Analysis method and program

Abstract

This makes it possible to predict the behavior of oxygen molecules within the pores of a carbon support. [Solution] The analysis method comprises a modeling step, a setting step, a simulation step, and a calculation step. In the modeling step, the carbon support of the hydrogen fuel cell is modeled as a cylindrical carbon nanotube model. In the setting step, the number of water molecule models, oxygen molecule models, and nitrogen molecule models to be placed within the carbon nanotube model is set. In the simulation step, a simulation is performed on the diffusion of water molecule models, oxygen molecule models, and nitrogen molecule models within the carbon nanotube model. In the calculation step, the diffusion coefficient of the oxygen molecule model is calculated based on the simulation results.

Description

[Technical Field]

[0001] This disclosure relates in general to analytical methods and programs, and more specifically to analytical methods and programs for the behavior of oxygen. [Background technology]

[0002] Patent Document 1 discloses a parameter determination method for fuel cells. This parameter determination method is used in simulations to determine the gas transportability within the pore space of a carbon support. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2019-186200 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] Incidentally, a fuel cell (hydrogen fuel cell) is a battery that generates electricity by releasing electrons during the reaction process that produces water molecules. In a hydrogen fuel cell, hydrogen molecules injected into the anode pass through the gas diffusion layer, are decomposed into hydrogen ions by a carbon support in the catalyst layer, pass through the electrolyte membrane, and react with oxygen molecules in the catalyst layer on the cathode side to produce water molecules. In such hydrogen fuel cells, it is desirable to generate more electrons.

[0005] To generate more electrons in hydrogen fuel cells, improving the effectiveness of the carbon support is conceivable. However, it is difficult to experimentally confirm the effectiveness of the carbon support, such as whether oxygen molecules are effectively in contact with it. Therefore, it is desirable to confirm the diffusion behavior of oxygen in the microscopic region through computer simulation analysis.

[0006] This disclosure is made in view of the above-mentioned reasons and aims to provide an analysis method and program that makes it possible to predict the behavior of oxygen molecules within the pores of a carbon support. [Means for solving the problem]

[0007] An analysis method according to one aspect of this disclosure comprises a modeling step, a setting step, a simulation step, and a calculation step. In the modeling step, the carbon support of the hydrogen fuel cell is modeled as a cylindrical carbon nanotube model. In the setting step, the number of water molecule models, oxygen molecule models, and nitrogen molecule models to be placed within the carbon nanotube model is set. In the simulation step, a simulation is performed on the diffusion of the water molecule models, oxygen molecule models, and nitrogen molecule models within the carbon nanotube model. In the calculation step, the diffusion coefficient of the oxygen molecule model is calculated based on the results of the simulation.

[0008] A program according to one aspect of this disclosure is a program for causing one or more processors to execute the analysis method described above. [Effects of the Invention]

[0009] According to this disclosure, it is possible to predict the behavior of oxygen molecules within the pores of a carbon support. [Brief explanation of the drawing]

[0010] [Figure 1] Figure 1 is a flowchart showing the processing steps of the analysis method according to Embodiment 1. [Figure 2] Figure 2 is a schematic diagram of the carbon support model. [Figure 3] Figure 3 is a schematic diagram of the carbon nanotube model used in the analysis method described above. [Figure 4] Figure 4 is an explanatory diagram illustrating the modeling method for carbon nanotubes. [Figure 5]Figure 5 is a graph showing the relationship between the diameter of carbon nanotubes and the density of water. [Figure 6] Figure 6 is a schematic diagram showing a water molecule model. [Figure 7] Figure 7 is a schematic diagram showing an oxygen molecule model. [Figure 8] Figure 8 is a schematic diagram showing a nitrogen molecule model. [Figure 9] Figure 9 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy is 0% in the same analysis method as above. [Figure 10] Figure 10 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy is 25% in the same analysis method as above. [Figure 11] Figure 11 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy is 50% in the same analysis method as above. [Figure 12] Figure 12 is an explanatory diagram for explaining the calculation method of the mean squared displacement in the same analysis method as above. [Figure 13] Figure 13 is another explanatory diagram for explaining the calculation method of the mean squared displacement in the same analysis method as above [Figure 14] Figure 14 is a graph showing the mean squared displacement when the liquid water occupancy is 0%. [Figure 15] Figure 15 is a graph showing the mean squared displacement when the liquid water occupancy is 25%. [Figure 16] Figure 16 is a graph showing the mean squared displacement when the liquid water occupancy is 50%. [Figure 17] Figure 17 is a graph showing the relationship between the liquid water occupancy in the simulation and the diffusion coefficient of the water molecule model. [Figure 18] Figure 18 is a graph obtained by partially enlarging Figure 17. [Figure 19] Figure 19 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy is 0% in the analysis method according to Embodiment 2. [Figure 20]Figure 20 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water content is 25% using the same analysis method. [Figure 21] Figure 21 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy rate is 50% using the same analysis method. [Figure 22] Figure 22 is a graph showing the mean square displacement when the liquid water content is 25%. [Figure 23] Figure 23 is a graph showing the mean square displacement when the liquid water content is 50%. [Figure 24] Figure 24 is a graph showing the relationship between the liquid water occupancy rate and the diffusion coefficient of the water molecule model in the simulation. [Figure 25] Figure 25 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy rate is 0% in the analysis method according to Embodiment 3. [Figure 26] Figure 26 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water content is 25% using the same analysis method. [Figure 27] Figure 27 is a schematic diagram showing the molecular model within the carbon nanotube model when the liquid water occupancy rate is 50% using the same analysis method as above. [Figure 28] Figure 28 is a graph showing the relationship between the liquid water occupancy rate and the diffusion coefficient of the water molecule model in the simulation. [Modes for carrying out the invention]

[0011] Preferred embodiments of this disclosure will be described in detail below with reference to the drawings. Common elements in the embodiments described below are denoted by the same reference numerals, and redundant descriptions of common elements may be omitted. The following embodiments and modifications represent only a portion of the various embodiments of this disclosure. Furthermore, the following embodiments and modifications can be modified in various ways depending on the design, etc., as long as the objectives of this disclosure are achieved. It is also possible to combine the configurations of the following embodiments and modifications as appropriate.

[0012] The figures described herein are schematic diagrams, and the ratios of the size and thickness of each component in each figure do not necessarily reflect the actual dimensional ratios.

[0013] (Embodiment 1) (1) Overview First, an overview of the analysis according to Embodiment 1 will be described with reference to Figure 1. The analysis method of Embodiment 1 is an analysis method concerning the behavior of oxygen molecules within the pores of the carbon support of a hydrogen fuel cell.

[0014] As shown in Figure 1, the analysis method of Embodiment 1 includes a modeling step (step S1), a setting step (step S2), a simulation step (step S3), and a calculation step (step S4).

[0015] In the modeling step, the carbon support for the hydrogen fuel cell is modeled as a cylindrical carbon nanotube model 2 (see Figure 3).

[0016] In the setup step, the number of water molecule model 3 (see Figure 6), oxygen molecule model 4 (see Figure 7), and nitrogen molecule model 5 (see Figure 8) to be placed inside the carbon nanotube model 2 is set.

[0017] The simulation step involves simulating the diffusion of water molecule model 3, oxygen molecule model 4, and nitrogen molecule model 5 within carbon nanotube model 2.

[0018] In the calculation step, the diffusion coefficient of oxygen molecule model 4 is calculated based on the simulation results.

[0019] The diffusion coefficient serves as an indicator or guideline for how much a molecule is moving. According to the analysis method of Embodiment 1, the behavior of oxygen molecules within the pores of the carbon support can be inferred. In other words, according to the analysis method of Embodiment 1, the behavior of oxygen molecules in regions where the carbon support and oxygen molecules are likely to come into contact can be inferred.

[0020] (2) Details The details of the analysis method according to Embodiment 1 will be described below with reference to Figures 1 to 18.

[0021] As described above, the analysis method of Embodiment 1 is a method for analyzing the behavior of oxygen within the pores of a carbon support in a hydrogen fuel cell. More specifically, the analysis method of Embodiment 1 performs a simulation using an analysis model to analyze the behavior of oxygen within the pores of the carbon support. The analysis method of Embodiment 1 is executed on a computer system such as a personal computer. In this disclosure, "model" refers to an analysis model used by a computer system to perform simulations.

[0022] In a hydrogen fuel cell, hydrogen molecules injected into the anode pass through the gas diffusion layer and are decomposed into hydrogen ions by a carbon support in the catalyst layer. The hydrogen ions then move through the electrolyte membrane to the catalyst layer on the cathode side. In the catalyst layer on the cathode side, hydrogen ions and oxygen molecules react to produce water molecules. The catalyst layer supports a catalyst, such as platinum, on a carbon support. The carbon support has multiple pores that penetrate the carbon support.

[0023] The analysis method of Embodiment 1 is used for analyzing the behavior of molecular models in a hydrogen fuel cell model. The hydrogen fuel cell model is a model for analyzing the behavior of each molecule within a hydrogen fuel cell. As shown in Figure 2, the hydrogen fuel cell model has a plurality of catalyst models 11 and a carbon support model 12.

[0024] The carbon support model 12 supports multiple catalyst models 11. The carbon support model 12 has multiple pores 121. Molecular models such as water molecule model 3 and oxygen molecule model 4 are arranged within the pores 121.

[0025] In analyzing the behavior of molecular models within pores 121, it is preferable to consider the contact between the walls 122 forming the pores 121 and the molecular models. However, the pores of carbon carriers have very complex shapes, making it difficult to create accurate models. In this case, the analysis method of Embodiment 1 uses a carbon nanotube model 2 that simulates the pores of a carbon carrier.

[0026] In other words, in the modeling step of the analysis method of Embodiment 1, the pores of the carbon support are modeled as a cylindrical carbon nanotube model 2. More specifically, in the modeling step, the carbon nanotube model 2 is modeled using a graphene model 6 (see Figure 4) and chiral vectors.

[0027] Graphene Model 6 is a model of graphene. Graphene is a film (or sheet) with a honeycomb structure in which carbon atoms are arranged in a hexagonal lattice. Carbon nanotube Model 2 is modeled by winding graphene Model 6 into a cylindrical shape using chiral vectors. Chiral vectors are expressed by the following equation (1).

[0028]

number

[0029] In equation (1), "a1" and "a2" are basis vectors of the graphene lattice. Also, "n" and "m" in equation (1) are coefficients and are integers. The combination of "n" and "m" (n,m) is called the chiral index (chirality). The structure of carbon nanotube model 2 is determined by graphene model 6 and the chiral index.

[0030] The opening diameter D1 (see Figure 9) and the axial length D2 (see Figure 3) of the carbon nanotube model 2 are uniquely determined according to the chiral index. In the modeling step of Embodiment 1, the opening diameter D1 of the carbon nanotube model 2 is determined by determining the chiral index. Also in the modeling step, the axial length D2 of the carbon nanotube model 2 is determined by determining the chiral index. The opening diameter D1 and length D2 are determined based on user operations on a user interface such as a personal computer. Since the opening diameter D1 and length D2 can be set, simulations can be performed using carbon nanotube models 2 of various sizes.

[0031] For example, if the chiral index is (15,15), the aperture diameter D1 is 2 nm and the length D2 is 10 nm. Also, for example, if the chiral index is (29,29), the aperture diameter D1 is 4 nm and the length D2 is 10 nm. Also, for example, if the chiral index is (44,44), the aperture diameter D1 is 6 nm and the length D2 is 10 nm. Also, for example, if the chiral index is (58,58), the aperture diameter D1 is 8 nm and the length D2 is 10 nm. Also, for example, if the chiral index is (73,73), the aperture diameter D1 is 10 nm and the length D2 is 10 nm.

[0032] In the setup step, the number of water molecule models 3, oxygen molecule models 4, and nitrogen molecule models 5 to be placed inside the carbon nanotube model 2 is set. Figure 5 is a graph showing the relationship between the opening diameter of the carbon nanotube and the density of water inside the carbon nanotube. In the setup step, the number of water molecule models 3 to be contained inside the carbon nanotube model 2 is determined based on the volume of the carbon nanotube model 2 and the graph shown in Figure 5. In other words, in the setup step, the number of water molecule models 3 to be contained inside the carbon nanotube model 2 is determined based on the opening diameter D1, length D2, and the graph shown in Figure 5.

[0033] In the setup step, the number of oxygen molecule models 4 and nitrogen molecule models 5 to be contained within carbon nanotube model 2 is determined based on the volume of carbon nanotube model 2 and the density of air within carbon nanotube model 2. Furthermore, in the setup step, the number of oxygen molecule models 4 and nitrogen molecule models 5 is set based on the ratio of oxygen molecules to nitrogen molecules in the air. This improves the accuracy of the analysis. In Embodiment 1, the ratio of oxygen molecules to nitrogen molecules is set to approximately 1:4.

[0034] Embodiment 1 illustrates a case where the user determines the number of each molecular model to be contained within the carbon nanotube model 2. However, the number of each molecular model to be contained within the carbon nanotube model 2 may be determined by a computer system based on the volume of the carbon nanotube model 2 and the graph shown in Figure 5.

[0035] Embodiment 1 illustrates the case where the aperture diameter D1 is 4 [nm] and the simulation is performed accordingly. The simulation conditions are shown in Table 1.

[0036] [Table 1]

[0037] Furthermore, Embodiment 1 illustrates a case where the simulation is performed while varying the liquid-water occupancy rate. More specifically, Embodiment 1 performs simulations under three conditions: liquid-water occupancy rates of 0%, 25%, and 50%. Note that the simulation conditions shown in Table 1 are for the case where the liquid-water occupancy rate is 50%.

[0038] Here, "liquid water occupancy rate" is the ratio of the number of water molecule models 3 placed within the carbon nanotube model 2 to 100%, where the number of water molecule models 3 determined based on the volume of the carbon nanotube model 2 and the graph (density of water) shown in Figure 5 is set to 100%. The liquid water occupancy rate is changed by changing the number of water molecule models 3 placed within the carbon nanotube model 2 in the setting step (step S2 in Figure 1) or the modification step (step S7 in Figure 1).

[0039] The analysis method of Embodiment 1 further includes a placement step. As shown in Figures 9 to 11, in the placement step, the number of water molecule models 3, oxygen molecule models 4, and nitrogen molecule models 5 set in the setting step are placed inside the carbon nanotube model 2. Figure 9 shows the molecular model inside the carbon nanotube model when the liquid water occupancy rate is 0%. Figure 10 shows the molecular model inside the carbon nanotube model when the liquid water occupancy rate is 25%. Furthermore, Figure 11 shows the molecular model inside the carbon nanotube model 2 when the liquid water occupancy rate is 50%. Here, the space R1 between the wall of the carbon nanotube model 2 and the molecular model is the space due to the repulsive force acting between the wall of the carbon nanotube model 2 and the molecular model.

[0040] In the simulation step, for example, molecular dynamics analysis software is used to simulate the diffusion of water molecule model 3, oxygen molecule model 4, and nitrogen molecule model 5 within carbon nanotube model 2. In the simulation step of Embodiment 1, the simulation is performed using molecular dynamics. First, in the simulation step, initial coordinates and initial velocities are given to each molecular model. Next, the forces acting between multiple molecular models at a certain time (timing) are determined. In the simulation step of Embodiment 1, the forces acting on oxygen molecule model 4 and nitrogen molecule model 5 are determined using the GAFF (General Amber Force Field) force field. Also, in the simulation step of Embodiment 1, the force acting on water molecule model 3 is determined using the SPC / E (Extended Simple Point Charge model) force field. Then, each molecular model is moved according to the equation of motion. Then, the time is advanced by Δt (advance one step), the forces acting between multiple intermolecular models are determined, and the process of moving each molecular model according to the equation of motion is repeated sequentially. In Embodiment 1, one step is 1 femtosecond.

[0041] In the simulation step, a simulation is performed to calculate the diffusion coefficient of oxygen molecule model 4. In Embodiment 1, the simulation to calculate the diffusion coefficient is performed for 1 million steps. The number of steps in the simulation to calculate the diffusion coefficient can be set as appropriate.

[0042] In the calculation step, the diffusion coefficient of oxygen molecule model 4 is calculated based on the simulation results. More specifically, the diffusion coefficient of oxygen molecule model 4 is calculated using the Mean Square Displacement (MSD) applied to the simulation results. More specifically, the diffusion coefficient of oxygen molecule model 4 is calculated using the total displacement, which is the sum of the displacements in the X, Y, and Z directions. Note that "displacement" refers to the distance between the initial position of oxygen molecule model 4 at the start of the simulation and the position of oxygen molecule model 4 at a given point in time.

[0043] In the calculation step of Embodiment 1, a linear interval is selected from the mean squared displacement of the simulation results (for example, the graphs shown in Figures 12 and 13) that is close to linear (proportional), and the diffusion coefficient is calculated based on the slope of the linear interval. For example, in the graph of Figure 12, interval X1 is selected as the linear interval, and the diffusion coefficient is calculated based on the slope of interval X1. Also, for example, in the graph of Figure 13, interval X3 is selected as the linear interval, and the diffusion coefficient is calculated based on the slope of interval X3. In other words, in the calculation step of Embodiment 1, for example, interval X2 in Figure 13 is treated as the nonlinear interval. Figures 14 to 16 are graphs of the linear intervals of the mean squared displacement of the simulation results.

[0044] Figure 14 is a graph showing the mean square displacement when carbon nanotube model 2 has an aperture diameter of 4 nm and a liquid water occupancy rate of 0%. Figure 15 is a graph showing the mean square displacement when carbon nanotube model 2 has an aperture diameter of 4 nm and a liquid water occupancy rate of 25%. Figure 16 is a graph showing the mean square displacement when carbon nanotube model 2 has an aperture diameter of 4 nm and a liquid water occupancy rate of 50%.

[0045] In Embodiment 1, the diffusion coefficient is calculated by performing a linear approximation on the linear interval of the mean squared displacement. Here, the diffusion coefficient is expressed by the following equation (2). In equation (2), "D" is the diffusion coefficient. Also, "x 2 (t) is the displacement in the X direction, and t is the simulation time.

[0046] x 2 (t) = 6Dt (2) For example, if the aperture diameter of carbon nanotube model 2 is 4 nm and the liquid water occupancy is 50%, the diffusion coefficient is approximately 2.5 × 10⁻¹⁰ from equations (3) and (4) below. -9 [m 2 This becomes / s].

[0047] 6D = 0.0152 [nm] 2 / ps]=15.2×10 -9 [m 2 / s] (3) D = 2.53×10 -9 [m 2 / s] ≒ 2.5×10 -9 [m 2 / s] (4) FIG. 17 is a graph showing the relationship between the diffusion coefficient of the oxygen molecule model 4 and the liquid water occupancy. FIG. 18 is an enlarged view of FIG. 17 with the scale of the vertical axis reduced. As shown in FIGS. 17 and 18, in the simulation results of the analysis method according to Embodiment 1, the diffusion coefficient decreases as the liquid water occupancy increases.

[0048] As shown in FIG. 9, when the liquid water occupancy is 0%, the water molecule model 3 does not exist in the carbon nanotube model 2, and the empty space in the carbon nanotube model 2 becomes wider. Therefore, when the liquid water occupancy is 0%, it is considered that the influence of the carbon nanotube model 2 is almost negligible.

[0049] As shown in FIG. 10, when the liquid water occupancy is 25%, although the water molecule model 3 exists in the carbon nanotube model 2, the empty space in the carbon nanotube model 2 is relatively wide. Therefore, when the liquid water occupancy is 25%, it is considered that the influence of the carbon nanotube model 2 is relatively small.

[0050] As shown in FIG. 11, when the liquid water occupancy is 50%, the proportion occupied by the liquid water increases, and the empty space in the carbon nanotube model 2 becomes narrower. As a result, contact between the carbon nanotube model 2 and the oxygen molecule model 4 occurs, and it is considered that the carbon nanotube model 2 has a relatively large influence on the movement of the oxygen molecule model 4. Note that the fluctuation of the mean square displacement in FIG. 16 indicates that the carbon nanotube model 2 affects the movement of the oxygen molecule model 4.

[0051] As described above, according to the analysis method of Embodiment 1, the relationship between the liquid water occupancy and the oxygen molecule model 4 can be confirmed.

[0052] (3) Flow of the analysis method Next, the flow of the analysis method of Embodiment 1 will be described with reference to Figure 1. Note that the flowchart shown in Figure 1 is merely an example, and the order of processing may be changed as appropriate, or processing may be added or deleted as appropriate.

[0053] First, a modeling step is performed (Step S1). In the modeling step, the carbon support for the hydrogen fuel cell is modeled as a cylindrical carbon nanotube model 2.

[0054] Next, the setup step is performed (step S2). In the setup step, the number of water molecule model 3, oxygen molecule model 4, and nitrogen molecule model 5 to be placed inside the carbon nanotube model 2 is set.

[0055] Next, the placement step is performed (step S3). In the placement step, each molecular model is placed inside the carbon nanotube model 2.

[0056] Next, a simulation step is performed (step S4). In the simulation step, a simulation is performed on the diffusion of water molecule model 3, oxygen molecule model 4, and nitrogen molecule model 5 within carbon nanotube model 2.

[0057] Next, the calculation step is performed (step S5). In the calculation step, the diffusion coefficient of oxygen molecule model 4 is calculated based on the simulation results.

[0058] Next, a decision is made as to whether or not to change parameters such as the aperture diameter D1, length D2, and the number of each molecular model (step S5). Embodiment 1 illustrates a case where the user decides whether or not to change the parameters. However, the decision on whether or not to change the parameters may be made by the computer system based on a plurality of simulation conditions set in advance by the user.

[0059] If the parameter is to be changed (Step S6: Yes), the parameter is changed (Step S7: Change Step), and the process from Step S3 to Step S5 is repeated. On the other hand, if the parameter is not to be changed (Step S6: No), the series of processes shown in Figure 1 is terminated.

[0060] (Embodiment 2) The analysis method of Embodiment 2 simulates the behavior of oxygen molecules when functional groups are present in the pores of the carbon support of a hydrogen fuel cell. The functional group is, for example, a hydrophilic functional group, such as a carboxyl group.

[0061] In the setup step, it is possible to set whether or not to include the functional group model 7 (see Figure 19). In other words, in the setup step, it is possible to set whether or not to place the functional group model 7 within the carbon nanotube model 2. Embodiment 2 exemplifies the case where the functional group model 7 is placed within the carbon nanotube model 2.

[0062] Embodiment 2 illustrates the case where the aperture diameter D1 is set to 4 [nm] for the simulation. Furthermore, Embodiment 2 performs simulations under three conditions: liquid water occupancy of 0%, 25%, and 50%.

[0063] As shown in Figures 19 to 21, in the placement step, the number of water molecule models 3, oxygen molecule models 4, and nitrogen molecule models 5, along with the functional group model 7, set in the setting step, are placed inside the carbon nanotube model 2. Figure 19 shows the molecular model inside the carbon nanotube model when the liquid water occupancy is 0%. Figure 20 shows the molecular model inside the carbon nanotube model when the liquid water occupancy is 25%. Furthermore, Figure 21 shows the molecular model inside the carbon nanotube model 2 when the liquid water occupancy is 50%.

[0064] In the calculation step, the diffusion coefficient of oxygen molecule model 4 is calculated based on the simulation results. Similar to the calculation step of Embodiment 1, in the calculation step of Embodiment 2, the diffusion coefficient of oxygen molecule model 4 is calculated using the mean square displacement of the simulation results. Similar to the calculation step of Embodiment 1, in the calculation step of Embodiment 2, a linear interval is selected from the mean square displacement of the simulation results, and the diffusion coefficient is calculated based on the slope of the linear interval. Figures 22 and 23 are graphs of the linear interval of the mean square displacement of the simulation results.

[0065] Figure 22 is a graph showing the mean square displacement when carbon nanotube model 2 has an aperture diameter of 4 nm, a liquid water occupancy of 25%, and functional group model 7 is placed inside carbon nanotube model 2. Figure 23 is a graph showing the mean square displacement when carbon nanotube model 2 has an aperture diameter of 4 nm, a liquid water occupancy of 50%, and functional group model 7 is placed inside carbon nanotube model 2.

[0066] Similar to the calculation step in Embodiment 1, the calculation step in Embodiment 2 involves performing a linear approximation on the linear interval of the mean squared displacement to calculate the diffusion coefficient.

[0067] Figure 24 is a graph showing the relationship between the diffusion coefficient of oxygen molecule model 4 and the liquid water occupancy rate. As shown in Figure 24, the simulation results in the analysis method according to Embodiment 2 show that the diffusion coefficient decreases as the liquid water occupancy rate increases.

[0068] Furthermore, the diffusion coefficient calculated using the analysis method of Embodiment 2 is smaller at each liquid water occupancy rate compared to the diffusion coefficient calculated using the analysis method of Embodiment 1, which uses an analysis model without functional group model 7 (see Figure 17). When the liquid water occupancy rate is 0%, the diffusion coefficient calculated using the analysis method of Embodiment 2 is particularly smaller than the diffusion coefficient calculated using the analysis method of Embodiment 1. It is thought that the functional group model 7 restricts the movement of oxygen molecule model 4 moving along the wall (or near space R1) of carbon nanotube model 2, which is the reason why the diffusion coefficient calculated using the analysis method of Embodiment 2 is smaller.

[0069] (Embodiment 3) As described above, the analysis method of this disclosure allows for the modification of simulation parameters such as the aperture diameter D1 of carbon nanotube model 2. Embodiment 3 of the analysis method exemplifies the case where the simulation is performed with an aperture diameter D1 of carbon nanotube model 2 set to 10 nm. The simulation conditions are shown in Table 2.

[0070] [Table 2]

[0071] Furthermore, simulations are performed by varying the liquid water occupancy rate. More specifically, in Embodiment 3, simulations are performed for three conditions: liquid water occupancy rates of 0%, 25%, and 50%. In Embodiment 3, the case in which the functional group model 7 is not placed inside the carbon nanotube model 2 is illustrated as an example. Note that the simulation conditions shown in Table 2 are for the case where the liquid water occupancy rate is 50%.

[0072] As shown in Figures 25 to 27, in the placement step, the number of water molecule models 3, oxygen molecule models 4, and nitrogen molecule models 5 set in the setting step are placed inside the carbon nanotube model 2. Figure 25 shows the molecular model inside the carbon nanotube model when the liquid water occupancy rate is 0%. Figure 26 shows the molecular model inside the carbon nanotube model when the liquid water occupancy rate is 25%. Furthermore, Figure 27 shows the molecular model inside the carbon nanotube model 2 when the liquid water occupancy rate is 50%.

[0073] Figure 28 is a graph showing the relationship between the diffusion coefficient of oxygen molecule model 4 and the liquid water occupancy rate in the analysis method of Embodiment 3. As shown in Figure 28, in the simulation results of the analysis method according to Embodiment 3, the diffusion coefficient decreases as the liquid water occupancy rate increases.

[0074] Furthermore, the diffusion coefficient calculated using the analysis method of Embodiment 3 is larger than the diffusion coefficient calculated using the analysis method of Embodiment 1 (see Figure 17) at each liquid water occupancy rate. In the analysis method of Embodiment 3, the opening diameter D1 of the carbon nanotube model 2 is larger than in the analysis method of Embodiment 1, so the space in which the oxygen molecule model 4 can move within the carbon nanotube model 2 is wider. This is thought to be why the diffusion coefficient calculated using the analysis method of Embodiment 3 is larger.

[0075] (modified version) The following lists some modifications of the above embodiment.

[0076] Functionality equivalent to the analysis method according to the above embodiment may be embodied in a (computer) program or a non-temporary recording medium on which the program is stored. A program according to one embodiment is a program that causes one or more processors to execute the analysis method according to the above embodiment.

[0077] The entity that executes the analysis method in this disclosure includes a computer system. The computer system mainly consists of a processor and memory as hardware. The processor executes a program recorded in the memory of the computer system, thereby realizing the function of the entity that executes the analysis method in this disclosure. The program may be pre-recorded in the memory of the computer system, provided via a telecommunications line, or provided on a non-temporary recording medium such as a memory card, optical disk, or hard disk drive that can be read by the computer system. The processor of the computer system consists of one or more electronic circuits including semiconductor integrated circuits (ICs) or large-scale integrated circuits (LSIs). The integrated circuits such as ICs and LSIs referred to here are named differently depending on the degree of integration, and include integrated circuits called system LSIs, VLSIs (Very Large Scale Integration), or ULSIs (Ultra Large Scale Integration). Furthermore, FPGAs (Field-Programmable Gate Arrays) that are programmed after the manufacture of LSIs, or logic devices that allow for the reconfiguration of junction relationships or circuit compartments within LSIs, can also be used as processors. Multiple electronic circuits may be integrated onto a single chip or distributed across multiple chips. Multiple chips may be integrated onto a single device or distributed across multiple devices. The computer system referred to here includes a microcontroller having one or more processors and one or more memories. Therefore, the microcontroller also consists of one or more electronic circuits, including semiconductor integrated circuits or large-scale integrated circuits.

[0078] In the above embodiment, an example was given in which the diffusion coefficient of oxygen molecule model 4 is calculated in the calculation step. However, in the analysis method, the diffusion coefficient of water molecule model 3 or nitrogen molecule model 5 may be calculated in place of or in addition to oxygen molecule model 4 in the calculation step.

[0079] (Appearance) As is clear from the embodiments and modifications described above, the analysis method according to the first embodiment comprises a modeling step, a setting step, a simulation step, and a calculation step. In the modeling step, the carbon support of the hydrogen fuel cell is modeled as a cylindrical carbon nanotube model (2). In the setting step, the number of water molecule models (3), oxygen molecule models (4), and nitrogen molecule models (5) to be placed inside the carbon nanotube model (2) is set. In the simulation step, a simulation is performed on the diffusion of water molecule models (3), oxygen molecule models (4), and nitrogen molecule models (5) inside the carbon nanotube model (2). In the calculation step, the diffusion coefficient of the oxygen molecule model (4) is calculated based on the simulation results.

[0080] According to this embodiment, the behavior of oxygen molecules within the pores of the carbon support can be predicted.

[0081] In the second embodiment of the analysis method, in the first embodiment, the setting step allows setting whether or not to place a functional group model (7) within the carbon nanotube model (2).

[0082] According to this embodiment, it is possible to predict the behavior of oxygen molecules when functional groups are present in the pores of the carbon support.

[0083] The analysis method according to the third embodiment involves determining the opening diameter (D1) of the carbon nanotube model (2) in the modeling step, as in the first or second embodiment.

[0084] According to this embodiment, simulations can be performed using carbon nanotube models of various sizes (2).

[0085] The analysis method according to the fourth embodiment involves determining the axial length (D2) of the carbon nanotube model (2) in the modeling step, according to any of the first to third embodiments.

[0086] According to this embodiment, simulations can be performed using carbon nanotube models of various sizes (2).

[0087] The analysis method according to the fifth embodiment is as follows: In any of the first to fourth embodiments, in the setting step, the number of oxygen molecule models (4) and nitrogen molecule models (5) is set based on the ratio of oxygen molecules to nitrogen molecules in the air.

[0088] According to this embodiment, the accuracy of the analysis can be improved.

[0089] The analysis method according to the sixth embodiment involves, in any of the first to fifth embodiments, modeling a carbon nanotube model (2) using a graphene model (6) and chiral vectors in the modeling step.

[0090] The analysis method according to the seventh embodiment involves performing a simulation using molecular dynamics in the simulation step according to any of the first to sixth embodiments.

[0091] Configurations other than those in the first embodiment are not essential to the analysis method and can be omitted as appropriate.

[0092] The program relating to the eighth aspect is a program that causes one or more processors to execute the analysis method relating to any of the first to seventh aspects.

[0093] According to this embodiment, the behavior of oxygen molecules within the pores of the carbon support can be predicted. [Explanation of Symbols]

[0094] 2. Carbon Nanotube Model 3. Water molecule model 4. Oxygen Molecular Model 5. Nitrogen Molecular Model 6 Graphene Models 7 Functional Group Model D1 Opening diameter D2 Length

Claims

1. A modeling step to model the carbon support of a hydrogen fuel cell as a cylindrical carbon nanotube model, A setting step of setting the number of water molecule models, oxygen molecule models, and nitrogen molecule models to be placed within the carbon nanotube model, A simulation step in which simulations are performed on the diffusion of the water molecule model, the oxygen molecule model, and the nitrogen molecule model within the carbon nanotube model, A calculation step to calculate the diffusion coefficient of the oxygen molecule model based on the results of the simulation, Having, Analysis method.

2. In the setting step, it is possible to set whether or not to place the functional group model within the carbon nanotube model. The analysis method according to claim 1.

3. In the modeling step, the aperture diameter of the carbon nanotube model is determined. The analysis method according to claim 1.

4. In the modeling step, the axial length of the carbon nanotube model is determined. The analysis method according to claim 1.

5. In the setting step, the number of each of the oxygen molecule model and the nitrogen molecule model is set based on the ratio of oxygen molecules to nitrogen molecules in the air. The analysis method according to claim 1.

6. In the modeling step described above, the carbon nanotube model is modeled using a graphene model and chiral vectors. The analysis method according to claim 1.

7. In the simulation step, the simulation is performed using molecular dynamics. The analysis method according to any one of claims 1 to 6.

8. To cause one or more processors to execute the analysis method described in any one of claims 1 to 6, program.

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