V to -0.6V to avoid possible damage to the electrode at higher overpotentials, especially in the three-electrode system, where the overall battery potential may exceed the risk of -2V. Nevertheless, the LSV experiments and simulations were extended to -1.0V. This is because, although the EIS test provides important data on the relationship between impedance and overpotential, the LSV scan is able to quickly explore a wider potential range while reducing potential damage to the electrode. The larger overpotential range of the LSV curve provides a more comprehensive validation of the model and helps to more fully understand the electrochemical behavior of the electrode under different operating conditions.

Claims

1. A method for fitting the chemical capacitance of a solid oxide battery, characterized in that: Includes steps: S1. Modeling: Input the geometric parameters of the battery into the multi-physics model for geometric modeling, and input the initial chemical capacitance value C chem ; S2, fitting generated current I total :According to the geometric model fitting, the current in the current-voltage curve is the current I generated by the fitting. total , the fitting generates a current I total is the fitting reaction current I reac With the fitted chemical capacitance current I c The sum of the fitting reaction current I reac According to the calculation of chemical reaction rate, the fitted chemical capacitance current I c is the ratio of potential difference to resistance; S3. Get the real chemical capacitance value C chem,real :Compare the fitted generated current I under the same voltage total and experimental current, the experimental current is measured under the same conditions, when the fitting generated current I at different scanning voltage rates total If the current is consistent or close to the experimental current, then input the initial chemical capacitance value C of the model. chem is the actual chemical capacitance value C chem,real .

2. The method according to claim 1, characterized in that The fitted reaction current I reac Satisfies the following formula: I reac =F*k*c(e - ) 4 *c reac Formula (1) In formula (1), F is the Faraday constant; k is the material heterogeneous reaction rate constant; c(e - ) is the electrode electron concentration; c reac is the concentration of the reactant.

3. The method according to claim 2, characterized in that When fitting the cathode chemical capacitance of solid oxide, the reactant concentration c in equation (1) is reac Satisfies the following formula: Preferably, the cathode reaction current I reac,cath Satisfies the following formula: In formula (2) and formula (3), F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(CO 2(ad) ) is the surface adsorbed carbon dioxide concentration, c(e - ) is the electrode electron concentration, is the oxygen vacancy concentration of the electrode.

4. The method according to claim 2, characterized in that: When fitting the anode chemical capacitance of solid oxide, the reactant concentration c in equation (1) is reac Satisfies the following formula: Preferably, the fitting anode reaction current I reac,ano Satisfies the following formula: In formula (4) and formula (5), F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(e - ) is the electrode electron concentration, c reac is the reactant concentration, is the lattice oxygen concentration.

5. The method according to any one of claims 1 to 4, characterized in that: The fitted chemical capacitance current I c for: In formula (6), F is the Faraday constant, E is the applied overvoltage, is the lattice oxygen concentration, C chem is the initial chemical capacitance value, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

6. The method according to claim 5, characterized in that The fitting generates a current I total for: Preferably, the total cathode current I total,cath for: Preferably, the total anode current I total,ano for: In formula (7) to formula (9), F is the Faraday constant, k is the material heterogeneous reaction rate constant, c(e - ) is the electrode electron concentration, c reac is the concentration of reactants, c(e - ) is the electrode electron concentration, is the electrode oxygen vacancy concentration, E is the applied overvoltage, and E cath is the cathode overvoltage, E ano is the anode applied overvoltage, = is the lattice oxygen concentration, C chem is the initial chemical capacitance value, R ohm is the ohmic impedance, vol eff is the effective volume of the electrode.

7. The method according to claim 6, characterized in that The actual chemical capacitance value C chem,real Follow the Arrhenius equation; Preferably, the actual chemical capacitance value C chem,real The calculation formula is: In formula (10), F is the Faraday constant and E is the applied overvoltage.

8. The method according to claim 1, characterized in that The geometric parameters of the battery in step S1 include the diameter and thickness of the electrolyte and the working electrode.

9. The method according to claim 1, characterized in that: The experimental conditions fitted in step S2 include temperature, gas concentration, flow rate, and scanning voltage rate.

10. A method for calculating electrode current according to the method for fitting chemical capacitance of solid oxide batteries according to any one of claims 1 to 9, characterized in that: The steps include: according to the actual chemical capacitance value C chem,real Calculate the real electrode current I total,real , the real electrode current I total,real is the real reaction current I reac,real The real chemical capacitance current I c,real sum.

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