Rate change matrix acquisition method, apparatus, medium for electrochemical impedance analysis

Abstract

The application relates to a rate of change matrix acquisition method, device and medium for electrochemical impedance analysis, which comprises the following steps: acquiring corresponding electrochemical impedance data at different frequencies, acquiring corresponding electrochemical admittance data and converting the same into an admittance vector in a preset form, establishing a solving matrix containing at least one unknown element based on the admittance vector in the preset form, solving the unknown element value based on the solving matrix and the electrochemical impedance data, judging whether the unknown element value meets a preset stop condition, if not, increasing the order of the solving matrix and the admittance vector by 1, generating a new solving matrix, and repeating the step, and if yes, acquiring a target matrix based on the current solving matrix and the unknown element value; and analyzing the rate of change of substances and / or processes participating in the electrochemical reaction based on each element value in the target matrix. Compared with the prior art, the application has the advantages of strong robustness and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of impedance spectrum analysis, and in particular to a rate of change matrix acquisition method, device and medium for electrochemical impedance analysis. BACKGROUND

[0002] As a non-destructive testing and diagnosis method, electrochemical impedance analysis technology is widely used in the field of electrochemistry, especially in the field of electrocatalytic material research and electrochemical energy device development. Electrochemical impedance spectroscopy (EIS) measures the impedance change with the frequency of the sine wave, and then analyzes the electrode process dynamics, double layer and diffusion, etc., to study the mechanism of electrode materials, solid electrolytes, conductive polymers and corrosion protection.

[0003] Electrochemical impedance data contains the dynamic information of multiple substances, interfaces and processes in the test system, which needs to be evaluated and diagnosed by analyzing the corresponding numerical parameters. The current commonly used data analysis methods are equivalent circuit model (ECM) and distribution of relaxation times (DRT). The ECM method regards the electrochemical system as an equivalent circuit, which is composed of basic elements such as resistance (R), capacitance (C) and inductance (L) combined in series and parallel. Through EIS, the composition of the equivalent circuit and the size of each element can be determined, and the structure of the electrochemical system and the nature of the electrode process can be analyzed by using the electrochemical meaning of these elements. The criterion for selecting the equivalent circuit is to match the spectrum, and the ECM method has strong personal subjective judgment, which is prone to overfitting or oversimplification, making the simulation results unable to reflect the true situation. The DRT method has the problem of solving ill-conditioned matrix in the solving process, which is easily affected by data errors, and the results are difficult to form a reasonable explanation with the actual phenomenon in mechanism.

[0004] In summary, there is currently a lack of an analysis method to solve the problem that the traditional ECM method uses matching spectrum as the criterion for selecting the equivalent circuit, which is prone to overfitting or oversimplification, making the simulation results unable to reflect the true situation. SUMMARY

[0005] The present application aims at overcoming the defects of the prior art and provides a rate matrix acquisition method, device and medium for electrochemical impedance analysis, which solves a specific matrix from collected impedance data, thereby solving or partially solving the problem that the traditional ECM method is prone to overfitting or oversimplification when taking the fitting graph as the criterion for selecting the equivalent circuit, so that the simulation result cannot reflect the real situation.

[0006] The object of the present application can be achieved by the following technical solutions.

[0007] According to one aspect of the present application, a rate matrix acquisition method for electrochemical impedance analysis is provided, comprising the following steps:

[0008] Obtaining corresponding electrochemical impedance data at different frequencies, obtaining corresponding electrochemical admittance data and converting the same into a preset form of admittance vector, and establishing a solving matrix containing at least one unknown element based on the admittance vector converted into the preset form;

[0009] Solving the value of the unknown element based on the solving matrix and the electrochemical impedance data, judging whether the preset stop condition is met based on the value of the unknown element, if not, increasing the order of the solving matrix and the admittance vector by 1, generating a new solving matrix, and repeating the step, and if yes, obtaining a target matrix based on the current solving matrix and the value of the unknown element, the target matrix including the rate information of the dynamics rate between each substance and / or process participating in the electrochemical reaction process;

[0010] Analyzing the rate of the substance and / or process participating in the electrochemical reaction based on each element value in the target matrix.

[0011] As a preferred technical solution, the structure of the solving matrix or its transpose is:

[0012]

[0013] In the formula, D is the solving matrix, the element jω is at any position on the diagonal line of the matrix, and the element values of the row or column where the element jω is located are all 0, D mn is the unknown element in the mth row and the nth column, and N is the order of the solving matrix.

[0014] As a preferred technical solution, the preset form of the admittance vector includes at least one constant.

[0015] As a preferred technical solution, the preset form of the admittance vector or its transpose is:

[0016] Y X= [y1... y k-1 a y k+1 ... y N ] T

[0017] Wherein, a is a constant, the position in the admittance vector is same as the row k in which jω is located in the solving matrix, y1, y2,..., y N are frequency function variables.

[0018] As a preferred technical solution, the order of the solving matrix is 2 when initially established.

[0019] As a preferred technical solution, the solving includes the following steps:

[0020] By taking the admittance vector and the corresponding frequency value as the eigenvector and eigenvalue of the solving matrix respectively, a determinant is established, and the unknown element value is obtained by solving the determinant.

[0021] As a preferred technical solution, the determinant is the following formula or the transpose form of the following formula or the submatrix operation form obtained via the following formula:

[0022] (D-jω·I)×Y X =0

[0023] In the formula, D is the solving matrix, I is the unit matrix, Y X is the admittance vector converted into a preset form.

[0024] As a preferred technical solution, the preset stopping condition is:

[0025] The change measurement index of the value of the unknown element under different frequencies is less than a preset threshold.

[0026] Another aspect of the present application provides an electronic device, comprising: one or more processors and a memory, the memory having stored therein one or more programs, the one or more programs including instructions for performing the above-described method for obtaining a rate of change matrix for electrochemical impedance analysis.

[0027] Another aspect of the present application provides a computer-readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs including instructions for performing the above-described method for obtaining a rate of change matrix for electrochemical impedance analysis.

[0028] Compared with the prior art, the present application has the following advantages:

[0029] (1) The target matrix is solved by the collected impedance data. Since each value in the target matrix corresponds to the dynamic change rate of the physical quantity to be investigated relative to other physical quantities, and the dynamic change rate feeds back the kinetic information of various internal processes and mass transfer and reaction of the tested electrochemical system, the present application does not need to know the specific electrochemical reaction process of the test system. The solved matrix is obtained through the iterative solving process of the impedance data and the matrix, which avoids the data overfitting and underfitting caused by the artificial selection of parameters, solves or partially solves the problem that the traditional ECM method uses the fitting graph as the criterion for selecting the equivalent circuit, which is easy to cause overfitting or oversimplification, so that the simulation result cannot reflect the true situation.

[0030] (2) The values of each element in the matrix D obtained finally are the change rates of the kinetics of each substance and process involved in the electrochemical reaction process, which directly reflect the parameters in each physical and chemical process in the tested system, and are beneficial to understanding and analysis. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The flowchart of the change rate matrix acquisition method for electrochemical impedance analysis in Example 1;

[0032] Figure 2 The impedance spectrum obtained;

[0033] Figure 3 The calculation result in Example 1. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present application.

[0035] Example 1

[0036] As Figure 1 described, the present embodiment provides a change rate matrix acquisition method for electrochemical impedance analysis, which comprises the following steps:

[0037] Step S1, collecting electrochemical impedance data (ω, Z) at different frequencies, and converting the impedance into admittance data (ω, Y), wherein Y = 1 / Z

[0038] Step S2, converting the admittance value into a vector form Y X , wherein an element value of Y X is a constant.

[0039] The vector form of admittance is

[0040] Y X = [y1…y k-1 a y k+1 …y N ] T and its transpose form,

[0041] where a is a constant, the position in the vector is consistent with the row index k in the matrix D where jω is located; y1, y2,..., y N are function variables of frequency ω.

[0042] Step S3, given the initial structure of the matrix D used for calculation and the initial order N = 2, where one element value of D is and when Y X is a column vector, other element values in D in the same row as jω are 0, and when Y X is a row vector, other element values in D in the same column as jω are 0.

[0043] The structure of the matrix D is

[0044] and its transpose form,

[0045] where jω is on the diagonal of the matrix, and the row number or column number (for the transpose form) is not limited, as long as the other element values in the matrix in the same row or column (for the transpose form) as jω are 0, it is the structure of the matrix D described in the present claim.

[0046] Step S4, Y X and the corresponding frequency value are taken as the eigenvector and eigenvalue of the initial matrix D, and the matrix D is solved by solving the determinant (D - jω·I) x Y X = 0, if the values of the elements in the matrix obtained by solving change with the frequency value, then the order of the matrix D is increased by 1, and step S3 is repeated.

[0047] Step S5, the final matrix D obtained without changing with the frequency value is used to evaluate the change rate of the corresponding substances and processes involved in the electrochemical reaction according to the element values in the matrix.

[0048] The diffusion impedance model widely used in the literature Theoretical models for ac impedance of finite diffusion layers exhibiting low frequency dispersion. Journal of Electroanalytical Chemistry 1999, 475(2), 152-163 is analyzed as follows. As shown inFigure 2 The obtained impedance spectrum is shown in Table 1, and the impedance data is as described in Table 1.

[0049] Table 1 Impedance Data

[0050]

[0051] The diffusion impedance model is as follows:

[0052]

[0053] Where j is the imaginary unit, satisfying ω is the angular frequency, RW is a reference quantity with impedance units, and Z... f For diffusion resistance, ω d R represents the feature frequency values ​​of the model. W Z f and ω d It all depends on the specific research subject.

[0054] Admittance vectorization: Take Y X =[1 y(ω)] T E = [e1 e2], where e1 and e2 are constants, and y(ω) is a function of ω, satisfying

[0055]

[0056] Given matrix D in the following form: Where D 21 D 22 It is an unknown.

[0057] Solve for the determinant (D-jω·I)×Y X =0:

[0058] Depend on Solving Substituting the result of y(ω) obtained from the vectorization of the first admittance, and after separating the real and imaginary parts, we get the following: Figure 3 The results are described, where the horizontal axis represents the frequency of the impedance, and the vertical axis represents the unknown quantity D in matrix D. 21 and D 22 The specific calculated value. When the frequency is below 100Hz, e2D 21 It is always equal to -35421.6, D 22 It is always equal to -10698.6, but when the frequency is higher than 100Hz, e2D 21 The absolute value of D decreases as the frequency increases. 22 The absolute value of increases with increasing frequency. On the one hand, e2D 21 and D 22 The existence of regions that remain constant with frequency (low-frequency region) and regions that vary with frequency (mid-to-high-frequency region) indicates that the above Z...ec (jω) is only valid in the low frequency region; on the other hand, in this example, e2D 21 and D 22 represent the rate of change of the concentration of the reactants with the electrode potential and the rate of change of the concentration itself, respectively. By measuring the frequency value corresponding to the inflection point of the change of both with the frequency, in this example 100 Hz, the value of the concentration diffusion rate of the object under test is obtained. When the ion or molecular species involved in the test object changes, the values of e2D 21 and D 22 and the frequency value corresponding to the inflection point of the change of both also change. By comparing or estimating the change, it can be determined which ion or molecule is involved in the electrochemical reaction.

[0059] The method has the following advantages:

[0060] 1. The method does not need to know the specific electrochemical reaction process of the test system. The final physical parameters are obtained by iterative solution of the impedance data and the matrix, avoiding data overfitting and underfitting caused by manual selection of parameters.

[0061] 2. The values of the elements in the matrix D obtained by the method are the rates of change of the dynamics of the substances and processes involved in the electrochemical reaction process, which directly reflect the parameters in the physical and chemical processes in the test system, facilitating understanding and analysis.

[0062] Example 2

[0063] The embodiment provides an electronic device, comprising one or more processors and a memory, the memory storing one or more programs, the one or more programs comprising instructions for performing the rate matrix acquisition method for electrochemical impedance analysis as described in embodiment 1.

[0064] Example 3

[0065] The embodiment provides a computer-readable storage medium comprising one or more programs for execution by one or more processors of an electronic device, the one or more programs comprising instructions for performing the rate matrix acquisition method for electrochemical impedance analysis as described in embodiment 1.

[0066] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for obtaining the rate of change matrix for electrochemical impedance analysis, characterized in that, Includes the following steps: Obtain electrochemical impedance data at different frequencies, obtain the corresponding electrochemical admittance data and convert it into an admittance vector in a preset form, and establish a solution matrix containing at least one unknown element based on the admittance vector converted into a preset form. Based on the solution matrix and the electrochemical impedance data, the values ​​of unknown elements are solved. Based on the values ​​of unknown elements, it is determined whether the preset stopping condition is met. If not, the order of the solution matrix and the admittance vector is increased by 1 to generate a new solution matrix, and this step is repeated. If yes, based on the current solution matrix and the values ​​of unknown elements, the target matrix is ​​obtained. The target matrix includes information on the rate of change of kinetic rates between the various substances and / or processes involved in the electrochemical reaction. Based on the element values ​​in the target matrix, the rate of change of substances and / or processes involved in the electrochemical reaction is analyzed. The structure of the solution matrix or its transpose is as follows: In the formula, To solve the matrix, elements At any position on the diagonal of the matrix, and the element The element value in the row or column is 0. For the first Line 1 Unknown elements in the column, To solve for the order of a matrix, The preset admittance vector or its transpose is: in, The position of the constant in the admittance vector and in the solution matrix is... If the rows k are the same, then y1, y2, ..., y N For frequency, The preset stopping condition is as follows: The measure of the change in the value of an unknown element at different frequencies is less than a preset threshold.

2. The method for obtaining the rate of change matrix for electrochemical impedance analysis according to claim 1, characterized in that, The preset admittance vector includes at least one constant.

3. The method for obtaining the rate of change matrix for electrochemical impedance analysis according to claim 1, characterized in that, The solution matrix is ​​of order 2 when it is initially established.

4. The method for obtaining the rate of change matrix for electrochemical impedance analysis according to claim 1, characterized in that, Solving for the value of an unknown element involves the following steps: By using the admittance vector and the corresponding frequency value as the eigenvector and eigenvalue of the solution matrix, respectively, a determinant is established, and the unknown element values ​​are obtained by solving the determinant.

5. The method for obtaining the rate of change matrix for electrochemical impedance analysis according to claim 4, characterized in that, The determinant is the following formula, or the transpose of the following formula, or the submatrix operation form obtained by the following formula: In the formula, To solve the matrix, It is the identity matrix. This is to convert the admittance vector into a preset form.

6. An electronic device, characterized in that, include: One or more processors and a memory, wherein the memory stores one or more programs, the one or more programs including instructions for executing the method for obtaining the rate of change matrix for electrochemical impedance analysis as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, It includes one or more programs that are executed by one or more processors of an electronic device, the one or more programs including instructions for performing the method for obtaining the rate of change matrix for electrochemical impedance analysis as described in any one of claims 1-5.

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