JP5007963B2 - Calculation method of interface resistance - Google Patents

Description

  The present invention relates to a method for measuring an interface resistance at the time of operation of a fuel cell, specifically, a method for calculating an interface resistance at an interface between a fuel electrode and an electrolyte and an interface resistance at an interface between an air electrode and an electrolyte. .

The fuel cell has a cell for a fuel cell configured to sandwich an electrolyte between a fuel electrode and an air electrode. The fuel cell will be described with reference to FIG. FIG. 14 is a schematic view showing a fuel cell. In FIG. 14, the fuel cell 44 is formed so that the electrolyte 41 is sandwiched between the fuel electrode 42 and the air electrode 43.
Since the resistance value during operation of the fuel cell 44 is one of the important factors related to the performance of the fuel cell, it is important to grasp the resistance value during operation of the fuel cell 44. It is. The resistance of the fuel cell 44 during operation mainly includes an ohm resistance of the electrolyte 41 itself, an ohm resistance of the fuel electrode 42 itself, an ohm resistance of the air electrode 43 itself, and the fuel electrode 42 during operation. The sum of the interface resistance at the interface with the electrolyte 41 and the interface resistance at the interface between the air electrode 43 and the electrolyte 41 during operation. Hereinafter, the sum of the ohmic resistance of the electrolyte 41 itself, the ohmic resistance of the fuel electrode 42 itself, and the ohmic resistance of the air electrode 43 itself is also referred to as the cell ohmic resistance Rb, and the interface between the fuel electrode and the electrolyte. The interface resistance is also referred to as the fuel electrode side interface resistance Ria, and the interface resistance at the interface between the air electrode and the electrolyte is also referred to as the air electrode side interface resistance Ric.
Of the above resistances, the ohmic resistance of the fuel electrode 42 itself is measured by measuring the resistance of the fuel electrode 42 before being joined to the electrolyte 41, or the resistance of the fuel electrode 42 not joined to the electrolyte 41. It is calculated | required by producing and measuring the resistance. The same applies to the ohmic resistance of the electrolyte 41 itself and the ohmic resistance of the air electrode 43 itself.
On the other hand, since the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric are resistances at the interface between the fuel electrode 42 or the air electrode 43 and the electrolyte 41, the fuel electrode 42 or the air electrode actually The resistance cannot be measured unless 43 is bonded to the electrolyte 41.
Therefore, a conventional method for measuring the interface resistance will be described with reference to FIG. FIG. 15 is a schematic diagram showing a conventional method for measuring interface resistance, and is a schematic diagram of a cross section of a cell for a fuel cell at the time of measuring interface resistance. First, each ohm resistance before joining the fuel electrode 42a and the air electrode 43a to the electrolyte 41a, that is, the ohm resistance of the electrolyte 41a, the ohm resistance of the fuel electrode 42a, and the ohm resistance of the air electrode 43a is measured. Next, as shown in FIG. 15, the electrolyte cell 41a is sandwiched between the fuel electrode 42a and the air electrode 43a to form a fuel cell 44a, and a reference electrode 51 is formed at an intermediate potential point 55a. Provide. Usually, the position where the reference electrode 51 is installed is the side surface of the electrolyte 41a, and the middle point in the thickness direction of the electrolyte 41a. Next, the resistance between the fuel electrode terminal 53 and the reference electrode 51 and the resistance between the reference electrode 51 and the air electrode terminal 54 are measured under the same operating conditions as the fuel cell 44a. And the following formula (5):
The fuel electrode side interface resistance Ria = resistance _53-51- (Rba + 0.5Rbs) (5)
( _Wherein , resistance _53-51 indicates the resistance between the fuel electrode terminal 53 and the reference electrode 51, Rba indicates the ohmic resistance of the fuel electrode 42a, and Rbs indicates the ohmic resistance of the electrolyte 41a. Is shown.)
Thus, the fuel electrode side interface resistance Ria is calculated, and the following equation (6):
The air Kikyoku side interface resistance Ric = resistance _{51-54 - (Rbc + 0.5Rbs) (} 6)
(In the formula, resistors _51-54 indicate the resistance between the reference electrode 51 and the air electrode terminal 54, Rbc indicates the ohmic resistance of the air electrode 43a, and Rbs indicates the ohmic resistance of the electrolyte 41a. Is shown.)
Thus, the air electrode side interface resistance Ric is calculated. The intermediate potential point 55a refers to a point that bisects the ohmic resistance of the electrolyte 41a.
In the conventional method for calculating the interfacial resistance as described above, the reference electrode can be installed without any problem as long as the thickness of the electrolyte is sufficient. However, since the thickness of the electrolyte of the fuel cell currently in practical use is as extremely thin as about 5 to 100 μm, it is difficult to install the reference electrode on the electrolyte of the fuel cell currently in practical use. there were. That is, in the case of the fuel cell currently in practical use, there is a problem that the interface resistance cannot be calculated.
In the case of the fuel cell 44a shown in FIG. 15, the area and shape of the junction between the electrolyte 41a and the fuel electrode 42a are the same as the area and shape of the junction between the electrolyte 41a and the air electrode 43a. Therefore, the change in potential in the electrolyte 41a is subject to up and down. That is, when the equipotential line 52a in the electrolyte 41a is shown, in the case of the fuel cell 44a, the equipotential line 52a spreads from the fuel electrode 42a and the air electrode 43a in the shape of the vertical object. Therefore, in the fuel cell 44a, the intermediate potential point 55a appears on the side surface of the electrolyte 41a and becomes the intermediate point in the thickness direction of the electrolyte 41a.
FIG. 16 is a schematic cross-sectional view showing a fuel cell cell in which the area or shape of the joint between the electrolyte and the fuel electrode is not the same as the area or shape of the joint between the electrolyte and the air electrode. In FIG. 16, in the fuel cell 44b, the area and shape of the junction between the electrolyte 41b and the fuel electrode 42b are not the same as the area and shape of the junction between the electrolyte 41b and the air electrode 43b. In this case, the equipotential line 52b extends from the fuel electrode 42b and the air electrode 43b in a non-target shape. Therefore, in the fuel cell 44b, the intermediate potential point 55b does not appear on the side surface of the electrolyte 41b, but appears on the surface 56 to which the fuel electrode 42b is joined, and depending on the area or shape of the joined portion. Since the position where the intermediate potential point 55b appears changes, in the case of the fuel cell 44b, there is a problem in that the reference electrode cannot be installed at an accurate position and an accurate interface resistance cannot be measured. .
Therefore, the problem of the present invention is that even if the thickness of the electrolyte of the fuel cell is small, or the area or shape of the junction between the electrolyte and the fuel electrode is the area or shape of the junction between the electrolyte and the air electrode. An object of the present invention is to provide a method for calculating an interface resistance that can calculate the interface resistance even if they are not the same.

The present invention (1) is an interface resistance calculation method for calculating the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric during operation of the calculation target fuel cell.
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
In the Cole-Cole plot of the calculation target fuel cell obtained in the first step, the maximum value of the resistance value of the real part of the arc recognized as the arc derived from the fuel electrode side interface in the second step The difference between Rra (max) and the minimum value Rra (min) of the real part resistance value is expressed by the following formula (3):
Ria = Rra (max) −Rra (min) (3)
To obtain the fuel electrode side interface resistance Ria, and then derived from the air electrode side interface in the third step during the Cole-Cole plot of the calculation target fuel cell obtained in the first step The difference between the maximum value Rrc (max) of the real part resistance value and the minimum value Rrc (min) of the real part resistance value of the arc recognized as an arc to be obtained is expressed by the following formula (4):
Ric = Rrc (max) −Rrc (min) (4)
And calculating an interface resistance Ric to obtain an air electrode side interface resistance Ric.
Further, the present invention (2) is an interface resistance calculation method for calculating the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric during operation of the calculation target fuel cell.
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
An equivalent circuit having (i) a first resistor connected in series, (ii) a second resistor and a first capacitor connected in parallel, and (iii) a third resistor and a second capacitor connected in parallel; Fitting with the Cole-Cole plot of the calculation target fuel cell obtained in the first step to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric;
It is intended to provide a method for calculating an interface resistance characterized by comprising:
According to the present invention, even if the thickness of the electrolyte of the fuel cell cell is small, or the area or shape of the junction between the electrolyte and the fuel electrode is the same as the area or shape of the junction between the electrolyte and the air electrode. Even if it is not, it is possible to provide an interface resistance calculation method capable of calculating the interface resistance.

  FIG. 1 is a schematic diagram of a call / call plot of the calculation target fuel cell comprising two arcs, and FIG. 2 is a call / call plot of the calculation target fuel cell comprising three arcs. FIG. 3 is a schematic diagram of a plot, and FIG. 3 is a schematic diagram of a Cole-Cole plot of the cell for calculation target fuel cell when complex impedance is measured under the first measurement condition and the second measurement condition. FIG. 4 is a schematic diagram showing the real part resistance difference first graph 14 and the real part resistance difference second graph 141, and FIG. 5 shows the complex impedance under the third measurement condition and the fourth measurement condition. FIG. 6 is a schematic diagram of a Cole-Cole plot of the calculation target fuel cell when measured, FIG. 6 is a diagram showing an equivalent circuit 21, and FIG. 7 is a diagram showing an equivalent circuit 30. Figure 8 shows the call code for measurement 1. Fig. 9 is a diagram showing a plot, Fig. 9 is a diagram showing a Cole-Cole plot of measurement 2, Fig. 10 is a diagram showing a Cole-Cole plot of measurement 3, and Fig. 11 is a diagram FIG. 12 is a graph showing a Cole-Cole plot of measurement 4, FIG. 12 is a graph showing a real part resistance value difference first graph and a real part resistance value difference second graph, and FIG. 13 is an example. FIG. 14 is a diagram showing a Cole-Cole plot at the time of fitting obtained in the fitting step in FIG. 1, FIG. 14 is a schematic diagram showing a fuel cell, and FIG. 15 is a conventional method for measuring interface resistance. FIG. 16 is a schematic diagram showing a fuel cell cell in which the area or shape of the joint between the electrolyte and the fuel electrode is not the same as the area or shape of the joint between the electrolyte and the air electrode. FIG.

The interface resistance measuring method according to the first aspect of the present invention is a method for calculating an interface resistance for calculating a fuel electrode side interface resistance Ria and an air electrode side interface resistance Ric during operation of a calculation target fuel cell.
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
In the Cole-Cole plot of the calculation target fuel cell obtained in the first step, the maximum value of the resistance value of the real part of the arc recognized as the arc derived from the fuel electrode side interface in the second step The difference between Rra (max) and the minimum value Rra (min) of the real part resistance value is expressed by the following formula (3):
Ria = Rra (max) −Rra (min) (3)
To obtain the fuel electrode side interface resistance Ria, and then derived from the air electrode side interface in the third step during the Cole-Cole plot of the calculation target fuel cell obtained in the first step The difference between the maximum value Rrc (max) of the real part resistance value and the minimum value Rrc (min) of the real part resistance value of the arc recognized as an arc to be obtained is expressed by the following formula (4):
Ric = Rrc (max) −Rrc (min) (4)
An interface resistance calculation step of calculating the air electrode side interface resistance Ric.
The calculation target fuel cell according to the interface resistance calculation method of the first aspect of the present invention is a fuel cell for which the interface resistance is calculated.
In the first step, first, the complex impedance of the calculation target fuel cell is measured under the operating condition for calculating the interface resistance.
The operating condition for calculating the interface resistance is a specific operating condition that requires calculation of the interface resistance. That is, in the first step, first, complex impedance measurement of the calculation target fuel cell is performed under a specific operating condition for which calculation of interface resistance is desired.
There are various operating conditions for calculating the interface resistance, such as the fuel electrode side gas fuel concentration, the air electrode side gas oxygen concentration, the cell operating temperature, the fuel electrode side gas water vapor concentration, and the air electrode side gas water vapor concentration. It is composed of elements. The operating conditions for calculating the interface resistance always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.
The calculation target fuel cell is not particularly limited as long as it is a fuel cell formed by sandwiching an electrolyte between a fuel electrode and an air electrode. For example, a solid oxide fuel cell, phosphoric acid Examples include a fuel cell, a molten carbonate fuel cell, and a polymer electrolyte fuel cell.
The complex impedance measurement means that when a voltage is applied by applying a slight voltage AC component of 100 mV or less between the fuel electrode and the air electrode of the calculation target fuel cell, the frequency of the AC component is 100 kHz. It is to measure the current and its phase difference when changing from about 1 to about 1 mHz. The method for performing the complex impedance measurement is not particularly limited as long as it is a complex impedance measurement method usually used for grasping the characteristics of the fuel cell. The complex impedance measurement is also called AC impedance measurement. Further, the complex impedance measurement according to the second step and the complex impedance measurement according to the third step, which will be described later, are the same as the complex impedance measurement according to the first step.
Then, based on the current obtained by performing the complex impedance measurement and its phase difference, the real part resistance value Z ′ (Ω) and the imaginary part resistance value Z ″ (Ω) for each frequency when the frequency is changed, The horizontal axis is plotted with the real part resistance value Z ′ and the vertical axis is plotted with the imaginary part resistance value Z ″ to obtain a Cole-Cole plot of the calculation target fuel cell. The method for obtaining the Cole-Cole plot of the calculation target fuel cell is also called a complex plane display method.
The Cole-Cole plot of the calculation target fuel cell obtained in the first step will be described with reference to FIG. 1 and FIG. FIG. 1 is a schematic diagram of a call / call plot of the calculation target fuel cell comprising two arcs, and FIG. 2 is a call / call plot of the calculation target fuel cell comprising three arcs. -It is a schematic diagram of a plot. Of the call-call plots of the calculation target fuel cell obtained in the first step, the simplest one has two arcs, that is, the first arc 2a and the first arc 2a as shown in FIG. This is a Cole-Cole plot 1a composed of two arcs 3a. In addition, as the Cole-Cole plot of the calculation target fuel cell obtained in the first step, there are three arcs, that is, a first arc 2b and a second arc as shown in FIG. Cole call plot 1b composed of 3b and third arc 4, and four or more arcs, that is, call call composed of two or more arcs other than the first arc and the second arc, and the first arc and the second arc・ Plots are listed. Many of the Cole-Cole plots of the calculation target fuel cell obtained in the first step are composed of two or three arcs.
In the present invention, the first arc is defined by counting from the side with the smaller real part resistance value among the arcs of the call / call plot of the fuel cell for calculation obtained in the first step. The second arc is the number of arcs of the Cole-Cole plot of the calculation target fuel cell obtained in the first step, counted from the side with the smaller real part resistance value. Refers to the second arc. One of the first arc and the second arc is an arc derived from the fuel electrode side interface, and the other is an arc derived from the air electrode side interface.
In addition, the Cole-Cole plot curve of the calculation target fuel cell obtained by actually performing the complex impedance measurement hardly has the same shape as a perfect circular arc. Although it becomes a similar shape, the wording of the arc is used in the present invention.
In FIG. 1, in the Cole-Cole plot 1a, the smaller the real part resistance value, the higher the frequency, that is, the higher the frequency in the direction of the arrow 5, while the real part resistance value increases. The lower the frequency, the lower the frequency in the direction of arrow 6. Similarly, in the case of the Cole-Cole plot of the calculation target fuel cell comprising three or more arcs, the smaller the real part resistance value, the higher the frequency, while the real part resistance value increases. The lower the frequency.
In the second step, first, the complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas.
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition in which only the gas composition of the fuel electrode side gas is different. Among the elements constituting the measurement condition, the fuel electrode This means that the complex impedance measurement of the calculation target fuel cell is performed under two measurement conditions in which the gas composition other than the side gas is fixed and only the gas composition of the fuel electrode side gas is changed. Specifically, for example, the hydrogen concentration of the fuel electrode side gas in the first measurement condition is set to 100% by volume, the hydrogen concentration of the fuel electrode side gas in the second measurement condition is set to 10% by volume, and other measurement conditions are set. Regarding the constituent elements, the complex impedance measurement of the calculation target fuel cell is performed under the same conditions of the first measurement condition and the second measurement condition. The measurement conditions according to the first measurement condition and the second measurement condition are as follows: the fuel concentration of the fuel electrode side gas, the oxygen concentration of the air electrode side gas, the operating temperature of the cell, the water vapor concentration of the fuel electrode side gas, and the air electrode side gas. It is composed of various elements such as water vapor concentration. The measurement conditions always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.
FIG. 3 shows a schematic diagram of a Cole-Cole plot of the fuel cell for calculation under the first measurement condition or the second measurement condition. FIG. 3 shows the calculation target fuel cell in which the number of arcs of the call / call plot of the calculation target fuel cell obtained by performing the first step is 2, the first measurement condition and the It is a Cole-Cole plot of the calculation target fuel cell when complex impedance is measured under the second measurement condition, and a Cole-Cole plot 11 of the calculation target fuel cell under the first measurement condition is The call arc / call plot 12 of the calculation target fuel cell cell under the second measurement condition includes a first arc 2d and a second arc 3d.
Next, a difference ΔR (1-2) rn between the real part resistance value R1rn when the frequency in the first measurement condition is n and the real part resistance value R2rn when the frequency in the second measurement condition is n is Following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To obtain ΔR (1-2) rn for each frequency.
Specifically, for example, when a point at which the frequency in the call call plot 11 is 1000 Hz is a point E1, and a point at which the frequency in the call call plot 12 is 1000 Hz is a point E2, the call call call From the plot 11, the real part resistance value R1r of the point E1 is shown. ₁₀₀₀ From the Cole-Cole plot 12, the real part resistance value R2r at the point E2 ₁₀₀₀ Ask for. Next, the real part resistance value R1r of the point E1 ₁₀₀₀ And the real part resistance value R2r of the point E2 ₁₀₀₀ Difference (R1r ₁₀₀₀ -R2r ₁₀₀₀ ) And ΔR (1-2) r when the frequency is 1000 Hz ₁₀₀₀ Ask for. Such calculation of ΔR (1-2) rn is performed over the entire area of the Cole-Cole plot 11 and the Cole-Cole plot 12, and ΔR (1-2) rn for each frequency is obtained. . The calculation of ΔR (1-2) rn is performed by observing changes in ΔR (1-2) rn with respect to changes in frequency over the entire area of the Cole-Cole plot 11 and the Cole-Cole plot 12. It is only necessary to be performed at a frequency interval that can be performed, and ΔR (1-2) rn corresponding to each frequency at a constant interval may be obtained, or the frequency interval may not be constant.
Next, ΔR (1-2) rn for each frequency is plotted with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, thereby obtaining a real part resistance difference first graph.
FIG. 4 is a schematic diagram of the first real part resistance difference graph. In FIG. 4, a graph indicated by reference numeral 14 is a real part resistance difference first graph 14, and the real part resistance difference first graph 14 always includes ΔR (1-2) compared to other frequency ranges. ) There is a frequency range where the amount of change in rn becomes large. That is, a peak 15 always exists in the real part resistance difference first graph 14. Then, the frequency of the peak top 16 of the peak 15 is read from the first real part resistance difference graph 14, and the calculation target fuel cell cell obtained in the first step is obtained from the frequency value of the peak top 16. In the Cole-Cole plot, the arc derived from the fuel electrode side interface is recognized. For example, if the frequency of the peak top of the first real part resistance difference graph is x, the frequency is x in the Cole-Cole plot of the calculation target fuel cell obtained in the first step. The arc including the point is identified as an arc derived from the fuel electrode side interface.
In the second step, since only the gas composition of the fuel electrode side gas is changed, the fact that the peak top is present at the frequency x in the first real part resistance difference graph indicates the influence of the change on the fuel electrode side. Is strongly affected by the frequency region in the vicinity of the frequency x in the Cole-Cole plot of the calculation target fuel cell, the calculation target fuel cell obtained in the first step. In the Cole-Cole plot of the cell, an arc including a point having a frequency x can be recognized as an arc derived from the fuel electrode side interface.
The fuel contained in the fuel electrode side gas is not particularly limited, and examples thereof include hydrogen and methane.
In the third step, first, the complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition that are different only in the gas composition of the air electrode side gas.
The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition in which only the gas composition of the air electrode side gas is different. Among the elements constituting the measurement condition, the air electrode It means that the complex impedance measurement of the calculation target fuel cell is performed under two measurement conditions in which the gas composition other than the side gas is fixed and only the gas composition of the air electrode side gas is changed. Specifically, for example, the oxygen concentration of the air electrode side gas in the third measurement condition is set to 100% by volume, the oxygen concentration of the air electrode side gas in the fourth measurement condition is set to 10% by volume, and other measurement conditions are set. Regarding the constituent elements, the complex impedance measurement of the calculation target fuel cell is performed with the third measurement condition and the fourth measurement condition being the same. The measurement conditions according to the third measurement condition and the fourth measurement condition are: fuel electrode side gas fuel concentration, air electrode side gas oxygen concentration, cell operating temperature, fuel electrode side gas water vapor concentration, air electrode side gas It is composed of various elements such as water vapor concentration. The measurement conditions always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.
FIG. 5 shows a schematic diagram of the Cole-Cole plot of the calculation target fuel cell under the third measurement condition or the fourth measurement condition. FIG. 5 shows the calculation target fuel cell in which the number of arcs of the call / call plot of the calculation target fuel cell obtained by performing the first step is 2, the third measurement condition and the It is a Cole-Cole plot of the calculation target fuel cell when the complex impedance is measured under the fourth measurement condition, and a Cole-Cole plot of the calculation target fuel cell under the third measurement condition is The call arc / call plot 18 of the calculation target fuel cell cell under the fourth measurement condition includes a first arc 2f and a second arc 3f.
Next, a difference ΔR (3-4) rn between the real part resistance value R3rn when the frequency in the third measurement condition is n and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is Following formula (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency.
Specifically, for example, when a point where the frequency in the call call plot 17 is 1000 Hz is a point G1, and a point where the frequency is 1000 Hz in the call call plot 18 is a point G2, the call call call From the plot 17, the real part resistance value R3r of the point G1 ₁₀₀₀ From the Cole-Cole plot 18, the real part resistance value R4r of the point G2 ₁₀₀₀ Ask for. Next, the real part resistance value R3r of the point G1 ₁₀₀₀ And the real part resistance value R4r of the point G2 ₁₀₀₀ Difference (R3r ₁₀₀₀ -R4r ₁₀₀₀ ) And ΔR (3-4) r when the frequency is 1000 Hz ₁₀₀₀ Ask for. Such calculation of ΔR (3-4) rn is performed over the entire area of the Cole-Cole plot 17 and the Cole-Cole plot 18 to obtain ΔR (3-4) rn for each frequency. . The calculation of ΔR (3-4) rn is performed by observing changes in ΔR (3-4) rn with respect to changes in frequency over the entire area of the Cole-Cole plot 17 and the Cole-Cole plot 18. It is only necessary to be performed at such a frequency interval, and ΔR (3-4) rn corresponding to each frequency at a certain interval may be obtained, or the frequency interval may not be constant.
Next, ΔR (3-4) rn for each frequency is plotted with the horizontal axis representing frequency and the vertical axis representing ΔR (3-4) rn, thereby obtaining a real part resistance difference second graph.
FIG. 4 is a schematic diagram of the second real part resistance difference graph. In FIG. 4, a graph denoted by reference numeral 141 is a real part resistance difference second graph 141, and the real part resistance difference second graph 141 always includes the ΔR (3-4) as compared with other frequency ranges. ) There is a frequency range where the amount of change in rn becomes large. That is, the peak 151 is always present in the second real part resistance difference graph 141. The frequency of the peak top 161 of the peak 151 is read from the real part resistance difference second graph 141, and the calculation target fuel cell cell obtained in the first step is obtained from the frequency value of the peak top 161. In the Cole-Cole plot, the arc derived from the air electrode side interface is recognized. For example, if the frequency of the peak top of the real part resistance difference second graph is y, the frequency is y in the Cole-Cole plot of the calculation target fuel cell obtained in the first step. The arc including the point is identified as an arc derived from the air electrode side interface.
In the third step, since only the gas composition of the air electrode side gas is changed, the fact that the peak top is present at the frequency y in the second real part resistance difference graph indicates the influence of the change on the air electrode side. Is strongly affected by the frequency range in the vicinity of the frequency y in the Cole-Cole plot of the calculation target fuel cell, the calculation target fuel cell obtained in the first step. In the Cole-Cole plot of the cell, an arc including a point having a frequency y can be recognized as an arc derived from the air electrode side interface.
In the interface resistance calculation step, in the Cole-Cole plot of the calculation target fuel cell obtained in the first step, the arc determined to be an arc derived from the fuel electrode side interface in the second step The difference between the maximum value Rra (max) of the real part resistance value and the minimum value Rra (min) of the real part resistance value is expressed by the following equation (3):
Ria = Rra (max) −Rra (min) (3)
To obtain the fuel electrode side interface resistance Ria, and in the Cole-Cole plot of the calculation target fuel cell obtained in the first step, the arc derived from the air electrode side interface in the third step The difference between the maximum value Rrc (max) of the real part resistance value and the minimum value Rrc (min) of the real part resistance value of the arc that has been determined to be present is expressed by the following equation (4):
Ric = Rrc (max) −Rrc (min) (4)
To calculate the air electrode side interface resistance Ric.
The interface resistance calculation step will be described with reference to FIG. As a result of performing the second step and the third step, in the Cole-Cole plot 1a, the first arc 2a is an arc derived from the fuel electrode side interface, and the second arc 3a is air. The description will be made assuming that the arc is derived from the pole-side interface. In the Cole-Cole plot 1a, the point of intersection of the first arc 2a and the horizontal axis, that is, the point at which the imaginary part resistance value of the first arc 2a is “0”, the first arc 2a and the second arc 3a is the point B1, and the second arc 3a and the horizontal axis is the intersection, that is, the point where the imaginary part resistance value of the second arc 3a is "0" is the point C1. In this case, the Rra (min) is the real part resistance value of the point A1, the Rra (max) is the real part resistance value of the point B1, and the Rc (min) is the point B1. The Rrc (max) is the real part resistance value of the point C1. Then, the fuel electrode side interface resistance Ria is obtained from the above equation (3), and the air electrode side interface resistance Ric is obtained from the above equation (4).
Further, a case where the Cole-Cole plot of the calculation target fuel cell obtained by performing the first step is composed of three arcs will be described with reference to FIG. As a result of performing the second step and the third step, in the Cole-Cole plot 1b, the first arc 2b is an arc derived from the fuel electrode side interface, and the second arc 3b is air. The description will be made assuming that the arc is derived from the pole-side interface. In the Cole-Cole plot 1b, the intersection of the first arc 2b and the horizontal axis, that is, the point where the imaginary part resistance value of the first arc 2b is “0” is the point A2, the first arc If the intersection of 2b and the second arc 3b is a point B2, and the intersection of the second arc 3b and the third arc 4 is a point C2, in this case, Rra (min) is the real part of the point A2. A resistance value, the Rra (max) is a real part resistance value at the point B2, the Rc (min) is a real part resistance value at the point B2, and the Rrc (max) is a real number at the point C2. Resistance value. Then, the fuel electrode side interface resistance Ria is obtained from the above equation (3), and the air electrode side interface resistance Ric is obtained from the above equation (4).
Further, when the Cole-Cole plot of the calculation target fuel cell obtained by performing the first step is composed of four arcs, the number of arcs increases on the side where the real part resistance value is larger than the third arc. However, since the relationship between the first arc, the second arc, and the third arc does not change, the call / call plot of the calculation target fuel cell obtained by performing the first step has three arcs. It is the same as the case where consists of.
The method for measuring the interface resistance according to the second aspect of the present invention is a method for calculating the interface resistance for calculating the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric during operation of the calculation target fuel cell.
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
An equivalent circuit having (i) a first resistor connected in series, (ii) a second resistor and a first capacitor connected in parallel, and (iii) a third resistor and a second capacitor connected in parallel; Fitting with the Cole-Cole plot of the calculation target fuel cell obtained in the first step to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric;
It is the calculation method of the interface resistance which has this.
The first step, the second step and the third step according to the method for measuring the interfacial resistance according to the second aspect of the present invention are the first step and the second step according to the method for measuring the interfacial resistance according to the first aspect of the present invention. And it is the same as that of a 3rd process.
In the fitting step, first, the equivalent circuit is constructed. When the Cole-Cole plot of the calculation target fuel cell obtained in the first step is the Cole-Cole plot 1a shown in FIG. 1, that is, obtained in the first step. When the Cole-Cole plot of the cell to be calculated is composed of two arcs, the equivalent circuit to be constructed is the equivalent circuit 21 shown in FIG. In FIG. 6, the equivalent circuit 21 includes (i) a first resistor 22a, (ii) a second resistor 24a and a first capacitor 23a connected in parallel, and (iii) a third resistor 26a connected in parallel. And the 2nd capacitor | condenser 25a is connected in series.
Next, fitting is performed between the equivalent circuit 21 and the Cole-Cole plot 1a of the calculation target fuel cell obtained in the first step.
In the fitting, the circuit diagram of the equivalent circuit, the resistance value of the resistor in the equivalent circuit, the capacitance value of the capacitor in the equivalent circuit, and the reactance are input, and the Cole-Cole plot is calculated and the shape is output. Can use existing software. The existing software used for the fitting is not particularly limited, and examples include Z View2-Equivalent-Circuits.
In the fitting, first, the soft circuit diagram of the equivalent circuit 21, the initial value of the first resistor 22a, the initial value of the second resistor 24a, the initial value of the first capacitor 23a, the third resistor The initial value of 26a, the initial value of the second capacitor 25a, and input values necessary for calculation of reactance, etc. are input, and then the calculation by the software is repeated while changing the input value little by little. The shape of the Cole Cole plot obtained by the calculation in is approximated to the shape of the Cole Cole plot of the calculation target fuel cell obtained in the first step. When the shape of the Cole-Cole plot obtained by the calculation in the software matches or substantially matches the shape of the Cole-Cole plot of the calculation target fuel cell obtained in the first step An input value is obtained as an input value at the time of fitting.
The relationship between the equivalent circuit 21 and the Cole-Cole plot 1a of the calculation target fuel cell obtained in the first step will be described. By the second step and the third step, (1) the call When it is determined that the first arc 2a of the Cole plot 1a is an arc derived from the fuel electrode side interface and the second arc 3a is an arc derived from the air electrode side interface, the second resistance 24a is In the fuel electrode side interface resistance Ria, the first capacitor 23a is a capacitor component at the fuel electrode side interface, the third resistor 26a is in the air electrode side interface resistance Ric, and the second capacitor 25a is a capacitor component in the air electrode side interface. Respectively. Further, by the second step and the third step, (2) the first arc 2a of the Cole-Cole plot 1a is an arc derived from the air electrode side interface, and the second arc 3a is the fuel electrode side. When the arc is derived from the interface, the second resistor 24a is the air electrode side interface resistance Ric, the first capacitor 23a is the capacitor component at the air electrode side interface, and the third resistor 26a is the fuel electrode side. The second capacitor 25a corresponds to the interface resistance Ria and the capacitor component at the fuel electrode side interface.
Therefore, if (1) the first arc 2a is an arc derived from the fuel electrode side interface and the second arc 3a is an arc derived from the air electrode side interface, the input at the time of fitting is performed. Among the values, the input value of the second resistor 24a is the fuel electrode side interface resistance Ria, and the input value of the third resistor 26a is the air electrode side interface resistance Ric. In addition, when it is determined that (2) the first arc 2a is an arc derived from the air electrode side interface and the second arc 3a is an arc derived from the fuel electrode side interface, the input value at the time of fitting Of these, the input value of the second resistor 24a is the air electrode side interface resistance Ric, and the input value of the third resistor 26a is the fuel electrode side interface resistance Ria.
Further, when the Cole-Cole plot of the calculation target fuel cell obtained in the first step is the Cole-Cole plot 1b shown in FIG. 2, that is, obtained in the first step. When the Cole-Cole plot of the calculated calculation target fuel cell is composed of three arcs, the equivalent circuit to be constructed is the equivalent circuit 30 shown in FIG. 7, the equivalent circuit 30 includes (i) a first resistor 22b, (ii) a second resistor 24b and a first capacitor 23b connected in parallel, (iii) a third resistor 26b connected in parallel, and The second capacitor 25b, and (iv) the fourth resistor 28b and the third capacitor 27b connected in parallel are connected in series.
In the fitting, first, the soft circuit diagram of the equivalent circuit 30 and the initial value of the first resistor 22b, the initial value of the second resistor 24b, the initial value of the first capacitor 23b, the third resistor Except for inputting an initial value of 26b, an initial value of the second capacitor 25b, an initial value of the fourth resistor 28b, an initial value of the third capacitor 27b, an input value necessary for calculation of reactance, etc. An input value at the time of fitting is obtained by the same method as in the case where the Cole-Cole plot of the calculation target fuel cell obtained in the first step is composed of two arcs.
The relationship between the equivalent circuit 30 and the Cole-Cole plot 1b of the calculation target fuel cell obtained in the first step will be described. By the second step and the third step, (3) the call When it is determined that the first arc 2b of the Cole plot 1b is an arc derived from the fuel electrode side interface and the second arc 3b is an arc derived from the air electrode side interface, the second resistor 24b is In the fuel electrode side interface resistance Ria, the first capacitor 23b is a capacitor component at the fuel electrode side interface, the third resistor 26b is in the air electrode side interface resistance Ric, and the second capacitor 25b is a capacitor component in the air electrode side interface. Respectively. Further, by the second step and the third step, (4) the first arc 2b of the Cole-Cole plot 1b is an arc derived from the air electrode side interface, and the second arc 3b is the fuel electrode side. When the arc is derived from the interface, the second resistor 24b is the air electrode side interface resistance Ric, the first capacitor 23b is the capacitor component at the air electrode side interface, and the third resistor 26b is the fuel electrode side. The second capacitor 25b corresponds to the interface resistance Ria and the capacitor component on the fuel electrode side interface.
Therefore, if it is determined that (3) the first arc 2b is an arc derived from the fuel electrode side interface and the second arc 3b is an arc derived from the air electrode side interface, the input at the time of fitting is performed. Among the values, the input value of the second resistor 24b is the fuel electrode side interface resistance Ria, and the input value of the third resistor 26b is the air electrode side interface resistance Ric. Further, when it is determined that (4) the first arc 2b is an arc derived from the air electrode side interface and the second arc 3b is an arc derived from the fuel electrode side interface, the input value at the time of fitting Among these, the input value of the second resistor 24b is the air electrode side interface resistance Ric, and the input value of the third resistor 26b is the fuel electrode side interface resistance Ria.
Further, when the Cole / Cole plot of the calculation target fuel cell obtained in the first step is composed of four or more arcs, the equivalent circuit 30 shown in FIG. 7 regardless of the number of arcs. And fitting.
In the calculation method of the interfacial resistance according to the first aspect of the present invention and the interfacial resistance calculation method according to the second aspect of the present invention, the Cole-Cole plot of the calculation target fuel cell obtained in the first step (1) The first measurement in the second step in that it is easy to determine whether the first arc and the second arc are from the fuel electrode side interface or the air electrode side interface. And the second measurement condition is a measurement condition in which only the fuel concentration in the fuel electrode side gas is different, and the third measurement condition and the fourth measurement condition in the third step are the air electrode side gas. It is preferable that the measurement conditions differ only in the oxygen concentration therein. (2) The first measurement condition and the second measurement condition in the second step differ only in the hydrogen concentration in the fuel electrode side gas. And the third measurement condition in the third step and the fourth It is particularly preferable that the constant condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different. (3) The first measurement condition and the second measurement condition in the second step are the fuel electrode side. Only the water vapor concentration in the gas is a different measurement condition, and the third measurement condition and the fourth measurement condition in the third step are different measurement conditions only in the oxygen concentration in the air electrode side gas. Further preferred.
In the calculation method of the interfacial resistance according to the first aspect of the present invention and the interfacial resistance calculation method according to the second aspect of the present invention, the complex impedance measurement of the calculation target fuel cell in the second step and the second The temperature at which the complex impedance measurement of the calculation target fuel cell in the three steps is not particularly limited, is appropriately selected depending on the type of cell and the operating conditions, and is usually −10 to 1200 ° C., for example, solid oxidation In the case of a physical fuel cell, the temperature is 600 to 1200 ° C.
Conventionally, it has been known to obtain a Cole-Cole plot by measuring complex impedance of a fuel cell cell under operating conditions during operation. However, it has not been possible to determine whether the arc in the obtained Cole-Cole plot is derived from the fuel electrode side interface or the air electrode side interface. Therefore, the fuel electrode side interface resistance and the air electrode side interface resistance during operation could not be calculated.
On the other hand, in the calculation method of the interfacial resistance of the first aspect of the present invention and the calculation method of the interfacial resistance of the second aspect of the present invention, by performing the second step and the third step, It can be reliably identified from which interface the first arc and the second arc in the obtained Cole-Cole-Plot of the calculated fuel cell for calculation are derived. Therefore, according to the calculation method of the interfacial resistance according to the first aspect of the present invention and the interfacial resistance calculation method according to the second aspect of the present invention, the fuel cell to be calculated is calculated under a specific operating condition desired to be calculated. When operated, the fuel electrode side interface resistance and the air electrode side interface resistance can be calculated.
EXAMPLES Next, although an Example is given and this invention is demonstrated more concretely, this is only an illustration and does not restrict | limit this invention.

そして、第一工程の界面抵抗の算出を行う作動条件を測定１とし、第二工程の第一測定条件を測定４、第二測定条件を測定２、第二工程の第三測定条件を測定１、第四測定条件を測定２として、実数部抵抗値差第一グラフ及び実数部抵抗値差第二グラフを求めた。その結果を第６表及び第１２図に示す。

（円弧の認定）
第１２図中、実数部抵抗値差第一グラフのピークトップは、周波数１００Ｈｚ付近であるので、周波数１００Ｈｚ近辺に、燃料極側の変化の影響が強く出ていることがわかった。そして、第２表から、第８図の測定１のコール・コール・プロット中の円弧のうち、周波数１００Ｈｚの点を含む円弧である第一円弧３１が、燃料極側に由来する円弧であると認定できる。同様に、実数部抵抗値差第二グラフのピークトップは、周波数１０Ｈｚ付近であるので、周波数１０Ｈｚ近辺に、空気極側の変化の影響が強く出ていることがわかった。そして、第２表から、第８図の測定１のコール・コール・プロット中の円弧のうち、周波数１０Ｈｚの点を含む円弧である第二円弧３２が、空気極側に由来する円弧であると認定できる。
（フィッティング工程）
第７図に示す等価回路を構築した。上記円弧の認定結果から、第７図中、第二抵抗２４ｂが燃料極側界面抵抗Ｒｉａに相当し、第二抵抗２６ｂが空気極側界面抵抗Ｒｉｃの相当する。次いで、既存ソフトＺ Ｖｉｅｗ２−Ｅｑｕｉｖａｌｅｎｔ−Ｃｉｒｃｕｉｔｓを用いて、第８図に示す測定１のコール・コール・プロットとのフィッティングを行い、第１３図に示すコール・コール・プロットを得た。第１３図に示すコール・コール・プロットとなる時の第二抵抗２４ｂの入力値は、０．９６９７６Ωであり、第三抵抗２６ｂの入力値は、０．５５５２７Ωであった。
従って、該燃料電池用セルＡを、燃料極側のガス組成が水素濃度１００％、空気極側のガス組成が酸素濃度１０％、セルの作動温度が１０００℃の作動条件で作動させた時、該燃料電池用セルＡの燃料極側界面抵抗Ｒｉａは０．９６９７６Ω、空気極側界面抵抗Ｒｉｃは０．５５５２７Ωである。Example 1
(Production of cell)
A fuel electrode forming slurry containing a mixed powder of nickel oxide (NiO) and scandiaceria-stabilized zirconia (10Sc1CeSZ) having a mixing ratio of 50:50 is prepared, and then the fuel electrode forming slurry is used to screen. A slurry layer for forming a fuel electrode having a film thickness of 100 μm was formed by a printing method, dried, and then fired at 1400 ° C. for 5 hours to produce a fuel electrode.
・ Nickel oxide; average particle size 0.8μm
Scandia ceria stabilized zirconia; scandia content in zirconia 10 mol%, ceria content 1 mol%, average particle size 0.6 μm
Next, an electrolyte forming slurry containing scandiaceria-stabilized zirconia (10Sc1CeSZ) used for the preparation of the fuel electrode layer forming slurry is prepared, and then the electrolyte forming slurry is screen-printed on the surface of the fuel electrode layer. The film was applied by a method so that the film thickness became 0.3 mm, dried, and then fired at 1400 ° C. for 5 hours to obtain a fuel electrode on which an electrolyte was formed.
Next, an air electrode forming slurry containing lanthanum strontium manganate (Ln _0.8 Sr _0.2 Mn _1.0 O ₃ ) is prepared, and then the air electrode forming slurry is formed on the surface of the electrolyte. By applying a screen printing method so as to have a film thickness of 100 μm and drying, baking was performed at 1200 ° C. for 3 hours to produce a cell A for a fuel cell.
(Complex impedance measurement)
The complex impedance of the fuel cell A is measured under the conditions of the cell operating temperature of 1000 ° C. and the gas composition of the hydrogen concentration of the fuel electrode side gas and the oxygen concentration of the air electrode side gas as shown in Table 1. Tension stat, set potential: 0.0 V, current range: 10 A, delay time: 0.1 second, number of sweep measurement data: 50 times, number of integrations: 10 times, maximum frequency: 100 kHz, minimum frequency: 0.1 Hz, sine Wave voltage: 0.03 Vrms, EM measurement time: 5 seconds, polarization holding time: 0.2 seconds. The results are shown in Tables 2-5. Also, Cole-Cole plots of measurements 1 to 4 are shown in FIGS.

The operating condition for calculating the interfacial resistance in the first step is taken as measurement 1, the first measuring condition in the second step is measured 4, the second measuring condition is measured 2, and the third measuring condition in the second step is measured 1. Using the second measurement condition as measurement 2, a real part resistance value difference first graph and a real part resistance value difference second graph were obtained. The results are shown in Table 6 and FIG.

(Circuit certification)
In FIG. 12, since the peak top of the first real part resistance value difference graph is near the frequency of 100 Hz, it was found that the influence of the change on the fuel electrode side is strongly around the frequency of 100 Hz. From Table 2, the first arc 31 that is an arc including a point of a frequency of 100 Hz among the arcs in the call call plot of the measurement 1 in FIG. 8 is an arc derived from the fuel electrode side. Can be certified. Similarly, since the peak top of the real part resistance value difference second graph is near the frequency of 10 Hz, it was found that the influence of the change on the air electrode side is strongly around the frequency of 10 Hz. And from Table 2, the second arc 32 that is an arc including a point of frequency 10 Hz among the arcs in the call call plot of the measurement 1 in FIG. 8 is an arc derived from the air electrode side. Can be certified.
(Fitting process)
The equivalent circuit shown in FIG. 7 was constructed. From the result of the above-mentioned arc recognition, in FIG. 7, the second resistance 24b corresponds to the fuel electrode side interface resistance Ria, and the second resistance 26b corresponds to the air electrode side interface resistance Ric. Next, using the existing software Z View2-Equivalent-Circuits, fitting with the call-call plot of measurement 1 shown in FIG. 8 was performed, and the call-call plot shown in FIG. 13 was obtained. The input value of the second resistor 24b in the Cole-Cole plot shown in FIG. 13 was 0.96976Ω, and the input value of the third resistor 26b was 0.55527Ω.
Therefore, when the fuel cell A is operated under the operating conditions where the gas composition on the fuel electrode side is 100% hydrogen concentration, the gas composition on the air electrode side is 10% oxygen concentration, and the cell operating temperature is 1000 ° C. The fuel cell side interface resistance Ria of the fuel cell A is 0.96976Ω, and the air electrode side interface resistance Ric is 0.55527Ω.

Explanation of symbols

1a, 1b, 11, 12, 17, 18 Cole-Cole plot 2a, 2b, 2c, 2d, 2e, 2f, 31 First arc 3a, 3b, 3c, 3d, 3e, 3f, 32 Second arc 4 Second Three arcs 14 Real part resistance difference first graph 141 Real part resistance difference second graph 15, 151 Peak 16, 161 Peak top 21, 30 Equivalent circuit 22a, 22b First resistor 23a, 23b First capacitor 24a, 24b Second resistance 25a, 25b Second capacitor 26a, 26b Third resistor 27b Third capacitor 28b Fourth resistor 41, 41a, 41b Electrolyte 42, 42a, 42b Fuel electrode 43, 43a, 43b Air electrode 44, 44a, 44b Fuel cell 51 Reference electrode 52a, 52b Equipotential line 53 Fuel electrode terminal 54 Air electrode terminal 55a, 55b Intermediate potential point 56 Fuel electrode 4 Surface b is bonded

  According to the present invention, since the interface resistance of the fuel cell can be grasped under the operating condition, it is easy to construct a power generation system having the fuel cell.

Claims (5)

A calculation method of an interface resistance for calculating a fuel electrode side interface resistance Ria and an air electrode side interface resistance Ric during operation of a calculation target fuel cell,
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
In the Cole-Cole plot of the calculation target fuel cell obtained in the first step, the maximum value of the resistance value of the real part of the arc recognized as the arc derived from the fuel electrode side interface in the second step The difference between Rra (max) and the minimum value Rra (min) of the real part resistance value is expressed by the following formula (3):
Ria = Rra (max) −Rra (min) (3)
To obtain the fuel electrode side interface resistance Ria, and then derived from the air electrode side interface in the third step during the Cole-Cole plot of the calculation target fuel cell obtained in the first step The difference between the maximum value Rrc (max) of the real part resistance value and the minimum value Rrc (min) of the real part resistance value of the arc recognized as an arc to be obtained is expressed by the following formula (4):
Ric = Rrc (max) −Rrc (min) (4)
And calculating an interface resistance Ric to obtain the air electrode side interface resistance Ric. A calculation method of an interface resistance for calculating a fuel electrode side interface resistance Ria and an air electrode side interface resistance Ric during operation of a calculation target fuel cell,
A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;
The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference ΔR (1-2) rn between the partial resistance value R1rn and the real part resistance value R2rn when the frequency in the second measurement condition is n is expressed by the following formula (1):
ΔR (1-2) rn = R1rn−R2rn (1)
To calculate ΔR (1-2) rn for each frequency, and then plot ΔR (1-2) rn for each frequency with the horizontal axis representing frequency and the vertical axis representing ΔR (1-2) rn, A real part resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the call cell call call of the calculation target fuel cell obtained in the first step is obtained. Of the arcs in the plot, the second step of certifying arcs derived from the fuel electrode side interface;
Under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, the complex impedance measurement of the calculation target fuel cell is performed, and then the frequency in the third measurement condition is n The difference ΔR (3-4) rn between the real part resistance value R3rn and the real part resistance value R4rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):
ΔR (3-4) rn = R3rn−R4rn (2)
To obtain ΔR (3-4) rn for each frequency, and then plot the frequency on the horizontal axis and ΔR (3-4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak top frequency in the real part resistance value difference second graph, the arc side in the Cole-Cole plot of the calculation target fuel cell obtained in the first step is connected to the air electrode side interface. A third step of certifying the arc of origin,
An equivalent circuit having (i) a first resistor connected in series, (ii) a second resistor and a first capacitor connected in parallel, and (iii) a third resistor and a second capacitor connected in parallel; Fitting with the Cole-Cole plot of the calculation target fuel cell obtained in the first step to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric;
A method for calculating the interfacial resistance, comprising: The first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the fuel concentration in the fuel electrode side gas, and the third measurement condition and the fourth measurement in the third step. The interface resistance calculation method according to claim 1, wherein the measurement condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different. The interface resistance calculation method according to claim 3, wherein the first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the hydrogen concentration in the fuel electrode side gas. The first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the water vapor concentration in the fuel electrode side gas, and the third measurement condition and the fourth measurement in the third step. The interface resistance calculation method according to claim 1, wherein the measurement condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different.

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