A method and system for reconstructing microstructure of aerogel based on potential energy driving

Abstract

The application relates to an aerogel microstructure reconstruction method and system based on potential energy driving, and belongs to the technical field of aerogel materials, solving the problems of low aerogel microstructure reconstruction precision and difficult porosity control in the prior art. The method comprises the following steps: generating a target particle based on aerogel particle characteristics, generating current Brownian motion parameters based on a random diffusion model, calculating aggregation potential when the target particle after displacement based on the current Brownian motion parameters contacts an existing aggregated particle cluster, and determining the target particle and the existing aggregated particle cluster as a current aggregated particle cluster when the potential energy threshold is reached; calculating the number of particles in the current aggregated particle cluster, calculating the current porosity of the current aggregated particle cluster when the contact particle number requirement is met, and outputting the microstructure of the current aggregated particle cluster as the microstructure of the reconstructed target aerogel if the target porosity is reached. The effective control and accurate reconstruction of the porosity of the aerogel microstructure are realized.

Description

Technical Field

[0001] This invention relates to the field of aerogel materials technology, and in particular to a method and system for reconstructing the microstructure of aerogels based on potential energy. Background Technology

[0002] With the development of high technology, aerogel materials, due to their unique nanoporous structure, possess extremely low density, high specific surface area, and excellent thermal insulation / mechanical properties, making them irreplaceable in key fields such as aerospace thermal protection, new energy battery separators, and high-end equipment insulation. Among them, nanoporous overlapping aerogels, through the controllable overlapping of particles to construct a "cross-linking-pore" synergistic structure, significantly improve the material's mechanical stability and optimize heat transfer barrier efficiency, becoming a research hotspot for high-end functional materials.

[0003] However, the complexity of the microstructure of nanoporous-overlapping aerogels (nanoparticle size, dynamically changing particle overlap interfaces, and fractal pore distribution) poses a significant technical challenge for aerosol microstructure reconstruction and analysis. Current technologies rely solely on "geometric contact (center-to-center distance ≤ sum of particle radii)" to determine particle aggregation, failing to consider that particle aggregation in nanoporous-overlapping aerogels essentially depends on a "weak attraction-stable crosslinking" mechanism. This approach deviates from the true physical properties of aerosols and cannot provide a reliable structural basis for simulating the heat transfer and mechanical properties of aerogels. Furthermore, existing technologies assume "no particle overlap" in aerogel nanoparticles, making precise control of porosity impossible.

[0004] Therefore, there is an urgent need for a method to reconstruct the microstructure of aerogels that better matches the physical properties of aerogels, providing a reliable structural basis for simulating the heat transfer and mechanical properties of aerogel materials, which can be widely applied to the analysis and research and development of aerogel materials. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a potential energy-driven aerogel microstructure reconstruction method and system to solve the problems of low accuracy and difficulty in porosity control in existing aerogel microstructure reconstruction.

[0006] On one hand, embodiments of the present invention provide a potential energy-driven method for reconstructing the microstructure of aerogels, comprising the following steps:

[0007] Step 1: Generate target particles based on the characteristics of aerogel particles, and generate current Brownian motion parameters based on a random diffusion model;

[0008] Step 2: Control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster;

[0009] Step 3: When the target particle comes into contact with the existing aggregated particle cluster, calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster, and determine whether the aggregation potential energy reaches the potential energy threshold.

[0010] Step 4: When the aggregation potential energy reaches the potential energy threshold, the target particle and the existing aggregated particle cluster are identified as the current aggregated particle cluster;

[0011] Step 5: Calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle count requirement;

[0012] Step 6: When the number of particles meets the requirement for the number of contact particles, calculate the current porosity of the current aggregated particle cluster and determine whether the current porosity has reached the target porosity;

[0013] Step 7: If the target porosity is achieved, the microstructure of the current aggregated particle cluster is output as the microstructure of the reconstructed target aerogel.

[0014] Furthermore, the particle features include particle size features and the boundary of the simulated region;

[0015] Target particles are generated based on aerogel particle characteristics, including:

[0016] Obtain the boundary and particle size characteristics of the simulated region;

[0017] Based on the particle size characteristics, the particle radius is generated using a normal distribution.

[0018] Based on the boundary, the simulation region is divided into an internal sub-region and an edge sub-region, and an initial position is generated in the internal sub-region or the edge sub-region; wherein the initial position is generated with the same probability in the internal sub-region and the edge sub-region.

[0019] The target particle is generated based on the initial position and the particle radius.

[0020] Further, determining whether the displaced target particle comes into contact with the existing aggregated particle cluster includes:

[0021] Calculate the distance between the target particle after displacement and each aerogel particle in the existing aggregated particle cluster;

[0022] Determine whether the distance reaches the contact distance threshold;

[0023] If the contact distance threshold is reached, the target particle after displacement is considered to be in contact with the existing aggregated particle cluster.

[0024] Further, when the target particle comes into contact with the existing aggregated particle cluster, the aggregation potential energy of the target particle and the existing aggregated particle cluster is calculated, and it is determined whether the aggregation potential energy reaches a potential energy threshold, including:

[0025] Extract the aerogel particles that are in contact with the target particles from the existing aggregated particle clusters and use them as contact particles;

[0026] The aggregation potential energy corresponding to the target particle and each of the contacting particles is calculated using the LJ potential energy function; wherein, the LJ potential energy function is expressed as:

[0027] In the formula The gathering potential energy, The depth of the LJ potential well. d is the distance from the zero potential energy point of LJ, and d is the distance between the target particle and the contacting particle;

[0028] Determine whether the accumulated potential energy has reached the potential energy threshold.

[0029] Furthermore, when the accumulation potential energy does not reach the potential energy threshold, new Brownian motion parameters are generated based on the random diffusion model as the current Brownian motion parameters;

[0030] Repeat steps 2-3.

[0031] Further, calculating the current porosity of the currently aggregated particle cluster includes:

[0032] Calculate the total volume of the currently aggregated particle cluster;

[0033] Calculate the total overlap volume of the currently aggregated particle cluster;

[0034] The current porosity is calculated based on the total volume and the total overlapping volume.

[0035] Further, the total overlap volume of the currently aggregated particle cluster is calculated, including:

[0036] Select any two aerogel particles from the current aggregated particle cluster as the current particle pair;

[0037] Calculate the spacing between the current particle pairs;

[0038] The overlap of the current particle pair is determined based on the spacing.

[0039] Based on the aforementioned overlap, an overlap volume calculation method is selected to calculate the overlap volume of the current particle pair;

[0040] The total overlap volume of the current aggregated particle cluster is determined based on the overlap volume of all the current particle pairs.

[0041] Further, two aerogel particles are randomly selected from the current aggregated particle cluster as the current particle pair, including:

[0042] The spatial distribution density of the current aggregated particle cluster is determined by using a real-time density statistical method based on spatial grids.

[0043] Based on the spatial distribution density of the particles, the current aggregated particle cluster is divided into multiple aggregated particle sub-clusters; wherein, the aggregated particle sub-clusters include multiple aerogel particles;

[0044] Select one aerogel particle from the aggregated particle sub-cluster as the current particle, and select one aerogel particle other than the current particle from the current aggregated particle cluster as the paired particle. The current particle and the paired particle are then considered as the current particle pair.

[0045] Furthermore, if the target porosity is not achieved, the current aggregated particle cluster is considered as the existing aggregated particle cluster.

[0046] New aerogel particles are generated based on the particle characteristics as the target particles, and new Brownian running parameters are generated based on the random diffusion model as the current Brownian running parameters.

[0047] Repeat steps 2 through 6.

[0048] On the other hand, embodiments of the present invention provide a potential energy-driven aerogel microstructure reconstruction system, comprising:

[0049] The particle generation module is used to generate target particles based on the characteristics of aerogel particles;

[0050] The Brownian motion simulation module is used to generate current Brownian motion parameters based on a random diffusion model, control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster.

[0051] The potential energy calculation module is used to calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster when the target particle comes into contact with the existing aggregated particle cluster, and to determine whether the aggregation potential energy reaches the potential energy threshold.

[0052] The particle cluster generation module is used to determine the target particle and the existing aggregated particle cluster as the current aggregated particle cluster when the aggregation potential energy reaches the potential energy threshold.

[0053] The particle cluster generation module is also used to calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle number requirement.

[0054] The porosity calculation module is used to calculate the current porosity of the current aggregated particle cluster when the number of particles meets the contact particle number requirement, and to determine whether the current porosity reaches the target porosity.

[0055] The microstructure determination module is used to output the microstructure of the current aggregated particle cluster as the microstructure of the reconstructed target aerogel when the target porosity is reached.

[0056] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0057] 1. By introducing aggregation potential energy and using a dual control mechanism of contact conditions and potential energy threshold, the true aggregation mechanism of aerogel particles, characterized by "weak attraction and stable cross-linking," is restored, improving physical realism and enabling an accurate description of the physical mechanism of aerosols. This results in a more precise output aerogel microstructure, providing a reliable structural basis for simulating the heat transfer and mechanical properties of aerogels. Furthermore, by controlling the number of contact particles, the frequency of porosity calculations is reasonably controlled, reducing computational resource consumption.

[0058] 2. The LJ potential energy function is used to describe the physical properties of "weak attraction-stable cross-linking" of aerogel particles. The 12th term characterizes the short-range repulsive force between particles, avoiding structural distortion caused by excessive particle compression; the 6th term characterizes the long-range attractive force between particles, accurately describing the weak interaction dominated by van der Waals forces; by adjusting the potential well depth and the distance to the zero potential energy point, the interaction strength and range in the aggregation of different types of aerogel particles can be adapted.

[0059] 3. Considering particle overlap, the overlapping volume of particles is introduced and the problem of repeated counting of overlapping volume is corrected to improve the accuracy of porosity calculation. The porosity reaching the target porosity is used as the reconstruction stopping condition to achieve precise control of porosity.

[0060] 4. Based on the spatial distribution density of particles, the current aggregated particle cluster is divided into multiple aggregated particle sub-clusters. Multiple sub-clusters can calculate the particle overlap volume in parallel, which effectively improves the porosity calculation efficiency when large-scale aerogel particle aggregation occurs.

[0061] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0062] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0063] Figure 1 This is a schematic flowchart of a potential energy-driven aerogel microstructure reconstruction method in an embodiment of the present invention.

[0064] Figure 2 This is an example of aerogel microstructure visualization output from an embodiment of the present invention;

[0065] Figure 3 This is an example graph showing the current porosity variation curve in an embodiment of the present invention;

[0066] Figure 4 This is a schematic diagram of the main modules of a potential energy-driven aerogel microstructure reconstruction system in an embodiment of the present invention;

[0067] Figure 5 This is an example diagram of a visual parameter input interface in an embodiment of the present invention. Detailed Implementation

[0068] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0069] A specific embodiment of the present invention discloses a potential energy-driven method for reconstructing the microstructure of aerogels, such as... Figure 1 As shown, including

[0070] Step 1: Generate target particles based on aerogel particle characteristics, and generate current Brownian motion parameters based on a random diffusion model.

[0071] Specifically, it includes:

[0072] Step S11: Generate aerogel particles (i.e., target particles) based on aerogel particle characteristics. Based on the particle characteristic constraints of the aerogel, corresponding target particles are generated for different types of organic aerogels (such as phenolic, melamine-formaldehyde, and silica aerogels). This ensures a high degree of consistency between the generated target particles and the constituent particles of the aerogel to be reconstructed (i.e., the target aerogel), improving the physical realism of subsequent particle aggregation and reconstruction.

[0073] The particle features include particle size features and the boundary of the simulated region. Target particles are generated based on these aerogel particle features, specifically including:

[0074] First, the boundary and particle size characteristics of the simulated region are obtained. Specifically, the boundary and particle size characteristics can be extracted from a database or input through a visualization interface; there are no restrictions here. Furthermore, the obtained boundary and particle size characteristics can be validated to avoid errors in the basic data. For example, setting the particle radius to 1m in the particle size characteristics does not conform to the typical size range of aerogel particles, or setting the target porosity to 1 does not conform to the aerogel aggregation characteristics; these will be flagged.

[0075] Secondly, based on the particle size characteristics, the particle radius is generated using a normal distribution. Specifically, in this embodiment, the particle size characteristics include the mean and standard deviation of the particle diameter, and the particle radius is generated using a normal distribution. For example, In the formula, r is the particle radius. It is an absolute value function, ensuring that the radius is positive. is a function used to generate random samples that conform to a normal distribution, where mean is the mean particle diameter and std is the standard deviation.

[0076] Next, based on the boundary, the simulation region is divided into an internal sub-region and an edge sub-region, and an initial position is generated in either the internal or edge sub-region; wherein the initial position is generated with the same probability in both the internal and edge sub-regions. Specifically, the simulation region is divided into internal and edge sub-regions based on the boundary, and an initial position is randomly generated in either the internal or edge sub-region, with the probability of generating the initial position in either the internal or edge sub-region being controlled to be the same. For example, if the boundary is a cube with a side length of d, then the internal sub-region is a cube with a side length of d. The center of the internal sub-region is the center of the simulated region, and other regions are the edge sub-regions. The internal sub-regions are connected by... Uniformly distributed within the simulated sub-region, the edge sub-regions can be defined by randomly selecting x / y / z axis boundaries, with the corresponding axis coordinates fixed as "". " or" The remaining axis coordinates are evenly distributed to simulate the actual path of particle diffusion from the edge of the system to the interior during aerogel aggregation.

[0077] Finally, the target particle is generated based on the initial position and the particle radius. Based on the initial position and particle radius, an aerogel particle is generated with its center at the initial position and its radius equal to the particle radius; this is the target particle.

[0078] Understandably, each time a target particle is generated, it can be numbered, a particle index can be established, and the particle radius, initial position, and position after each displacement can be recorded, for example... Let be the particle radius of the target particle generated in the kth generation.

[0079] In this embodiment, target particles are generated one by one each time to achieve precise control of the aggregation process. This avoids structural distortion caused by the large-scale, unconstrained accumulation of aerogel particles without aggregation determination, and ensures that each aerogel particle undergoes subsequent physical mechanism verification.

[0080] Step S12: Generate the current Brownian motion parameters based on the stochastic diffusion model.

[0081] Specifically, a random diffusion model with a fixed displacement size is used to generate the current Brownian motion parameters, balancing physical realism and ease of use. Generate the current Brownian motion parameters, where, Given the current Brownian motion parameters, The standard deviation can be set based on the statistical characteristics of aerogel nanoparticles. This ensures that the single displacement of particles is much smaller than the particle diameter, avoiding non-physical "jump diffusion" and conforming to the slow diffusion characteristics of nanoparticles in sol-gel systems. This represents the number of random numbers. For example, That is, three independent random numbers are generated with a standard deviation of 1.0, which are then used to form a one-dimensional array of length 3. These three random numbers correspond to the displacement components of the particle in three-dimensional space (x-axis, y-axis, z-axis), and together they form a "three-dimensional displacement vector".

[0082] Step 2: Control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster.

[0083] Specifically, based on the current Brownian motion parameters determined in step 1, the coordinate position information of the target particle is updated to achieve the displacement of the target particle. For example, if the initial position coordinates of the target particle are (0,0,0) and the Brownian motion parameters are (1,2,3), then the position coordinates of the target particle are updated to (1,2,3), completing the displacement of the target particle.

[0084] Furthermore, to avoid simulation anomalies caused by particle overflow and to ensure the integrity of the simulation system, by... The system trims particle positions that extend beyond the simulation region. When a particle's displacement exceeds the simulation region's boundary, automatic trimming correction is performed. For example, using periodic boundary conditions, when a particle exceeds the physical boundary of the simulation region after Brownian motion, it is allowed to re-enter the simulation region from the opposite boundary. This approach can eliminate boundary effects and better characterize infinitely large materials with a finite simulation region.

[0085] For the target particle after displacement, update the center coordinates of the target particle and determine whether the target particle is in contact with the existing aggregated particle cluster, specifically including:

[0086] First, the distance between the displaced target particle and each aerogel particle in the existing aggregated particle cluster is calculated. Specifically, the distance between the target particle and each aerogel particle in the existing aggregated particle cluster is calculated, and the minimum distance is selected as the distance between the target particle and the existing aggregated particle cluster. The distance is calculated using the three-dimensional Euclidean distance formula. In the formula, Let x be the distance between the target particle and the m-th aerogel particle. k y k , z k (x) represents the center coordinates of the target particle. m y m , z m () represents the center coordinates of the m-th aerogel particle in the existing aggregated particle cluster.

[0087] Secondly, it is determined whether the spacing reaches the contact distance threshold. Specifically, the contact distance threshold between the target particle and each aerogel particle in the existing aggregated particle cluster is calculated, and the relationship between the spacing and the contact distance threshold is determined one by one. The contact distance threshold is calculated using the formula... Calculate, where, Let be the contact distance threshold between the target particle and the m-th aerogel particle. This is a spacing correction factor, for example, 0.9, used to avoid structural distortion caused by excessive particle compression and to ensure the stability of the cross-linking state. Let be the particle radius of the target particle. Let be the particle radius of the m-th aerogel particle.

[0088] Understandably, one could simultaneously calculate the distance and contact distance threshold between the target particle and a certain aerogel particle in an existing aggregated particle cluster, determine whether the distance reaches the contact distance threshold, and iterate through the aerogel particles in the existing aggregated particle cluster one by one; or one could first calculate the distance and contact distance threshold between the target particle and all aerogel particles in the existing aggregated particle cluster, record the corresponding relationship, and then determine the relationship between the distance and the contact distance threshold one by one according to the corresponding relationship.

[0089] Finally, if the contact distance threshold is reached, the displaced target particle is considered to be in contact with the existing aggregated particle cluster. Specifically, if the existing aggregated particle cluster contains aerogel particles, and the corresponding spacing is less than the contact clustering threshold, for example... If so, it is determined that the target particle after displacement is in contact with the existing aggregated particle cluster.

[0090] It should be noted that if no aggregated particle cluster is found, that is, if there are only target particles in the simulation area, for example, the number of times the target particles are generated can be used to determine this. For example, if the number of generation times is 1, there are only target particles, then the target particles are regarded as existing aggregated particle clusters, and new target particles are generated according to step 1.

[0091] In other embodiments, after generating the target particle, it can be determined whether the target particle is in contact with the existing aggregated particle cluster. If they are not in contact, the position of the target particle is controlled based on the current Brownian motion parameters, and then it can be determined whether the target particle after displacement is in contact with the existing aggregated particle cluster.

[0092] Step 3: When the target particle comes into contact with the existing aggregated particle cluster, calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster, and determine whether the aggregation potential energy reaches the potential energy threshold.

[0093] By employing both contact assessment and potential energy threshold determination, the true aggregation behavior of aerogel particles is reconstructed, achieving accurate assessment of "stable cross-linking." When a target particle comes into contact with an existing aggregated particle cluster, the aggregation potential energy of the target particle and the existing aggregated particle cluster is calculated, and it is determined whether the aggregation potential energy reaches the potential energy threshold. Specifically, this includes:

[0094] First, aerogel particles in contact with the target particle from the existing aggregated particle cluster are extracted as contact particles. Specifically, the center-to-center distance and contact distance threshold between the target particle and the aerogel particles in the existing aggregated particle cluster, as determined in step 2, can be used to identify aerogel particles in the existing aggregated particle cluster whose distance from the target particle is less than the contact distance threshold as contact particles. In other embodiments, the principle of step 2 can be followed, and the aggregate spacing correction coefficient can be set to different values ​​for contact determination; this is not limited here.

[0095] Secondly, the aggregation potential energy corresponding to the target particle and each of the contacting particles is calculated using the LJ potential energy function; wherein, the LJ potential energy function is expressed as:

[0096] ,

[0097] In the formula, To concentrate potential energy, the unit is joule, representing the strength of the attraction between particles. The LJ potential well depth is expressed in joules. LJ zero potential energy point distance, in nanometers, represents the distance between two particles when the aggregation potential energy is 0, and d is the distance between the target particle and the contacting particle, in nanometers.

[0098] in, The larger the value, the stronger the binding energy and the stronger the interaction between the two particles. This represents the distance between two particles when the aggregation potential energy is 0. It can be set according to the type of the target aerogel; for example, for carbon aerogel... Set it to 1.2. Set to 1.0. The spacing d is the same as the spacing in step 2. The calculation principle is the same, so it will not be repeated here.

[0099] The 12th term in the LJ potential energy function (i.e.) This describes the short-range repulsive force between the target particle and the contacting particles: when the particle spacing... At this time, the repulsive force increases rapidly, avoiding structural distortion caused by excessive particle compression, which matches the aggregation characteristic of aerogel particles of "contact but not dense"; the 6th term (i.e. Describes the long-range attractive force between particles: when the distance between particles... At this time, attraction plays a dominant role, accurately simulating the "weak attraction" effect dominated by van der Waals forces at the nanoscale, and accurately simulating the core physical mechanism between nanoscale aerogel particles; when At this time, the particles are in a net attraction state. Combined with the geometric spacing condition limited by the contact distance threshold, the accurate determination of "stable cross-linking" is achieved, which solves the problem of loose structure caused by "only geometric contact" in traditional methods.

[0100] Finally, it is determined whether the aggregation potential energy reaches the potential energy threshold. Specifically, it is determined whether the aggregation potential energy between the target particle and each contacting particle reaches the potential energy threshold. In this embodiment, the potential energy threshold is set to 0.

[0101] Step 4: When the aggregation potential energy reaches the potential energy threshold, the target particle and the existing aggregated particle cluster are identified as the current aggregated particle cluster.

[0102] Specifically, when the aggregation potential energy of the target particle and each contacting particle reaches the potential energy threshold, it is determined that the aggregation potential energy of the target particle and the existing aggregated particle cluster has reached the potential energy threshold. At this time, the target particle and the existing aggregated particle cluster form a "weak attraction-stable cross-linking" aggregation state, and the target particle and the existing aggregated particle cluster are identified as the current aggregated particle cluster.

[0103] Furthermore, when the aggregation potential energy does not reach the potential energy threshold, that is, the aggregation potential energy between the target particle and a certain contacting particle does not reach the potential energy threshold, a new Brownian motion parameter is generated based on the random diffusion model as the current Brownian motion parameter, and steps 2-3 are repeated. That is, the target particle is controlled to move based on the new Brownian motion parameter, and it is determined whether the target particle after the second movement is in contact with the existing aggregated particle cluster. When in contact, the aggregation potential energy between the target particle and the existing aggregated particle cluster is calculated, and it is determined whether the aggregation potential energy reaches the potential energy threshold. If it does, step 5 is executed; if it does not, the process is repeated.

[0104] Step 5: Calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle count requirement.

[0105] Specifically, the number of particles in the current aggregated particle cluster is calculated. In this embodiment, the number of times the target particles are generated can be recorded as the number of particles in the current aggregated particle cluster. It is then determined whether the number of particles meets the particle count requirement. The frequency of current porosity calculation is controlled based on the particle count requirement, reducing computational resource consumption. The particle count requirement can be set dynamically. For example, when the number of particles does not exceed 1000, the particle count requirement is an integer multiple of 50, meaning the current porosity is calculated every 50 newly added particles. When the number of particles exceeds 1000, the particle count requirement is an integer multiple of 20, achieving a balance between wide-interval calculations of the current porosity in the early stages and relatively dense calculations in the later stages, thus balancing computational resources and the need for precise porosity control. In other embodiments, time can also be controlled; this is not limited here.

[0106] Step 6: When the number of particles meets the requirement for the number of contact particles, calculate the current porosity of the current aggregated particle cluster and determine whether the current porosity has reached the target porosity.

[0107] Specifically, it includes:

[0108] Step S61: Calculate the total volume of the current aggregated particle cluster.

[0109] The total volume of the current aggregated particle cluster, representing the sum of the volumes of each particle in the current aggregated particle cluster, is calculated using the following formula:

[0110] ,

[0111] In the formula The total volume is N, where N represents the total number of aerogel particles in the current aggregated particle cluster. Let be the particle radius of the nth aerogel particle.

[0112] Step S62: Calculate the total overlap volume of the current aggregated particle cluster.

[0113] Specifically, the total overlap volume of the current aggregated particle cluster is calculated by calculating the overlap volume of every two aerogel particles in the current aggregated particle cluster one by one.

[0114] First, two aerogel particles are randomly selected from the current aggregated particle cluster as the current particle pair. Alternatively, two aerogel particles can be directly selected from the current aggregated particle cluster as the current particle pair for overlapping volume calculation.

[0115] Furthermore, for situations with a large number of particles and a large computational workload, parallel computation can be performed by grouping particles according to their spatial distribution density. Specifically, this includes:

[0116] 1) The spatial distribution density of the current aggregated particle cluster is determined using a real-time density statistical method based on spatial grids. Specifically, the real-time density statistical method based on spatial grids is an effective spatial data analysis method that can monitor and analyze spatial distribution in real time through grid division and density estimation. In this embodiment, the spatial distribution density of the current aggregated particle cluster is determined using a real-time density statistical method based on spatial grids, which can be implemented using existing technologies and will not be elaborated here.

[0117] 2) Based on the spatial distribution density of the particles, the current aggregated particle cluster is divided into multiple aggregated particle sub-clusters; wherein, each aggregated particle sub-cluster includes multiple aerogel particles. Specifically, based on the spatial distribution density of the particles, and according to the task mapping of load prediction, the computational tasks are divided and weighted. For example, the mapping relationship between the spatial distribution density of particles and the number of task processes or the number of computer CPU cores is used. Based on the spatial distribution density of the particles in the current aggregated particle cluster, the number of task processes is selected or different computers are allocated for grouped parallel computation. Computational resources are increased for densely populated areas and reduced for sparsely populated areas, further improving parallel computing efficiency and memory utilization efficiency, and solving the problem of uneven computational load caused by particle aggregation during aerogel reconstruction.

[0118] 3) Select one aerogel particle from the aggregated particle sub-cluster as the current particle, and select one aerogel particle from the current aggregated particle sub-cluster other than the current particle as the paired particle. The current particle and the paired particle are then considered as a current particle pair. Specifically, for an aggregated particle sub-cluster, select one aerogel particle as the current particle, and select one aerogel particle from the current aggregated particle sub-cluster other than the current particle as the paired particle (i.e., the paired particle may or may not be in the same aggregated particle sub-cluster as the current particle). The current particle and the paired particle are then considered as a current particle pair.

[0119] Next, the spacing between the current particle pairs is calculated.

[0120] Specifically, the spacing between the current particle pairs is calculated using the three-dimensional Euclidean distance formula. In the formula, (x i y i , z i ), (x j y j , z j ) are the center coordinates of the two aerogel particles in the current particle pair.

[0121] Next, the overlap of the current particle pair is determined based on the spacing.

[0122] Specifically, when the spacing is greater than or equal to the sum of the radii of the two aerogel particles in the current particle pair, the current particle pair is determined to be in a non-overlapping state; when the spacing is less than or equal to the difference in the radii of the two aerogel particles, the current particle pair is determined to be in a completely overlapping state; when the spacing is less than the sum of the radii of the two aerogel particles but greater than the difference in the radii of the two aerogel particles, the current particle pair is determined to be in a partially overlapping state.

[0123] Then, based on the overlap situation, an overlap volume calculation method is selected to calculate the overlap volume of the current particle pair.

[0124] Specifically, when the current particle pair is in a non-overlapping state, the overlap volume is the default value, which is 0; when the current particle pair is in a fully overlapping state, the overlap volume is determined by the formula... Calculate, where This represents the overlap volume of the current particle pair. , These are the radii of the two aerogel particles in the current particle pair, respectively; that is, the volume of the smaller of the two aerogel particles is taken as the overlap volume. When the current particle pair is in a partially overlapping state, the overlap volume is calculated using the formula... Calculation, where , , In the formula, a and b are auxiliary parameters in the partially overlapping scene, with the unit being nanometers, representing the "semi-major axis" and "semi-minor axis" in the direction of the line connecting the centers of the aerogel particles, respectively. The height of the overlapping area is expressed in nanometers to ensure the accuracy of the 3D volume calculation.

[0125] Finally, the total overlap volume of the current aggregated particle cluster is determined based on the overlap volumes of all the current particle pairs.

[0126] Iterate through the current particle pairs in the current aggregated particle cluster, and sum the overlapping volumes of all current particle pairs as the total overlapping volume of the current aggregated particle cluster.

[0127] In other embodiments, grouped parallel computing can split the task according to the "index of the current aggregated particle cluster". First, obtain the coordinates and radius arrays of all aggregated particles, and then split the particle index into multiple consecutive index groups according to the number of CPU cores. Each index group corresponds to a group of aerogel particles. During grouped parallel computing, each group will independently call the compute_overlap_volumes function to calculate the overlap volume of each particle in the group with each aerogel particle in the current aggregated particle cluster (including all aerogel particles in the group and other groups). The overlap volume of each "aerogel particle in the group" with other "all aerogel particles" is calculated to ensure that no cross-group particle pairs' overlap volume is missed, completely covering all possible particle interactions. The logic for summing the total overlap volume is as follows: After each index group is calculated, it will return an overlap volume array of "number of particles in the group × total number of particles". First, sum the local overlap volume of each array to obtain the local overlap volume of each group, and then sum the local sums of all groups. Since the overlap volume of any two particles will be calculated twice, the subsequent porosity calculation should be divided by 2 to correct for duplicate calculations.

[0128] Step S63: Calculate the current porosity based on the total volume and the total overlapping volume.

[0129] The current porosity is calculated based on the total volume and the total overlapping volume, using the following formula:

[0130] ,

[0131] In the formula, Given the current porosity, For the total volume, The total overlap volume represents the sum of the overlap volumes between all aggregated particles. Since each aerogel particle is calculated twice, it is corrected by dividing by 2. The total volume of the simulated region is calculated based on the boundary.

[0132] For example, if the boundary of the simulation region is a cube with side length l, then the total volume of the simulation region is... The boundary is a sphere with radius R; then the total volume of the simulated region is... .

[0133] Step 7: If the target porosity is achieved, the microstructure of the current aggregated particle cluster is output as the microstructure of the reconstructed target aerogel.

[0134] Specifically, when the current porosity reaches the target porosity, the microstructure of the current aggregated particle clusters is output as the microstructure of the reconstructed target aerogel. The target porosity can be set according to the needs of the target aerogel. When the difference between the current porosity and the target porosity is less than the error limit, the current porosity is considered to have reached the target porosity. For example, the error limit is set to 0.01. When the current porosity is considered to have reached the target porosity, then... Given the current porosity, The target porosity.

[0135] Furthermore, if the target porosity is not achieved, the current aggregated particle cluster is taken as the existing aggregated particle cluster; new aerogel particles are generated based on the particle characteristics as the target particles, and new Brownian running parameters are generated based on the random diffusion model as the current Brownian running parameters; steps 2-6 are repeated.

[0136] Specifically, when the current porosity does not reach the target porosity, it means that the aggregation structure of the current aggregated particle cluster does not meet the requirements of the target aerogel. The current aggregated particle cluster is regarded as an existing aggregated particle cluster, and new aerogel particles are generated according to the particle characteristics as target particles. New Brownian running parameters are generated based on the random diffusion model as the current Brownian running parameters, and a new cycle begins until the current porosity reaches the target porosity.

[0137] Using the target porosity as the termination condition, the microstructure of the current aggregated particle cluster is used as the output microstructure of the target aerogel to ensure that the reconstruction result accurately matches the requirements of the target aerogel.

[0138] Furthermore, the microstructure output supports multiple formats to meet subsequent analysis needs. For example, the particle feature CSV file contains core parameters such as particle ID, three-dimensional coordinates (X / Y / Z), diameter, and radius, which can be directly imported into third-party software such as ANSYS and COMSOL for heat transfer / mechanical performance simulation; the porosity evolution CSV file contains data such as simulation steps, number of aggregated particles, real-time porosity, and deviation from the target porosity, facilitating the analysis of the porosity convergence process; and the simulation log file records information such as parameter configuration, simulation progress, and key calculation results, facilitating problem tracing and simulation reproduction.

[0139] Furthermore, the method in this embodiment supports particle motion visualization, such as three-dimensional microstructure visualization. It can utilize matplotlib 3D plotting technology to display the spatial distribution of aggregated particles, such as... Figure 2 As shown; the porosity evolution curve is visualized, outputting the current porosity and particle count for each iteration, and plotting the current porosity against the number of calculations to form a curve, as shown. Figure 3As shown (the horizontal axis step represents the number of times the current porosity has been calculated), the target porosity and the allowable deviation range are marked to visually verify the simulation convergence.

[0140] This invention provides a potential energy-driven aerogel microstructure reconstruction system, such as... Figure 4 As shown, it includes:

[0141] The particle generation module is used to generate target particles based on the characteristics of aerogel particles;

[0142] The Brownian motion simulation module is used to generate current Brownian motion parameters based on a random diffusion model, control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster.

[0143] The potential energy calculation module is used to calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster when the target particle comes into contact with the existing aggregated particle cluster, and to determine whether the aggregation potential energy reaches the potential energy threshold.

[0144] The particle cluster generation module is used to determine the target particle and the existing aggregated particle cluster as the current aggregated particle cluster when the aggregation potential energy reaches the potential energy threshold.

[0145] The particle cluster generation module is also used to calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle number requirement.

[0146] The porosity calculation module is used to calculate the current porosity of the current aggregated particle cluster when the number of particles meets the contact particle number requirement, and to determine whether the current porosity reaches the target porosity.

[0147] The microstructure determination module is used to output the microstructure of the current aggregated particle cluster as the microstructure of the reconstructed target aerogel when the target porosity is reached.

[0148] Furthermore, the particle generation module is also used to generate new target particles based on particle characteristics when the number of particles does not meet the contact particle number requirement, or when the current porosity does not reach the target porosity.

[0149] The particle generation module also provides a visual parameter input interface, such as... Figure 5 As shown, it provides an intuitive input space (numerical box) to manage and set key parameters, obtain the boundary and particle size characteristics of the simulation area, and thus determine the initial position and particle radius of the target particles. It also allows input of constraints used by the module, such as potential energy threshold, target porosity, and number of aggregated particle subclusters, and supports setting input parameters as templates for easy subsequent use.

[0150] The Brownian motion simulation module is further configured to generate new Brownian motion parameters based on the random diffusion model when the target particle is not in contact with the existing aggregated particle cluster or when the aggregation potential energy has not reached the potential energy threshold, and control the target particle to move based on the new Brownian motion parameters, determine whether the target particle after the second movement is in contact with the existing aggregated particle cluster, and if not, repeatedly execute the generation of Brownian motion parameters and control of the target particle displacement until the target particle is in contact with the existing aggregated particle cluster.

[0151] In summary, the potential energy-driven aerogel microstructure reconstruction method and system of this invention has at least one of the following beneficial effects:

[0152] 1. By introducing aggregation potential energy and using a dual control mechanism of contact conditions and potential energy threshold, the true aggregation mechanism of aerogel particles, characterized by "weak attraction and stable cross-linking," is restored, improving physical realism and enabling an accurate description of the physical mechanism of aerosols. This results in a more precise output aerogel microstructure, providing a reliable structural basis for simulating the heat transfer and mechanical properties of aerogels. Furthermore, by controlling the number of contact particles, the frequency of porosity calculations is reasonably controlled, reducing computational resource consumption.

[0153] 2. The LJ potential energy function is used to describe the physical properties of "weak attraction-stable cross-linking" of aerogel particles. The 12th term characterizes the short-range repulsive force between particles, avoiding structural distortion caused by excessive particle compression; the 6th term characterizes the long-range attractive force between particles, accurately describing the weak interaction dominated by van der Waals forces; by adjusting the potential well depth and the distance to the zero potential energy point, the interaction strength and range in the aggregation of different types of aerogel particles can be adapted.

[0154] 3. Considering particle overlap, the overlapping volume of particles is introduced and the problem of repeated counting of overlapping volume is corrected to improve the accuracy of porosity calculation. The porosity reaching the target porosity is used as the reconstruction stopping condition to achieve precise control of porosity.

[0155] 4. Based on the spatial distribution density of particles, the current aggregated particle cluster is divided into multiple aggregated particle sub-clusters. Multiple sub-clusters can calculate the particle overlap volume in parallel, which effectively improves the porosity calculation efficiency when large-scale aerogel particle aggregation occurs.

[0156] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0157] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing the microstructure of aerogels based on potential energy, characterized in that, Includes the following steps: Step 1: Generate target particles based on aerogel particle characteristics, and generate current Brownian motion parameters based on a random diffusion model; Step 2: Control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster; Step 3: When the target particle comes into contact with the existing aggregated particle cluster, calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster, and determine whether the aggregation potential energy reaches the potential energy threshold. Step 4: When the aggregation potential energy reaches the potential energy threshold, the target particle and the existing aggregated particle cluster are identified as the current aggregated particle cluster; Step 5: Calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle count requirement; Step 6: When the number of particles meets the requirement for the number of contact particles, calculate the current porosity of the current aggregated particle cluster and determine whether the current porosity has reached the target porosity; Step 7: If the target porosity is achieved, the microstructure of the current aggregated particle cluster is output as the microstructure of the reconstructed target aerogel.

2. The method according to claim 1, characterized in that, The particle features include particle size characteristics and the boundary of the simulated region; Target particles are generated based on aerogel particle characteristics, including: Obtain the boundary and particle size characteristics of the simulated region; Based on the particle size characteristics, the particle radius is generated using a normal distribution. Based on the boundary, the simulation region is divided into an internal sub-region and an edge sub-region, and an initial position is generated in the internal sub-region or the edge sub-region; wherein the initial position is generated with the same probability in the internal sub-region and the edge sub-region. The target particle is generated based on the initial position and the particle radius.

3. The method according to claim 1, characterized in that, Determining whether the target particle, after displacement, comes into contact with an existing aggregated particle cluster includes: Calculate the distance between the target particle after displacement and each aerogel particle in the existing aggregated particle cluster; Determine whether the distance reaches the contact distance threshold; If the contact distance threshold is reached, the target particle after displacement is considered to be in contact with the existing aggregated particle cluster.

4. The method according to claim 1, characterized in that, When the target particle comes into contact with the existing aggregated particle cluster, the aggregation potential energy of the target particle and the existing aggregated particle cluster is calculated, and it is determined whether the aggregation potential energy reaches a potential energy threshold, including: Extract the aerogel particles that are in contact with the target particles from the existing aggregated particle clusters and use them as contact particles; The aggregation potential energy corresponding to the target particle and each of the contacting particles is calculated using the LJ potential energy function; wherein, the LJ potential energy function is expressed as: In the formula The gathering potential energy, The depth of the LJ potential well. d is the distance from the zero potential energy point of LJ, and d is the distance between the target particle and the contacting particle; Determine whether the accumulated potential energy has reached the potential energy threshold.

5. The method according to claim 1, characterized in that, When the accumulation potential energy does not reach the potential energy threshold, new Brownian motion parameters are generated based on the random diffusion model as the current Brownian motion parameters. Repeat steps 2-3.

6. The method according to claim 1, characterized in that, Calculating the current porosity of the current aggregated particle cluster includes: Calculate the total volume of the currently aggregated particle cluster; Calculate the total overlap volume of the currently aggregated particle cluster; The current porosity is calculated based on the total volume and the total overlapping volume.

7. The method according to claim 6, characterized in that, Calculating the total overlap volume of the current aggregated particle cluster includes: Select any two aerogel particles from the current aggregated particle cluster as the current particle pair; Calculate the spacing between the current particle pairs; The overlap of the current particle pair is determined based on the spacing. Based on the aforementioned overlap, an overlap volume calculation method is selected to calculate the overlap volume of the current particle pair; The total overlap volume of the current aggregated particle cluster is determined based on the overlap volume of all the current particle pairs.

8. The method according to claim 7, characterized in that, Select any two aerogel particles from the current aggregated particle cluster as the current particle pair, including: The spatial distribution density of the current aggregated particle cluster is determined by using a real-time density statistical method based on spatial grids. Based on the spatial distribution density of the particles, the current aggregated particle cluster is divided into multiple aggregated particle sub-clusters; wherein, the aggregated particle sub-clusters include multiple aerogel particles; Select one aerogel particle from the aggregated particle sub-cluster as the current particle, and select one aerogel particle other than the current particle from the current aggregated particle cluster as the paired particle. The current particle and the paired particle are then considered as the current particle pair.

9. The method according to claim 1, characterized in that, If the target porosity is not achieved, the current aggregated particle cluster is taken as the existing aggregated particle cluster. New aerogel particles are generated based on the particle characteristics as the target particles, and new Brownian running parameters are generated based on the random diffusion model as the current Brownian running parameters. Repeat steps 2 through 6.

10. A potential energy-driven aerogel microstructure reconstruction system, characterized in that, include: The particle generation module is used to generate target particles based on the characteristics of aerogel particles; The Brownian motion simulation module is used to generate current Brownian motion parameters based on a random diffusion model, control the target particle to move based on the current Brownian motion parameters, and determine whether the target particle after displacement comes into contact with the existing aggregated particle cluster. The potential energy calculation module is used to calculate the aggregation potential energy of the target particle and the existing aggregated particle cluster when the target particle comes into contact with the existing aggregated particle cluster, and to determine whether the aggregation potential energy reaches the potential energy threshold. The particle cluster generation module is used to determine the target particle and the existing aggregated particle cluster as the current aggregated particle cluster when the aggregation potential energy reaches the potential energy threshold. The particle cluster generation module is also used to calculate the number of particles in the current aggregated particle cluster and determine whether the number of particles meets the contact particle number requirement. The porosity calculation module is used to calculate the current porosity of the current aggregated particle cluster when the number of particles meets the contact particle number requirement, and to determine whether the current porosity reaches the target porosity. The microstructure determination module is used to output the microstructure of the current aggregated particle cluster as the microstructure of the reconstructed target aerogel when the target porosity is reached.

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