WO2019124388A1

WO2019124388A1 - Analysis device and analysis method

Info

Publication number: WO2019124388A1
Application number: PCT/JP2018/046604
Authority: WO
Inventors: 重輔志村; 後藤　習志; 宮崎　武志
Original assignee: 株式会社村田製作所
Priority date: 2017-12-19
Filing date: 2018-12-18
Publication date: 2019-06-27
Also published as: JP6863482B2; JPWO2019124388A1

Abstract

This analysis device is provided with: a current supply unit that supplies an alternating current to a sample electrode; and a calculation unit that calculates an exchange current density and a charge transfer coefficient, which relate to the sample electrode, on the basis of an overvoltage response generated at the sample electrode in accordance with the alternating current supply from the current supply unit.

Description

Analyzer and analysis method

The present technology relates to an analysis device and an analysis method for analyzing a charge transfer reaction generated between a sample electrode and ion species present on the surface of the sample electrode.

An electrode releases and transfers charge to cause a redox reaction (charge transfer reaction) of ionic species present on the surface of the electrode. The behavior during the charge transfer reaction (the relationship between the current and the overvoltage) is represented by the Butler-Volmer equation.

The Butler-Volmer equation contains two parameters that represent the charge transfer characteristics of the electrode. The first parameter is the exchange current density that represents the reaction barrier of the charge transfer reaction, and the second parameter is the charge transfer coefficient that represents the symmetry of the charge transfer reaction. Since exchange current density and charge transfer coefficient are important to know the characteristics of the electrode, they are widely used in the research and development field of the electrode and the material used for the electrode, manufacturing control field, and the like.

Several methods have already been proposed as methods for determining the exchange current density and charge transfer coefficient.

Specifically, after measuring the current and overpotential under conditions where material transport can be sufficiently ignored, the relationship between log [i / (1-e ^f η)] and η is plotted with the current as i and overpotential as η Thus, the exchange current density and the charge transfer coefficient are calculated based on the intercept and the slope (see, for example, Non-Patent Document 1). However, f = nF / RT, n is the number of reaction electrons, F is the Faraday constant, R is the gas constant, and T is the absolute temperature. This method is called the Allen-Hickling method. Also, by plotting the relationship between log (i) and η using the Tafel equation in which the Butler-Volmer equation is simplified, the exchange current density and charge transfer coefficient are calculated based on the intercept and the slope. It is also good.

Alternatively, the exchange current density and the charge transfer coefficient may be calculated by linearly approximating the relationship between the current and the overvoltage (see, for example, Non-Patent Document 2). This method is called Stern-Geary method.

Besides, it has also been proposed to calculate the exchange current density and the charge transfer coefficient using a random number search method, a genetic algorithm method, a sequential search method or the like (see, for example, Patent Document 1).

In addition, as a method of examining the relationship between current and overvoltage, a method of measuring current and overvoltage under potential regulation or voltage regulation using a potentiostat, and current and overvoltage under current regulation using a galvanostat Methods are known (see, for example, Patent Document 2). Both methods are further classified into methods in which the constant potential state, constant voltage state or constant current state is maintained until the measured value is stabilized, and methods in which steady-state values are predicted by analysis of transient response. .

Patent No. 3669669 specification Patent No. 6026055 specification

Several methods have been proposed to determine the exchange current density and charge transfer coefficient, but both methods use the relationship between current and overvoltage. In this case, in order to investigate the relationship between the current and the overvoltage, it is necessary to keep the current flowing until the measured value of the overvoltage stabilizes, and also in the case of predicting the steady-state value by analyzing the transient response. It is necessary to flow a considerable amount of current. For this reason, when using an electrode whose composition changes due to the flow of current, the composition of the electrode changes with time during measurement of overvoltage, so the exchange current density and charge transfer coefficient can not be determined. . Thus, there is a need to determine exchange current density and charge transfer coefficients for various electrodes, including electrodes of varying composition.

The present technology has been made in view of such problems, and an object thereof is to provide an analysis apparatus and an analysis method capable of analyzing the charge transfer characteristics of various sample electrodes.

An analysis apparatus according to an embodiment of the present technology includes a current supply unit that supplies an alternating current to a sample electrode, and a sample electrode based on an overvoltage response generated in the sample electrode in response to the supply of the alternating current by the current supply unit. And an operation unit for calculating the exchange current density and the charge transfer coefficient.

An analysis method according to an embodiment of the present technology supplies an alternating current to a sample electrode, and based on an overvoltage response generated at the sample electrode in response to the supply of the alternating current, the exchange current density and charge transfer coefficient for the sample electrode Is calculated.

According to the analysis device or the analysis method of one embodiment of the present technology, an alternating current is supplied to the sample electrode, and the exchange current related to the sample electrode is generated based on the overvoltage response generated in the sample electrode in response to the supply of the alternating current. Since the density and charge transfer coefficient are calculated, the charge transfer characteristics of various electrode materials can be analyzed.

In addition, the effect described here is not necessarily limited, and may be any effect described in the present technology.

It is a block diagram showing composition of an analysis device of one embodiment of this art. It is sectional drawing which represents typically the structure of the sample containing the sample electrode shown in FIG. It is a figure showing the image which separated the resistance characteristic (Bode plot) of the sample electrode measured using an electrochemical impedance method (linear alternating current impedance method) into each resistance component. It is a flow chart for explaining the analysis method of one embodiment of this art. It is a figure showing the resistance characteristic (Cole-Cole plot) of a sample electrode. It is a figure showing the resistance characteristic (Bode plot) of a sample electrode.

Hereinafter, an embodiment of the present technology will be described in detail with reference to the drawings. The order to be described is as follows.

1. Analysis device 1-1. Overall configuration 1-2. Configuration of sample including sample electrode 1-3. Forming material of sample electrode Theory of operation 3. Method of setting frequency of alternating current 4. Operation (analysis method)
5. Action and effect 6. Modified example

<1. Analyzer>
First, an analysis device according to an embodiment of the present technology will be described.

The analysis device described here is a device that analyzes the charge transfer characteristic, which is an important characteristic regarding the sample electrode 121, by analyzing the sample electrode 121 (see FIG. 1) contained in the sample 12 described later. .

In particular, this analyzer calculates the exchange current density i ₀ (A / m ² ) and the charge transfer coefficient α, which are indices representing the charge transfer characteristics of the sample electrode 121. In this case, the analysis apparatus uses the new arithmetic expression derived based on the new arithmetic theory described later to convert the exchange current density i ₀ and the charge transfer coefficient α based on the overvoltage response of the sample electrode 121. In the calculation, the influence of the non-linear component of the over-voltage response is taken into consideration.

The type of the sample 12 is not particularly limited as long as the sample electrode 121 to be analyzed is included. Specifically, the sample 12 is, for example, a battery and a capacitor. The type of cell is not particularly limited, and examples thereof include primary cells, secondary cells, fuel cells, and dye-sensitized solar cells.

<1-1. Overall configuration>
First, the entire configuration of the analysis device will be described. FIG. 1 shows a block configuration of the analysis device.

This analyzer includes, for example, as shown in FIG. 1, a sample 12 including a sample electrode 121, a current supply unit 14 for supplying an alternating current I to the sample 12 (sample electrode 121), and a current supply unit 14 An arithmetic unit 17 for calculating the exchange current density i ₀ and the charge transfer coefficient α for the sample electrode 121 based on the overvoltage response generated in the sample 12 (sample electrode 121) in response to the supply of the alternating current I by There is.

More specifically, the analysis device includes, for example, the control unit 11, the function generation unit 13, the overvoltage measurement unit 15, and the overvoltage amplitude measurement unit 16 together with the sample 12, the current supply unit 14 and the calculation unit 17 described above. , A waveform display unit 18, an analysis display unit 19, and a storage unit 20.

[Control unit]
The control unit 11 controls the overall operation of the analysis device. The control unit 11 includes, for example, a central processing unit (CPU) and various memories. Specifically, the control unit 11 includes, for example, a personal computer and the like, and incorporates a control program for executing an operation (analysis method) of an analysis device described later.

[Sample containing sample electrode]
The sample 12 is an element that causes a charge transfer reaction to proceed between the sample electrode 121 and the ion species present on the surface of the sample electrode 121. The sample 12 causes the above-described charge transfer reaction to proceed when the alternating current I is supplied from the current supply unit 14 to the sample electrode 121. The number of samples 12 is not particularly limited. The detailed configuration of the sample 12 including the sample electrode 121 will be described later (see FIG. 2).

[Function generator]
The function generation unit 13 sets the frequency f (Hz) of the alternating current I supplied from the current supply unit 14 to the sample electrode 121, and sends an alternating current signal corresponding to the frequency f of the alternating current I to the current supply unit 14. Send. The function generator 13 includes, for example, a lock-in amplifier.

The frequency f of the alternating current I is not particularly limited, but is preferably a frequency f within a specific range (a specific frequency range Rf described later). As described later, since the influence of the resistance component caused by the diffusion resistance is suppressed, the analysis accuracy of the sample electrode 121, that is, the calculation accuracy of the exchange current density i ₀ and the charge transfer coefficient α is improved.

Specifically, for example, before the charge transfer characteristic of the sample electrode 121 is analyzed, the function generating unit 13 examines the resistance characteristic of the sample electrode 121 using an electrochemical impedance method (linear alternating current impedance method) in advance. To identify the specific frequency Rf.

In this case, the function generation unit 13 measures, for example, the impedance Z of the sample electrode 121 while changing the frequency f. As a result, for example, when the function generator 13 decreases again until the impedance Z decreases to be substantially constant according to the increase of the frequency f, a range in which the impedance Z becomes substantially constant (specific frequency range Rf The frequency f of the alternating current I is set so as to be a value in.

That is, for example, after specifying the specific frequency range Rf based on the resistance characteristic (the change pattern of the impedance Z) of the sample electrode 121 examined using the above-described electrochemical impedance method, the function generation unit 13 determines the specific frequency The frequency f of the alternating current I is set so as to be a value within the range Rf.

The value of the frequency f set by the function generation unit 13 is not particularly limited as long as it is an arbitrary value within the range of the specific frequency range Rf described above.

For example, when the frequency f of the alternating current I is set based on the specific frequency range Rf by specifying the specific frequency range Rf, the function generation unit 13 sets the frequency f of the alternating current I as described above. The corresponding AC signal is transmitted to the current supply unit 14.

A specific setting procedure of the frequency f of the alternating current I (including the details of the specific frequency range Rf) will be described later (see FIG. 3).

[Current supply unit]
The current supply unit 14 supplies an alternating current I to the sample electrode 121. The current supply unit 14 includes, for example, a current control device such as a galvanostat.

The reason why the current supply unit 14 supplies the alternating current I to the sample electrode 121 is that the composition of the sample electrode 121 is unlikely to change at the time of analysis using the analyzer (at the time of progress of charge transfer reaction).

Specifically, as described later, as a forming material of the sample electrode 121, in addition to a non-alloying material such as a carbon material, an alloying material such as silicon which forms an alloy at the time of progress of charge transfer reaction is also used. In the case where the sample electrode 121 contains an alloying material, when a direct current is supplied to the sample electrode 121, only one of the oxidation reaction and the reduction reaction proceeds according to the sign of the direct current. Do. As a result, the composition of the sample electrode 121 changes in the process of progress of the charge transfer reaction, so that the charge transfer characteristics of the sample electrode 121 in the original composition can not be analyzed. The alloying material described here is an example of a material whose composition changes in the course of the charge transfer reaction.

On the other hand, in the case where the sample electrode 121 contains an alloying material, when an alternating current I is supplied to the sample electrode 121, the alternating current for exactly N cycles (N is a natural number) After I is supplied, the time integral value of the alternating current I becomes zero. That is, the number of moles required for the oxidation reaction and the number of moles needed for the reduction reaction are equal to each other. Thus, the composition of the sample electrode 121 does not change in the process of progress of the charge transfer reaction, so that the charge transfer characteristic of the sample electrode 121 in the original composition can be analyzed.

The frequency f of the alternating current I supplied to the sample electrode 121 by the current supply unit 14 is not particularly limited. However, as described above, the value of the frequency f of the alternating current I is set by the function generation unit 13 It is preferable that the value is within the specific frequency range Rf. This is because the analysis accuracy of the sample electrode 121 is improved.

[Overvoltage measurement unit]
When the alternating current I is supplied to the sample electrode 121 by the current supply unit 14, the overvoltage measuring unit 15 measures the overvoltage E generated in the sample electrode 121. The overvoltage measurement unit 15 includes, for example, a galvanostat. For example, when measuring the overvoltage E, the overvoltage measuring unit 15 transmits the measurement result of the overvoltage E to the overvoltage amplitude measuring unit 16.

[Overvoltage amplitude measurement unit]
The overvoltage amplitude measurement unit 16 measures overvoltage amplitudes of two or more frequency components of the overvoltage E measured by the overvoltage measurement unit 15. More specifically, the overvoltage amplitude measurement unit 16 extracts a non-linear component of 2 or more n-th order (n is an integer of 2 or more) as the overvoltage amplitude of the above-mentioned 2 or more frequency components. The overvoltage amplitude V _n (V) of the two or more n-th nonlinear components is measured. The overvoltage amplitude measurement unit 16 includes, for example, a signal extraction device such as a lock-in amplifier. Note that two or more lock-in amplifiers may be used in combination to measure the overvoltage amplitude V _n of the two or more n-th nonlinear components.

The type of the overvoltage amplitude V _n of the _n-th non-linear component measured by the overvoltage amplitude measurement unit 16 is not particularly limited. Among them, the overvoltage amplitude measurement section 16, as an overvoltage amplitude V _n of 2 or more n-order nonlinear components described above, one or more overvoltage overvoltage amplitude V _n and one or more even-order non-linear components of odd-order nonlinear component Preferably, the amplitude V _n is measured. This is because the analysis accuracy of the sample electrode 121 is improved. The odd-order non-linear components are, for example, third-order non-linear components, fifth-order non-linear components, seventh-order non-linear components, and ninth-order non-linear components. The even-order nonlinear components include, for example, second-order nonlinear components, fourth-order nonlinear components, sixth-order nonlinear components, and eighth-order nonlinear components.

In this case, it is preferable that the overvoltage amplitude measurement unit 16 measure the overvoltage amplitude V _n of the lower order two or more nonlinear components, more specifically, the overvoltage amplitude V ₂ of the second order nonlinear component. and third order is preferable to measure the overvoltage amplitude V ₃ of the nonlinear components. This is because it is more difficult for the low-order non-linear component to include the high-order non-linear component, so that the analysis accuracy of the sample electrode 121 is further improved.

When the overvoltage amplitude measurement unit 16 measures, for example, the overvoltage amplitude V _n of the 2 or more n-th nonlinear component, the measurement result of the overvoltage amplitude V _n of the 2 or more n-th nonlinear component is Send.

[Operation unit]
Arithmetic unit 17 calculates exchange current density i ₀ and charge transfer coefficient α for sample electrode 121 based on the overvoltage response generated at sample electrode 121 in response to the supply of alternating current I by current supply unit 14.

Specifically, for example, based on the overvoltage amplitudes of two or more frequency components (the overvoltage amplitude V _{n of the n-th} non-linear component of 2 or more) measured by the overvoltage amplitude measuring unit 16, the operation unit 17 determines Calculate density i ₀ and charge transfer coefficient α. More specifically, when the over-voltage amplitude measurement unit 16 is over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component is measured, the arithmetic unit 17, for example, secondary The exchange current density i ₀ and the charge transfer coefficient α are calculated based on the overvoltage amplitude V ₂ of the non-linear component and the overvoltage amplitude V ₃ of the non-linear component of the third order.

When the overvoltage amplitude measurement unit 16 is over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component is measured, the arithmetic unit 17, for example, using Equation (1) below Charge transfer coefficient α is calculated. Further, the calculation unit 17 calculates the exchange current density i ₀ using, for example, the following equation (2) or (3) based on the calculation value of the charge transfer coefficient α calculated in advance.

(Α is the charge transfer coefficient, V ₂ is the overvoltage amplitude (V) of the second-order nonlinear component, V ₃ is the overvoltage amplitude (V) of the third-order nonlinear component, R is the gas constant (J / [K · mol]) , T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I ₀ is the exchange current density (A / m ² ), α is the charge transfer coefficient, I is the alternating current (A), V ₂ is the overvoltage amplitude (V) of the second-order nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I ₀ is the exchange current density (A / m ² ), α is the charge transfer coefficient, I is the alternating current (A), V ₃ is the overvoltage amplitude (V) of the third nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

As apparent from the equation (1), the charge transfer coefficient α calculated here is not the overvoltage amplitude V ₁ of the linear component but the overvoltage amplitude V _{n of the n-th} nonlinear component of 2 or more (the second nonlinear component It is calculated by using the over-voltage amplitude V ₃₎ of the overvoltage amplitude V ₂ and third-order nonlinear component of.

As is apparent from later-described equation (18), charge transfer coefficient α is because it is independent of the overvoltage amplitude V ₁ of the linear component, overvoltage amplitude V ₁ of the the linear component are not dependent parameter of the charge transfer coefficient α . Therefore, the charge transfer coefficient α can not be calculated based on the overvoltage amplitude V ₁ of the linear component.

On the other hand, as apparent from the equations (19) to (21) described later, since the charge transfer coefficient α depends on the overvoltage amplitude V _n of the _n-th nonlinear component, the n-th nonlinear The component overvoltage amplitude V _n is a dependent parameter of the charge transfer coefficient α. Therefore, the charge transfer coefficient α can be calculated based on the overvoltage amplitude V _n of the _n-th non-linear component.

Also, as is clear from the equation (2) or the equation (3), the exchange current density i ₀ computed here uses the computed value of the charge transfer coefficient α computed using the above equation (1) Is calculated.

In equation (1), all parameters (gas constant R, absolute temperature T, reaction electrons other than charge transfer coefficient α, overvoltage amplitude V _{2 of second-} order nonlinear component and overvoltage amplitude V ₃ of third-order nonlinear component The number n and the Faraday constant F) are constants (known values). Therefore, calculation unit 17, for example, based on the measured value of the overvoltage amplitude V ₃ of the actual measurement value and the third-order nonlinear component of the overvoltage amplitude V ₂ of the second-order nonlinear component obtained from the overvoltage amplitude measurement section 16, the formula The charge transfer coefficient α can be calculated using (1).

In equation (2), all parameters (gas constant R, absolute temperature T, number of reaction electrons n, and Faraday constant F) other than the charge transfer coefficient α and the overvoltage amplitude V ₂ of the second-order nonlinear component are constants. . Therefore, calculation unit 17, for example, the measured value of the overvoltage amplitude V ₂ of the second-order nonlinear component obtained from the overvoltage amplitude measurement section 16, based on the calculated value of the charge transfer coefficient α computed above formula The exchange current density i ₀ can be calculated using (2).

Similarly, in Formula (3), all parameters except the overvoltage amplitude V ₃ of charge transfer coefficient α and third-order nonlinear component (gas constant R, absolute temperature T, the number of reaction electrons n and the Faraday constant F) is a constant is there. Therefore, calculation unit 17, for example, the measured value of the overvoltage amplitude V ₃ of the third-order nonlinear component obtained from the overvoltage amplitude measurement section 16, based on the calculated value of the charge transfer coefficient α computed above formula The exchange current density i ₀ can be calculated using (3).

The calculation theory of the equations (1) to (3), that is, the background of the derivation of the equations (1) to (3) will be described later.

[Waveform display section]
The waveform display unit 18 displays the waveform of the overvoltage E measured by the overvoltage measurement unit 15. The waveform display unit 18 includes, for example, an oscilloscope.

[Analytical display section]
The analysis display unit 19 is a display device on which an operation screen for analysis, an analysis result, and the like are displayed. The operation screen for analysis is, for example, an input screen of various parameters. The analysis result is, for example, the calculation result of the exchange current density i ₀ and the charge transfer coefficient α.

[Storage unit]
The storage unit 20 stores information necessary for analysis, and includes, for example, a read only memory (ROM) and a random access memory (RAM). The type of information stored in the storage unit 20 is not particularly limited. Specifically, the information includes various constants such as, for example, the gas constant R, the absolute temperature T, the number of reaction electrons n, and the Faraday constant F described above. The information may also include a conversion table (see Table 1) and the like described later. Of course, the information stored in the storage unit 20 can be changed at any time, for example.

<1-2. Configuration of sample including sample electrode>
Next, the configuration of the sample 12 including the sample electrode 121 will be described. FIG. 2 schematically shows the cross-sectional configuration of the sample 12 including the sample electrode 121. As shown in FIG.

For example, as shown in FIG. 2, the sample 12 includes the sample electrode (working electrode) 121, the counter electrode 122, and the electrolyte 123 described above. An alternating current I is supplied to the sample 12 by the current supply unit 14 via the sample electrode 121 and the counter electrode 122.

Although FIG. 2 shows a configuration in which the electrolyte 123 is sandwiched between the sample electrode 121 and the counter electrode 122, the configuration is merely an example. Therefore, the configuration of the sample 12 can be arbitrarily changed according to, for example, the configuration of the electrolyte 123 and the like.

The sample electrode 121 is an electrode whose charge transfer characteristic is analyzed using an analyzer. Details of the forming material of the sample electrode 121 will be described later.

The counter electrode 122 is an electrode for advancing a charge transfer reaction with the sample electrode 121, and moves charges (ions) between the sample electrode 121 and the counter electrode 122 when the charge transfer reaction progresses. The counter electrode 122 includes, for example, any one or two or more materials capable of transferring and releasing charges, and details of the material may be, for example, the formation of a sample electrode 121 described later. The details are the same as for the material.

The electrolyte 123 is a medium for moving charges (ions) between the sample electrode 121 and the counter electrode 122. The configuration of the electrolyte 123 is not particularly limited as long as the charge can be moved between the sample electrode 121 and the counter electrode 122. Specifically, the electrolyte 123 may be, for example, a liquid electrolyte (electrolyte solution) or a gel electrolyte (gel electrolyte).

The electrolytic solution contains, for example, a solvent, an electrolyte salt, and the like, and in the electrolytic solution, for example, the electrolytic salt is dissolved or dispersed in the solvent. The electrolytic solution may be impregnated in, for example, a separator interposed between the sample electrode 121 and the counter electrode 123.

The gel electrolyte contains, for example, a polymer compound and the like together with the above-described electrolytic solution (solvent and electrolyte salt), and in the gel electrolyte, the electrolytic solution is held, for example, by the polymer compound.

The sample 12 may further include, for example, one or more of other components such as a reference electrode (not shown).

<1-3. Sample electrode forming material>
Next, the forming material of the sample electrode 121 will be described.

The type of the forming material of the sample electrode 121 is not particularly limited as long as it is any one type or two or more types of materials capable of releasing and transferring electric charge on the surface of the sample electrode 121. Specifically, the forming material of the sample electrode 121 is, for example, a carbon material and a metal-based material.

The carbon material is, for example, graphitizable carbon, non-graphitizable carbon, and graphite. More specifically, the carbon material is, for example, pyrolytic carbons, cokes, glassy carbon fibers, organic polymer compound fired bodies, activated carbon, carbon blacks and the like.

The metal-based material is a material containing one or more of metal elements and metalloid elements as constituent elements. The metal-based material may be a single material, an alloy, a compound, a mixture of two or more thereof, or a material including two or more phases thereof. The metal-based material may be, for example, an insertion material (or an intercalation material), a solid solution, a eutectic (eutectic mixture), or an intermetallic compound, or two of them. It may be a coexistence of the above. However, the alloy may be, for example, a material composed of two or more types of metal elements, or a material including one or more types of metal elements and one or more types of metalloid elements. The alloy may contain, for example, one or more types of nonmetallic elements. The insertion material, the solid solution, the intermetallic compound, and the like described here are, as with the above-described alloying material, representative examples of materials whose composition is likely to change in the course of the charge transfer reaction.

The type of metal element and metalloid element is not particularly limited. For example, magnesium (Mg), boron (B), aluminum (Al), gallium (Ga), indium (In), silicon (Si), germanium (Ge) ), Tin (Sn), lead (Pb), bismuth (Bi), cadmium (Cd), silver (Ag), zinc (Zn), hafnium (Hf), zirconium (Zr), yttrium (Y), palladium (Pd) And platinum (Pt).

<2. Operation theory>
Next, the operation theory of the above-described equations (1) to (3) will be described.

[Butler-Volmer type]
The behavior during the electrode reaction (charge transfer reaction) in the charge transfer limited state is represented by the Butler-Volmer equation, as described above. The Butler-Volmer equation is as shown in the following equation (4).

(J is current density (A / m ² ), j ₀ is exchange current density (A / m ² ), α is a charge transfer coefficient, η is an overvoltage (V), n is the number of reaction electrons, F is a Faraday constant (C / Mol), R is the gas constant (J / [K · mol]), T is the absolute temperature (K).

In this Butler-Volmer equation, the total current density is represented by the sum of the current density of the anode and the current density of the cathode. Here, since the current density of the anode is expressed by an exp function, it has large non-linearity. Similarly, the current density of the cathode is represented by the exp function, and thus has large non-linearity. For this reason, the sum of the current density of the anode and the current density of the cathode also has large non-linearity. The balance between the current density of the anode and the current density of the cathode is represented by the charge transfer coefficient α. In the case of α = 0.5, the curve representing the correlation between the current density j and the overvoltage η is a point-symmetrical curve (= odd function) about the origin.

In order to discuss the non-linearity of the Butler-Volmer equation, first, Taylor series expansion of the Butler-Volmer equation is performed. Since the Taylor series expansion of the exponential function is expressed as the following expression (5), the Taylor series expansion of the difference of the exponential function is expressed as the following expression (6).

By comparing the equation (6) with the equation (4), the Butler-Volmer equation is expressed as the following equation (7).

By the way, the Butler-Volmer equation is an equation solved with respect to the current density, that is, an equation expressing what kind of current flows when an overvoltage is applied to the electrode. In other words, the Butler-Volmer equation is an equation that is caused by an overvoltage and results in a current.

Here, by solving the Butler-Volmer equation with respect to the overvoltage 考える, it is considered to make an equation representing what overvoltage will occur when a current is supplied to the electrode.

[Inverse function of Butler-Volmer equation]
The Butler-Volmer equation can be simplified and expressed as the following equation (8).

As mentioned above, in order to solve the Butler-Volmer equation for over voltage 過電圧, first consider solving the simplified equation (8) for x. This Butler-Volmer expression contains two exp functions. Therefore, if α = 0.5, since the Butler-Volmer equation is represented by one sinh function, the inverse function of the Butler-Volmer equation is represented by one sinh ⁻¹ function.

On the other hand, when α ≠ 0.5, the Butler-Volmer equation is not represented by one sinh function, so the inverse function of the Butler-Volmer equation is also not represented by one sinh ⁻¹ function. However, using the formulas reported by Morse and Feshback, it can be expressed in the form of an infinite series as shown in the following equation (9).

The above-mentioned formulas reported by Morse and Feshback are formulas for directly obtaining the coefficients of Taylor series expansions related to inverse functions of the functions from coefficients of Taylor series expansion related to a function (PM Morse and H. Feshbach, Methods of Theoretical Physics, Part 1, New York: McGraw-Hill, pp. 411-413, 1953).

By applying the relationship of the equation (9) to the above-described non-simplified equation (1), the overvoltage 簡略 is expressed as the following equation (10). However, the first four terms (η ⁽¹⁾ , η ⁽²⁾ , η ⁽³⁾ and η ⁽⁴⁾ ) of η ⁽ⁱ⁾ (i is an integer of 1 or more) are It is expressed by the equations (11) to (14).

[Relationship between coefficients of Taylor series expansion and higher-order distortion in AC measurement]

Next, the relationship between the coefficients of the Taylor series expansion and the coefficients of the Fourier series expansion will be discussed. Here, it is assumed that the coefficient of the term of n-th power in the case of Taylor series expansion of a non-linear equation such as Equation (11) to Equation (14) into a polynomial is Tn (n is an integer of 1 or more). Further, it is assumed that the amplitude of the nth harmonic component of the nonlinear response when AC stimulation is given, that is, the coefficient of the Fourier series expansion is Fn (n is an integer of 1 or more). The relationship between Tn and Fn is represented by the following equation (15).

In this case, it should be noted that Tn ≠ Fn. This is because the amplitude of the harmonic component is different from the coefficient of Taylor series expansion. Although the process of specific derivation is omitted here, if the relationship shown in equation (15) holds identically for all θ, as shown in equation (16) below, Fn is expressed using Tn.

(Since _n C _k is a binomial coefficient, _n C _k = n! / {K! (N-k)!}.)

As an example, when each of F1 to F4 is subjected to Taylor series expansion, it is expressed as the following equation (17).

Here, when the relationship between n and Tn is graphed, Tn gradually decreases as n increases. That is, in F1 to F4, the foot base of Tn is wider at F2 than F1, the foot base of Tn is wider at F3 than F2, and the foot base of Tn is wider at F4 than F3. This is because higher order harmonic components are more susceptible to higher order terms.

From this result, the voltage and current supplied to the sample electrode 121 are not necessarily as large as possible, but rather, it is desirable that the voltage and current be as small as possible to the extent that the signal is not affected by noise.

Since the electrode reaction (charge transfer reaction) is inherently large in nonlinearity, a sufficiently large nonlinear component response can be obtained even with a small input (voltage and current). Care must be taken because if the input is larger than necessary, the signal is susceptible to higher order terms. In the case where the input is inevitably increased, it is desirable to devise a method such as finding the impedance when the input value becomes zero using extrapolation by examining the change in the signal while changing the input value.

[Calculating j ₀ and α in Butler-Volmer equation based on higher-order distortion in AC measurement]
By summarizing the above series of discussions, it is possible to express the response of the n-th non-linear component (overvoltage amplitude which is the over-voltage response) when an alternating current I is applied to the electrode. The basis in this case is the coefficients of the Taylor series expansion shown in equations (11) to (14). In order to make the coefficient of Taylor series expansion be a coefficient of Fourier series expansion, the rms (root mean square value) at the time of alternating current measurement is 1 / (2 ^1/2 ) of the peak value. Taking into consideration, the equations (11) to (14) are expressed as the following equations (18) to (21).

In the equations (18) to (21), all parameters (gas constant R, absolute temperature T, number of reaction electrons n, Faraday constant F and current density amplitude (effective value) except the exchange current density j ₀ and charge transfer coefficient α The value of) jrms) is known. Therefore, the exchange current density j ₀ and the charge transfer coefficient α can be calculated by solving the simultaneous equations using any two of the equations (18) to (21). The calculation method of the exchange current density j ₀ and the charge transfer coefficient α based on these calculation theory is a novel calculation method.

Note that, instead of the current density amplitude (effective value) jrms, an alternating current (effective value) I = irms = Ajrms (A is an area of the electrode) is used for simplification, and the exchange current density j ₀ Use exchange current density i ₀ instead of This is because the electrochemical measuring device can not know the area of the electrode. In this case, the amplitude of the nth harmonic component related to the overvoltage η ( _成分 ⁽ⁿ⁾ rms _jrms → ₀ ) when the current density amplitude (rms value) jrms is extrapolated to zero is V _n (n is 1 It is an integer greater than or equal to.). However, the amplitude of the opposite phase is negative.

The response of the linear component (voltage response, which is the voltage response) related to the overvoltage η includes the passive component (the electrical resistance R, the capacitance C and the inductance L) that the electrode inherently has. Therefore, in this case, attention is focused on the response of the second-order nonlinear component not including the passive element component described above and the response of the third-order nonlinear component. Then, when equations (19) and (20) are solved with respect to exchange current density i ₀ , positive real solutions are expressed as equations (2) and (3) described above.

Therefore, when the exchange current density i ₀ and the alternating current I are eliminated by solving the simultaneous equations using the equations (2) and (3), the above equation (1) is derived.

Using this equation (1), by measuring the over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component, it is possible to calculate the charge transfer coefficient alpha.

The procedure for specifically calculating the charge transfer coefficient α is as follows. First, based on the over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component, to calculate the β defined by the following formula (22). This β is the left side of equation (1). Here, the constant (= 0.7346) is a value derived from (2 ^3/4 × 18 ^1/3 ) / 6.

However, the value represented by the equation (1), that is, the value of β is a real number or an imaginary number depending on whether the overvoltage amplitude V ₂ of the second-order nonlinear component is positive or negative. However, here, for simplicity, we restrict β to real numbers. Instead, the overvoltage amplitude V ₂ of the second-order nonlinear component or is greater than zero, over-voltage amplitude V ₂ of the second-order nonlinear component depending on whether less than zero, case analysis.

When the measured value of the overvoltage amplitude V ₂ of the second-order nonlinear component is greater than or equal to zero (V ₂ 00), the charge transfer coefficient α satisfies the following equation (23) and the second-order nonlinear component When the measured value of the overvoltage amplitude V ₂ is less than zero (V ₂ <0), the charge transfer coefficient α satisfies the following equation (24). However, solving equation (23) or equation (24) for the charge transfer coefficient α is difficult. Therefore, β may be converted to the charge transfer coefficient α by numerically analyzing the equation (23) or the equation (24). Alternatively, the value of β may be converted to the value of the charge transfer coefficient α by using the conversion table shown in Table 1 below.

In Table 1, when the measured value of the overvoltage amplitude V ₂ of the second-order nonlinear component is greater than zero and (V ₂ ≧ 0), the measured value of the overvoltage amplitude V ₂ of the second-order nonlinear component is less than zero The case is divided into cases (V ₂ <0), and the correspondence between the value of β and the value of the charge transfer coefficient α is shown. Therefore, if β is calculated, the value of β can be converted into the value of the charge transfer coefficient α quickly and accurately using the conversion table shown in Table 1.

Incidentally, by calculating the charge transfer coefficient alpha, by actually measuring the over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ or third-order nonlinear component of the second-order nonlinear component, the above-mentioned formula (2) or equation (3) The exchange current density i ₀ can be calculated using this.

<3. How to set the frequency of alternating current>
Next, a method of setting the frequency f of the alternating current I will be described. The frequency f of the alternating current I is set by, for example, the function generator 13 as described above.

FIG. 3 shows an image in which the resistance characteristics (Bode plot) of the sample electrode 121 measured using the electrochemical impedance method (linear AC impedance method) are separated into respective resistance components. FIG. 3 shows the correlation between the absolute value of impedance | Z | (Ω cm ² ) and the frequency f (Hz).

When the absolute value | Z | of the impedance of the sample electrode 121 is measured while changing the frequency f of the alternating current I, as shown in FIG. 3, the absolute value | Z | of the impedance increases as the frequency f increases. It will decrease gradually. More specifically, when the frequency f increases, the absolute value | Z | of impedance gradually decreases (region with large inclination L1), then becomes substantially constant (region with small inclination L2), (Region L3 with a large inclination), it becomes substantially constant again (region L4 with a small inclination). Note that “substantially constant” described with respect to the area L2 means that the slope of the impedance | Z | in the area L2 is sufficiently smaller than the slope of the absolute value | Z | of the areas L1 and L3. means.

In this case, the absolute value | Z | of the impedance mainly includes four types of resistance components R1 to R4 described below.

The resistance component R1 is, for example, a component resulting from a diffusion resistance in which charges (ions) present on the surface of the sample electrode 121 diffuse in a direction toward the electrolyte 123. The resistance component R1 disappears in the regions L2 to L4, for example, as the frequency f increases, the resistance component R1 gradually decreases in the region L1.

The resistance component R2 is, for example, a component resulting from diffusion resistance in which charges (ions) present on the surface of the sample electrode 121 are diffused in a direction toward the inside of the sample electrode 121. The resistance component R2 disappears in the regions L2 to L4 by decreasing gradually in the region L1 as the frequency f increases, for example, similarly to the above-described resistance component R1.

The resistance component R3 is, for example, a charge transfer resistance component resulting from a charge transfer reaction generated between the sample electrode 121 and a charge (ion) present on the surface of the sample electrode 121. The resistance component R3 disappears in the region L4 by, for example, becoming substantially constant in the regions L1 and L2 when the frequency f increases, and then rapidly decreasing in the region L3.

The resistance component R4 is, for example, a component resulting from a solution resistance, an electrode coating (SEI: Solid Electrolyte Interphase) resistance, and an electronic resistance. The solution resistance is the resistance of the electrolyte itself when the electrolyte 123 contains the electrolyte. The SEI resistance is the resistance of the film formed on the surface of the sample electrode 121 or the like due to the decomposition reaction of the electrolyte 123 or the like during the charge transfer reaction. The electron resistance is a resistance when electrons move in the electrolyte 123. The resistance component R4 is, for example, substantially constant in the regions L1 to L4 without depending on the frequency f.

Considering these resistance components R1 to R4, the absolute value | Z | of the impedance changes as described below as the frequency f increases. First, in the region L1, the impedance Z gradually decreases while including the resistance components R1 to R4. Subsequently, in the region L2, as the resistance components R1 and R2 have already disappeared, the absolute value | Z | of the impedance becomes substantially constant while including the resistance components R3 and R4. Subsequently, in the region L3, the absolute value | Z | of the impedance continues to rapidly decrease while including the resistance components R3 and R4. In this case, the resistance component R4 sharply decreases while the resistance component R4 is substantially constant. Finally, in the region L4, as the resistance component R3 has already disappeared, the impedance Z becomes substantially constant while including only the resistance component R4.

Here, focusing on the frequency f (f1) at which each of the resistance components R1 and R2 disappears and the frequency f (f2) at which the resistance component R3 starts to decrease in response to the increase of the frequency f, The frequency range Rf is a range between the frequencies f1 and f2. If the frequency f set by the function generation unit 13 is within the range of the specific frequency range Rf, the resistance components R1 and R2 caused by the diffusion of electric charges hardly affect the analysis accuracy, and the analysis accuracy is improved. It is from.

The value of the frequency f set by the function generation unit 13 is not particularly limited as long as it is a value within the specific frequency range Rf as described above. Above all, when the overvoltage amplitude V _n of the _nth nonlinear component is measured between the frequencies f 1 and f 2, the imaginary part of the overvoltage amplitude V _n of the _nth nonlinear component is close to zero. It is preferable that it is a value. Since the overvoltage amplitude V _n of the _nth nonlinear component of the charge transfer resistance is theoretically zero, the fact that the imaginary part described above is close to zero means that the resistance component at that frequency f is almost only the charge transfer resistance It is because it is thought.

<4. Operation (analysis method)>
Next, the operation of the analysis device will be described.

In addition, the analysis method of one embodiment of the present technology is described by the operation of the analysis device described below. Therefore, an analysis method according to an embodiment of the present technology will be described together below. In the following, reference will be made to FIG. 4 together with FIGS. 1 to 3 described above.

FIG. 4 illustrates the flow of an analysis method using an analysis apparatus. The analyzer analyzes the charge transfer characteristics (exchange current density i ₀ and charge transfer coefficient α) of the sample electrode 121 according to the procedure shown in FIG. 4, for example.

First, the function generation unit 13 sets the frequency f of the alternating current I supplied to the sample 12 (sample electrode 121) in the later process (FIG. 4: step S1).

In this case, for example, as described above, the function generation unit 13 checks the change behavior (FIG. 3) of the absolute value | Z | of the impedance of the sample electrode 121 using the electrochemical impedance method to obtain the specific frequency. After specifying the range Rf, the value of the frequency f is set to be a value within the range of the specific frequency range Rf.

Subsequently, the current supply unit 14 supplies an alternating current I of frequency f to the sample 12 via the sample electrode (working electrode) 121 and the counter electrode 122 based on the frequency f set by the function generation unit 13 (see FIG. 4: Step S2).

Thereby, the charge transfer reaction of ion species present on the surface of the sample electrode 121 proceeds. More specifically, in response to the supply of alternating current I, the oxidation reaction and reduction reaction of ion species present on the surface of sample electrode 121 are repeated.

Subsequently, the overvoltage measuring unit 15 measures the overvoltage E generated in the sample electrode 121 in response to the supply of the alternating current I (FIG. 4: step S3).

Subsequently, the overvoltage amplitude measuring unit 16 determines the overvoltage amplitude V of the second-order nonlinear component as the overvoltage amplitude of two or more frequency components (the overvoltage amplitude V _{n of the n-th} nonlinear component of two or more) based on the overvoltage E. overvoltage amplitude V ₃ of ₂ and third-order nonlinear component measuring (Figure 4: step S4, S5). The waveform of the overvoltage E measured by the overvoltage amplitude measurement unit 16 is displayed on the waveform display unit 18. In the following, the “non-linear alternating current impedance method” is a method of measuring the overvoltage amplitude V _{n of} 2 or more n-th nonlinear components (the overvoltage amplitude V _{2 of the second} nonlinear component and the overvoltage amplitude V _{3 of the third} nonlinear component) It is called.

Subsequently, the operating unit 17, based on the measured value of the overvoltage amplitude V ₃ of the actual measurement value and the third-order nonlinear component of the overvoltage amplitude V ₂ of the second-order nonlinear component, charge transfer coefficient using equation (1) alpha Are calculated (FIG. 4: step S6). In this case, the calculation unit 17 reads a series of constants (gas constant R, absolute temperature T, number of reaction electrons n, and Faraday constant F) stored in the storage unit 20. In addition, the calculation unit 17 converts the value of β into the value of the charge transfer coefficient α by reading the conversion table (Table 1) stored in the storage unit 20 as necessary. The calculation result of the charge transfer coefficient α is displayed on the analysis display unit 19.

Finally, the calculation unit 17, based on the AC current I, to the measured value of the overvoltage amplitude V ₂ of the second-order nonlinear component, the measured value of the overvoltage amplitude V ₃ of the third-order non-linear component, equation (2) or it calculates the exchange current density i ₀ using equation (3) (Fig. 4: step S7). In this case, the calculation unit 17 reads a series of constants (gas constant R, absolute temperature T, number of reaction electrons n, and Faraday constant F) stored in the storage unit 20. The calculation result of the exchange current density i ₀ is displayed on the analysis display unit 19.

Thereby, the charge transfer characteristics (exchange current density i ₀ and charge transfer coefficient α) of the sample electrode 121 are analyzed.

<5. Action and effect>
Finally, the operation and effects of the analysis device will be described.

According to the analysis apparatus of the present embodiment, the alternating current I is supplied to the sample electrode 121, and the exchange current density of the sample electrode 121 is changed based on the overvoltage response generated in the sample electrode 121 in response to the supply of the alternating current I. i ₀ and charge transfer coefficient α are calculated. Therefore, the charge transfer characteristics of various electrode materials can be analyzed for the reasons described below.

As another analysis device (analyzer of a comparative example) which analyzes the charge transfer characteristic of sample electrode 121, for example, as mentioned above, while examining direct current to sample electrode 121 and examining the relation between current and overvoltage Thus, an apparatus that analyzes the charge transfer characteristic of the sample electrode 121 using the Tafel equation can be mentioned.

However, in the analysis device of the comparative example for supplying a direct current to the sample electrode 121, as described above, the composition of the sample electrode 121 changes in the progress of the charge transfer reaction, so the charge transfer of the sample electrode 121 in the original composition Characteristics can not be analyzed. Therefore, the sample electrode 121 capable of analyzing the charge transfer characteristic is limited to only the sample electrode 121 whose composition does not change in the process of the charge transfer reaction, and thus the charge transfer characteristic of various sample electrodes 121 can not be analyzed.

On the other hand, in the analysis apparatus of the present embodiment for supplying the alternating current I to the sample electrode 121, as described above, the composition of the sample electrode 121 does not change in the process of charge transfer reaction. The charge transfer characteristics of the electrode 121 can be analyzed. Therefore, the sample electrode 121 capable of analyzing the charge transfer characteristic is not limited to only the sample electrode 121 whose composition does not change in the process of the charge transfer reaction, so that the charge transfer characteristic of various sample electrodes 121 can be analyzed.

In particular, in the analysis apparatus of the present embodiment, the overvoltage amplitude of two or more frequency components (the overvoltage amplitude V _n of the n-order non-linear component of 2 or more) is measured based on the overvoltage response (overvoltage E). If the exchange current density i ₀ and the charge transfer coefficient α are calculated based on the overvoltage amplitude V _n of the n-th nonlinear component described above, the influence of the overvoltage amplitude V _n of the two or more n-th nonlinear components is taken into consideration. Thus, the exchange current density i ₀ and the charge transfer coefficient α are calculated. Therefore, since analysis accuracy is further improved, higher effects can be obtained.

In this case, by measuring the over-voltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component, the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component If the exchange current density i ₀ and the charge transfer coefficient α are calculated based on the overvoltage amplitude V ₃ , the analysis accuracy is further improved, and a higher effect can be obtained.

Further, after calculating charge transfer coefficient α using equation (1), if exchange current density i ₀ is calculated using equation (2) or equation (3) based on the calculated value of charge transfer coefficient α Since the analysis accuracy is sufficiently improved, a sufficiently high effect can be obtained.

Also, by examining the change behavior (FIG. 3) of the absolute value | Z | of the impedance of the sample electrode 121 using the electrochemical impedance method (linear alternating current impedance method), it becomes a value within the specific frequency range Rf If the frequency f of the alternating current I is set as described above, as described above, the resistance components R1 and R2 resulting from the diffusion of the charge hardly affect the analysis accuracy. Therefore, since the analysis accuracy is improved, a higher effect can be obtained.

In addition, a series of operations and effects relating to the analysis apparatus of the present embodiment described above can be obtained similarly in the analysis method of the present embodiment.

<6. Modified example>
The configuration of the analysis apparatus described above and the procedure of the analysis method can be changed as appropriate.

Specifically, if it is possible to perform the above-described analysis, that is, if it is possible to calculate the exchange current density i ₀ and the charge transfer coefficient α in which the influence of the overvoltage amplitude V _n of the _nth nonlinear component is taken into account, an analyzer The configuration of can be arbitrarily changed. Similar effects can be obtained also in the case described below.

For example, although the analysis apparatus is provided with the function generation unit 13, the current supply unit 14, the overvoltage measurement unit 15, and the overvoltage amplitude measurement unit 16, one of them may serve as two or more roles. . Specifically, for example, if a galvanostat is used, the galvanostat can also serve as each of the current supply unit 14 and the overvoltage measurement unit 15. Also, for example, if a lock-in amplifier is used, the lock-in amplifier can serve as each of the functions of the function generation unit 13 and the overvoltage amplitude measurement unit 16.

Further, for example, although the analysis device includes the operation unit 17 and the like together with the control unit 11, the control unit 11 may also play a role of one or more of the operation unit 17 and the like. Good. In this case, for example, since the control unit 11 includes a central processing unit or the like, the control unit 11 can also play a role of one or more of the calculation unit 17 and the like.

Besides, for example, since the specific frequency range Rf is known, the frequency f of the alternating current I is made to be an appropriate value in advance without setting the frequency f of the alternating current I by the function generating unit 13. When the setting can be performed, the setting operation of the frequency of the alternating current I by the function generation unit 13 may be omitted. In this case, for example, an appropriate value (a value within the specific frequency range Rf) of the frequency f of the alternating current I may be stored in the storage unit 20 in advance, and the user of the analysis device An appropriate value of the frequency f of the alternating current I may be input.

An embodiment of the present technology will be described. The order to be described is as follows.

1. Analysis method of this technology Analysis method of comparative example 3. Comparison between the analysis method of the present technology and the analysis method of the comparative example

<1. Analysis method of this technology>
The charge transfer characteristics (exchange current density i ₀ and charge transfer coefficient α) of the sample electrode were analyzed using the analysis method of the present technology.

When analyzing the charge transfer characteristics of a sample electrode, first, a sample including the sample electrode was prepared. Here, as a sample, a sample electrode (platinum disk electrode, diameter = 5 mm), a reference electrode (silver / silver chloride electrode, an internal solution is a sodium chloride aqueous solution having a concentration = 3 mol / dm ³ ) and a counter electrode (platinum wire, An electrochemical measurement system including a diameter of 0.5 mm × length of 3 cm and an electrolytic solution (an aqueous solution containing iron (II) sulfate, iron (III) sulfate, magnesium sulfate and sulfuric acid) was used. The concentration of each component in the electrolytic solution is: concentration of iron (II) sulfate = 0.05 mol / dm ³ , concentration of iron (III) sulfate = 0.05 mol / dm ³ , concentration of magnesium sulfate = 1 mol / dm ³ , The concentration of sulfuric acid was 1 mol / dm ³ . In the preparation of the electrolyte, water-saturated nitrogen gas was sufficiently blown into the electrolyte during preparation so that the iron (II) sulfate was not oxidized due to oxygen in the air.

Subsequently, when the resistance characteristics of the sample electrode were examined using an electrochemical impedance method (linear alternating current impedance method), the results shown in FIGS. 5 and 6 were obtained. FIG. 5 shows a Cole-Cole plot (horizontal axis: real part ReZ (Ωcm ² ) of impedance, vertical axis: imaginary part ImZ (Ωcm ² ) of impedance), and FIG. 6 shows Bode plot (horizontal axis) : Frequency f (Hz), vertical axis: absolute value of impedance | Z | (Ω cm ² )). In this case, the start value of the frequency f = 100 kHz, the end value of the frequency f = 100 mHz, and the current amplitude = 0.5 mA.

In the Cole-Cole plot (FIG. 5), a semicircular arc-shaped curve P1 was obtained in the high frequency region, and a straight line P2 having a slope of 45 ° was obtained in the low frequency region. That is, the Cole-Cole plot depicts the shape of a typical Randles-type equivalent circuit. The high frequency region in which the semicircular arc P1 is obtained is considered to be a region belonging to the charge transfer resistance, and the low frequency region in which the straight line P2 is obtained is considered to be a region belonging to the diffusion resistance.

On the other hand, in the Bode plot (FIG. 6), as described with reference to FIG. 3, the absolute value | Z | of the impedance changes while including the regions L1 to L4 according to the change of the frequency f. In this case, a frequency range in which the frequency f is smaller than approximately 1 Hz corresponds to the range L1, and a frequency range in which the frequency f is approximately 1 Hz to 100 Hz corresponds to the range L2, and the frequency f is greater than approximately 100 Hz. The large frequency range corresponds to the range L3, L4. Based on this Bode plot, it was confirmed that the specific frequency range Rf is about 1 Hz to 100 Hz, and the boundary between the high frequency region and the low frequency region is about 1 Hz to 100 Hz in the Cole-Cole plot.

That is, the resistance components generated in the frequency region (regions L3 and L4) in which the frequency f is larger than about 100 Hz are mainly electronic resistance and charge transfer resistance. The resistance components that occur in the frequency region (region L1) where the frequency f is smaller than about 1 Hz are mainly electronic resistance, charge transfer characteristics and diffusion resistance. The resistive components occurring in the frequency range (range L2) where the frequency f is about 1 Hz to 100 Hz are mainly electronic resistance and charge transfer resistance.

Finally, using samples having the configuration described above, was measured overvoltage amplitude V ₃ of the overvoltage amplitude V ₂ and third-order nonlinear component of the second-order nonlinear component using a non-linear alternating current impedance method described above. In this case, the start value of the frequency f = 100 Hz, the end value of the frequency f = 1 Hz, and the current amplitude = 1 mA. As a result, when the exchange current density i ₀ and the charge transfer coefficient α were calculated using the above-mentioned equations (1) to (3), the results shown in Table 2 were obtained.

As shown in Table 2, after the charge transfer coefficient α is calculated by the analysis method of the present technology using the above-described calculation theory (equations (1) to (3)), the charge transfer coefficient α is calculated. The exchange current density i ₀ was calculated using the value. The charge transfer coefficient α and the exchange current density i ₀ fluctuated according to the frequency f of the alternating current I supplied to the charge transfer device.

<2. Analysis method of comparative example>
For comparison, charge transfer characteristics of the sample electrode (exchange current density i ₀ and charge transfer coefficient α) are obtained by the same procedure except that the sample having the same configuration is used and the above-mentioned Allen-Hickling method is used. Was analyzed.

In this case, the start potential is 410 mV, the end potential is 550 mV, and the measurement interval of potential is 10 mV. The current after holding for 200 seconds at each potential is measured, and the current is log i The exchange current density i ₀ and the charge transfer coefficient α were calculated based on the intercept and the slope by plotting the relationship between / (1−e ^f η)] and および. As a result, the equilibrium potential was 485 mV, the charge transfer coefficient α was 0.54, and the exchange current density i ₀ was 0.24 mA / cm ² .

<3. Comparison of the analysis method of the present technology and the analysis method of the comparative example>
When the analysis result by the analysis method of the present technology and the analysis result by the analysis method of the comparative example are compared with each other, the following tendency is obtained.

First, while the charge transfer coefficient α calculated by the analysis method of the comparative example is 0.54 as described above, the charge transfer coefficient α calculated by the analysis method of the present technology is an alternating current The frequency f of I was about 0.50 in the vicinity of about 10 Hz within the range of the specific frequency range Rf. Therefore, the value of the charge transfer coefficient α calculated by the analysis method of the present technology has a value substantially close to the value of the charge transfer coefficient α calculated by the analysis method of the comparative example.

Further, while the exchange current density i ₀ calculated by the analysis method of the comparative example was 0.24 mA / cm ² as described above, the exchange current density i calculated by the analysis method of the present technology is ₀ (frequency f = 10 Hz) was about 0.79 mA / cm ² . Therefore, the value of the exchange current density i ₀ calculated by the analysis method of the present technology is a value substantially close to the value of the exchange current density i ₀ calculated by the analysis method of the comparative example, that is, the value of the same digit .

From these results, the alternating current is supplied to the sample electrode, and the charge transfer characteristic (exchange current density i ₀ and the charge transfer coefficient for the sample electrode) based on the overvoltage response generated in the sample electrode in response to the supply of the alternating current. By analyzing α), charge transfer characteristics of various sample electrodes were analyzed.

In addition, the effect described in this specification is an illustration to the last, is not limited, and may have other effects.

The present technology can also be configured as follows.
(1)
A current supply unit for supplying an alternating current to the sample electrode;
An operation unit configured to calculate an exchange current density and a charge transfer coefficient of the sample electrode based on an overvoltage response generated at the sample electrode in response to the supply of the alternating current by the current supply unit.
(2)
further,
An overvoltage measuring unit that measures an overvoltage generated at the sample electrode according to the supply of the alternating current by the current supply unit;
An overvoltage amplitude measurement unit that measures overvoltage amplitudes of two or more frequency components of the overvoltage measured by the overvoltage measurement unit;
The calculation unit calculates the exchange current density and the charge transfer coefficient based on the overvoltage amplitudes of the two or more frequency components measured by the overvoltage amplitude measurement unit.
The analyzer described in (1) above.
(3)
The overvoltage amplitude measurement unit measures an overvoltage amplitude of a second nonlinear component and an overvoltage amplitude of a third nonlinear component as the overvoltage amplitude of the two or more frequency components.
The analyzer described in (2) above.
(4)
The computing unit computes the charge transfer coefficient using the following equation (1), and then uses the following equation (2) or (3) based on the computed value of the charge transfer coefficient: Calculate the density,
The analyzer described in (3) above.

(I ₀ is the exchange current density (A / m ² ), α is the charge transfer coefficient, I is the alternating current (A), V ₃ is the overvoltage amplitude (V) of the third nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)
(5)
Furthermore, as a result of measuring the impedance of the sample electrode using the electrochemical impedance method, when the impedance decreases until it becomes substantially constant, when it decreases again, the impedance becomes a value within a range where it becomes substantially constant. And setting a frequency of the alternating current as well as a function generating unit which transmits an alternating current signal corresponding to the frequency of the alternating current to the current supply unit.
The analyzer according to any one of (1) to (4) described above.
(6)
Supply alternating current to the sample electrode,
The exchange current density and charge transfer coefficient for the sample electrode are calculated based on the overvoltage response generated at the sample electrode in response to the supply of the alternating current.
analysis method.
(7)
Furthermore, an overvoltage generated at the sample electrode in response to the supply of the alternating current is measured;
By measuring the overvoltage amplitude of two or more frequency components of the overvoltage,
The exchange current density and the charge transfer coefficient are calculated based on overvoltage amplitudes of the two or more frequency components,
The analysis method described in (6) above.
(8)
The overvoltage amplitude of the second-order nonlinear component and the overvoltage amplitude of the third-order nonlinear component are measured as the overvoltage amplitudes of the two or more frequency components.
The analysis method described in (7) above.
(9)
After the charge transfer coefficient is calculated using the following equation (1), the exchange current density is calculated using the following equation (2) or (3) based on the calculated value of the charge transfer coefficient:
The analysis method described in (8) above.

(I ₀ is the exchange current density (A / m ² ), α is the charge transfer coefficient, I is the alternating current (A), V ₃ is the overvoltage amplitude (V) of the third nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)
(10)
Furthermore, as a result of measuring the impedance of the sample electrode using the electrochemical impedance method, when the impedance decreases until it becomes substantially constant, when it decreases again, the impedance becomes a value within a range where it becomes substantially constant. To set the frequency of the alternating current,
The analysis method according to any one of (6) to (9) described above.

Claims

A current supply unit for supplying an alternating current to the sample electrode;
An operation unit configured to calculate an exchange current density and a charge transfer coefficient of the sample electrode based on an overvoltage response generated at the sample electrode in response to the supply of the alternating current by the current supply unit.
further,
An overvoltage measuring unit that measures an overvoltage generated at the sample electrode according to the supply of the alternating current by the current supply unit;
An overvoltage amplitude measurement unit that measures overvoltage amplitudes of two or more frequency components of the overvoltage measured by the overvoltage measurement unit;
The calculation unit calculates the exchange current density and the charge transfer coefficient based on the overvoltage amplitudes of the two or more frequency components measured by the overvoltage amplitude measurement unit.
The analysis device according to claim 1.
The overvoltage amplitude measurement unit measures an overvoltage amplitude of a second nonlinear component and an overvoltage amplitude of a third nonlinear component as the overvoltage amplitude of the two or more frequency components.
The analysis device according to claim 2.
The computing unit computes the charge transfer coefficient using the following equation (1), and then uses the following equation (2) or (3) based on the computed value of the charge transfer coefficient: Calculate the density,
The analyzer according to claim 3.

(Α is the charge transfer coefficient, V 2 is the overvoltage amplitude (V) of the second-order nonlinear component, V 3 is the overvoltage amplitude (V) of the third-order nonlinear component, R is the gas constant (J / [K · mol]) , T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I 0 is the exchange current density (A / m 2 ), α is the charge transfer coefficient, I is the alternating current (A), V 2 is the overvoltage amplitude (V) of the second-order nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I 0 is the exchange current density (A / m 2 ), α is the charge transfer coefficient, I is the alternating current (A), V 3 is the overvoltage amplitude (V) of the third nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)
Furthermore, as a result of measuring the impedance of the sample electrode using the electrochemical impedance method, when the impedance decreases until it becomes substantially constant, when it decreases again, the impedance becomes a value within a range where it becomes substantially constant. And setting a frequency of the alternating current as well as a function generating unit which transmits an alternating current signal corresponding to the frequency of the alternating current to the current supply unit.
The analyzer according to any one of claims 1 to 4.
Supply alternating current to the sample electrode,
The exchange current density and charge transfer coefficient for the sample electrode are calculated based on the overvoltage response generated at the sample electrode in response to the supply of the alternating current.
analysis method.
Furthermore, an overvoltage generated at the sample electrode in response to the supply of the alternating current is measured;
By measuring the overvoltage amplitude of two or more frequency components of the overvoltage,
The exchange current density and the charge transfer coefficient are calculated based on overvoltage amplitudes of the two or more frequency components,
The analysis method according to claim 6.
The overvoltage amplitude of the second-order nonlinear component and the overvoltage amplitude of the third-order nonlinear component are measured as the overvoltage amplitudes of the two or more frequency components.
The analysis method according to claim 7.
After the charge transfer coefficient is calculated using the following equation (1), the exchange current density is calculated using the following equation (2) or (3) based on the calculated value of the charge transfer coefficient:
The analysis method according to claim 8.

(Α is the charge transfer coefficient, V 2 is the overvoltage amplitude (V) of the second-order nonlinear component, V 3 is the overvoltage amplitude (V) of the third-order nonlinear component, R is the gas constant (J / [K · mol]) , T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I 0 is the exchange current density (A / m 2 ), α is the charge transfer coefficient, I is the alternating current (A), V 2 is the overvoltage amplitude (V) of the second-order nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)

(I 0 is the exchange current density (A / m 2 ), α is the charge transfer coefficient, I is the alternating current (A), V 3 is the overvoltage amplitude (V) of the third nonlinear component, R is the gas constant (J / [K · mol]), T is the absolute temperature (K), n is the number of reaction electrons, and F is the Faraday constant (C / mol).)
Furthermore, as a result of measuring the impedance of the sample electrode using the electrochemical impedance method, when the impedance decreases until it becomes substantially constant, when it decreases again, the impedance becomes a value within a range where it becomes substantially constant. To set the frequency of the alternating current,
The analysis method according to any one of claims 6 to 9.