Method and apparatus for determining percolation performance of carbon black network, device, and storage medium

Abstract

The present application relates to a method and apparatus for determining the percolation performance of a carbon black network, a device, and a storage medium. The method comprises: constructing a percolation model of a carbon black network in a three-dimensional space on the basis of model parameters (S202); gradually inserting new carbon black particles into the percolation model to obtain an updated percolation model (S204); searching a plurality of carbon black particles comprised in the updated percolation model for a target conductive path (S206), the target conductive path being a conductive path passing through a first surface and a second surface in the three-dimensional space; updating the model parameters, and returning to the step of constructing a percolation model of a carbon black network in a three-dimensional space on the basis of model parameters until a cycle end condition is satisfied (S208); and determining the percolation performance of the carbon black network on the basis of the probabilities of respectively searching for the target conductive path in a plurality of cycles (S210).

Description

Methods, apparatus, equipment, and storage media for determining the percolation properties of carbon black networks.

[0001] Related applications

[0002] This application claims priority to Chinese patent application filed on February 21, 2025, with application number 2025101968662, entitled "Method, Apparatus, Device and Storage Medium for Determining the Percolation Properties of Carbon Black Networks", the entire contents of which are incorporated herein by reference. Technical Field

[0003] This application relates to the field of materials modeling technology, and in particular to a method, apparatus, computer device, computer-readable storage medium, and computer program product for determining the percolation properties of a carbon black network. Background Technology

[0004] Semiconducting shielding material is a crucial and decisive material in high-voltage cables, mainly composed of a matrix resin, conductive filler, crosslinking agent, antioxidant, and other processing aids, obtained through melt blending. The conductive filler is a key component of the semiconducting shielding material, determining its critical electrical, mechanical, thermal, processability, and surface finish properties. Conductive carbon black, due to its excellent electrical properties and low cost, has become the primary choice for conductive filler in the production of high-voltage cable semiconducting shielding materials. The properties of conductive carbon black are crucial in determining the performance of the semiconducting shielding material. In high-voltage cable shielding materials, the use of conductive carbon black can improve the material's conductivity, enhance the shielding effect, and improve the overall performance of the cable. Studies have shown that the distribution and concentration of carbon black have a significant impact on the electrical properties of the shielding material.

[0005] Percolation models for conductive carbon black are crucial for optimizing material formulations and improving product performance. Percolation theory is an important tool for studying the electrical conductivity of materials, allowing us to understand how the distribution and bonding of conductive particles in the matrix affect the overall conductivity of the material. The formation mechanism of carbon black percolation is complex and influenced by various factors, including particle size distribution, content ratio, and matrix material properties. Therefore, by constructing percolation models, we can better simulate the bonding patterns of carbon black at different particle sizes and contents, and predict its percolation performance.

[0006] In traditional techniques, percolation models are typically constructed using cellular automata methods to study percolation phase transitions on two-dimensional planar regular lattices. This modeling approach is relatively simple, but when constructing a three-dimensional percolation model that conforms to the conductivity binding characteristics, the accuracy of determining percolation performance is low. Summary of the Invention

[0007] According to various embodiments disclosed in this application, a method, apparatus, computer device, computer-readable storage medium, and computer program product for determining the percolation properties of a carbon black network are provided, which can improve the accuracy of determining percolation properties.

[0008] A method for determining the percolation properties of a carbon black network, comprising:

[0009] Based on model parameters, a percolation model of a carbon black network is constructed in three-dimensional space; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space.

[0010] New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model.

[0011] The target conductive path is searched among the multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold.

[0012] Update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and

[0013] The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations.

[0014] An apparatus for determining the percolation properties of a carbon black network, comprising:

[0015] A construction module is used to construct a percolation model of a carbon black network in three-dimensional space based on model parameters; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space.

[0016] The update module is used to gradually insert new carbon black particles into the percolation model to obtain an updated percolation model.

[0017] The search module is used to search for target conductive paths among multiple carbon black particles included in the updated percolation model, and record the percolation probability of finding the target conductive path; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold.

[0018] The update module is further configured to update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and

[0019] A determination module is used to determine the percolation performance of the carbon black network based on the percolation probabilities recorded in multiple cycles.

[0020] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the above-described method.

[0021] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0022] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0023] Details of one or more embodiments of this application are set forth in the following drawings and description. Other features, objects, and advantages of this application will become apparent from the specification, drawings, and claims. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the disclosed drawings without creative effort.

[0025] Figure 1 shows the application environment of a method for determining the percolation performance of a carbon black network in one embodiment;

[0026] Figure 2 is a flowchart illustrating a method for determining the percolation performance of a carbon black network in one embodiment.

[0027] Figure 3 is a schematic diagram of a conductive path in one embodiment;

[0028] Figure 4 is a schematic diagram showing the changes in the percolation threshold and percolation probability of a percolation model in one embodiment;

[0029] Figure 5 shows a device for determining the percolation performance of a carbon black network in one embodiment.

[0030] Figure 6 is an internal structure diagram of a computer device in one embodiment. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0033] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0034] It is understood that the terms "first," "second," etc., used herein may be used to describe various elements, but these elements are not limited by these terms. These terms are used only to distinguish one element from another. "A plurality of" means two or more. "At least a part of an element" means part or all of an element. It is understood that "connection" in the following embodiments should be understood as "electrical connection," "communication connection," etc., if the connected circuits, modules, units, etc., have the transmission of electrical signals or data between them. When used herein, the singular forms "a," "an," and "the" may also include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms "comprising / including" or "having," etc., specify the presence of the stated features, integrals, steps, operations, components, parts, or combinations thereof, but do not exclude the possibility of the presence or addition of one or more other features, integrals, steps, operations, components, parts, or combinations thereof.

[0035] The method for determining the percolation performance of a carbon black network provided in this application embodiment can be applied to the application environment shown in Figure 1. In this environment, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104 or placed on a cloud or other network server. Terminal 102 constructs a percolation model of a carbon black network in three-dimensional space based on model parameters. The percolation model simulates the distribution of individual carbon black particles in the carbon black network in three-dimensional space. Terminal 102 progressively inserts new carbon black particles into the percolation model to obtain an updated percolation model. Terminal 102 searches for target conductive paths among the multiple carbon black particles included in the updated percolation model. The target conductive path is a conductive path that runs through the first and second surfaces in three-dimensional space. The height difference between the first and second surfaces in three-dimensional space is greater than a difference threshold. Terminal 102 updates the model parameters and returns to the step of constructing the percolation model of the carbon black network in three-dimensional space based on the model parameters until the loop termination condition is met. Terminal 102 determines the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops. Terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, smart in-vehicle devices, projection devices, etc. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted displays. Head-mounted displays can be virtual reality (VR) devices, augmented reality (AR) devices, smart glasses, etc. Server 104 can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server providing cloud computing services.

[0036] In an exemplary embodiment, as shown in FIG2, a method for determining the percolation performance of a carbon black network is provided. Taking the application of this method to terminal 102 in FIG1 as an example, the method includes:

[0037] Step S202: Based on the model parameters, construct the percolation model of the carbon black network in three-dimensional space.

[0038] The model parameters can refer to the initial conditions and constraints used to construct the three-dimensional percolation model, including but not limited to the particle size or particle size distribution of carbon black particles, the spatial size or geometry of the three-dimensional space, the connection distance between particles (such as the critical distance of the tunneling effect), the concentration or distribution density of carbon black particles, the number of carbon black particle sets composed of carbon black particles, and the range of the number of carbon black particles contained in each carbon black particle set.

[0039] The three-dimensional space can be a virtual modeling region that simulates the carbon black network, such as a three-dimensional cube or other shape with clear boundaries, which can provide a spatial range for the distribution of carbon black particles.

[0040] The percolation model of the carbon black network can be a mathematical and physical model used to describe the distribution of carbon black particles in three-dimensional space and how they are interconnected. The percolation model can be used to simulate the process of carbon black particles forming a conductive network and to evaluate whether the carbon black network has reached the percolation state.

[0041] The percolation model is used to simulate the distribution of individual carbon black particles in the carbon black network in three-dimensional space.

[0042] In practice, the terminal can distribute carbon black particles in three-dimensional space according to model parameters to form an initial network structure. The positions of the carbon black particles are initialized according to particle distribution rules (random distribution, clustered distribution). Simultaneously, the connection relationships between carbon black particles are set according to particle connection rules (the distance between two carbon black particles cannot be less than a set critical value, which can be the tunneling distance). Through this step, the terminal obtains the initially constructed percolation model, providing a foundation for subsequent particle insertion and model update steps.

[0043] Step S204: New carbon black particles are gradually inserted into the percolation model to obtain the updated percolation model.

[0044] Since the progressive insertion of carbon black particles can alter the carbon black particle distribution, connectivity, and conductive paths in the original percolation model, an updated percolation model can be obtained after the insertion of new carbon black particles. This updated percolation model can be used to reflect the dynamic changes in the carbon black network structure after the insertion of carbon black particles.

[0045] In practice, the terminal can gradually add carbon black particles based on the original percolation model. At each step, one or more carbon black particles can be inserted, and the target conductive path can be searched among the multiple carbon black particles in the updated percolation model. If no target conductive path is found, the next carbon black particle insertion can be performed until the target conductive path is found among the multiple carbon black particles in the updated percolation model.

[0046] In practice, the terminal gradually inserts new carbon black particles into the percolation model. This can be done by randomly generating new carbon black particle positions in a uniform distribution within three-dimensional space; or by prioritizing insertion at locations with efficient connections (such as near existing conductive clusters) based on the distribution of existing particles. After each insertion of a new carbon black particle, it is checked whether it meets the connection conditions (such as whether it satisfies the tunneling distance); otherwise, the position is regenerated.

[0047] Step S206: Search for target conductive paths among the multiple carbon black particles included in the updated percolation model.

[0048] The updated percolation model can be a three-dimensional model that includes the current distribution and connection relationships of all carbon black particles after inserting new carbon black particles into the original percolation model and updating it, reflecting the real-time state of the carbon black network.

[0049] The target conductive path is a conductive path that runs through the first and second surfaces in three-dimensional space; the height difference between the first and second surfaces in three-dimensional space is greater than the difference threshold.

[0050] The target conductive path can refer to the interconnected path formed between carbon black particles in the percolation model through physical contact or tunneling effect, marking the formation of the percolation state.

[0051] The first and second surfaces can be two surfaces in three-dimensional space with a significant height difference, such as the upper and lower surfaces in three-dimensional space, or the top and bottom of a percolation model. Optionally, the difference threshold can be 80% or 90% of the height in three-dimensional space.

[0052] In one embodiment, the terminal searches for a target conductive path among multiple carbon black particles included in the updated percolation model. This can be achieved using breadth-first search (BFS) or depth-first search (DFS) between the first and second surfaces. Specifically, the terminal can sequentially traverse the carbon black particles in three-dimensional space, searching for connecting paths from carbon black particles on the first surface to those on the second surface. When the distance between carbon black particles is less than a preset tunneling distance or physical contact distance, the two carbon black particles are considered connected. The terminal then recursively or iteratively determines whether the current carbon black particle can connect the first and second surfaces through existing connectivity. During the path search, the found path information can be recorded to analyze the impact of different carbon black particle distributions on the conductive path. By using search algorithms such as BFS or DFS, connecting paths between upper and lower surfaces can be efficiently found in a large-scale three-dimensional space, improving the accuracy and stability of path searching.

[0053] In practice, the terminal can perform multiple searches for the target conductive path on the updated percolation model, thereby recording the number of times the target conductive path is successfully found in the updated percolation model and calculating the percolation probability. This percolation probability can be used to evaluate percolation performance. Specifically, the percolation probability can be the probability of successfully finding the target conductive path under specific carbon black particle distribution conditions, and can be used to quantify the likelihood of the percolation model reaching the percolation state.

[0054] Step S208: Update the model parameters and return to the step of constructing a percolation model of the carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met.

[0055] The updated model parameters can be key parameters of the percolation model, such as particle size, particle distribution density, particle content, and connection distance. The updated model parameters are used to reflect changes in carbon black particle distribution and electrical conductivity under different conditions, thereby analyzing their impact on percolation performance.

[0056] After updating the model parameters, the terminal returns to step S202 to reconstruct the percolation model of the carbon black network. This is an iterative loop process that continues until a preset loop termination condition is met. The loop termination condition can be used to determine whether the loop has terminated, and may include determining whether all model parameters such as particle size and particle content have been tested, or whether the preset number of loops has been reached.

[0057] For example, updating model parameters can be done by changing the particle size of carbon black particles, such as adjusting it from 10 nanometers (nm) to 15 nanometers (nm); it can be done by changing the effective connection distance of the tunneling effect between carbon black particles to reflect different conductivity conditions; or it can be done by changing the content of carbon black particles.

[0058] Step S210: Determine the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops.

[0059] In this context, multiple iterations can refer to the process of updating model parameters, rebuilding the percolation model, and conducting simulations multiple times.

[0060] In the specific implementation, in each loop, the terminal first constructs a percolation model of the carbon black network in three-dimensional space based on the model parameters. Then, new carbon black particles can be gradually inserted into the percolation model. This gradual insertion can involve increasing the number of carbon black particles one at a time, rather than adding all the carbon black particles at once. After inserting one or more new carbon black particles each time, a search for the target conductive path can be performed. As new carbon black particles are gradually inserted, the probability of finding the target conductive path changes continuously. After each insertion of a carbon black particle, a path search is performed on the entire updated percolation model to determine if a connected path exists from the first surface to the second surface. If a connected path is found, it is recorded as "successful"; if no connected path is found, the next carbon black particle insertion continues until the target conductive path is found among multiple carbon black particles in the updated percolation model. Finally, based on the number of successful searches for the target conductive path and the total number of searches in the current updated percolation model, the probability of finding the target conductive path, i.e., the percolation probability, can be obtained. For example, if only a small number of new carbon black particles are needed to find the target conductive path, it indicates that the percolation model built based on these parameters has a high percolation probability; conversely, if a large number of new carbon black particles are required to find the target conductive path, it indicates that the percolation model built based on these parameters has a low percolation probability. After finding the target conductive path, the model parameters are updated, and the next iteration is performed until the loop termination condition is met. Then, based on the probability of finding the target conductive path in each iteration, the percolation performance of the carbon black network is determined.

[0061] The probability of finding the target conductive path can also be called the percolation probability, which reflects the conductivity of the percolation model under the given model parameters. The level of the percolation probability, to a certain extent, reflects the degree of development of the conductive network of carbon black particles in the percolation system.

[0062] The percolation performance can include the conductivity and global connectivity of the carbon black network. The percolation probability can be used to quantify the conductivity and percolation behavior of the carbon black network under different conditions.

[0063] In practice, the terminal can summarize the percolation probability of multiple cycles, plot the relationship curve between different model parameters (such as particle size or particle content) and percolation probability, and obtain the percolation probability curve under different model parameters. This allows for the simulation of the bonding mode of carbon black particles under different particle sizes and contents, and the determination of the influence of different particle sizes and contents on percolation performance. This helps to understand how the distribution and connection mode of carbon black particles in the matrix affects the overall conductivity of the material.

[0064] In the above-mentioned method for determining the percolation performance of the carbon black network, the terminal constructs a percolation model of the carbon black network in three-dimensional space based on model parameters. The percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in three-dimensional space. New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model. Target conductive paths are searched among the multiple carbon black particles included in the updated percolation model. The target conductive path is a conductive path that runs through the first and second surfaces in three-dimensional space, and the height difference between the first and second surfaces in three-dimensional space is greater than a difference threshold. The model parameters are updated, and the process returns to the step of constructing the percolation model of the carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met. The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple loops. By progressively inserting carbon black particles and dynamically updating the percolation model, combined with the search for the target conductive path and the statistics of percolation probability, the distribution and connection characteristics of carbon black particles can be accurately simulated in three-dimensional space, constructing a high-precision percolation model. This significantly improves the accuracy of percolation performance determination, providing a scientific basis for optimizing the formulation of semi-conductive shielding materials for high-voltage cables, and further enhancing the conductivity, processing performance, and overall cable performance of the material.

[0065] In one embodiment, a percolation model of a carbon black network is constructed in three-dimensional space based on model parameters, including: obtaining a preset carbon black particle diameter, a preset number of carbon black particle sets, and a preset number of carbon black particles contained in each carbon black particle set; during the construction of the current carbon black particle set, generating several new carbon black particles around the existing carbon black particles in the current carbon black particle set according to a preset particle distance; the diameter of the several new carbon black particles conforms to the preset carbon black particle diameter; and, provided that the several new carbon black particles are located in three-dimensional space and do not overlap with other carbon black particles in the current carbon black particle set, adding the several new carbon black particles to the current carbon black particle set. Then return to the step of generating a number of new carbon black particles around the existing carbon black particles in the current carbon black particle set according to the preset particle distance, until the number of carbon black particles in the current carbon black particle set meets the preset number of carbon black particles; continue to construct the next carbon black particle set, take the next carbon black particle set as the current carbon black particle set, and return to the step of generating a number of new carbon black particles around the existing carbon black particles in the current carbon black particle set according to the preset particle distance during the construction of the current carbon black particle set, until multiple carbon black particle sets that meet the preset number of carbon black particle sets are generated; and based on the multiple carbon black particle sets, construct a percolation model of the carbon black network in three-dimensional space.

[0066] In practical applications, carbon black exhibits a multi-layered, structured distribution in the matrix resin. Individual carbon black particles, acting as basic units, are uniformly distributed in the resin through the action of surfactants or dispersants, forming a primary particle distribution. Subsequently, these particles attract each other through van der Waals forces, forming grape-like aggregates composed of several to dozens of primary particles. These grape-like aggregates are distributed randomly and with a certain orientation in the matrix, constituting a grape-like aggregate distribution. As the carbon black content increases, the distance between the grape-like aggregates decreases, making it easier to form conductive pathways. These pathways are achieved through direct contact or tunneling effects between carbon black particles, thus constructing an effective conductive network in the matrix resin. Furthermore, the interfacial forces between carbon black particles and the resin also affect their distribution in the matrix. Good interfacial interactions contribute to more uniform particle dispersion and enhance the formation of the conductive network, collectively determining the conductivity of carbon black-filled composite materials. Therefore, this distribution pattern can be mimicked to construct carbon black particle assemblies, and subsequently, a percolation model of the carbon black network can be built.

[0067] Among them, the carbon black particle set can be a grape-like set of carbon black particles. Each set of carbon black particles can be regarded as a local "grape bunch" structure. By combining these sets, an overall carbon black network is formed.

[0068] Optionally, model parameters may include the spatial dimensions in three-dimensional space, the diameter of carbon black particles, the number of carbon black particles, the number of bunches (the number of carbon black particle sets), and the range of the number of spheres in each bunch (the number of carbon black particle sets). Based on these model parameters, the terminal can generate multiple bunch-like carbon black particle sets. Specifically, the terminal can generate bunch-like carbon black particle sets using an iterative algorithm starting from a random position, ensuring that the newly generated carbon black particles do not overlap with existing carbon black particles and are within a predetermined range. The terminal divides the generated carbon black particles into sets for a first surface and a second surface, recording the corresponding coordinate information. The recursively generated bunch-like carbon black particles are evenly distributed, avoiding particle overlap and ensuring the rationality and effectiveness of the structure.

[0069] In practice, the terminal can set a starting point in three-dimensional space and construct the first carbon black particle based on the starting point position. The particle size of this carbon black particle conforms to the preset carbon black particle diameter. New carbon black particles are generated from the current carbon black particle at random angles and fixed distances. Each time, several new carbon black particles are generated (e.g., 2 to 6). It is checked whether the newly generated carbon black particles are within the range of three-dimensional space and whether they overlap with existing carbon black particles. If both conditions are met, the new carbon black particles can be added to the carbon black particle set. Based on the position of the new carbon black particles, it is determined whether they are located on the first or second surface of three-dimensional space and added to the corresponding list. If the number of carbon black particles in the current carbon black particle set reaches the preset number of carbon black particles, or the number of attempts to generate particles reaches 1000, the generation of the current carbon black particle set can be stopped, and the generation of the next carbon black particle set can continue until the number of carbon black particle sets meets the preset number of carbon black particle sets. Based on multiple carbon black particle sets, a percolation model of the carbon black network is constructed to simulate the distribution and conductivity of carbon black particles in the material.

[0070] For example, the size of the three-dimensional space can be set to 1000nm×1000nm×1000nm, the diameter of the carbon black particles can be adjusted between 10nm and 60nm, the number of particles contained in a single bunch of carbon black particles can be set to 15 to 30, and the number of carbon black particles in a set can be 200 to 300.

[0071] For example, the terminal can record the volume percentage of the generated carbon black particle ensemble in the entire three-dimensional space to determine the density of the generated structure. This calculation helps to evaluate the filling effect of carbon black particles in the matrix material.

[0072] In this embodiment, the terminal generates carbon black networks with different properties (such as particle size and density) by adjusting parameters; through step-by-step generation and rigorous inspection, a high-precision carbon black percolation model is constructed in three-dimensional space; it is suitable for simulating the distribution of carbon black particles in actual materials and is used to study percolation performance or optimize material design.

[0073] In one embodiment, the process of progressively inserting new carbon black particles into a percolation model to obtain an updated percolation model includes: progressively inserting new carbon black particles into the percolation model; determining the conductive group to which the new carbon black particles belong in the percolation model based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, to obtain an updated conductive group; the conductive group is a collection of multiple carbon black particles that form a conductive path; and obtaining an updated percolation model based on the updated conductive group.

[0074] Among them, a conductive cluster can refer to a collection of multiple carbon black particles connected by physical contact or tunneling effect. Conductive clusters are the basis for forming conductive paths in the percolation model.

[0075] In practice, the terminal dynamically inserts new carbon black particles into the existing percolation model, gradually expanding or adjusting the conductive network (conductive clusters) in the model. Based on the distance between the new particle and existing particles, it determines whether the new particle is connected to a specific conductive cluster. If the distance between the new particle and a particle in a conductive cluster is less than a preset connection threshold, the new particle is added to that conductive cluster. If the new particle simultaneously meets the connection conditions with multiple conductive clusters, these conductive clusters are merged into a larger cluster. If the new particle is not connected to any existing particle, a new independent conductive cluster is formed. The new carbon black particles are then regrouped with existing particles to form updated conductive clusters. Based on these updated conductive clusters, the structure of the entire percolation model is adjusted to obtain an updated percolation model, which reflects the current distribution and connection relationships of the carbon black particles.

[0076] The technical solution of this embodiment reflects the process of carbon black particles gradually connecting to form a conductive network from independent distribution. The terminal updates the conductive clusters in real time to ensure the model accurately describes the connectivity and conductivity of the carbon black particles. This provides a reliable modeling method for studying the relationship between carbon black particle concentration, distribution, and percolation performance. By progressively inserting carbon black particles and dynamically updating the conductive clusters and percolation model, accurate simulation of the carbon black network evolution process is achieved. This method is suitable for studying the formation law of conductive networks and provides important basis for optimizing material formulations and improving conductivity.

[0077] In one embodiment, determining the conductive group to which the new carbon black particles belong in the percolation model based on the distance between the new carbon black particles and the original carbon black particles in the percolation model includes: identifying target particles from the original carbon black particles whose distance is less than a preset limit distance based on the distance between the new carbon black particles and the original carbon black particles in the percolation model; and determining that the new carbon black particles belong to the same conductive group if each target particle belongs to the same conductive group; and merging the different conductive groups into a new conductive group if each target particle belongs to one or more different conductive groups, and determining that the new carbon black particles belong to the new conductive group.

[0078] The preset limit distance is the critical distance used to determine whether two particles can connect, and it is usually set based on the range of physical contact or tunneling effect.

[0079] The target particle can be a carbon black particle that meets the preset limit distance condition with the new carbon black particle among the existing carbon black particles.

[0080] In practice, each time a new carbon black particle is inserted into the terminal, the composition of the conductive group is adjusted according to the affiliation of the new carbon black particle. For example, it may expand an existing conductive group, merge multiple conductive groups, or create a new conductive group (if the new particle is not connected to any target particle).

[0081] For example, in the percolation model, when interpolating new carbon black particles, it is necessary to determine whether the carbon black particle forms a new independent conductive group and connects to an existing conductive group, or whether it connects two independent conductive groups. Therefore, the terminal needs to use the neighborhood relationship in the data structure to determine whether there are other carbon black particles around the interpolated carbon black particle within a given range (within a preset limit distance). For each interpolated carbon black particle, its neighboring region is checked to find nearby carbon black particles. The label values ​​of the neighboring carbon black particles are recorded to identify the conductive group to which they belong. The neighboring carbon black particles found during the search are connected. Each time a new carbon black particle is interpolated, it is immediately labeled, and its status information is recorded. As carbon black particles are interpolated step by step, after each interpolation, the neighboring particles of the new carbon black particle are searched, and their label values ​​are checked. If carbon black particles with the same label value are found within a given preset limit distance, the new carbon black particle is added to the same conductive group. If carbon black particles with different label values ​​are found, the two conductive groups are connected together and the label values ​​are unified. Alternatively, a conductive group can be randomly selected, and the label values ​​of all related carbon black particles can be updated to make them consistent. This ensures that the relationship between particles and conductive groups can be correctly judged and processed during the particle interpolation process, and realizes the dynamic generation and connection of conductive groups.

[0082] As an example, in the established percolation model, setting a preset limit distance for the connection between carbon black particles is crucial. When the spacing between carbon black particles is relatively small, leakage current is generated in the medium, which also increases the conductivity of the system. From the formula for the tunneling probability of charge carriers crossing the barrier, it can be calculated that the tunneling effect decreases exponentially with increasing distance; therefore, the preset limit distance can be set to 2 nanometers (nm).

[0083] As another example, the terminal can determine a preset limiting distance based on the particle size of the carbon black particles. Assuming the particle size of the carbon black particles is w, the limiting distance d between particles can be determined as: d = 2r * 10⁻⁶ -3 In the percolation model, model parameters such as model size, particle size, and particle connection conditions are set. Particles are interpolated step by step in the percolation model, and repeated searches and connections are made to find other carbon black particles within a preset limit distance range in the 360-degree direction of any particle.

[0084] In this embodiment, the terminal determines the relationship between the newly inserted carbon black particles and existing carbon black particles based on their positions, identifies the conductive group to which the particles belong, and merges the conductive groups when necessary. This enables dynamic adjustment of the conductive network, reflecting the gradual connection and evolution of the carbon black network. It can reflect the impact of new particle insertion on the connectivity of the conductive network in real time and supports the gradual evolution of the carbon black network. By merging conductive groups, it ensures that the conductive paths of the model gradually form and tend to be complete. By filtering target particles by distance, calculations are only performed on particles that may be connected, reducing unnecessary operations.

[0085] In one embodiment, searching for a target conductive path among multiple carbon black particles included in the updated percolation model includes: searching for the largest conductive group among the conductive groups included in the updated percolation model; the largest conductive group is the conductive group containing the most carbon black particles; and determining the target conductive path from the conductive paths contained in the largest conductive group if the largest conductive group penetrates a first surface and a second surface in three-dimensional space.

[0086] The largest conductive cluster is the one containing the most carbon black particles, representing the most important conductive network in the model. In practice, all conductive clusters in the updated percolation model can be traversed, the number of carbon black particles in each cluster can be counted, and the conductive cluster with the most particles is identified as the largest conductive cluster.

[0087] The largest conductive cluster must connect the first and second surfaces in three-dimensional space; that is, the largest conductive cluster must contain a connected path from the first surface to the second surface. If the largest conductive cluster traverses the three-dimensional space, the traversing path is selected from all its conductive paths as the target conductive path. The target conductive path is the most important connected path in the model, indicating that the model has reached a percolation state.

[0088] For example, as the number of interpolated carbon black particles in the percolation model increases, the connections between the carbon black particles form conductive clusters. When the largest conductive cluster penetrates the first and second surfaces of the system (e.g., the upper and lower surfaces), the percolation model can be considered to have reached the percolation state. When the three-dimensional spatial dimensions are a square or cube with a side length of 1000, and the number of carbon black particles contained is n with a volume fraction of V, the relationship between V and n when the percolation state is reached can be calculated using the following formula:

[0089] Where r is the particle size and l is the preset limit distance between carbon black particles.

[0090] In this embodiment, the terminal searches and analyzes the largest conductive cluster in the percolation model to find the target conductive path that can penetrate the upper and lower surfaces of the three-dimensional space, thus achieving a precise assessment of the global conductivity of the carbon black network. By determining whether the target conductive path penetrates the three-dimensional space, the percolation state can be dynamically analyzed, providing a scientific basis for studying the percolation performance of the carbon black network.

[0091] In one embodiment, the percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations, including: determining that the updated percolation model has reached a percolation state when the probability of finding the target conductive path is greater than or equal to a probability threshold; the percolation state is the state in which the target conductive path exists in the updated percolation model; and determining the percolation threshold of the carbon black network based on the average carbon black particle content corresponding to when the updated percolation model reaches the percolation state in multiple iterations.

[0092] In practice, during each loop, the terminal calculates the probability of finding the target conductive path based on the updated percolation model. If the probability of finding the target conductive path is greater than or equal to a preset probability threshold (e.g., 50%), the updated percolation model is considered to have reached the percolation state. The percolation state means that a conductive path exists in the carbon black network from the first surface to the second surface in three-dimensional space.

[0093] In each iteration, the terminal records the carbon black particle content at which the percolation model reaches the percolation state. The carbon black particle content can refer to the proportion or number of carbon black particles in the total space of the model. The average carbon black particle content corresponding to the percolation state across multiple iterations is calculated and used as the percolation threshold for the carbon black network.

[0094] The percolation threshold can be used to characterize how easily a carbon black network reaches a percolation state. A higher percolation threshold indicates that a higher particle concentration is required for the carbon black network to form conductive pathways; a lower percolation threshold indicates that a conductive state can be achieved at a lower concentration.

[0095] For example, the percolation threshold obtained through a single modeling step is random. To eliminate random errors, the terminal performs multiple iterations, interpolating carbon black particles multiple times in each iteration until the percolation model reaches a percolation state. The carbon black particle content is calculated, and the average carbon black particle content in each iteration is calculated. This average value can be determined as the percolation threshold, and percolation probability curves are plotted for different particle sizes. The percolation threshold represents the ease with which the carbon black network reaches a percolation state. If the percolation probability of the carbon black network is not less than 50%, the carbon black network can be considered to have reached a percolation state. The level of the percolation probability, to some extent, reflects the degree of development of the conductive network of particles in the percolation system.

[0096] The technical solution of this embodiment dynamically evaluates the conductivity of the carbon black network at the terminal and accurately determines the percolation state by setting a probability threshold. By using the percolation threshold, the influence of carbon black particle distribution on the network conductivity is quantified, improving the accuracy of determining percolation performance and providing a scientific basis for optimizing the design and production of conductive materials. This method can simulate the binding mode of carbon black particles under different parameters such as different particle sizes and contents, and analyze the impact of changes in particle content and particle size on the overall percolation threshold.

[0097] In one embodiment, the terminal can generate a visual image of the three-dimensional structure and conductive path of the percolation model, plot the results using a graphics library and save them to a designated folder, generating both easily viewable results and original-size result images. The probability of finding the target conductive path in multiple simulations is recorded, the overall algorithm runtime and the runtime of each step are calculated and printed, and relevant images are displayed when needed. The generated three-dimensional structure and path are graphically displayed, facilitating observation and analysis and providing strong support for further research.

[0098] For the convenience of those skilled in the art, Figure 3 provides an exemplary schematic diagram of a conductive path.

[0099] To facilitate understanding by those skilled in the art, Figure 4 provides an exemplary schematic diagram illustrating the changes in the percolation threshold and percolation probability of a percolation model.

[0100] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0101] Based on the same inventive concept, this application also provides a device for determining the percolation performance of a carbon black network to implement the above-described method for determining the percolation performance of a carbon black network. The solution provided by this device is similar to the solution described in the above-described method. Therefore, the specific limitations of one or more embodiments of the device for determining the percolation performance of a carbon black network provided below can be found in the limitations of the method for determining the percolation performance of a carbon black network described above, and will not be repeated here.

[0102] In an exemplary embodiment, as shown in FIG5, a percolation performance determination apparatus for a carbon black network is provided, comprising:

[0103] The construction module 510 is used to construct a percolation model of a carbon black network in three-dimensional space based on model parameters; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space.

[0104] The update module 520 is used to gradually insert new carbon black particles into the percolation model to obtain an updated percolation model.

[0105] Search module 530 is used to search for target conductive paths among multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through a first surface and a second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than a difference threshold.

[0106] Update module 520 is also used to update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and

[0107] The determination module 540 is used to determine the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops.

[0108] In one embodiment, the updating module 520 is specifically used to progressively insert new carbon black particles into the percolation model; determine the conductive group to which the new carbon black particles belong in the percolation model based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, so as to obtain an updated conductive group; the conductive group is a collection of multiple carbon black particles that form a conductive path; and obtain the updated percolation model based on the updated conductive group.

[0109] In one embodiment, the updating module 520 is specifically configured to: determine target particles whose distance is less than a preset limit distance from the original carbon black particles based on the distance between the new carbon black particles and the original carbon black particles in the percolation model; and determine that the new carbon black particles belong to the same conductive group when each of the target particles belongs to the same conductive group; and merge the different conductive groups into a new conductive group when each of the target particles belongs to one or more different conductive groups, and determine that the new carbon black particles belong to the new conductive group.

[0110] In one embodiment, the search module 530 is specifically configured to search for the largest conductive group among the conductive groups included in the updated percolation model; the largest conductive group is the conductive group containing the largest number of carbon black particles; and, if the largest conductive group penetrates the first surface and the second surface in the three-dimensional space, determine the target conductive path from the conductive paths contained in the largest conductive group.

[0111] In one embodiment, the determining module 540 is specifically configured to determine that the updated percolation model has reached a percolation state when the probability of finding the target conductive path is greater than or equal to a probability threshold; the percolation state is the state in which the target conductive path exists in the updated percolation model; and to determine the percolation threshold of the carbon black network based on the average carbon black particle content corresponding to when the updated percolation model reaches the percolation state in the multiple iterations; the percolation threshold is used to characterize the ease with which the carbon black network reaches the percolation state.

[0112] In one embodiment, the construction module 510 is specifically used to obtain the preset carbon black particle diameter, the preset number of carbon black particle sets, and the preset number of carbon black particles contained in each carbon black particle set from the model parameters; during the construction of the current carbon black particle set, according to the preset particle distance, several new carbon black particles are generated around the original carbon black particles in the current carbon black particle set; the diameter of the several new carbon black particles conforms to the preset carbon black particle diameter; when the several new carbon black particles are located in the three-dimensional space and do not overlap with other carbon black particles in the current carbon black particle set, the several new carbon black particles are added to the current carbon black particle set, and the process returns to the preset particle distance. The process involves several steps: generating new carbon black particles around existing carbon black particles in the current carbon black particle set according to a preset particle distance, until the number of carbon black particles in the current carbon black particle set meets the preset number of carbon black particles; continuing to construct the next carbon black particle set, using the next carbon black particle set as the current carbon black particle set, and returning to the step of generating new carbon black particles around existing carbon black particles in the current carbon black particle set according to a preset particle distance during the construction of the current carbon black particle set, until multiple carbon black particle sets meeting the preset number of carbon black particle sets are generated; and constructing a percolation model of the carbon black network in the three-dimensional space based on the multiple carbon black particle sets.

[0113] Each module in the aforementioned device for determining the percolation performance of carbon black networks can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware within or independently of the processor in a computer device, or stored in software within the memory of a computer device, so that the processor can invoke and execute the corresponding operations of each module.

[0114] In an exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram is shown in Figure 6. The computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are connected to the system bus via the input / output interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The input / output interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When the computer program is executed by the processor, it implements a method for determining the percolation performance of a carbon black network. The display unit of the computer device is used to form a visually visible image and may be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0115] Those skilled in the art will understand that the structure shown in Figure 6 is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0116] A computer device includes a memory and one or more processors. The memory stores computer-readable instructions, which, when executed by the one or more processors, cause the one or more processors to perform the following steps: constructing a percolation model of a carbon black network in a three-dimensional space based on model parameters; the percolation model simulating the distribution of individual carbon black particles in the carbon black network in the three-dimensional space; progressively inserting new carbon black particles into the percolation model to obtain an updated percolation model; searching for a target conductive path among the multiple carbon black particles included in the updated percolation model; the target conductive path being a conductive path traversing a first surface and a second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space being greater than a difference threshold; updating the model parameters and returning to the step of constructing a percolation model of the carbon black network in a three-dimensional space based on the model parameters, until a loop termination condition is met; and determining the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops.

[0117] One or more computer-readable storage media storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the following steps: constructing a percolation model of a carbon black network in three-dimensional space based on model parameters; the percolation model simulating the distribution of individual carbon black particles in the carbon black network in the three-dimensional space; progressively inserting new carbon black particles into the percolation model to obtain an updated percolation model; searching for a target conductive path among the multiple carbon black particles included in the updated percolation model; the target conductive path being a conductive path traversing a first surface and a second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space being greater than a difference threshold; updating the model parameters and returning to the step of constructing a percolation model of the carbon black network in three-dimensional space based on the model parameters, until a loop termination condition is met; and determining the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops.

[0118] A computer program product includes a computer program that, when executed by a processor, performs the following steps:

[0119] Based on model parameters, a percolation model of a carbon black network is constructed in three-dimensional space. The percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space. New carbon black particles are progressively inserted into the percolation model to obtain an updated percolation model. A target conductive path is searched among the multiple carbon black particles included in the updated percolation model. The target conductive path is a conductive path that runs through a first surface and a second surface in the three-dimensional space. The height difference between the first surface and the second surface in the three-dimensional space is greater than a difference threshold. The model parameters are updated, and the process returns to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met. The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple loops.

[0120] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0121] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for determining the percolation properties of a carbon black network, the method comprising: Based on the model parameters, a percolation model of carbon black network is constructed in three-dimensional space; The percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space; New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model. The target conductive path is searched among the multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold. Update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations.

2. The method of claim 1, wherein, The stepwise insertion of new carbon black particles into the percolation model to obtain an updated percolation model includes: New carbon black particles are gradually inserted into the percolation model; Based on the distance between the new carbon black particles and the existing carbon black particles in the percolation model, the conductive cluster to which the new carbon black particles belong in the percolation model is determined to obtain the updated conductive cluster; the conductive cluster is a collection of multiple carbon black particles forming a conductive path; and Based on the updated conductive group, the updated percolation model is obtained.

3. The method according to claim 2, wherein, The step of determining the conductive group to which the new carbon black particles belong in the percolation model based on the distance between the new carbon black particles and the original carbon black particles in the percolation model includes: Based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, target particles whose distance is less than a preset limit distance are determined from the original carbon black particles; and When each of the target particles belongs to the same conductive group, the new carbon black particle is determined to belong to the same conductive group. When each of the target particles belongs to one or more different conductive groups, the different conductive groups are merged into a new conductive group, and the new carbon black particles are determined to belong to the new conductive group.

4. The method according to claim 2, wherein, The process of searching for the target conductive path among the multiple carbon black particles included in the updated percolation model includes: The maximum conductive group is searched among the conductive groups included in the updated percolation model; the maximum conductive group is the conductive group containing the largest number of carbon black particles; and In the case where the largest conductive group penetrates the first and second surfaces in the three-dimensional space, the target conductive path is determined from the conductive paths contained in the largest conductive group.

5. The method according to claim 1, wherein, The determination of the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple iterations includes: If the probability of finding the target conductive path is greater than or equal to a probability threshold, the updated percolation model is determined to have reached a percolation state; the percolation state is the state in which the target conductive path exists in the updated percolation model; and The percolation threshold of the carbon black network is determined based on the average carbon black particle content corresponding to the percolation state when the updated percolation model reaches the percolation state in the multiple iterations; the percolation threshold is used to characterize the ease with which the carbon black network reaches the percolation state.

6. The method according to claim 1, wherein, The percolation model for constructing a carbon black network in three-dimensional space based on model parameters includes: Obtain the preset carbon black particle diameter, preset carbon black particle set quantity, and preset carbon black particle quantity contained in each carbon black particle set from the model parameters. During the construction of the current carbon black particle set, according to the preset particle distance, several new carbon black particles are generated around the original carbon black particles in the current carbon black particle set; the diameter of the several new carbon black particles conforms to the preset carbon black particle diameter. When the several new carbon black particles are located in the three-dimensional space and do not overlap with other carbon black particles in the current carbon black particle set, the several new carbon black particles are added to the current carbon black particle set, and the process returns to the step of generating several new carbon black particles around the original carbon black particles in the current carbon black particle set according to the preset particle distance, until the number of carbon black particles contained in the current carbon black particle set meets the preset number of carbon black particles; Continue constructing the next set of carbon black particles, using this next set of carbon black particles as the current set of carbon black particles, and return to the step in the process of constructing the current set of carbon black particles, where, according to a preset particle distance, a certain number of new carbon black particles are generated around the existing carbon black particles in the current set of carbon black particles, until multiple sets of carbon black particles that meet the preset number of carbon black particle sets are generated; and Based on the multiple sets of carbon black particles, a percolation model of the carbon black network is constructed in the three-dimensional space.

7. An apparatus for determining the percolation properties of a carbon black network, the apparatus comprising: The building block is used to construct a percolation model of a carbon black network in three-dimensional space based on model parameters. The percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space; The update module is used to gradually insert new carbon black particles into the percolation model to obtain an updated percolation model. The search module is used to search for the target conductive path among the multiple carbon black particles included in the updated percolation model. The target conductive path is a conductive path that passes through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold. The update module is also used to update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met. and A determination module is used to determine the percolation performance of the carbon black network based on the probability of finding the target conductive path in multiple loops.

8. A computer device comprising a memory and one or more processors, the memory storing computer-readable instructions that, when executed by the one or more processors, cause the one or more processors to perform the following steps: Based on model parameters, a percolation model of a carbon black network is constructed in three-dimensional space; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space. New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model. The target conductive path is searched among the multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold. Update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations.

9. The computer device according to claim 8, wherein, When the processor executes the computer-readable instructions, it also performs the following steps: New carbon black particles are gradually inserted into the percolation model; Based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, the conductive group to which the new carbon black particles belong in the percolation model is determined, so as to obtain the updated conductive group. The conductive group is a collection of multiple carbon black particles that form a conductive path. and Based on the updated conductive group, the updated percolation model is obtained.

10. The computer device according to claim 9, wherein, When the processor executes the computer-readable instructions, it also performs the following steps: Based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, target particles whose distance is less than a preset limit distance are determined from the original carbon black particles; and When each of the target particles belongs to the same conductive group, the new carbon black particle is determined to belong to the same conductive group. When each of the target particles belongs to one or more different conductive groups, the different conductive groups are merged into a new conductive group, and the new carbon black particles are determined to belong to the new conductive group.

11. The computer device according to claim 9, wherein, When the processor executes the computer-readable instructions, it also performs the following steps: The maximum conductive group is searched among the conductive groups included in the updated percolation model; the maximum conductive group is the conductive group containing the largest number of carbon black particles. and In the case where the largest conductive group penetrates the first and second surfaces in the three-dimensional space, the target conductive path is determined from the conductive paths contained in the largest conductive group.

12. The computer device according to claim 8, wherein, When the processor executes the computer-readable instructions, it also performs the following steps: If the probability of finding the target conductive path is greater than or equal to a probability threshold, the updated percolation model is determined to have reached a percolation state; the percolation state is the state in which the target conductive path exists in the updated percolation model. and The percolation threshold of the carbon black network is determined based on the average carbon black particle content corresponding to the percolation state when the updated percolation model reaches the percolation state in the multiple iterations; the percolation threshold is used to characterize the ease with which the carbon black network reaches the percolation state.

13. The computer device according to claim 8, wherein, When the processor executes the computer-readable instructions, it also performs the following steps: Obtain the preset carbon black particle diameter, preset carbon black particle set quantity, and preset carbon black particle quantity contained in each carbon black particle set from the model parameters. During the construction of the current carbon black particle set, according to the preset particle distance, several new carbon black particles are generated around the original carbon black particles in the current carbon black particle set; the diameter of the several new carbon black particles conforms to the preset carbon black particle diameter. When the several new carbon black particles are located in the three-dimensional space and do not overlap with other carbon black particles in the current carbon black particle set, the several new carbon black particles are added to the current carbon black particle set, and the process returns to the step of generating several new carbon black particles around the original carbon black particles in the current carbon black particle set according to the preset particle distance, until the number of carbon black particles contained in the current carbon black particle set meets the preset number of carbon black particles; Continue constructing the next set of carbon black particles, using this next set of carbon black particles as the current set of carbon black particles, and return to the step in the process of constructing the current set of carbon black particles, where, according to a preset particle distance, a certain number of new carbon black particles are generated around the existing carbon black particles in the current set of carbon black particles, until multiple sets of carbon black particles that meet the preset number of carbon black particle sets are generated; and Based on the multiple sets of carbon black particles, a percolation model of the carbon black network is constructed in the three-dimensional space.

14. One or more computer-readable storage media storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the following steps: Based on model parameters, a percolation model of a carbon black network is constructed in three-dimensional space; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space. New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model. The target conductive path is searched among the multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold. Update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations.

15. The storage medium according to claim 14, wherein, When the computer-readable instructions are executed by the processor, the following steps are also performed: New carbon black particles are gradually inserted into the percolation model; Based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, the conductive group to which the new carbon black particles belong in the percolation model is determined, so as to obtain the updated conductive group. The conductive group is a collection of multiple carbon black particles that form a conductive path. and Based on the updated conductive group, the updated percolation model is obtained.

16. The storage medium according to claim 15, wherein, When the computer-readable instructions are executed by the processor, the following steps are also performed: Based on the distance between the new carbon black particles and the original carbon black particles in the percolation model, target particles whose distance is less than a preset limit distance are determined from the original carbon black particles; and When each of the target particles belongs to the same conductive group, the new carbon black particle is determined to belong to the same conductive group. When each of the target particles belongs to one or more different conductive groups, the different conductive groups are merged into a new conductive group, and the new carbon black particles are determined to belong to the new conductive group.

17. The storage medium according to claim 15, wherein, When the computer-readable instructions are executed by the processor, the following steps are also performed: The maximum conductive group is searched among the conductive groups included in the updated percolation model; the maximum conductive group is the conductive group containing the largest number of carbon black particles. and In the case where the largest conductive group penetrates the first and second surfaces in the three-dimensional space, the target conductive path is determined from the conductive paths contained in the largest conductive group.

18. The storage medium according to claim 14, wherein, When the computer-readable instructions are executed by the processor, the following steps are also performed: If the probability of finding the target conductive path is greater than or equal to a probability threshold, the updated percolation model is determined to have reached a percolation state; the percolation state is the state in which the target conductive path exists in the updated percolation model. and The percolation threshold of the carbon black network is determined based on the average carbon black particle content corresponding to the percolation state when the updated percolation model reaches the percolation state in the multiple iterations; the percolation threshold is used to characterize the ease with which the carbon black network reaches the percolation state.

19. The storage medium according to claim 14, wherein, When the computer-readable instructions are executed by the processor, the following steps are also performed: Obtain the preset carbon black particle diameter, preset carbon black particle set quantity, and preset carbon black particle quantity contained in each carbon black particle set from the model parameters. During the construction of the current carbon black particle set, according to the preset particle distance, several new carbon black particles are generated around the original carbon black particles in the current carbon black particle set; the diameter of the several new carbon black particles conforms to the preset carbon black particle diameter. When the several new carbon black particles are located in the three-dimensional space and do not overlap with other carbon black particles in the current carbon black particle set, the several new carbon black particles are added to the current carbon black particle set, and the process returns to the step of generating several new carbon black particles around the original carbon black particles in the current carbon black particle set according to the preset particle distance, until the number of carbon black particles contained in the current carbon black particle set meets the preset number of carbon black particles; Continue constructing the next set of carbon black particles, using this next set of carbon black particles as the current set of carbon black particles, and return to the step in the process of constructing the current set of carbon black particles, where, according to a preset particle distance, a certain number of new carbon black particles are generated around the existing carbon black particles in the current set of carbon black particles, until multiple sets of carbon black particles that meet the preset number of carbon black particle sets are generated; and Based on the multiple sets of carbon black particles, a percolation model of the carbon black network is constructed in the three-dimensional space.

20. A computer program product comprising a computer program that, when executed by a processor, performs the following steps: Based on model parameters, a percolation model of a carbon black network is constructed in three-dimensional space; the percolation model is used to simulate the distribution of each carbon black particle in the carbon black network in the three-dimensional space. New carbon black particles are gradually inserted into the percolation model to obtain an updated percolation model. The target conductive path is searched among the multiple carbon black particles included in the updated percolation model; the target conductive path is a conductive path that runs through the first surface and the second surface in the three-dimensional space; the height difference between the first surface and the second surface in the three-dimensional space is greater than the difference threshold. Update the model parameters and return to the step of constructing a percolation model of a carbon black network in three-dimensional space based on the model parameters, until the loop termination condition is met; and The percolation performance of the carbon black network is determined based on the probability of finding the target conductive path in multiple iterations.

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