Differential Electrochemical Impedance Spectroscopy

Abstract

To solve a problem such that with a conventional electrochemical impedance analysis method, it is essentially impossible to evaluate only a spectrum that changes a state.SOLUTION: According to an analysis method of the present invention, first impedance data in which electrochemical impedance of a reference sample is measured at first plurality of frequencies and second impedance data in which a sample after change in a state is measured at second plurality of frequencies are prepared. Of these data, data measured at a common frequency is selected. Difference impedance data is obtained by calculating difference of the first impedance data from the second impedance data for each measurement frequency for each of real and imaginary parts. These are graphically displayed as a differential impedance spectrum. Next, an equivalent circuit model that conforms to this spectrum is determined and model parameters are optimized. The optimized parameter is defined as a numerical value representing a magnitude of change in a state of the sample.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an analysis method of electrochemical impedance for measuring the deterioration and the magnitude of state change of an electrochemical device such as a secondary battery.

Background Art

[0002] As a non-destructive measurement method for measuring the deterioration and performance change (hereinafter referred to as state change) of electrochemical devices such as storage batteries and fuel cells, the electrochemical impedance method is widely used. In the conventional evaluation method of state change by the electrochemical impedance method, the electrochemical impedance of the initial state and the state after deterioration is measured, an equivalent circuit model capable of reproducing the spectrum is set for each impedance spectrum, the least squares method is applied to optimize the parameters of the equivalent circuit model, and then the degree of state change of the device is evaluated from the difference in the numerical values of the optimized parameters.

[0003] In addition, in recent years, there is also an example of applying the relaxation time distribution (DRT) analysis method as a new evaluation method. In this method, similar to the conventional method, the electrochemical impedance of the initial state and the state after deterioration is measured, the DRT analysis method is applied to each impedance spectrum, and the degree of deterioration is evaluated from the change in the obtained DRT spectrum.

[0004] For example, in FIG. 10(a) of Non-Patent Document 1, while flowing 15% hydrogen, 12% water vapor, 15% carbon monoxide, 13% carbon dioxide, 45% nitrogen, and a trace amount of hydrogen sulfide (0.5 ppm) through a SOFC (Solid Oxide Fuel Cell), the change in the electrochemical impedance spectrum over a elapsed time of 300 to 400 hours is shown. Although it can be qualitatively understood that the spectrum is changing, it does not quantitatively show the degree of change. In the analysis by the conventional method, each spectrum is analyzed with an equivalent circuit model to obtain the optimal value of the parameter, but the optimal value is not the change value itself. Further, FIG. 10(b) shows the analysis result by DRT (distribution of relaxation times) corresponding to (a). Although it can be qualitatively understood that the peak existing near a certain frequency changes with time in the DRT spectrum, this also does not quantitatively show the parameter change.

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0006] In order to evaluate the degree of state change, it is necessary to finally quantify the change in the spectrum. However, in the conventional analysis method, since the evaluation of the change is performed using the entire electrochemical impedance spectra before the initial state and each of the electrochemical impedance spectra after the state change, there is an essential problem that it is impossible to evaluate only the spectrum of the part that changes due to deterioration. Furthermore, in the optimization of the parameters of the equivalent circuit in each analysis before and after the state change, the parameters include errors before and after the state change, and when comparing the two, these multiple errors are involved, resulting in a problem that the analysis sensitivity decreases. Therefore, there has been a demand for the development of a simple and new method that extracts only the change elements of the state change and quantitatively converts the change of the change elements into the change of the parameter values by model analysis.

[0007] An object of the present invention is to provide a simple and new electrochemical impedance analysis method that extracts only the change of the change elements before and after the state change, and by performing model analysis on it, quantitatively converts the change amount into the change of the parameter values. The present invention further provides an analysis processing system and an analysis processing program based on it.

Means for Solving the Problems

[0008] The analysis method of the present invention is a method of quantifying the impedance spectrum parameters for this change by taking the difference between each value of the impedance spectrum changed due to the state change and each value of the impedance spectrum before the change, and analyzing the obtained difference impedance spectrum by an equivalent circuit model. Since this method analyzes the changed numerical values themselves, it is possible to extract the change elements and directly quantify the change of the parameters.

[0009] The main steps of the analysis method of the present invention are as follows. (1) Prepare first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample at a plurality of first frequencies. (2) Prepare second electrochemical impedance data obtained by measuring the electrochemical impedance of the sample after the state change at a second plurality of frequencies including a frequency common to the first plurality of frequencies. (3) Select a plurality of measured values measured at a common measurement frequency from among the first electrochemical impedance data and the second electrochemical impedance data, and for each measurement frequency, obtain difference impedance data by taking the difference between the real part and the imaginary part of the first electrochemical impedance data from the second electrochemical impedance data. (4) Graphically display the difference impedance data as a difference impedance spectrum. (5) Determine an equivalent circuit model that fits the graphically displayed difference impedance spectrum and optimize the model parameters of the equivalent circuit model. (6) Use the optimized model parameters as a numerical value representing the magnitude of the state change of the sample.

[0010] The sample used as the reference may be the sample before the state change. On the other hand, the sample after the state change refers to a sample whose characteristics have changed after performing a repeated charge-discharge test or the like.

[0011] When obtaining the difference impedance data, it may be performed when there are a preset number or more of common frequencies, and this number is preferably set to 40 or more. Also, the first plurality of frequencies and the second plurality of frequencies are preferably set such that their logarithmic values are equally spaced.

[0012] The complex non-linear least squares method can be used to optimize the model parameters. Also, the determination of the equivalent circuit model and the optimization of the model parameters may be performed using existing electrochemical impedance analysis software.

Advantages of the Invention

[0013] The present invention has the advantage that only the changing elements of the spectrum can be extracted by a simple method, and the amount of change can be quantified by model analysis. Since only the amount of change is extracted, the quantification of the change can be performed simply and accurately. The analysis method according to the present invention can be applied not only to the degradation analysis of storage batteries, fuel cells, etc., but also to all fields where the electrochemical impedance measurement method of an electrochemical system accompanied by a state change is used. In particular, if it is applied to the degradation monitor of a storage battery, large-scale implementation in automotive storage batteries can be expected in the future.

Brief Description of Drawings

[0014]

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Best Mode for Carrying Out the Invention

[0015] A typical flow of the electrochemical impedance analysis method according to the present invention is shown in FIG. 1. First, first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample at a plurality of first frequencies is prepared (S110). The reference sample refers to, for example, an unused sample after being prototyped. A charge-discharge test is repeatedly performed on this sample under desired conditions and number of times, and second electrochemical impedance data obtained by measuring the sample after the internal state has changed due to this repeated charge-discharge is prepared at a plurality of second frequencies (S120).

[0016] Normally, the plurality of second frequencies are set to the same frequencies as the plurality of first frequencies and are measured with the same measuring device. However, for example, when it is desired to compare with a sample measured with another measuring device or under another setting in the past, the measurement frequency may be different from the currently set measurement frequency. In order to perform the impedance analysis of the present invention in such a case, first, a plurality of measured values measured at a common measurement frequency among the first electrochemical impedance data and the second electrochemical impedance data are selected. It is desirable that the number of common frequencies be as large as possible, and at least 40 or more in order to obtain highly accurate analysis results. The number of common measurement frequencies can be set in advance. When the number of selected common frequencies is less than the set number (S130), the plurality of second frequencies are reset to be equal to or more than the set number and measured again, and this is used as the second electrochemical impedance data. Note that since the ranges of the plurality of first and second measurement frequencies usually span several digits from low frequency to high frequency, it is desirable to set the logarithmic values to be equally spaced for easy viewing when the impedance spectrum is graphically displayed.

[0017] In this way, when the second electrochemical impedance data is obtained, for the data of each common measurement frequency, a difference is taken for each of the real part and the imaginary part of the first electrochemical impedance data from the second electrochemical impedance data to obtain difference impedance data (S140). This difference impedance data is stored in a data storage unit such as a semiconductor memory or a hard disk, and is graphically displayed as a difference impedance spectrum on a display unit such as a liquid crystal display (S150).

[0018] Next, it is determined whether this difference impedance spectrum can be analyzed by an equivalent circuit model (S160). This determination can also be made using known software pre-installed in a computer attached to this analysis device. If it is determined that it is not possible, the difference impedance data is recalculated or re-measured. On the other hand, if it is determined that it is possible, an equivalent circuit model and model parameters that match the difference impedance spectrum are obtained, and the model parameters are optimized (S170). The determination of the equivalent circuit model can also be performed using existing electrochemical impedance analysis software. For the optimization of the model parameters, it is desirable to use the complex non-linear least squares method. As specific methods, any of the Levenberg-Marquardt method, Nelder-Mead method, Powell method, conjugate gradient method, and a method combining these methods with a regularization method can be used. Alternatively, any other method may be used as long as it is a least squares method for obtaining optimal parameters for a non-linear function. Finally, with this optimized model parameter as a numerical value representing the state change of the sample, it is displayed on the display unit together with the equivalent circuit, and the analysis is completed (S180).

[0019] Next, an electrochemical impedance analysis processing system for performing the electrochemical impedance analysis of the present invention described with reference to FIG. 1 will be described. A block diagram thereof is shown in FIG. 2. The electrochemical impedance analysis processing system 200 of the present invention includes at least a control unit 210, a data storage unit 220, a data analysis unit 230, and a display unit 240, and may be data-connected to an electrochemical impedance measurement device 300.

[0020] The data storage unit 220 stores in advance the first electrochemical impedance data of a reference sample measured at a first plurality of frequencies using the electrochemical impedance measurement device 300, and the electrochemical impedance data of the sample after the state change measured at a second plurality of frequencies including frequencies common to the first plurality of frequencies (corresponding to S110 and S120 in FIG. 1). The data storage unit 220 can use a built-in or external semiconductor memory or a hard disk drive (HDD) in the system. First, the control unit 210 transfers the first electrochemical impedance data and the second electrochemical impedance data to the data analysis unit 230. The function of the control unit 210 can be performed by a central processing unit (CPU) of a computer built into the system.

[0021] The function of the data analysis unit 230 may also be performed by the above CPU. The data analysis unit 230 first determines whether the number of the second plurality of frequencies including frequencies common to the first plurality of frequencies is greater than a preset number (corresponding to S130 in FIG. 1). If it is less, the user is displayed on the display unit 240 to reset the frequency and perform the measurement again. If it is equal to or greater than the preset number, the current second electrochemical impedance data is used.

[0022] Next, among the above-described first electrochemical impedance data and second electrochemical impedance data, a plurality of sets of measured values measured at a common frequency are selected, and the difference between the first electrochemical impedance data and the second electrochemical impedance data is calculated for each set for each of the real part and the imaginary part (corresponding to S140 in FIG. 1). The control unit 210 stores the plurality of values (difference impedance data) calculated in this way in the data storage unit 220 together with data related to the sample such as the structure of the sample and test conditions, and causes the display unit 240 to display the difference impedance data as a difference impedance spectrum in a two-dimensional graph (corresponding to S150 in FIG. 1). The display unit 240 can be a built-in or external liquid crystal display or an organic display.

[0023] Next, in the data analysis unit 230, an equivalent circuit model capable of reproducing the displayed difference impedance spectrum is selected. If it is determined that analysis using the equivalent circuit model is impossible, the display unit 240 may display a message prompting the user to reset the measurement frequency or perform remeasurement (corresponding to S160 in FIG. 1). The model parameters of the circuit elements of the equivalent circuit model are optimized so that the difference between the spectrum reproduced on the display unit 240 using this equivalent circuit and the above-described difference impedance spectrum is minimized (corresponding to S170 in FIG. 1). Since the optimized model parameters can be regarded as values representing the magnitude of the state change of the measurement sample, the control unit 210 finally causes the display unit 240 to display this value as a numerical value representing the magnitude of the state change of the measurement sample (corresponding to S180 in FIG. 1), and the analysis of the present invention is completed.

[0024] Next, an analysis processing program executed on the CPU of a computer built into the electrochemical impedance analysis processing system for performing the electrochemical impedance analysis of the present invention described with reference to FIG. 1 will be described.

[0025] The program pre-downloaded to the computer reads into the data analysis unit 230 the first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample stored in advance in the data storage unit 220 at a first plurality of frequencies, and the second electrochemical impedance data obtained by measuring the electrochemical impedance of the sample after the state change at a second plurality of frequencies including frequencies common to the first plurality of frequencies (corresponding to S110 and S120 in FIG. 1).

[0026] Next, a set of a plurality of measured values measured at common frequencies among the first electrochemical impedance data and the second electrochemical impedance data is selected, and for each set, the difference between the first electrochemical impedance data and the second electrochemical impedance data is calculated for each of the real part and the imaginary part to obtain difference impedance data (corresponding to S140 in FIG. 1). At this time, in order to obtain highly accurate difference impedance, when the number of common frequencies is equal to or more than a preset number, preferably 40 or more, the difference is calculated, and when it is less than that, it may be configured to display a confirmation of the continuation of the step to the user (corresponding to S130 in FIG. 1). Then, the difference impedance data calculated in this way is stored in the data storage unit 220 and displayed as an electrochemical impedance spectrum on the display unit 240 in a two-dimensional graph (corresponding to S150 in FIG. 1). Further, in the electrochemical impedance measurement, since the measurement frequency ranges from a low frequency to a high frequency over several digits, it is preferable that these multiple frequencies are such that their logarithmic values are equally spaced in the graph display.

[0027] Next, it is determined whether this differential impedance data can be analyzed using an equivalent circuit model (corresponding to S160 in FIG. 1). If it is determined that it can be analyzed, an equivalent circuit model that can fit the electrochemical impedance spectrum is determined, and the model parameters are optimized so that the difference between the theoretical curve calculated using this equivalent circuit model and the electrochemical impedance spectrum is minimized (corresponding to S170 in FIG. 1). The complex nonlinear least squares method can be used for optimization. Also, the determination of the equivalent circuit model and the optimization of the model parameters may be performed by downloading and using existing electrochemical impedance analysis software pre-installed on a computer. Finally, the optimized model parameters are displayed on the display unit 240 as a numerical value representing the magnitude of the change in the state of the sample and stored in the data storage unit 220 (corresponding to S180 in FIG. 1).

[0028] The following shows the analysis results of the electrochemical impedance before and after repeated charge and discharge using a prototype all-solid-state lithium battery as a sample. The layer structure of the all-solid-state lithium battery is schematically shown on the left side of FIG. 3. The solid electrolyte is an inorganic lithium-ion conducting solid electrolyte, the positive electrode is a mixture of LiNi 0.8 Co 0.15 Al 0.05 O2 and the solid electrolyte, the positive electrode active material is LiNi 0.8 Co 0.15 Al 0.05 O2, and the negative electrode uses an InLi alloy. The current enters and exits through current collectors joined to the positive and negative electrodes respectively. The measurement was performed by measuring the electrochemical impedance by constant current charge and discharge measurement using a measurement system schematically shown on the right side of FIG. 3.

Example

[0029] First, the impedance of the discharged prototype battery was measured at a charge / discharge rate of 0.1C, in the second cycle, and at a charge rate of 100%, to obtain a reference impedance spectrum. Here, 1C is defined as the current value at which the theoretical capacity of the battery is discharged to its rated capacity and discharge is completed in 1 hour, and 0.1C is the current value at which discharge is completed in 10 hours. The reference impedance spectrum measured in this way is shown in Figure 4. Following a flattened arc-shaped bulge pattern on the left side of the graph (high frequency side), a linearly rising pattern was observed on the right side (low frequency side).

[0030] Next, the same prototype battery as above was discharged at 0.1C, then charged and discharged 10 times at a charge / discharge rate of 0.2C, and then further charged to 100% at 0.1C, and the impedance was measured as an impedance spectrum after the change in state. This is shown in Figure 5. As with the reference impedance spectrum in Figure 4, a flattened arc-like rise pattern was observed on the left side of the graph, followed by a linear rise pattern on the right side. However, it is difficult to tell the difference between the two figures by comparing them.

[0031] Next, the impedance spectra shown in Figures 4 and 5 were analyzed using the equivalent circuit model method. Figure 6 shows the equivalent circuit obtained for both impedance spectra. Here, R is the resistance, CPE is the constant phase element, and its impedance is

[0032]

number

[0033]

number

[0034] The values of the optimized parameters calculated using the equivalent circuit shown in FIG. 6 are summarized in Table 1. Among the parameters, R1, T1, and α1 correspond to the high-frequency arc (the left side of the figure), and R2, T2, and α2 correspond to the low-frequency arc (the central part of the figure). The right column of Table 1 shows the results of simply calculating the differences in the parameter values of the reference spectrum and the spectrum after the state change. From this, it can be seen that the change in the resistance value, especially the increase in the resistance component (R1) of the high-frequency arc, is large. However, T1 of the constant-phase element shows a negative value and is not recognized as having a significant value, making it impossible to quantify the difference. Also, the parameter T W of the Warburg impedance Z W related to the straight-line part in the low-frequency range

[0035]

Number

[0036]

Table 1

[0037] Next, by the method of the present invention, the difference value between the value of the impedance spectrum after the state change and the value of the reference impedance spectrum was calculated, and only the change in the sample due to charge and discharge at a charge and discharge rate of 0.2C for 10 cycles was extracted. Specifically, using a computer, a plurality of measurement values with equal measurement frequency values were selected from the impedance data after the state change and the reference impedance data, and the real part and the imaginary part of the complex impedance data were subtracted for each measurement frequency to obtain a complex difference value. This difference value was stored in a semiconductor memory or HDD, and a difference impedance spectrum was displayed on a liquid crystal display with the real part of the complex difference value on the horizontal axis and the imaginary part on the vertical axis. This is shown in FIG. 7. It can be seen that the spectral changes in the collapsed arc spectrum portions shown in FIGS. 4 and 5 can be accurately extracted, and even a slight change in the linear change region in the low-frequency range is extracted.

[0038] Next, the impedance spectrum shown in FIG. 7 was analyzed using the equivalent circuit model method. FIG. 8 shows the obtained equivalent circuit. Analysis was possible with the same equivalent circuit as the one shown in FIG. 6. Table 2 shows the results of optimizing the parameters using this equivalent circuit. From this, it can be seen that the resistance (R1 and R2) of the arc is increasing, that it is possible to quantify the change in the CPE parameters (T, α), and furthermore that the change value of the Warburg impedance parameter can be directly calculated from Equation 3. The impedance spectrum reproduced using these parameter values is the solid line in FIG. 7.

[0039]

Table 2

[0040] The difference by the analysis method of the present invention is the difference in each of the real part and the imaginary part, not just the difference in the vertical axis as shown in Table 1. Therefore, in FIG. 7, not only the vertical axis but also the scale of the horizontal axis is changing. As a result of taking the difference in each of the real part and the imaginary part for the values of the same frequency, the information of the measurement frequency, which was originally implicitly included as a parameter in the complex impedance data, can be accurately reflected between different impedance data, so that it becomes possible to obtain a highly accurate differential impedance spectrum.

Example

[0041] Using the battery prototyped under the same conditions as in Example 1, for the prototyped battery in a discharged state, the impedance at a charge-discharge rate of 0.1C, the second cycle, and a discharge rate of 50% was measured as the reference impedance spectrum. The results are shown in Fig. 9. Two arcs, an arc on the high-frequency side (left side of the figure) and an arc on the low-frequency side (central part of the figure), and a subsequent linearly rising part were observed. Then, using this battery, after charge-discharge at a charge-discharge rate of 0.2C for 10 cycles, and then discharging to 50% at 0.1C, the impedance was measured as the impedance spectrum after the state change. The results are shown in Fig. 10. The shape of the spectrum is the same as that in Fig. 9, and it is difficult to distinguish the changes between the two from the impedance spectrum even when comparing the two.

[0042] Next, in the same manner as in Example 1, each of the impedance spectra shown in Figs. 9 and 10 was analyzed using the equivalent circuit model method. The equivalent circuit model could be analyzed using the same equivalent circuit as the one shown in Fig. 6. The parameters obtained therefrom, R1, T1, α1 correspond to the arc on the high-frequency side (left side of the figure), and R2, T2, α2 correspond to the arc on the low-frequency side (central part of the figure). These parameters and the differences in the parameter values of the two are shown in Table 3. Similar to the case of Example 1, the differences in the T1, T2, α1, α2 parameters of the constant phase element have large variations and also have negative values, and it is not recognized that they show significant values, making quantification impossible.

[0043]

Table 3

[0044] Next, in the same manner as in Example 1, the difference between the spectrum values in FIG. 10 and those in FIG. 9 was obtained for each of the real part and the imaginary part, and only the change due to charge and discharge at a charge and discharge rate of 0.2C for 10 cycles was extracted to obtain a differential impedance spectrum. This is shown in FIG. 11. It can be seen that there is an increase of about 10% in the two arcs. As a result of analyzing this differential impedance spectrum using an equivalent circuit model, the same equivalent circuit as that shown in FIG. 6 was applicable. And the parameters could be optimized accurately by this equivalent circuit. The results are shown in Table 4. The differential impedance spectrum reproduced using these optimized parameters is shown by the solid line in FIG. 11.

[0045]

Table 4

[0046] The change in the state of the battery revealed from the experimental results of Example 1 and Example 2 for batteries with the same structure, considering that the negative electrode is an alloy with high reversibility, can be presumed to be due to the change in the state of the positive electrode. Specifically, it can be presumed to be due to the decrease in the lithium insertion / desorption ability of the positive electrode active material. Thus, by the electrochemical impedance analysis method of the present invention, it becomes possible to more accurately estimate the specific factors of battery deterioration.

[0047] Note that the description of the present invention has been made based on the above examples, but the present invention is not limited thereto, and it is obvious to those skilled in the art that various changes and modifications can be made within the spirit of the present invention and the scope of the appended claims. As an analysis method of the differential impedance spectrum, other methods such as a relaxation time distribution analysis method may be applied in addition to the equivalent circuit model analysis. Also, any method may be used as long as it is a least squares method for obtaining optimal parameters for a non-linear function instead of the complex non-linear least squares method used for optimizing the model parameters.

Claims

1. Preparing first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample at a first plurality of frequencies; Preparing second electrochemical impedance data obtained by measuring the electrochemical impedance of the sample after the state change at a second plurality of frequencies including frequencies common to the first plurality of frequencies; Selecting a plurality of measured values measured at the common frequencies from among the first electrochemical impedance data and the second electrochemical impedance data, and obtaining difference impedance data by taking the difference between the real part and the imaginary part of the second electrochemical impedance data and the first electrochemical impedance data for each measurement frequency; Graphically displaying the difference impedance data as a difference impedance spectrum; Determining an equivalent circuit model that fits the graphically displayed difference impedance spectrum and optimizing the model parameters of the equivalent circuit model; Taking the optimized model parameters as a numerical value representing the magnitude of the state change of the sample; An electrochemical impedance analysis method including the above steps.

2. The electrochemical impedance analysis method according to claim 1, wherein the reference sample is the sample before the state change.

3. The electrochemical impedance analysis method according to claim 1 or 2, wherein a complex nonlinear least squares method is used for optimizing the model parameters.

4. The electrochemical impedance analysis method according to any one of claims 1 to 3, wherein the difference impedance data is obtained when the number of the common frequencies is equal to or more than a preset number.

5. The electrochemical impedance analysis method according to claim 4, wherein the preset number is 40.

6. The electrochemical impedance analysis method according to any one of claims 1 to 5, wherein the first plurality of frequencies and the second plurality of frequencies are set such that their logarithmic values are equally spaced.

7. An electrochemical impedance analysis processing system including a control unit, a data storage unit, a data analysis unit, and a display unit, The control unit reads into the data analysis unit the first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample, which was previously stored in the data storage unit, at a first plurality of frequencies, and the second electrochemical impedance data obtained by measuring the electrochemical impedance of the sample after the state change at a second plurality of frequencies including frequencies common to the first plurality of frequencies. The data analysis unit selects a plurality of measured values measured at the common frequencies from among the first electrochemical impedance data and the second electrochemical impedance data, and obtains differential impedance data by taking the difference between the real part and the imaginary part of the second electrochemical impedance data and the first electrochemical impedance data for each measurement frequency. The control unit stores the differential impedance data in the data storage unit and causes it to be graphically displayed as a differential impedance spectrum on the display unit. The data analysis unit determines an equivalent circuit model that fits the graphically displayed differential impedance spectrum and optimizes the model parameters of the equivalent circuit model. The control unit displays the optimized model parameters on the display unit as a numerical value representing the magnitude of the state change of the sample and stores them in the data storage unit. An electrochemical impedance analysis processing system.

8. The electrochemical impedance analysis processing system according to claim 7, wherein a complex non-linear least squares method is used for the optimization of the model parameters.

9. The electrochemical impedance analysis processing system according to claim 7 or 8, wherein the differential impedance data is obtained when there are a preset number or more of the common frequencies.

10. The electrochemical impedance analysis processing system according to claim 9, wherein the preset number is 40.

11. The electrochemical impedance analysis processing system according to any one of claims 7 to 10, wherein the first plurality of frequencies and the second plurality of frequencies are set such that their logarithmic values are equally spaced. An analysis processing program executed on a CPU of a computer incorporated in an electrochemical impedance analysis processing system including a control unit, a data storage unit, a data analysis unit, and a display unit, wherein the computer A step of reading into the data analysis unit the first electrochemical impedance data obtained by measuring the electrochemical impedance of a reference sample stored in advance in the data storage unit at a first plurality of frequencies, and the second electrochemical impedance data obtained by measuring the electrochemical impedance of the sample after the state change at a second plurality of frequencies including frequencies common to the first plurality of frequencies; A step of selecting a plurality of measured values measured at the common frequencies from among the first electrochemical impedance data and the second electrochemical impedance data, and obtaining difference impedance data by taking the difference between the real part and the imaginary part of the second electrochemical impedance data and the first electrochemical impedance data for each measurement frequency; A step of storing the difference impedance data in the data storage unit and graphically displaying the difference impedance data as an electrochemical impedance spectrum on the display unit; A step of determining an equivalent circuit model that fits the electrochemical impedance spectrum and optimizing the model parameters of the equivalent circuit model in the data analysis unit; A step of displaying the optimized model parameters on the display unit as a numerical value representing the magnitude of the state change of the sample and storing them in the data storage unit; An electrochemical impedance analysis processing program for executing the above.

13. The electrochemical impedance analysis processing program according to claim 12, wherein a complex nonlinear least squares method is used for optimizing the model parameters.

14. The electrochemical impedance analysis processing program according to claim 12 or 13, wherein the difference impedance data is obtained when there are a preset number or more of the common frequencies.

15. The electrochemical impedance analysis processing program according to claim 14, wherein the preset number is 40.

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