Method for predicting macroscopic elastic modulus and strength of porous materials and applications thereof

Abstract

This invention provides a method for predicting the macroscopic elastic modulus and strength of porous materials and its application, relating to the technical field of new material design and performance prediction. The method includes the following steps: obtaining the tertiary pore structure parameters of the porous material; obtaining the deformation mechanism index of each pore level in the porous material; obtaining the fracture strength index of each pore level in the porous material; substituting the tertiary pore structure parameters and deformation mechanism index into the tertiary extended Gibson-Ashby model formula for predicting the modulus to obtain the predicted modulus value; and substituting the tertiary pore structure parameters and fracture strength index into the tertiary extended Gibson-Ashby model formula for predicting the strength to obtain the predicted strength value. This invention classifies pores into three levels: macropores, mesopores, and micropores, and describes the contribution of pores of different scales to mechanical properties through cascaded attenuation functions, enabling accurate prediction of elastic modulus and strength.

Description

Technical Field

[0001] This invention relates to the technical field of new material design and performance prediction, and in particular to a method for predicting the macroscopic elastic modulus and strength of porous materials and its application. Background Technology

[0002] Currently, the Gibson-Ashby model is the most classic theoretical framework for describing the mechanical properties of porous materials, and its basic form is as follows: Elastic modulus: ; strength: ; in, and These are the elastic modulus and strength of porous materials, respectively. and For the corresponding properties of dense matrix materials, For relative density, , is a geometric constant, and n and m are exponents (usually n=2, m=1.5 for open-hole structures; n=2, m=2 for closed-hole structures).

[0003] Existing porous materials typically employ the Gibson-Ashby model to characterize their mechanical properties using average porosity (or relative density), but this model neglects the hierarchical structural differences in pore size distribution. Experiments show that, with the same total porosity, samples with different pore size distributions exhibit significant differences in skeletal strength.

[0004] The traditional Gibson-Ashby model is only applicable to materials with single-scale porosity and cannot accurately predict the mechanical properties of materials with multi-level complex pore structures. Meanwhile, experiments show that macropores (>50nm), mesopores (2nm-50nm), and micropores (<2nm) play different roles in mechanical load-bearing: macropores form the overall framework structure and dominate the overall stiffness; mesopores weaken the moment of inertia of beams / walls, reducing local bending resistance; micropores change the effective cross-sectional area of ​​the skeleton and affect local strength through surface energy effects.

[0005] Existing material design methods rely heavily on trial and error, making it impossible to quantitatively predict the macroscopic modulus and strength of a specific pore structure before preparation, resulting in long development cycles and high costs.

[0006] For applications such as silicon-carbon anodes, the modulus of the carbon framework directly affects its ability to constrain silicon volume expansion and cycle life, but there is a lack of precise design guidelines that correlate pore structure with modulus. When silicon undergoes volume expansion, the carbon framework with a low modulus is prone to irreversible structural collapse, leading to failure of internal electrical contacts, shedding of active material, and consequently, rapid capacity decay.

[0007] For brittle porous materials (such as porous carbon), fracture strength is often more critical than modulus, directly determining the material's damage resistance and cycle life. Failure in porous materials is often initiated by fracture, rather than uniform deformation. Traditional density-based strength models cannot distinguish the influence of pores of different scales on crack initiation and propagation. Mesopores and micropores, as inherent defects, weaken fracture strength far more than they weaken modulus, necessitating quantitative models. Current technologies lack methods for predicting fracture strength from a pore topology perspective, leading to blind design of materials for damage resistance.

[0008] Therefore, significantly improving the mechanical confinement capacity of the carbon framework while ensuring ion transport channels, and maintaining its structural integrity during repeated volume changes, is crucial for achieving stable cycling of silicon-carbon anodes with "zero expansion" or "high confinement." Thus, there is an urgent need to develop an accurate and universal method for predicting and optimizing the macroscopic elastic modulus and strength of porous materials.

[0009] In view of this, the present invention is hereby proposed. Summary of the Invention

[0010] One of the objectives of this invention is to provide a method for predicting the macroscopic elastic modulus and strength of porous materials. This method can predict the macroscopic elastic modulus and strength of three-level porous materials with macropores, mesopores, and micropores. It breaks through the limitation of the traditional Gibson-Ashby model, which only considers the total porosity. It can accurately predict the elastic modulus and strength of materials and is applicable to various material systems such as porous carbon, ceramics, and metals. It is especially suitable for the mechanical performance design and optimization of silicon-carbon composite anode carbon skeletons in lithium-ion batteries.

[0011] The second objective of this invention is to provide an application of a method for predicting the macroscopic elastic modulus and strength of porous materials, which is beneficial for optimizing material structure design, effectively shortening the research and development cycle, and reducing development costs.

[0012] The three-level porosity model constructed in this invention differs fundamentally from the traditional Gibson-Ashby model. Its core innovation lies in abandoning the macroscopic description of a single "total porosity" and establishing a quantitative system of "nested porosity," achieving a precise characterization of the spatial distribution and synergistic effects of pores at each level. Based on this, this invention further proposes a three-level exponential model, breaking through the limitations of the traditional single exponential model. By assigning independent exponential values ​​n and m to pore structures at different scale levels, a constitutive relation that accurately reflects the evolution of multi-scale pore structures is constructed. Furthermore, this invention not only achieves high-precision prediction of the material's elastic modulus but also extends to establish a synergistic prediction model for fracture strength, forming a dual-parameter evaluation system for modulus and strength. This overcomes the deficiency of traditional models, which can only predict modulus but cannot assess the material's load-bearing failure behavior.

[0013] In order to achieve the above-mentioned objectives of the present invention, the following technical solution is adopted: In a first aspect, a method for predicting the macroscopic elastic modulus and strength of porous materials includes the following steps: (1) Obtain the third-order pore structure parameters of the porous material, including: Nested porosity based on the total volume of the material Nested porosity based on the solid volume of macropore walls And nested porosity based on mesoporous wall solid volume. ; (2) Determine the deformation mechanism index and fracture strength index corresponding to each level of porosity, including: Deformation mechanism indices include the large-pore deformation index n M Mesoporous deformation index n m and the micropore deformation index n µ ; Fracture strength index includes macroporous strength index m M Mesoporous strength index m m and the micropore strength index m µ ; (3) Based on the three-level nested pore structure, a modulus prediction model is constructed to calculate the predicted value of the macroscopic elastic modulus of porous materials: ; E* is the macroscopic elastic modulus of porous materials, and E0 is the elastic modulus of dense matrix materials; C M C is the topological geometric constant of the macropore. m For mesoporous topological geometric constants; (4) Construct a fracture strength prediction model based on a three-level nested pore structure and calculate the predicted macroscopic strength of porous materials: ; * For the macroscopic fracture strength of porous materials, For dense matrix materials, K is the geometric constant sensitive to large pore defects; (5) Based on the predicted elastic modulus and strength values, optimize the pore structure or predict the performance of the porous material.

[0014] Furthermore, the nested porosity satisfies: ; Φ total The total porosity of the porous material.

[0015] Furthermore, the large hole deformation index n M Determined based on the macroporous topology: Open-cell foam structure n M = 2; Closed-cell foam structure n M = 1; Truss structure n M = 1.

[0016] Furthermore, the mesoporous deformation index n m Determined based on mesoporous connectivity: Bending dominant structure n m = 2; Tension-dominant structure n m = 1.

[0017] Furthermore, the micropore deformation index n µ The range of values ​​is 2 ≤ n µ ≤ 4.

[0018] Furthermore, the macroporous strength index m m Determined based on the shape of the large hole: For perforated truss structures with smooth perforation edges and robust connections, m M =1.5; For random foam structures with sharp, crack-like pore edges, m M =2.0~2.5.

[0019] Furthermore, the mesoporous strength index m m Determined based on mesoporous connectivity: For isolated, spherical mesopores, m m =1; For highly interconnected mesopores that form through channels, m m =2.0~3.0.

[0020] Furthermore, the micropore strength index m µ The range of values ​​is 2 ≤ m µ ≤ 4.

[0021] Furthermore, the macropore parameters in the three-level pore structure parameters are obtained by SEM or X-ray CT; The mesopore parameters of the tertiary pore structure were obtained by gas adsorption. The micropore parameters in the three-level pore structure parameters are obtained by BET or density method.

[0022] Furthermore, the fracture strength index includes the macroporous strength index m. M The shape of the macropores was determined by SEM or TEM analysis. The fracture strength index and the intermediate hole strength index m m Determined by gas adsorption and nanoindentation; The fracture strength index includes the micropore strength index m. µ Determined by Raman or XPS analysis.

[0023] Furthermore, when the predicted elastic modulus is lower than the target value, the total porosity Φ total Under fixed conditions, by adjusting , , The allocation ratio is determined to obtain the maximum elastic modulus.

[0024] Furthermore, the predicted values ​​of elastic modulus and strength are calculated simultaneously, and isomodulus lines and isostrength lines are established to obtain a pore structure design window that meets the strength and modulus requirements.

[0025] Secondly, the application of any of the above-mentioned prediction methods in materials design and performance prediction.

[0026] Furthermore, the material includes at least one of porous carbon, porous ceramics, metal foam, porous polymers, biological scaffolds, and aerogels.

[0027] Compared with the prior art, the present invention has at least the following beneficial effects: The method for predicting the macroscopic elastic modulus and strength of porous materials provided by this invention is a method for predicting the mechanical properties of porous materials based on multi-scale pore hierarchy and morphological characteristics. It not only boasts high prediction accuracy and strong guidance but also good universality. Specifically, high prediction accuracy refers to the fact that it considers the coupling weakening effect of multi-level pores for the first time, and the prediction results show a significantly higher agreement with experiments than classical models, breaking through the limitations of estimating modulus or strength solely based on porosity. Strong guidance refers to the fact that the indices in the model have clear physical meanings, can diagnose the fundamental pore causes leading to material fragility, can quantitatively reveal the contribution of each level of pore to modulus and strength, and clarify optimization directions (such as indicating that macropore topology should be changed first rather than blindly reducing mesopore ratio). Furthermore, good universality means that it is applicable to porous carbon materials obtained by various preparation methods (template method, 3D printing, activation method). In summary, this invention breaks through the limitation of the traditional Gibson-Ashby model, which only considers total porosity, and can accurately predict the elastic modulus and strength of materials, applicable to various material systems such as porous carbon, ceramics, and metals.

[0028] The application of the method for predicting the macroscopic elastic modulus and strength of porous materials provided by this invention is beneficial for optimizing the structural design of materials, especially in fields with stringent requirements for the mechanical properties of materials, such as long-life lithium-ion battery anodes, lightweight and high-strength structural materials, and durable design of catalyst supports. It can effectively shorten the research and development cycle and reduce development costs. Attached Figure Description

[0029] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of the three-order pore structure of porous carbon. Figure 2 Comparison of macropore structures (open-pore vs. closed-pore). Figure 3 This is a partially enlarged schematic diagram of the mesoporous structure inside the skeleton beam. Figure 4 This is a schematic diagram of the atomic-scale distribution of micropores in a carbon matrix. Figure 5 This is a flowchart for the prediction and optimization design of the macroscopic elastic modulus and strength of porous materials based on a three-level pore structure of macropores-mesopores-micropores. Detailed Implementation

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

[0032] In real materials, tertiary porosity is usually not parallel; rather, mesopores and micropores are located within the solid framework that forms the walls of macropores. Figure 1 , Figure 2 , Figure 3 and Figure 4 ; Figure 1 This demonstrates the hierarchical pore structure of porous carbon materials, consisting of macropores, mesopores, and micropores. Macropores form the overall framework structure of the material, mesopores are distributed within the framework, and micropores are distributed within the carbon matrix. The left side of the figure shows an open-pore macropore framework structure, and the right side shows a closed-pore macropore structure. Figure 2 yes Figure 1 A partially enlarged schematic diagram of a medium-to-large porous skeleton beam is used to show the distribution of mesopores inside the carbon skeleton beam. The diagram contrasts and illustrates the interconnected mesopore structure and the closed mesopore structure, where the interconnected mesopores form a through channel, and the closed mesopores appear as independent pores. Figure 3 yes Figure 2A further enlarged schematic diagram of the medium-carbon matrix is ​​used to show the distribution of micropores in the carbon matrix; micropores are nanoscale voids formed by interlayer stacking defects or disordered structures of carbon atoms. Figure 4 This is a comparative schematic diagram of open-pore and closed-pore structures in porous carbon materials. In the open-pore structure, the pores are interconnected, forming continuous channels; while in the closed-pore structure, the pores are closed cavities and are not interconnected. Construct a three-level nested model: Level 1: Macroscopic Structure of Macropores Assuming the total volume of the material's appearance is The volume fraction occupied by macropores is ; The volume of the "primary solid framework" including the macropore walls is ; Notice: It is not a final non-porous solid; it also contains mesopores and micropores. Second level: Mesoporous structure (located within the wall of macropores) First-level solid skeleton Internally, mesopores exist; Assume the volume of mesopores accounts for The proportion is (This is a fraction based on the volume of the primary skeleton.) Therefore, the absolute volume of the mesopore is ; After subtracting the mesopores, the volume of the "secondary solid framework" containing micropores is obtained: ; Level 3: Microporous structure (located within the carbon matrix of the mesoporous walls) Second-level solid framework Inside, there are micropores; Assume the volume of micropores accounts for The proportion is (This is a fraction based on the volume of the secondary skeleton). Therefore, the absolute volume of the micropores is ; Finally, the volume of a completely non-porous solid is: .

[0033] Based on the nested model described above, the relative density can be derived: Final solid mass: ; Therefore, absolute density: ; Substituting the relationships at each level, we get: .

[0034] Gibson-Ashby extended model of tertiary porosity systems: The classic Gibson-Ashby (GA) model assumes that all pores have a single characteristic size and are uniformly distributed. It cannot distinguish between a "solid skeleton containing 50% macropores" and a "skeleton containing 30% macropores and 20% mesopores." At the same total relative density, the mechanical properties of the latter are usually much lower than those of the former because the mesopores weaken the "beams" or "walls" that transmit loads. The solid framework itself is also porous, and its intrinsic modulus is no longer constant, but varies with the content of mesopores and micropores. The material can be divided into three layers from the inside out: Layer I: Microporous carbon matrix This is the most basic solid material, composed of carbon atoms but containing micropores; Level II: Mesoporous solid framework (composed of microporous carbon matrix) The framework material is the microporous carbon matrix of layer I; Level III: Macroporous materials (composed of mesoporous solid frameworks) Macropores form tertiary pores within the mesoporous framework.

[0035] By associating the three-level pore structure with three key fracture mechanisms—crack initiation, crack propagation path, and brittle fracture criterion—and introducing strength indices corresponding to the fracture mechanisms, a power-law relationship model between fracture strength and porosity at each level can be established, enabling accurate prediction of fracture strength in porous materials.

[0036] According to a first aspect of the present invention, a method for predicting the macroscopic elastic modulus and strength of porous materials is provided, comprising the following steps: Obtain the tertiary pore structure parameters of porous materials; Tertiary pore structure parameters include nested porosity based on the total material volume. Nested porosity based on the solid volume of macropore walls And nested porosity based on mesoporous wall solid volume. ; Obtain the deformation mechanism index of each pore level in porous materials; Deformation mechanism indices include the large-pore deformation index n M Mesoporous deformation index n m and the micropore deformation index n µ ; Obtain the fracture strength index of each pore level in a porous material; Fracture strength index includes macroporous strength index m M Mesoporous strength index m m and the micropore strength index mµ ; The tertiary pore structure parameters and deformation mechanism index are substituted into the tertiary extended Gibson-Ashby model formula for predicting modulus to obtain the predicted modulus value. The strength prediction value is obtained by substituting the tertiary pore structure parameters and fracture strength index into the formula of the tertiary extended Gibson-Ashby model for predicting strength.

[0037] This invention not only boasts high prediction accuracy and strong guidance, but also good universality. Specifically, high prediction accuracy refers to the fact that it considers the coupling weakening effect of multi-level pores for the first time, and the prediction results are in significantly better agreement with experiments than classical models, breaking through the limitations of estimating modulus or strength solely based on porosity. Strong guidance refers to the fact that the indices in the model have clear physical meanings, can diagnose the root causes of porosity leading to material fragility, can quantitatively reveal the contribution of each level of pores to modulus and strength, and can clarify the optimization direction (such as indicating that macropore topology should be changed first rather than blindly reducing mesopores). At the same time, good universality means that it is applicable to porous carbon materials obtained by various preparation methods (template method, 3D printing, activation method).

[0038] In summary, this invention breaks through the limitation of the traditional Gibson-Ashby model, which only considers total porosity, and can accurately predict the elastic modulus and strength of materials. It is applicable to a variety of material systems, including porous carbon, ceramics, and metals.

[0039] In a preferred embodiment, the formula for the third-level extended Gibson-Ashby model of the prediction modulus is as follows: ; E* is the predicted modulus value, and E0 is the modulus of the fully dense, non-porous material that constitutes the skeleton. C M C is the topological geometric constant of the macropore. m For mesoporous topological geometric constants; , as well as The parameters all refer to nested porosity definitions, which are based on the total material volume, the solid volume of macropore walls, and the solid volume of mesopore walls, respectively. n M n is the large hole deformation index. m n is the mesoporous deformation index. µ The micropore deformation index.

[0040] This model decomposes the macroscopic modulus of a material into a product of macroporous topological weakening factors, mesoporous framework weakening factors, and microporous matrix weakening factors. It also introduces for the first time a deformation mechanism index based on the inherent properties of pores at each level.

[0041] In this invention, step one involves obtaining the tertiary pore structure parameters of the porous material, including nested porosity. (Based on total material volume), nested porosity (Based on the solid volume of the macroporous wall) and nested porosity (Based on the solid volume of the mesoporous wall); Step 2, obtain the deformation mechanism index of each level of pores in the porous material, including the macropore deformation index n. M Mesoporous deformation index n m and the micropore deformation index n µ Step 3: Calculate the macroscopic relative modulus of the porous material by substituting the numerical value into the third-order extended Gibson-Ashby model formula. Step 4: Calculate the macroscopic absolute modulus by substituting the known numerical value into the third-order extended Gibson-Ashby model formula to obtain the predicted value of the macroscopic absolute modulus.

[0042] In a preferred embodiment, the method of the present invention further includes the following steps: Design optimization: If the predicted modulus value is lower than the application requirements, adjust the input parameters and, under the constraint of a fixed total porosity, use the model to find the optimal parameters. , , This allocation maximizes the modulus.

[0043] In a preferred embodiment, the method of the present invention further includes the following steps: Experimental verification and model calibration: Porous materials were prepared based on the optimized parameters; The macroscopic modulus was measured using nanoindentation, AFM, and / or the microcantilever beam method. The measured modulus values ​​were compared with the predicted modulus values, and the exponent n in the model was adjusted. M n m n µ and the constant C M and C m This allows for model calibration for specific material systems, thereby improving the accuracy of subsequent predictions.

[0044] In a preferred embodiment, the formula for the third-level extended Gibson-Ashby model for predicting intensity is as follows: ; * This is the predicted intensity value. The intrinsic strength of a completely dense, non-porous material that forms the framework; K is a geometric constant related to the sensitivity to macroscopic large-pore defects; m M m m and mµ These are the fracture strength indices, representing the strength indices corresponding to macropores, mesopores, and micropores, respectively.

[0045] In this invention, step one involves obtaining the tertiary pore structure parameters of the porous material, including nested porosity. (Based on total material volume), nested porosity (Based on the solid volume of the macroporous wall) and nested porosity (Based on the solid volume of the mesoporous wall); Step 2, obtain the fracture strength index of each level of pores in the porous material, including the macropore strength index m. M Mesoporous strength index m m and the micropore strength index m µ Step 3: Calculate the fracture strength. Substitute the numerical values ​​into the third-order extended Gibson-Ashby model formula to calculate the relative fracture strength. The fracture strength of the dense phase can be obtained through micropillar compression or theoretical values ​​to calculate the predicted value of macroscopic fracture strength.

[0046] In a preferred embodiment, the shape of the macropore and the radius of curvature of the connecting neck can be analyzed using SEM / TEM images to assess stress concentration, thereby determining the macropore strength index m. M .

[0047] In a preferred embodiment, the mesopore connectivity can be analyzed by gas adsorption, and the carbon wall brittleness can be assessed by combining nanoindentation and / or micromechanical testing, thereby determining the mesopore strength index m. m .

[0048] In a preferred embodiment, the micropore strength index m can be determined by analyzing the disorder (ID / IG ratio) and / or defect density of carbon using Raman spectroscopy and / or XPS, and correlating this with the micropore defect concentration. µ .

[0049] In a preferred embodiment, the method of the present invention further includes the following steps: Simultaneously calculate the predicted values ​​of elastic modulus and strength, establish isomodulus lines and isostrength lines, and obtain a pore structure design window that meets the strength and modulus requirements.

[0050] According to a second aspect of the present invention, an application of the prediction method described in any of the above claims in materials design and performance prediction is provided.

[0051] The application of the prediction method of this invention is beneficial to the optimization of material structure design, especially in fields with stringent requirements for material mechanical properties, such as long-life lithium-ion battery anodes, lightweight and high-strength structural materials, and durable design of catalyst supports. It can effectively shorten the research and development cycle and reduce development costs.

[0052] In a preferred embodiment, the materials used in this invention include, but are not limited to, at least one of porous carbon, porous ceramics, metal foam, porous polymers, biological scaffolds, and aerogels.

[0053] The present invention will be further illustrated by the following examples. Unless otherwise specified, the materials in the examples are prepared according to existing methods or purchased directly from the market.

[0054] Examples 1-6 Examples 1-6 provide a method for predicting the macroscopic elastic modulus and strength of porous materials: Modulus prediction and performance optimization of porous materials, see flowchart. Figure 5 This includes the following steps: Step 1: Obtain or design the target tertiary pore structure parameters Obtain the following parameters for the porous material to be predicted or designed: Macroporous structure parameters: Macroporous porosity And large-pore topology types (such as open-cell foam, closed-cell foam, truss structure). Mesoporous structure parameters: mesoporous porosity ; Micropore structure parameters: micropore porosity ; In practical characterization, what is more commonly obtained is the volume of pores at each level. , and The corresponding porosity is given by the following formula: ; ; ; In nested models The relationship is: ; ; ; Step 2: Determine the deformation mechanism index of pores at each level. Based on pore structure and solid material properties, three key indices were determined: Large hole deformation index The topology of the large hole is determined; typically, the dominant structures are those with openings and bends. =2, closed-cell, membrane stretching dominant structure is taken =1, for tension-dominated truss structures, take =1; Mesoporous deformation index The deformation is determined based on the slenderness ratio and connectivity of the mesopore wall; when the mesopore wall is thick and the connectivity is good, the deformation is mainly axial tension and compression, and the following values ​​are taken: =1, when the mesopore wall is slender and easily bent, take =2; Micropore deformation index Micropores, acting as point defects, uniformly weaken the matrix; typically, they are taken as... =2~3, recommended value =3 (corresponding to a strong weakening effect); Step 3: Calculate the macroscopic relative modulus of the porous material Substitute the above values ​​into the formula of the third-order extended Gibson-Ashby model to calculate the macroscopic relative modulus of the material. ; E* is the predicted modulus value, and E0 is the modulus of the fully dense, non-porous material that constitutes the skeleton. C M C is a geometric constant related to the topology of macropores. m These are geometric constants related to mesoporous topology; Step 4: Calculate the macroscopic absolute modulus and provide design feedback Predicted modulus: Substitute the known values ​​into the formula of the third-level extended Gibson-Ashby model to calculate the predicted value of the macroscopic absolute modulus; Design optimization: If the predicted modulus is lower than the application requirements (such as the minimum constraint modulus required for silicon-carbon anodes), adjust the input parameters: prioritize increasing the modulus. (Change the topology of the macropore) or reduce (Reduce macroporosity), and secondly consider reducing... and Under the constraint of a fixed total porosity, the optimal value is sought using a model. , , Allocation to maximize the modulus; Step 5: Experimental Verification and Model Calibration (Optional). Prepare porous carbon materials based on the optimized parameters; measure their macroscopic modulus using nanoindentation, AFM, or the microcantilever beam method; compare the measured values ​​with the predicted values; and fine-tune the exponents in the model. , and ,constant This enables model calibration for specific material systems, improving the accuracy of subsequent predictions; Strength prediction and performance optimization of porous materials, see flowchart. Figure 5 This includes the following steps: Step 1: As described above, obtain the tertiary pore parameters; Step 2: Determine the fracture strength index of each porosity level; By analyzing the shape of the macropore and the radius of curvature of the connecting neck using SEM / TEM images, stress concentration was assessed and determined. ; The connectivity of mesopores (adsorption-desorption hysteresis loop shape) was analyzed by gas adsorption, and the carbon wall brittleness was assessed by nanoindentation or micromechanical testing to determine... ; By analyzing the disorder (ID / IG ratio) or defect density of carbon using Raman spectroscopy or XPS, and correlating it with the micropore defect concentration, m can be determined. µ ; Step 3: Calculate the fracture strength and perform damage resistance design. Substitute the above values ​​into the model formula to calculate the relative fracture strength; obtain the fracture strength of the dense carbon phase through micropillar compression or theoretical values, and calculate the predicted value of macroscopic fracture strength. ; * This is the predicted intensity value. The intrinsic strength of a completely dense, non-porous material that forms the framework; K is a geometric constant related to the sensitivity to macroscopic large-pore defects; Step 4: Damage Resistance Design Optimization: If the prediction strength is insufficient, the model will quantitatively indicate which index value is too high; Targeted optimization: If If the height is too high, optimize the large hole topology, increase the radius of curvature of the hole edge, and thicken the connecting neck; if... If the concentration is too high, it will reduce mesopore connectivity, or the toughness of the carbon wall can be enhanced through doping or graphitization; if... If the temperature is too high, reduce the micropores, increase the carbonization temperature, or use a graphitized catalyst. Step 5: Experimental verification and calibration. The actual fracture strength is measured by three-point bending, compression or single-sided notched beam experiments at the micron or macro scale, and compared with the predicted value to calibrate the index.

[0055] Stiffness-strength collaborative design: Simultaneously calculate the modulus and strength, and plot them as follows: , and Find the isomodulus and isostrength lines of the variables in the figure to locate the "safe design window" that meets the minimum modulus and minimum strength requirements, and use it to guide material synthesis.

[0056] The effects of different mesopore distributions on the modulus and strength of porous carbon materials in Examples 1-6 (same as total porosity) are shown in the table below.

[0057] Taking Example 1 as an example, the calculation process is as follows: Φ macro=0.6, Φ meso =0.3, Φ micro =0.1 Substitute: E* / E0 = (1-0.6) 2 (1-0.3) 1 (1-0.1) 3 =0.082 σ* / σ0 = (1-0.6) 1.5 (1-0.3) 1 (1-0.1) 2 =0.093 The modulus prediction results E*, from high to low, are Example 4, Example 3, Example 1, Example 2, Example 5, and Example 6.

[0058] Intensity prediction results * From highest to lowest, they are Example 4, Example 3, Example 1, Example 2, Example 5, and Example 6.

[0059]

[0060] The results show that, under the same total porosity, allocating as many pores as possible to mesopores and minimizing the pore volume fraction occupied by micropores can result in higher predicted modulus and strength.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the macroscopic elastic modulus and strength of porous materials, characterized in that, Includes the following steps: (1) Obtain the third-order pore structure parameters of the porous material, including: Nested porosity based on the total volume of the material Nested porosity based on the solid volume of macropore walls And nested porosity based on mesoporous wall solid volume. ; (2) Determine the deformation mechanism index and fracture strength index corresponding to each level of porosity, including: Deformation mechanism indices include the large-pore deformation index n M Mesoporous deformation index n m and the micropore deformation index n µ ; Fracture strength index includes macroporous strength index m M Mesoporous strength index m m and the micropore strength index m µ ; (3) Based on the three-level nested pore structure, a modulus prediction model is constructed to calculate the predicted value of the macroscopic elastic modulus of porous materials: ； E* is the macroscopic elastic modulus of porous materials, and E0 is the elastic modulus of dense matrix materials; C M C is the topological geometric constant of the macropore. m For mesoporous topological geometric constants; (4) Construct a fracture strength prediction model based on a three-level nested pore structure and calculate the predicted macroscopic strength of porous materials: ； * For the macroscopic fracture strength of porous materials, For dense matrix materials, K is the geometric constant sensitive to large pore defects; (5) Based on the predicted elastic modulus and strength values, optimize the pore structure or predict the performance of the porous material.

2. The prediction method according to claim 1, characterized in that, The nested porosity satisfies: ； Φ total The total porosity of the porous material.

3. The prediction method according to claim 1, characterized in that, The large hole deformation index n M Determined based on the macroporous topology: Open-cell foam structure n M = 2; Closed-cell foam structure n M = 1; Truss structure n M = 1.

4. The prediction method according to claim 1, characterized in that, The mesoporous deformation index n m Determined based on mesoporous connectivity: Bending dominant structure n m = 2; Tension-dominant structure n m = 1.

5. The prediction method according to claim 1, characterized in that, The micropore deformation index n µ The range of values ​​is 2 ≤ n µ ≤ 4.

6. The prediction method according to claim 1, characterized in that, The macroporous strength index m m Determined based on the shape of the large hole: For perforated truss structures with smooth perforation edges and robust connections, m M =1.5; For random foam structures with sharp, crack-like pore edges, m M =2.0~2.

5.

7. The prediction method according to claim 1, characterized in that, The mesoporous strength index m m Determined based on mesoporous connectivity: For isolated, spherical mesopores, m m =1; For highly interconnected mesopores that form through channels, m m =2.0~3.

0.

8. The prediction method according to claim 1, characterized in that, The micropore strength index m µ The value range is 2 ≤ m µ ≤ 4.

9. The prediction method according to any one of claims 1-8, characterized in that, The macropore parameters in the three-level pore structure parameters were obtained by SEM or X-ray CT. The mesopore parameters of the tertiary pore structure were obtained by gas adsorption. The micropore parameters in the three-level pore structure parameters are obtained by BET or density method.

10. The prediction method according to any one of claims 1-8, characterized in that, The fracture strength index includes the macroporous strength index m. M The shape of the macropores was determined by SEM or TEM analysis. The fracture strength index and the intermediate hole strength index m m Determined by gas adsorption and nanoindentation; The fracture strength index includes the micropore strength index m. µ Determined by Raman or XPS analysis.

11. The prediction method according to any one of claims 1-8, characterized in that, When the predicted elastic modulus is lower than the target value, the total porosity Φ total Under fixed conditions, by adjusting , , The allocation ratio is determined to obtain the maximum elastic modulus.

12. The prediction method according to any one of claims 1-8, characterized in that, Simultaneously calculate the predicted values ​​of elastic modulus and strength, establish isomodulus lines and isostrength lines, and obtain a pore structure design window that meets the strength and modulus requirements.

13. The application of the prediction method according to any one of claims 1-12 in materials design and performance prediction.

14. The application according to claim 13, characterized in that, The material includes at least one of porous carbon materials, porous ceramics, metal foams, porous polymers, biological scaffolds, and aerogels.

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