A method for calculating the effective surface area of an electrode based on the alternating current impedance method

Abstract

This invention relates to a method for calculating the effective surface area of ​​an electrode based on the AC impedance method. Addressing the limitations of existing gas adsorption methods (non-in-situ testing) and the cumbersome fitting process and susceptibility to initial human intervention in traditional AC impedance spectroscopy models, this invention first acquires full-frequency AC impedance data by applying a small sinusoidal voltage perturbation signal to the electrode system; based on the equivalent circuit model of the electrode interface, a method is established using the reciprocal of the square of the angular frequency ω. ‑2 The product of the independent variable, the imaginary part of the complex impedance, and the angular frequency (ωZ) img ) ‑1 The model is a linear mapping of the dependent variable; the least squares method is used to perform linear fitting on the characteristic frequency band data, and the double-layer capacitance C at the electrode interface is directly obtained by extracting the intercept of the fitted line on the vertical axis. dl Finally, the effective active surface area of ​​the electrode in the electrolyte environment is calculated by combining the preset specific capacitance constant. This invention achieves high-precision, in-situ monitoring of the active area of ​​electrode materials with different particle sizes and morphologies without the need for complex iterative algorithms.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical testing and battery material performance characterization technology, specifically relating to a method for calculating the effective surface area of ​​an electrode based on AC impedance spectroscopy. Background Technology

[0002] The surface area of ​​an electrode is one of the core parameters determining the performance of electrochemical devices such as fuel cells, lithium-ion batteries, and supercapacitors. Accurately characterizing the surface area of ​​an electrode under actual operating conditions is of great significance for evaluating the utilization rate of active materials, optimizing electrode structure, and predicting device lifetime.

[0003] Currently, the most commonly used method for characterizing the surface area of ​​porous materials is the gas adsorption method (BET method). The BET method involves performing gas adsorption / desorption tests on electrode materials at low temperatures and calculating their specific surface area (S²) based on physical adsorption theory. BET Generally speaking, for an electrode material, the surface area and the double-layer capacitance formed by the electrode (C) are related factors. dl There is a direct proportional relationship between them (e.g.) Figure 1 However, in practical electrochemical applications, the BET method has the following significant limitations:

[0004] 1. Non-in-situ nature and environmental differences: BET testing must be performed under dry and high vacuum conditions, which is quite different from the actual working state of the electrode in the electrolyte. The wettability of the electrolyte to porous structures, the accessibility of ions, and the formation of the double layer all lead to a deviation between the "effective surface area" actually participating in the electrochemical reaction and the physical surface area under dry conditions.

[0005] 2. Inability to distinguish active regions: The BET method measures the surface area of ​​all physically open pores, and cannot distinguish which regions are actually in contact with the electrolyte and participate in charge transfer (active regions). Figure 2 ).

[0006] 3. Insufficient characterization of complex structures: For thin film electrodes or composite electrodes with complex morphologies, the BET method often requires a large sample volume to achieve measurement accuracy, making it difficult to achieve in-situ monitoring of micron- or nano-scale thin film electrodes.

[0007] Electrochemical impedance spectroscopy (EIS) is a non-destructive in-situ electrochemical characterization technique capable of extracting C... dl Studies have shown that, under specific systems, the charge on an electrode is related to the surface area (S) measured by the BET method. BET It exhibits an excellent linear proportional relationship. Figure 3Since the magnitude of the double-layer capacitance depends directly on the charge layer formed by the arrangement of ions on the electrode surface, C dl It can more accurately reflect the "effective surface area" under electrolyte wetting.

[0008] Specifically, the double-layer capacitance (C) corresponding to a unit BET surface area dl / S BET For similar materials in the same electrolyte system, this value is typically a constant. This means that by accurately measuring the total capacitance of the electrode using EIS and combining this constant, the effective surface area of ​​the electrode under operating conditions can be deduced.

[0009] However, existing EIS characterization methods often rely on complex equivalent circuit fitting (such as Randle circuits), and the calculation process is cumbersome and prone to human error when dealing with high-frequency or low-frequency deviations from ideal capacitance (such as diffusion effects). Therefore, the industry urgently needs a standardized calculation method that can quickly, accurately, and linearly extract capacitance components and reliably estimate the effective surface area of ​​electrodes.

[0010] To address the above problems, this invention proposes a method for extracting C based on the AC impedance method. dl A new scheme for calculating electrode surface area is proposed, aiming to achieve high-precision, in-situ monitoring of the effective surface area of ​​electrodes, providing key data support for the research and engineering application of electrochemical materials. Summary of the Invention

[0011] This invention aims to overcome the limitations of existing BET methods in measuring the effective active surface area of ​​electrodes in a liquid environment, as well as the drawbacks of traditional AC impedance fitting software, such as its complexity and susceptibility to human error. This invention provides a method for linearly extracting double-layer capacitance (C0) based on AC impedance. dl The method of calculating the effective surface area of ​​the electrode, through a specific data conversion model, enables high-precision and rapid in-situ characterization of the effective surface area of ​​electrode materials with different particle sizes and morphologies.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is:

[0013] A method for calculating the effective surface area of ​​an electrode based on the AC impedance method includes the following steps:

[0014] Acquire complex impedance spectrum data under controlled conditions: Assemble the electrode under test into the test system (such as a symmetrical cell or a three-electrode system), and control the electrode to be in a preset state of charge (SOC) and temperature environment. Apply a small sinusoidal voltage perturbation signal to perform AC impedance spectrum testing and obtain the complex impedance Z at different angular frequencies (ω).

[0015] Furthermore, an equivalent circuit for the AC impedance spectrum is established for the counter electrode reaction process of a secondary battery, and its total impedance (Z) total ) and solution resistance (Z) Rs ) and the capacitance impedance part (Z) parallel It satisfies the classic Randle equivalent circuit relationship:

[0016] [1];

[0017] Furthermore, based on the simplified Randle electrode interface model, the dimensionality reduction of the spectral data acquired in step 1 is performed using the following linearization transformation formula, where Z... Rs = R s (Pure resistance, no imaginary part); the impedance Z of the parallel section. parallel for

[0018] [2];

[0019] [3];

[0020] [4];

[0021] Wherein, the total impedance Z total In the middle, it is divided into the real part (Z) real ) and imaginary part (Z) img Their respective expressions are:

[0022] [5];

[0023] [6];

[0024] Furthermore, the processed data is linearly fitted in a complex plane coordinate system. By extracting the intercept of the fitted line on the vertical axis, the C-axis of the electrode / electrolyte interface is directly obtained. dl This intercept physically eliminates the polarization resistance R. ct By observing the effect of frequency variation, the capacitance component was extracted.

[0025] [7];

[0026] Furthermore, based on the fact that materials with different morphologies and particle sizes have a constant unit specific capacitance C in the same electrolyte system... spec Based on the characteristics, the effective surface area S of the electrode is calculated using the following formula:

[0027] [8];

[0028] Among them, C specThis refers to the pre-calibrated areal capacitance constant of this type of material in a specific electrolyte.

[0029] The present invention has the following significant advantages over the prior art:

[0030] 1. High precision and high sensitivity: The intercept is extracted using a linearization formula, effectively avoiding the impact of semicircular distortion or blurring effects on R in the Nyquist plot. ct and C dl The estimation introduced errors, and experiments have shown that this method can accurately distinguish the surface area differences of materials with different particle sizes (such as 2μm, 12μm, and 20μm).

[0031] 2. In-situ characterization capability: This method is carried out in a liquid phase environment, and the measured surface area is the "effective active area" that the electrolyte can truly wet and participate in charge transfer, which is more meaningful for engineering guidance than the dry-state BET method.

[0032] 3. Simple and fast calculation: No complex impedance fitting software is required for iterative calculations; only simple linear regression is needed to extract the core parameter C. dl This greatly improves testing efficiency.

[0033] 4. High versatility: Applicable to the performance evaluation of positive and negative electrode materials for lithium-ion batteries, electrodes for supercapacitors, and thin film materials under dynamic environments. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below.

[0035] Figure 1 : Relationship between different particle sizes and specific surface area of ​​ternary cathode materials and fitted curves.

[0036] Figure 2 Equivalent circuit diagram of AC impedance spectrum in a typical secondary battery system (Randles equivalent circuit model).

[0037] Figure 3 AC impedance spectra of electrode materials with different particle sizes.

[0038] Figure 4 The electrode capacitance C is derived and calculated using this invention for different particle sizes. dl Result image.

[0039] Figure 5 Specific surface area and capacitance (C) measured by the BET method dl The relationship between ).

[0040] Figure 6The relationship between electrode specific surface area and electrode capacitance calculated in this invention. Detailed Implementation

[0041] The present invention will be further described below with reference to embodiments.

[0042] A method for calculating the effective surface area of ​​an electrode based on the AC impedance method includes the following steps:

[0043] Step 1: Acquire AC impedance spectrum data. Place the electrode under test in the electrolyte system and acquire the imaginary part data Z of the complex impedance at different angular frequencies ω. img ;

[0044] Step 2: Establish a linearized mapping model for impedance data; based on the equivalent circuit model of the electrode interface, construct a model with respect to the square of the reciprocal of the angular frequency ω. -2 The product of the independent variable, the imaginary part of the complex impedance, and the angular frequency (ωZ) img ) -1 The linear discriminant equation for the dependent variable;

[0045] Step 3: Extract double-layer capacitance characteristic parameters; by performing linear fitting on the linear discriminant equation, extract the intercept of the fitted line on the vertical axis to obtain the double-layer capacitance C at the electrode / electrolyte interface. dl ;

[0046] Step 4: Calculate the effective surface area of ​​the electrode; combine this with the preset specific capacitance constant C. spec With the C dl The effective active surface area S of the electrode in the electrolyte system is obtained by inversion calculation.

[0047] This invention provides a specific implementation method in which, before acquiring complex impedance spectrum data in step 1, the electrode under test needs to be adjusted to a preset state of charge (SOC) and ambient temperature to eliminate the interference of concentration polarization on the imaginary part of the impedance.

[0048] This invention provides a specific implementation method, in step 2, the linear discriminant equation is specifically:

[0049] ;

[0050] ω is the angular frequency; Z imgl For the imaginary part of the complex impedance; C dl For double-layer capacitors, R ct It is the charge transfer resistance.

[0051] This invention provides a specific implementation method in which, in step 3, when extracting the feature parameters of the double-layer capacitor, the least squares method is used to perform linear regression fitting on the data points in the high-frequency response region, and the coordinates of the intersection of the fitted line and the y-axis are used as the double-layer capacitor value C. dl.

[0052] This invention provides a specific embodiment in which, in step 4, the specific capacitance constant C spec It is obtained by calibrating standard electrode materials with known physical surface areas and is used to characterize the charge storage capacity per unit effective area under a specific electrolyte system.

[0053] This invention provides a specific embodiment in which the effective surface area S of the electrode is calculated as follows:

[0054] ;

[0055] Among them, C spec This refers to the pre-calibrated areal capacitance constant of this type of material in a specific electrolyte.

[0056] The present invention provides a specific embodiment in which the electrode includes a lithium-ion battery positive electrode, a lithium-ion battery negative electrode, a supercapacitor electrode, or a fuel cell catalyst layer electrode.

[0057] The present invention provides a method for calculating the effective surface area of ​​an electrode based on the AC impedance method, which involves establishing a linear mapping relationship in a specific frequency domain to decouple the capacitive and resistive components in the electrode interface impedance, thereby accurately obtaining the surface area that reflects the true electrochemical activity.

[0058] This embodiment uses different median particle sizes D 50 Taking lithium nickel cobalt manganese oxide (NCM) ternary lithium-ion battery cathodes with particle sizes of (2μm, 12μm, and 20μm) as examples, the relationship between particle size and electrode surface area is as follows: Figure 1 (The same method for calculating the effective surface area of ​​electrodes can be used for other systems such as battery anodes, supercapacitor electrodes, or fuel cell catalyst layer electrodes, derived from the Randle circuit above.) The specific implementation steps are as follows:

[0059] First, the cathode material to be tested and the negative electrode lithium metal sheet are assembled into a coin cell, and an electrolyte (such as 1M LiPF6 dissolved in an EC:DEC = 1:1 solvent) is injected. The cell is placed in a constant temperature chamber, and the ambient temperature is adjusted to a preset point (such as 25ºC, 0ºC, or -10ºC). Using an electrochemical workstation, the cell is adjusted to an equilibrium state with a state of charge (SOC) of 0 to eliminate the interference of concentration polarization on the impedance spectrum.

[0060] A sinusoidal voltage disturbance signal with an amplitude of 5mV is applied to a battery in equilibrium. The test frequency range is set from 100 kHz to 0.1 Hz. The complex impedance data Z at each frequency point f is obtained through testing, and the angular frequency ω (ω=2πf) and its corresponding imaginary impedance Z are recorded. img .

[0061] For reference Figure 4 The simplified Randles equivalent circuit model shown fits the AC impedance spectrum results ( Figure 3 The imaginary part of its total impedance Z is Z0. img With angular frequency ω, charge transfer resistance R ct Double-layer capacitance C dl The mapping relationship is shown in Formula [6]. In this embodiment, a linear transformation function is constructed to obtain the linear discriminant equation shown in Formula [7].

[0062] like Figure 4 As shown, the intercept of the fitted straight line on the vertical axis is the C of the electrode in its current state. dl Because this linear mapping model eliminates the offset effect of the ohmic resistance Rs and suppresses R... ct Despite the interference from frequency fluctuations, the obtained intercept accurately reflects the charge storage capacity of the electrode / electrolyte interface. Experimental data show that the electrode with a particle size of 2 μm has the highest intercept value, while the electrode with a particle size of 20 μm has the lowest intercept value, which is highly consistent with the physical characteristics of the material's specific surface area.

[0063] Introducing the specific capacitance constant C of this material system spec (In this embodiment, the value was obtained through a calibration sample and was taken as 0.06 mF / cm) 2 The effective active surface area S of the electrode is calculated according to formula [8].

[0064] The calculated results were compared with those obtained by the Biosorption Spectrometry (BET) method. Compared to the traditional BET method, which yields results showing no correlation between electrode area and capacitance, the results show a more accurate comparison. Figure 5 ). Figure 6 The results show that the surface area measured using the method of the present invention is related to S BET It exhibits excellent linear correlation (R0). 2 > 0.99), and can more accurately capture the phenomenon of reduced wetting area of ​​the electrode due to changes in electrolyte viscosity at low temperatures (such as -10ºC or -20ºC).

[0065] The above description is merely a preferred embodiment of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. It should be specifically stated that any use of double-layer capacitors C... dlThe method and related algorithm variations for extracting feature parameters from the frequency domain mapping relationship between the electrode and the angular frequency ω, and decoupling and inverting accordingly to obtain the effective active surface area of ​​the electrode under electrolyte immersion, regardless of how the equivalent circuit model is locally added or subtracted or the mathematical formula is equivalently transformed, constitute an equivalent substitution of the core inventive point of this invention and should be fully covered within the protection scope of this invention.

Claims

1. A method for calculating the effective surface area of ​​an electrode based on the AC impedance method, characterized in that, Includes the following steps: Step 1: Acquire AC impedance spectrum data. Place the electrode under test in the electrolyte system and acquire the imaginary part data Z of the complex impedance at different angular frequencies ω. img ; Step 2: Establish a linearized mapping model for impedance data; based on the equivalent circuit model of the electrode interface, construct a model with respect to the square of the reciprocal of the angular frequency ω. -2 The product of the independent variable, the imaginary part of the complex impedance, and the angular frequency (ωZ) img ) -1 The linear discriminant equation for the dependent variable; Step 3: Extract double-layer capacitance characteristic parameters; by performing linear fitting on the linear discriminant equation, extract the intercept of the fitted line on the vertical axis to obtain the double-layer capacitance C at the electrode / electrolyte interface. dl ; Step 4: Calculate the effective surface area of ​​the electrode; combine this with the preset specific capacitance constant C. spec With the C dl The effective active surface area S of the electrode in the electrolyte system is obtained by inversion calculation.

2. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 1, characterized in that, Before acquiring complex impedance spectrum data in step 1, the electrode under test needs to be adjusted to the preset state of charge (SOC) and ambient temperature to eliminate the interference of concentration polarization on the imaginary part of the impedance.

3. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 1, characterized in that, In step 2, the linear discriminant equation is specifically as follows: ； ω is the angular frequency; Z imgl For the imaginary part of the complex impedance; C dl For double-layer capacitors, R ct It is the charge transfer resistance.

4. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 1, characterized in that, In step 3, when extracting the feature parameters of the double-layer capacitor, the least squares method is used to perform linear regression fitting on the data points in the high-frequency response region, and the coordinates of the intersection of the fitted line and the y-axis are used as the double-layer capacitor value C. dl .

5. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 1, characterized in that, In step 4, the specific capacitance constant C spec It is obtained by calibrating standard electrode materials with known physical surface areas and is used to characterize the charge storage capacity per unit effective area under a specific electrolyte system.

6. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 5, characterized in that, The effective surface area S of the electrode is calculated as follows: ； Among them, C spec This refers to the pre-calibrated areal capacitance constant of this type of material in a specific electrolyte.

7. The method for calculating the effective surface area of ​​an electrode based on the AC impedance method according to claim 1, characterized in that, The electrodes include lithium-ion battery positive electrode, lithium-ion battery negative electrode, supercapacitor electrode, or fuel cell catalyst layer electrode.

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