Method for reconstructing catalyst layer structure of proton exchange membrane fuel cell based on transmission electron microscope tomography technology

Abstract

A method for reconstructing a catalyst layer structure of a proton exchange membrane fuel cell based on a transmission electron microscope tomography technology comprises the following steps: determining the apparent density of carbon particles of a catalyst layer according to an initial feed ratio and the size of the catalyst layer, and obtaining the volume fraction of each component; cesium ion dyeing is conducted on the catalyst layer, distribution of all component elements (carbon, platinum and cesium) of the catalyst layer is extracted through transmission electron microscope tomography and an energy disperse spectroscopy technology, the gray threshold value is adjusted, and a three-dimensional structure of a carbon skeleton, an ionomer and platinum is separated out; segmenting the carbon skeleton by using a watershed algorithm, and extracting geometric information of each carbon particle; calculating a morphological parameter k of a carbon skeleton according to the geometrical information of the carbon particles; generating a carbon skeleton in a self-defined space according to the obtained morphological parameter k, and generating platinum particles and an ionomer by using a random four-parameter method to obtain a complete three-dimensional microstructure of the catalyst layer; the method can be applied to the fields of porous electrode structure characterization, morphological analysis, simulation structure generation and the like, and has the characteristics of high precision and capability of accurately capturing the structural characteristics of the catalyst layer porous medium.

Description

Technical Field

[0001] This invention relates to the field of energy device technology, and in particular to a method for reconstructing the catalytic layer structure of a proton exchange membrane fuel cell. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) are an important device for hydrogen energy utilization. The catalyst layer, as the most complex component of a PEMFC, presents significant challenges to experimental research due to its intricate multi-scale structure and complex coupled transport processes. In-situ, online observation of the reaction and transport processes occurring within the pore scale of the catalyst layer using existing experimental techniques remains extremely difficult. Numerical simulations are necessary to study these internal transport processes, and the consistency between the simulated and real structures affects the accuracy and reliability of the calculations. Therefore, to improve simulation accuracy, the internal structure needs to be reproduced as accurately as possible.

[0003] Currently, some methods have been developed to generate catalyst layer structures using random distributions, but most of these methods rely on empirical values ​​and lack supporting data from actual catalyst layers. For example, in the 2024 study by Song et al. [SONG H, SHAO X, ZHANG H, et al. Effects of Nafion content in the catalyst layer of PEMFC on the transport phenomenon among nanoscale particles [J]. International Journal of HydrogenEnergy, 2024, 67: 282–93.], the generation method for each component within the catalyst layer was based on random values, lacking a quantitative relationship between the actual structure and the generated structure. There is a lack of a highly accurate method for reconstructing the true structure of the catalyst layer, which could abstract parameters from the real structure and generate a new structure for further research into the microscopic mechanisms within the catalyst layer. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the present invention aims to provide a high-precision reconstruction method for the catalyst layer structure of proton exchange membrane fuel cells based on transmission electron microscopy tomography. Based on transmission electron microscopy tomography, image processing, structural parameter calculation and structure generation technology, the method achieves high-precision and high-reduction numerical reconstruction of the catalyst layer structure, which has the characteristics of high precision and accurate capture of the porous media structure features of the catalyst layer.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A high-precision method for reconstructing the catalyst layer structure of a proton exchange membrane fuel cell based on transmission electron microscopy tomography includes the following steps: Step 1: Calculate the volume fraction of carbon particle skeleton, platinum particles and ionomers in the catalyst layer based on the initial feed ratio, catalyst layer thickness and porosity of the fuel cell membrane electrode; wherein, the initial feed ratio includes platinum loading, the mass ratio of platinum catalyst to carbon support Pt / C, and the mass ratio of ionomers to carbon particles I / C. Step 2: Cesium ion staining is performed on the catalyst layer sample, and three-dimensional distribution images of carbon, platinum, and cesium elements are obtained by transmission electron microscopy tomography combined with energy dispersive spectroscopy; the carbon particle framework structure is separated from the three-dimensional distribution images by grayscale thresholding. Step 3: Apply the watershed algorithm to the carbon particle skeleton structure obtained in Step 2 to segment it into multiple independent carbon particles, and extract the center position, volume and surface area of ​​each carbon particle. Step 4: Based on the volume and surface area of ​​each carbon particle obtained in Step 3, calculate the equivalent sphere volume radius of each carbon particle and the equivalent surface area radius of the overall carbon skeleton; calculate the maximum center-to-center distance between carbon particles based on the center position of each carbon particle. L max Based on this, the morphological parameters of the carbon particle framework were calculated. k Simultaneously, the particle size distribution and overlap distance distribution of carbon particles were statistically analyzed. Step 5: In a custom three-dimensional space, using the sphere connection method, based on the morphological parameter k, carbon particle size distribution, and overlap distance distribution obtained in Step 4, a carbon particle skeleton structure with the volume fraction determined in Step 1 is generated. Step 6: On the surface of the carbon particle skeleton generated in step 5, platinum particles and ionomers are grown sequentially using the random growth four-parameter method QSGS until their volume fractions reach the volume fractions of platinum particles and ionomers calculated in step 1, thereby obtaining a complete three-dimensional microstructure of the catalyst layer.

[0006] The thickness of the catalyst layer mentioned in step 1 was obtained by scanning electron microscopy, and the porosity was determined by mercury intrusion porosimetry. The ionomer was a perfluorosulfonic acid (PFSA) ionomer, and the platinum particle density was 21.45 g·cm³. -3 The density of the ionomer is 1.9 g·cm³. -3 ; The mass and volume of each component are expressed as follows: (1) (2) (3) (4) (5) in, , and These represent the mass of platinum particles, porous carbon particles, and ionomers per unit area, respectively. This is the platinum loading; , and These represent the volumes of the porous carbon particle framework, platinum particles, and ionomers per unit area, respectively. , and The densities of porous carbon particles, platinum particles, and ionomers are represented respectively; the porosity of the catalyst layer is expressed as... (6) The apparent density of porous carbon particles is calculated by combining the porosity expression (6) with the mass-volume relationship of each component (3)-(5), and the volume fractions of carbon particle skeleton, platinum particles and ionomers are obtained by substituting them into equation (3)-(5).

[0007] The cesium ion staining in step 2 specifically includes: pulverizing the catalyst layer and adding it to 50–150 mL of deionized water containing 0.01–0.03 mol cesium sulfate, stirring for 5–15 minutes; then adding 0.1–0.2 g of catalyst layer powder, centrifuging at 8000–10000 rpm for 3–5 minutes, washing the precipitate with deionized water and centrifuging 3–5 times, and then vacuum drying at 60–100 ℃ for 8–16 hours; taking 0.05–0.2 g of the stained sample and dispersing it in a solution of deionized water and anhydrous ethanol at a volume ratio of 2:1 to 1:2, and sonicating for 15–20 minutes to obtain the cesium-stained catalyst layer, which is used as a transmission electron microscopy sample.

[0008] The tilt angle range of the transmission electron microscope tomography scan in step 2 is as follows: The angle ranges from 70° to +70°, with an interval of 1° to 2°. The three-dimensional structure in real space is reconstructed through Fourier transform and inverse transform, and the three-dimensional distribution images of C, Pt, and Cs elements are acquired simultaneously. Gaussian filtering is applied to the images of carbon, platinum, and cesium elements to remove noise. Then, the carbon element image is extracted by grayscale threshold binarization to extract the connected carbon particle skeleton structure.

[0009] The watershed algorithm described in step 3 divides the three-dimensional image of the carbon particle skeleton into multiple catchment basins. C ( m i Each water collection basin corresponds to one carbon particle; the volume and center position of the corresponding carbon particle are obtained by statistically analyzing the number of voxels and the mean coordinates within each water collection basin, as follows: First, the i-th water collection basin in the three-dimensional space occupied by the carbon particle skeleton is defined as: (7) in, C( m i () represents the i-th three-dimensional water collection basin; p Ω represents discrete points in three-dimensional space, which are the basic building blocks of the carbon particle skeleton to be segmented; Ω is the spatial domain of the entire three-dimensional image of the carbon particle skeleton, which includes all the pixels in the entire carbon particle skeleton. d ( p , m i () represents a discrete point in three-dimensional space. p To the seed point m i The distance; I ( m i The image intensity at the seed point is denoted as ; the water level hyperplane, i.e., the boundary of the water level within the carbon particle framework, is defined as: (8) T h For the water level hyperplane, h This is the water level threshold. I (p) represents the image intensity at a discrete point p in three-dimensional space; The process of setting up the expansion of the water collection basin: (9) The watershed surface, i.e., the ridge separating carbon particles, is defined as the set of points occupied by the carbon particle skeleton that does not belong to any catchment basin: (10) The three-dimensional segmentation results of each carbon particle within the carbon particle skeleton are obtained; and the center position, volume and surface area of ​​each carbon particle are extracted.

[0010] The specific method for step 4 is as follows: Carbon particles with an equivalent diameter of less than 5 nm were screened out to eliminate noise; the maximum center-to-center distance between carbon particles within the carbon particle framework was statistically determined using the center position of each carbon particle obtained in step 3. L max Finally, the morphological parameters of the carbon particle framework were obtained. k : (11) in, d The radius of the equivalent surface area of ​​the carbon particle skeleton; Overlap distance between carbon particles δ over Calculate using the following formula: (12) in, R This represents the equivalent spherical volume radius of each carbon particle. x , y , z Let each represent the coordinate of the center of each carbon particle. The particle size distribution of carbon particles in the carbon skeleton is obtained by sorting the equivalent sphere volume radius of each carbon particle from small to large. The overlap distance between carbon particles is obtained by sorting the overlap distance between carbon particles from small to large according to Equation (12).

[0011] In step 5, when generating the carbon particle framework structure with the volume fraction determined in step 1: the carbon particles are considered to be smooth spheres, and as the number of carbon particles increases, they gradually connect to form a carbon particle framework; when the number of carbon particles in the carbon particle framework is less than 2, the newly added carbon particles are randomly connected to the existing carbon particles; when the number of carbon particles is greater than 2, the framework is first determined according to morphological parameters. k and normalized distance d i Calculate the probability that each existing carbon particle is selected as a connection target. p i The connection object is determined by comparing it with a random number; then, the center position of the new carbon particle is determined in a region around the connection object with a width equal to the statistically obtained overlap distance, based on a similar probability mechanism; the above process is repeated until the carbon particle skeleton volume fraction satisfies the calculation result of step 1. (13) In step 6, during the growth of platinum particles, random numbers are generated at each pixel on the surface of the carbon particle framework. x i If it is less than the preset generation probability p ,0< p If the value is less than 1, it is marked as a platinum particle seed; then it expands along the six-neighbor direction with the same or different growth probabilities until the total integral of the platinum particles reaches the target value; the growth of the ionomer takes place on the composite surface of the carbon particle skeleton and the generated platinum particles, using the same random growth mechanism, until the volume fraction of the ionomer reaches the target value.

[0012] A high-precision proton exchange membrane fuel cell catalyst layer structure based on transmission electron microscopy tomography is constructed using the method described above.

[0013] Compared with the prior art, the present invention has at least the following beneficial effects: 1. This invention provides a high-precision method for reconstructing the catalyst layer structure of a proton exchange membrane fuel cell based on transmission electron microscopy (TEM) tomography. Step 4 characterizes the carbon particle framework morphology within the actual catalyst layer using the tomography technique from step 2, and segments the carbon particles using the image processing technique from step 3, calculating the carbon framework structure factor. kStep 5 utilizes this morphological factor k The generation of carbon particle framework, and the generation of platinum particles and ionomers in step 6, enables accurate characterization and three-dimensional reconstruction of the fuel cell catalyst layer structure, which has certain practical value for refined research on the internal mechanism of the catalyst layer.

[0014] 2. Steps 2, 3, and 4 of this invention provide a systematic method for extracting the morphology of the carbon particle framework within the catalyst layer. Step 2 utilizes advanced transmission electron microscopy tomography to obtain three-dimensional images of each component within the catalyst layer; Step 3 uses a watershed algorithm to process the three-dimensional images and extract each carbon particle within the carbon particle framework; Step 4 extracts the morphological factors of the carbon framework structure of the catalyst layer based on geometric calculations. k It captured the main morphological features, which are reflected in the morphological factors of the carbon particle skeleton. k This morphological factor can well reflect the extended state of the carbon particle skeleton.

[0015] 3. Steps 5 and 6 of this invention provide a multi-step structure generation method for carbon framework / ionomer platinum particles. Step 5 involves using the morphology factor obtained in step 4. k Step 1 involves determining the carbon particle size distribution and overlap distance distribution to generate the carbon particle framework structure. Step 6 uses a randomized four-parameter generation method to successively generate platinum particle structures and ionomer structures on the carbon particle framework. This process conforms to the actual growth law inside the fuel cell catalyst layer and can also satisfy the generation of various different catalyst layer structures.

[0016] In summary, the transmission electron microscopy tomography, image processing, and structure generation techniques employed in this invention have the advantages of good reproducibility of catalyst layer structure, rapid and accurate carbon particle skeleton segmentation, and structure generation that conforms to the characteristics of real catalyst layer structure. This method has broad application prospects in the study of various porous structures, including: extraction of membrane fuel cell catalyst layers and various porous electrode structures, and generation of various porous electrode structures. Attached Figure Description

[0017] Figure 1 This is a flowchart of the structural reconstruction process of the present invention.

[0018] Figure 2 This is a diagram illustrating the structural extraction process of the present invention.

[0019] Figure 3 This invention extracts a typical carbon particle size distribution map.

[0020] Figure 4 This invention extracts a typical overlap distribution map.

[0021] Figure 5 This invention generates a typical three-dimensional structural diagram.

[0022] Figure 6 This invention generates typical structural cross-sectional diagrams.

[0023] Figure 7 This is a comparison between the aperture distribution of the present invention and the actual structural distribution.

[0024] Figure 8 It is a comparison of error curves between multi-scale simulations of generated structures and empirical values. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] This invention proposes a high-precision method for reconstructing the catalyst layer structure of a proton exchange membrane fuel cell based on transmission electron microscopy tomography, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps: The data in step 1 mainly include: the initial feed ratio of the fuel cell membrane electrode assembly (Pt / C and I / C), the platinum loading of the catalyst layer, the catalyst layer thickness measured by scanning electron microscopy, and the catalyst layer porosity measured by mercury intrusion porosimetry. Given the above parameters of initial feed ratio, platinum loading, thickness, and porosity, the mass and volume of each component of the fuel cell can be expressed as follows: (1) (2) (3) (4) (5) in, , and These represent the mass of porous carbon particles, platinum particles, and ionomers per unit area, respectively. , and These represent the volumes of the porous carbon particle framework, platinum particles, and ionomers per unit area, respectively. , and These represent the densities of porous carbon particles, platinum particles, and ionomers, respectively. =21.45 g·cm -3 , =1.9 g·cm -3 According to formulas (1)-(5), the porosity of the catalyst layer is expressed as: (6) The apparent density of porous carbon particles and the volume fractions of carbon particle skeleton, platinum particles and ionomers can be calculated by combining these equations with equations (3)-(5). The steps for staining the sample and processing the three-dimensional structure based on transmission electron microscopy tomography in step 2 are as follows: 1) Sample staining treatment To improve the visibility of the ionomers, cesium ions were used to stain them. First, the cathode catalyst layer was pulverized. Then, 0.01 mol of cesium sulfate (CsSO4) was dissolved in 50 ml of deionized water and stirred for 10 minutes to prepare the staining solution. Next, 0.1 g of catalyst layer powder was added to the solution, and the mixture was centrifuged at 9000 rpm for 3 minutes. The resulting precipitate was washed with deionized water and centrifuged three times. Finally, the washed sample was vacuum-dried at 80 °C for 12 hours to obtain the stained sample. 0.1 g of the stained catalyst layer powder was dispersed in a 1:1 solution of deionized water and ethanol, and sonicated for 15 minutes to obtain the sample solution for transmission electron microscopy (TEM) tomography.

[0027] 2) Transmission electron microscopy (TEM) tomography technique was used to characterize the three-dimensional micro / nano structure of the catalyst layer. The prepared sample solution was placed under a field emission transmission electron microscope (FET) and tilted at 1° intervals to capture the maximum rotation range of the three-dimensional structure sample from -70° to +70°. A charge-coupled device (CCD) camera was used to record the original two-dimensional projection images of the catalyst layer at different tilt angles. A Fourier transform was performed on each captured projection image of the catalyst layer, and the images were filled into the corresponding sections in the three-dimensional Fourier space according to the projection direction. An inverse Fourier transform was then performed to obtain the three-dimensional structure of the catalyst layer in real space.

[0028] During the transmission electron microscope tomography scan of the catalyst layer structure, three-dimensional images of elements such as C, Pt, Cs, F, and S within the catalyst layer are captured simultaneously, including the three-dimensional position of each element and the gray value of each point. Based on the three-dimensional elemental structures obtained by energy dispersive spectroscopy (EDS), the original three-dimensional images of each element were processed. First, the carbon element, representing the carbon particle framework, was processed. Gaussian filtering was used to remove noise from the carbon element. Then, a grayscale threshold was set, and the grayscale data of the three-dimensional carbon element structure were binarized to extract the connected structure of the overall carbon particle framework within the catalytic layer. Subsequently, based on the extracted three-dimensional carbon framework structure, the volume ratios of the carbon particle framework, platinum particles, and ionomers were calculated according to the densities of platinum particles and ionomers, as well as the feed ratios (platinum loading, I / C, and Pt / C). Then, platinum (representing platinum particles) and cesium (representing ionomers) were binarized using threshold settings to ensure accurate volume ratios of each component within the catalyst layer. Finally, a three-dimensional catalyst layer structure consistent with the feed ratios set during preparation was obtained.

[0029] Step 3 uses the watershed algorithm to segment the carbon particle framework structure obtained in Step 2, extracting the position, volume, and surface area of ​​each carbon particle within the framework. The steps are as follows: Based on the carbon particle skeleton structure obtained in step 2, the watershed algorithm is used to identify and segment the regions connecting the carbon particles. The detailed steps of the watershed algorithm are as follows: First, each water collection basin within the three-dimensional space occupied by the carbon particle skeleton is defined as: (7) in, C ( m i ) represents the i-th three-dimensional water collection basin, which is the set of voxels (points occupied by carbon particle skeleton structures) belonging to the seed point in space, and is the basic regional unit of watershed division. p Ω represents a voxel (i.e., a discrete point in three-dimensional space) in a 3D image, which is the basic building block of the carbon particle skeleton to be segmented; Ω is the spatial domain of the entire 3D image of the carbon particle skeleton, which contains all the pixels in the carbon particle skeleton to be analyzed. d ( p , m i (voxel) p To the seed point m i The distance is used to quantify spatial relationships. I ( m i The image intensity at the seed point represents the attribute characteristics of that seed point. Secondly, the water level hyperplane is defined, i.e., the boundary of the water level determination region within the carbon particle framework, is: (8) T h The water level hyperplane is the strength. I (p) does not exceed the threshold h A collection of voxels h This is the water level threshold. I (p) sets the expansion process of the water basin for the image intensity at voxel p: (9) The watershed surface (the ridge separating carbon particles) is defined as a set of voxels that do not belong to any catchment basin, and can be represented as: (10) This method yields relatively accurate three-dimensional segmentation results for each carbon particle within the carbon particle framework, as shown in the following figure. Figure 2 As shown. Then, the number of pixels and the average coordinates within the water collection basin representing each carbon particle were counted to obtain the volume and center position of each carbon particle.

[0030] In step 4, the equivalent spherical volume radius of each carbon particle is calculated, and the morphological parameters of the carbon skeleton are calculated based on this. k Mainly includes: Based on the carbon particle framework and carbon particle information obtained in step 3, including the surface area of ​​the carbon particle framework, the center position and volume of each carbon particle, etc., the equivalent surface area radius of the carbon particle framework is calculated based on the statistically obtained surface area. d The equivalent volume radius of each carbon particle was calculated using the equivalent spherical volume radius method, and particles with a diameter less than 5 nm were screened out to eliminate noise from excessively small carbon particles. The maximum center-to-center distance between carbon particles within the carbon particle framework was calculated by statistically analyzing the center positions of each carbon particle. L max Finally, the morphology factor of the carbon particle framework was obtained. k : (11) in, d The radius of the equivalent surface area of ​​the carbon particle skeleton; Overlap distance between carbon particles δ over Calculate using the following formula: (12) in, δ over Indicates the overlap distance between carbon particles. R This represents the equivalent radius of the carbon particle. x , y , z Let represent the coordinates of the carbon particle centers, respectively. Based on this formula, the overlap distance for each overlap, represented by the difference between the sum of the equivalent volume radii of the carbon particles and the center distance, can be obtained, and the overlap distance distribution can be statistically analyzed. The statistical results are as follows: Figure 3 and Figure 4 As shown.

[0031] Step 5 involves using the carbon particle framework morphology factor obtained in step 4. kThe carbon particle radii and overlap distances obtained are used to generate a carbon particle framework, and the steps include: Assuming all carbon particles are smooth spheres, they gradually connect to form a carbon particle skeleton as the number of carbon particles increases. When the number of carbon particles in the skeleton is less than 2, newly added carbon particles are randomly connected to existing carbon particles. When the number of carbon particles is greater than 2, a new carbon particle is added by determining the positions of both the connected carbon particles and the newly added carbon particle. The first step in adding carbon particles to generate the carbon particle skeleton is to find potential carbon particles that can connect to the newly added carbon particle. First, the distance between the centers of the i-th and j-th carbon particles is calculated. Then, the maximum distance between all particles can be obtained. L max ; then, L max Dividing by the sum of the center-to-center distances of all carbon particles yields the normalized value di. The probability that the i-th carbon particle is a connected carbon particle is: (13) in, k This is the morphology factor for each carbon particle's framework; subsequently, when generating new carbon particles within the carbon particle framework, the existing i carbon particles are iterated sequentially, generating random numbers between 0 and 1 for each. x i According to its relationship with p i The relationship determines whether it is a new carbon particle to be bonded to. If x i Less than p i If the i-th existing carbon particle is selected, then the i-th existing carbon particle is set as the carbon particle to be connected. The second step is to generate a region where the center of the new carbon particle can be inserted, and the width of this region is the overlap distance between carbon particles calculated in step 4. The third step is to place the new carbon particle. Similar to the first step, the distance from the node in the region where the new carbon particle can be inserted to the center of all other carbon particles is denoted as . L i The probability that each point within the region will be the center of a new carbon particle is... p i At the same time, generate random numbers x i .if x i Less than p i If the desired carbon particle size is achieved, then this node is set as the center of the new carbon particle. The three-dimensional structure of the catalyst layer is set to 330×330×330, with each pixel representing 3 nm. This process is repeated within this space, continuously inserting new carbon particles until the volume fraction of the carbon particle framework calculated in step 1 is met, thus generating a complete carbon particle framework structure.

[0032] Step 6 uses a random four-parameter growth method (quartet structure generation set, QSGS) to generate platinum particles and ionomers on the surface of the carbon particle framework, respectively, to obtain a complete catalyst layer microstructure. The steps are as follows: Platinum particles are randomly distributed on the surface of the carbon particle framework. By traversing the carbon particle surface, a random number is generated at each node on the carbon particle surface. x .if x Less than probability p (Set to 0.001) If a point is designated as a platinum particle, it is considered a seed site. If a point in space has two adjacent points that are platinum particles, both points become seeds. Otherwise, growth begins from an isolated platinum particle seed in a 3D space containing both carbon and platinum particle seeds. Six random numbers are generated for each of the six points adjacent to the seed in the six directions (up, down, left, right, front, back). If the random number is less than the seed growth probability... p This point also becomes the seed. Platinum particles are repeatedly grown within the defined custom space until their volume reaches the volume fraction of platinum particles calculated in step 1. After this, the same random growth four-parameter method is used to traverse the carbon particle framework and the platinum particle surface, according to the set growth probability. p Ionomers are generated until the ionomer volume reaches the ionomer volume fraction calculated in step 1. Ultimately, a complete three-dimensional catalytic layer structure is generated, as shown below. Figure 5 and Figure 6 As shown.

[0033] To eliminate the randomness of single-generation structures, multiple sets of structures were generated to obtain more stable structural features. The pore size distribution of each set of structures was calculated using a thirteen-direction method. Following thirteen directions (3 coordinate axes, 6 planar diagonals, and 4 body diagonals) uniformly distributed in three-dimensional space within the catalyst layer, each pixel was traversed along each direction, recording the length of the longest continuous pore segment in that direction, i.e., the equivalent pore size of that pore. This was then compared and verified with the pore size distribution obtained by experimental methods. Figure 7 As shown, the generated structure accurately reproduces the pore characteristics of the real structure.

[0034] Subsequently, using a pore-scale simulation method based on the lattice-Boltzmann method, the effective transport coefficients of oxygen, protons, and electrons within the catalyst layer were calculated and input into a macroscopic model to predict fuel cell performance. The results showed that the simulated values ​​agreed well with the experimental values, and the average error was significantly reduced compared to the empirical values ​​used, decreasing from approximately 5% to below 2.5%. The error variation is shown below. Figure 8 As shown.

Claims

1. A method for reconstructing the catalyst layer structure of a proton exchange membrane fuel cell based on transmission electron microscopy tomography, characterized in that, Includes the following steps: Step 1: Calculate the volume fraction of carbon particle skeleton, platinum particles and ionomers in the catalyst layer based on the initial feed ratio, catalyst layer thickness and porosity of the fuel cell membrane electrode; wherein, the initial feed ratio includes platinum loading, the mass ratio of platinum catalyst to carbon support Pt / C, and the mass ratio of ionomers to carbon particles I / C. Step 2: Cesium ion staining is performed on the catalyst layer sample, and three-dimensional distribution images of carbon, platinum, and cesium elements are obtained by transmission electron microscopy tomography combined with energy dispersive spectroscopy; the carbon particle framework structure is separated from the three-dimensional distribution images by grayscale thresholding. Step 3: Apply the watershed algorithm to the carbon particle skeleton structure obtained in Step 2 to segment it into multiple independent carbon particles, and extract the center position, volume and surface area of ​​each carbon particle. Step 4: Based on the volume and surface area of ​​each carbon particle obtained in Step 3, calculate the equivalent sphere volume radius of each carbon particle and the equivalent surface area radius of the overall carbon skeleton; calculate the maximum center-to-center distance between carbon particles based on the center position of each carbon particle. L max Based on this, the morphological parameters of the carbon particle framework were calculated. k Simultaneously, the particle size distribution and overlap distance distribution of carbon particles were statistically analyzed. Step 5: Within the custom 3D space, using the sphere connection method, based on the morphological parameters obtained in Step 4... k The carbon particle size distribution and overlap distance distribution are determined to generate a carbon particle framework structure with the volume fraction determined in step 1. Step 6: On the surface of the carbon particle skeleton generated in step 5, platinum particles and ionomers are grown sequentially using the random growth four-parameter method QSGS until their volume fractions reach the volume fractions of platinum particles and ionomers calculated in step 1, thereby obtaining a complete three-dimensional microstructure of the catalyst layer.

2. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, The thickness of the catalyst layer mentioned in step 1 was obtained by scanning electron microscopy, and the porosity was determined by mercury intrusion porosimetry. The ionomer was a perfluorosulfonic acid (PFSA) ionomer, and the platinum particle density was 21.45 g·cm³. -3 The density of the ionomer is 1.9 g·cm³. -3 ; The mass and volume of each component are expressed as follows: （1） （2） （3） （4） （5） in, , and These represent the mass of platinum particles, porous carbon particles, and ionomers per unit area, respectively. This is the platinum loading; , and These represent the volumes of the porous carbon particle framework, platinum particles, and ionomers per unit area, respectively. , and Represent the densities of porous carbon particles, platinum particles, and ionomers, respectively; the porosity of the catalyst layer is expressed as... （6） The apparent density of porous carbon particles is calculated by combining the porosity expression (6) with the mass-volume relationship of each component (3)-(5), and the volume fractions of carbon particle skeleton, platinum particles and ionomers are obtained by substituting them into equation (3)-(5).

3. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, The cesium ion staining in step 2 specifically includes: pulverizing the catalyst layer and adding it to 50–150 mL of deionized water containing 0.01–0.03 mol cesium sulfate, stirring for 5–15 minutes; then adding 0.1–0.2 g of catalyst layer powder, centrifuging at 8000–10000 rpm for 3–5 minutes, washing the precipitate with deionized water and centrifuging 3–5 times, and then vacuum drying at 60–100 ℃ for 8–16 hours; taking 0.05–0.2 g of the stained sample and dispersing it in a solution of deionized water and anhydrous ethanol at a volume ratio of 2:1 to 1:2, and sonicating for 15–20 minutes to obtain the cesium-stained catalyst layer, which is used as a transmission electron microscopy sample.

4. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, The tilt angle range of the transmission electron microscope tomography scan in step 2 is as follows: The angle ranges from 70° to +70°, with an interval of 1° to 2°. The three-dimensional structure in real space is reconstructed through Fourier transform and inverse transform, and the three-dimensional distribution images of C, Pt, and Cs elements are acquired simultaneously. Gaussian filtering is applied to the images of carbon, platinum, and cesium elements to remove noise. Then, the carbon element image is extracted by grayscale threshold binarization to extract the connected carbon particle skeleton structure.

5. A high-precision method for reconstructing the catalyst layer structure of a proton exchange membrane fuel cell based on transmission electron microscopy tomography, characterized in that, The watershed algorithm described in step 3 divides the three-dimensional image of the carbon particle skeleton into multiple catchment basins. C ( m i Each water collection basin corresponds to one carbon particle; the volume and center position of the corresponding carbon particle are obtained by statistically analyzing the number of voxels and the mean coordinates within each water collection basin, as follows: First, the i-th water collection basin in the three-dimensional space occupied by the carbon particle skeleton is defined as: （7） in, C ( m i () represents the i-th three-dimensional water collection basin; p Ω represents discrete points in three-dimensional space, which are the basic building blocks of the carbon particle skeleton to be segmented; Ω is the spatial domain of the entire three-dimensional image of the carbon particle skeleton, which includes all the pixels in the entire carbon particle skeleton. d ( p , m i () represents the distance from a discrete point p in three-dimensional space to the seed point. m i The distance; I ( m i The image intensity at the seed point is denoted as ; the water level hyperplane, i.e., the boundary of the water level within the carbon particle framework, is defined as: （8） T h For the water level hyperplane, h This is the water level threshold. I (p) represents the image intensity at a discrete point p in three-dimensional space; The process of setting up the expansion of the water collection basin: （9） The watershed surface, i.e., the ridge separating carbon particles, is defined as the set of points occupied by the carbon particle skeleton that does not belong to any catchment basin: （10） The three-dimensional segmentation results of each carbon particle within the carbon particle skeleton are obtained; and the center position, volume and surface area of ​​each carbon particle are extracted.

6. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, The specific method for step 4 is as follows: Carbon particles with an equivalent diameter of less than 5 nm were screened out to eliminate noise; the maximum center-to-center distance between carbon particles within the carbon particle framework was statistically determined using the center position of each carbon particle obtained in step 3. L max Finally, the morphological parameters of the carbon particle framework were obtained. k : （11） in, d The radius of the equivalent surface area of ​​the carbon particle skeleton; Overlap distance between carbon particles δ over Calculate using the following formula: （12） in, R This represents the equivalent spherical volume radius of each carbon particle. x , y , z Let each represent the coordinate of the center of each carbon particle. The particle size distribution of carbon particles in the carbon skeleton is obtained by sorting the equivalent sphere volume radius of each carbon particle from small to large. The overlap distance between carbon particles is obtained by sorting the overlap distance between carbon particles from small to large according to Equation (12).

7. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, In step 5, when generating the carbon particle framework structure with the volume fraction determined in step 1: the carbon particles are considered to be smooth spheres, and as the number of carbon particles increases, they gradually connect to form a carbon particle framework; when the number of carbon particles in the carbon particle framework is less than 2, the newly added carbon particles are randomly connected to the existing carbon particles; when the number of carbon particles is greater than 2, the framework is first determined according to morphological parameters. k and normalized distance d i Calculate the probability that each existing carbon particle is selected as a connection target. p i The connection object is determined by comparing it with a random number; then, the center position of the new carbon particle is determined in a region around the connection object with a width equal to the statistically obtained overlap distance, based on a similar probability mechanism; the above process is repeated until the carbon particle skeleton volume fraction satisfies the calculation result of step 1. （13）。 8. The high-precision proton exchange membrane fuel cell catalyst layer structure reconstruction method based on transmission electron microscopy tomography technology according to claim 1, characterized in that, In step 6, during the growth of platinum particles, random numbers are generated at each pixel on the surface of the carbon particle framework. x i If it is less than the preset generation probability p 0 < p If the value is less than 1, it is marked as a platinum particle seed; then it expands along the six-neighbor direction with the same or different growth probabilities until the total integral of the platinum particles reaches the target value; the growth of the ionomer takes place on the composite surface of the carbon particle skeleton and the generated platinum particles, using the same random growth mechanism, until the volume fraction of the ionomer reaches the target value.

9. A high-precision proton exchange membrane fuel cell catalyst layer structure based on transmission electron microscopy tomography, constructed by any one of claims 1 to 8.

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