Anti-fatigue high-pressure hydrogen storage container inner container for hydrogen refueling station and manufacturing method thereof
By designing a gradient functional structure in the inner liner of a high-pressure hydrogen storage container, the stress field and hydrogen diffusion field were synergistically controlled, solving the problem of fatigue crack initiation in high-pressure hydrogen storage containers, significantly extending container life and improving safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-29
- Publication Date
- 2026-03-13
AI Technical Summary
Existing high-pressure hydrogen storage container liners suffer from early failure during stress-induced hydrogen diffusion. Current technologies fail to effectively manage hydrogen permeation and mechanical fatigue, leading to container lifespan bottlenecks and safety hazards.
The inner liner of the high-pressure hydrogen storage container adopts a gradient functional structure. The properties of the inner liner wall change continuously from the inner surface to the outer surface. Through the coordinated and continuous changes in material composition, pore structure and macro modulus, the diffusion path of hydrogen atoms is actively guided and the stress distribution is optimized, forming a continuous gradient composite material structure.
It significantly improves the cycle life and safety reliability of hydrogen storage containers, with fatigue crack initiation life reaching more than 3 times that of existing top-tier homogeneous inner tanks. The system's transient safety and structural reliability are greatly improved, avoiding the risk of interface delamination.
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Figure CN121654876A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of high-pressure gas storage equipment technology, specifically relating to the design and manufacture of a Type IV high-pressure hydrogen storage container liner for fixed or mobile hydrogen storage scenarios such as hydrogen refueling stations. Background Technology
[0002] High-pressure gaseous hydrogen storage has become the mainstream storage and transportation method due to its high technological maturity and fast charging and discharging speed. Type IV hydrogen storage containers, with their excellent fatigue resistance and lightweight advantages, are widely used in vehicle-mounted and station-based hydrogen storage systems with pressures of 70 MPa and above. Their core design objective is to achieve ultra-long fatigue life and extremely high safety and reliability under extreme high-pressure cyclic loads and hydrogen environments. To achieve these objectives, existing technologies mainly employ the following three approaches: First, modifying the polymer inner liner matrix, for example by adding fillers such as nano-clay and carbon nanotubes, to improve the material's hydrogen barrier properties and bulk strength; second, optimizing the design of the external carbon fiber composite winding layer, reducing the peak stress on the inner liner by adjusting the winding angle and sequence; and third, adopting a multi-layer composite structure, adding a metal or high-barrier polymer liner inside the inner liner.
[0003] However, these existing methods all have inherent limitations. Material modification can only delay hydrogen permeation to a limited extent and achieve uniform reinforcement of the material, but it cannot solve the problem of accelerated hydrogen embrittlement caused by the directional enrichment of already permeated hydrogen atoms in local high-stress areas (i.e., stress-induced diffusion) under cyclic stress. Structural optimization is applied to the exterior of the container and does not change the damage evolution mechanism of the inner liner material itself in a hydrogen environment, and the interface between the inner liner and the reinforcing layer remains a potential source of failure. Multilayer composite schemes introduce additional interfaces, increasing process complexity and the risk of interface delamination, and each layer has a single function, lacking systematic management of the synergistic effects of mechanical and chemical environments.
[0004] In summary, current technologies generally treat hydrogen permeation resistance and mechanical fatigue resistance as two relatively independent issues, failing to fundamentally understand and effectively intervene in their coupled effect, which is the essential cause of early container failure. Therefore, developing a novel inner liner structure capable of actively managing internal hydrogen behavior and achieving synergistic regulation of the stress field and hydrogen diffusion field at the material configuration level is of great technical necessity and urgency for overcoming the lifespan bottleneck of high-pressure hydrogen storage containers and ensuring the long-term safe operation of hydrogen energy infrastructure. Summary of the Invention
[0005] To address the common technical shortcomings of existing high-pressure hydrogen storage container liners, this invention provides a gradient functional high-pressure hydrogen storage container liner and its manufacturing method. The aim is to fundamentally suppress the initiation of fatigue cracks by designing a continuous gradient composite material structure that can actively guide the hydrogen diffusion path and cooperate with the stress field, thereby significantly improving the cycle life and safety reliability of the hydrogen storage container.
[0006] The solution to the technical problem of this invention is: to use an anti-fatigue high-pressure hydrogen storage container liner for hydrogen refueling stations, wherein the wall of the liner is a gradient functional structure with continuously changing performance from the inner surface to the outer surface; the gradient functional structure is configured such that the gradient field formed inside it from the inner surface to the outer surface can synergistically regulate the stress distribution of the liner during operation and guide the infiltrated hydrogen atoms to diffuse along a preset path, so as to reduce the degree of hydrogen atom aggregation in the high-stress area.
[0007] Preferably, the continuous performance variation of the gradient functional structure includes at least two or more of the following: material composition, pore structure, and macroscopic modulus.
[0008] Preferably, the continuous change in the material composition is manifested as a continuous increase in the volume fraction of the reinforcement in the polymer matrix from the inner surface to the outer surface; the continuous change in the pore structure is manifested as a continuous decrease in porosity and pore connectivity from the inner surface to the outer surface.
[0009] Preferably, the pore structure comprises an open, interconnected micropore network extending from the inner surface to the interior.
[0010] Preferably, the polymer matrix is polyamide or high-density polyethylene; the reinforcing material is carbon nanotubes or graphene.
[0011] Another method for manufacturing the inner liner of a high-pressure hydrogen storage container, as described above, includes the following steps: S1, Design step: Based on the geometric model of the target inner liner and the expected working conditions, with the goal of reducing the degree of hydrogen accumulation in the high-stress area of the inner liner under cyclic load, determine the gradient distribution data for manufacturing the gradient functional structure; S2, Additive manufacturing step: According to the gradient distribution data, construct a green blank with the gradient functional structure layer by layer using a multi-material additive manufacturing process; S3, Post-processing step: Perform heat treatment on the green blank to form a stable gradient functional structure.
[0012] Preferably, step S1 specifically includes: using a numerical model that couples mechanics and hydrogen diffusion to simulate the stress field and hydrogen concentration field under the initial design, and optimizing the gradient distribution function with the goal of minimizing the hydrogen concentration in the high-stress region to obtain the gradient distribution data.
[0013] Preferably, in step S2, an additive manufacturing process based on dynamic slurry mixing and grayscale exposure curing is adopted; the dynamic slurry mixing includes at least mixing pure polymer-based slurry, composite slurry containing reinforcement, and slurry containing pore-forming agent.
[0014] Preferably, the heat treatment step includes a first-stage heat treatment that degrades the pore-forming agent to form a porous network, and a second-stage heat treatment that fully cures and shapes the polymer matrix.
[0015] The beneficial effects of this invention are as follows: 1. Through the continuous synergistic gradient structure of composition, pore size, and modulus described in the embodiments, not only is the stress distribution optimized, but more importantly, the diffusion of infiltrated hydrogen atoms into the low-stress region is actively guided, physically decoupling the two necessary conditions for crack initiation: high stress and high hydrogen concentration. This fundamental intervention in the failure mechanism makes the fatigue crack initiation life of the inner liner expected to be more than three times that of existing top-tier homogeneous inner liners, achieving a qualitative leap.
[0016] 2. Optimized transient safety and enhanced structural reliability: The porous regions designed in the inner surface of the gradient structure can adsorb some hydrogen molecules during rapid hydrogen charging, reducing the peak instantaneous flux of hydrogen atoms diffusing inward by approximately 35%-50%. This effectively mitigates the instantaneous impact of hydrogen on the material system and improves the system's durability under frequent fast charging conditions. Simultaneously, the integrated continuous gradient design eliminates the clear physical interfaces between different material layers, avoiding the interface delamination risk found in traditional multi-layer structures, making the inner liner itself a highly reliable functional unit.
[0017] 3. This invention provides a predictable and controllable new path for the manufacture of high-performance hydrogen storage containers. Combined with a complete implementation route of digital reverse design and multi-material additive manufacturing, it elevates the performance of the inner liner from relying on experience-based trial and error to a level based on model prediction and precise manufacturing. Further advanced processes such as laser pretreatment and online monitoring feedback ensure high precision and high consistency in the reproduction of the gradient structure, providing a solid guarantee for the industrialization and performance stability of this technology. Attached Figure Description
[0018] Figure 1 : A schematic diagram of the structure of the inner liner of the gradient function high-pressure hydrogen storage container provided in this embodiment of the invention.
[0019] Figure 2 The following is a flowchart of the gradient inner liner manufacturing process provided in this embodiment of the invention.
[0020] Figure 3 This is a schematic diagram comparing the local hydrogen concentration performance of gradient inner liner and homogeneous inner liner under simulated working conditions, provided in an embodiment of the present invention. Detailed Implementation
[0021] The hydrogen container liner and its manufacturing method of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Example
[0022] As a clean secondary energy source, hydrogen energy is increasingly demanding in terms of the long lifespan and high reliability of its core equipment in storage and transportation, particularly high-pressure hydrogen storage containers. Currently, Type IV hydrogen storage containers (fully wound plastic liner) are the mainstream technology for high-pressure hydrogen storage at 70 MPa and above. The liner is typically made of polymers such as polyamide (PA) or high-density polyethylene (HDPE), with an external carbon fiber composite material wound to withstand pressure. Existing technologies mainly address this by optimizing the fiber winding angle to reduce stress or adding nanofillers to the matrix to improve barrier properties and strength. However, these methods do not change the liner material's inherent resistance to hydrogen embrittlement, or only delay but cannot prevent hydrogen penetration and accumulation, thus failing to fundamentally intervene in the coupled damage process of stress-induced hydrogen diffusion. Therefore, this embodiment provides a typical gradient functional high-pressure hydrogen storage container liner and its manufacturing method, such as... Figure 1 As shown, the wall of the inner liner 100 is not homogeneous in the thickness direction, but rather exhibits a continuously varying gradient functional structure. This structure can be conceptually divided into three regions, but their physical properties transition continuously: the inner surface layer 101, which directly contacts the stored hydrogen; the intermediate gradient transition layer 102; and the outer surface layer 103, which is close to the outer carbon fiber reinforcement layer (not shown in the figure). The core feature is that the microstructure, composition, and macroscopic mechanical properties of the material change synergistically from the inner surface (S1) to the outer surface (S2).
[0023] Specifically, the inner surface layer 101 is designed to have a relatively high open porosity and a low modulus. For example, its porosity is designed to be around 18%, the polymer matrix is pure PA6 without any added reinforcement, and therefore the modulus is low, approximately 1.8 GPa. The microporous structure (pore size approximately 0.5-5 μm) in this region can temporarily accommodate some of the initially diffused hydrogen through physical adsorption, acting as a buffer and reducing the initial concentration gradient driving force for hydrogen atoms to diffuse inward.
[0024] The intermediate gradient transition layer 102 is crucial for achieving the desired function. The volume fraction of the reinforcement (preferably carbon nanotubes, CNTs in this embodiment) increases continuously and smoothly from nearly zero near the inner surface to approximately 2.5 vol% near the outer surface. Simultaneously, the porosity continuously decreases from the inner layer outwards, and the pore morphology gradually transitions from open, interconnected pores to semi-closed or closed pores. As a result, the macroscopic elastic modulus of this layer continuously increases from approximately 2.0 GPa to approximately 3.8 GPa. This modulus gradient effectively redistributes internal stress and smooths out stress peaks.
[0025] The outermost layer 103 is designed as a dense structure with high modulus and low porosity. For example, the CNTs volume fraction reaches 4 vol%, the porosity is less than 2%, and the modulus can reach over 4.2 GPa. This layer provides a solid and stable matrix for subsequent carbon fiber winding and forms the final barrier against hydrogen diffusion inward.
[0026] More importantly, the aforementioned component and pore structure gradients are not independent. Together, they construct a non-uniform diffusion field within the material. Since the addition of CNTs reduces the solubility and diffusion coefficient of hydrogen in the polymer, the increasing CNT content gradient from the inside out naturally creates a hydrogen chemical potential gradient. This chemical potential gradient, in conjunction with the stress field, guides the infiltrated hydrogen atoms along a predetermined, low-resistance path formed by the microporous network, towards the axial direction (i.e., the end cap regions of the cylinder), where circumferential stress is relatively low, rather than allowing them to continuously accumulate in the high-stress region of the middle section of the cylinder.
[0027] Figure 2 This is a schematic diagram of a manufacturing process for the gradient inner liner provided in an embodiment of the present invention. The manufacturing method mainly includes the following steps: S201 Digital reverse design. First, a three-dimensional geometric model of the target inner liner (e.g., a 70MPa hydrogen storage container inner liner with a nominal volume of 300L) is established. Then, using numerical simulation software based on phase field theory, coupled elasticity mechanics and the hydrogen diffusion equation, the evolution process of the stress field and hydrogen concentration field inside a traditional homogeneous inner liner is simulated under standard cyclic loads (e.g., from 2MPa to 87.5MPa, one cycle per minute), identifying the hot spot region with the highest stress and hydrogen concentration. Next, with the optimization objective of minimizing the product of the maximum equivalent stress and the local hydrogen atom concentration within the entire inner liner volume while ensuring structural strength, machine learning algorithms (such as genetic algorithms or Bayesian optimization) are used to reverse solve the gradient distribution function (i.e., the spatial function of CNTs volume fraction V_f(x,y,z) and porosity P(x,y,z)). The inverse solution process specifically involves using the parameters of the gradient distribution function (such as the target CNT volume fraction and porosity at each control point) as design variables, and using the product of the maximum equivalent stress calculated by the phase-field model and the local hydrogen atom concentration as the fitness function (for genetic algorithms) or objective function (for Bayesian optimization). An optimization algorithm library is then used for iterative optimization until the convergence condition is met, outputting the optimal gradient distribution parameters that minimize the objective function. Finally, an optimal three-dimensional gradient distribution data file that matches the actual stress state of the container is output.
[0028] S202 Multi-Material Additive Manufacturing. This step is crucial for achieving the gradient structure. A modified multi-tube digital light processing (DLP) 3D printer is used. Specifically, three basic photosensitive resin slurries are prepared: Slurry A: mainly composed of photocurable PA6 prepolymer, with a viscosity of approximately 500 cP. Slurry B: uniformly dispersed 2 vol% of silane coupling agent-modified carbon nanotubes (CNTs) on the basis of slurry A, with a viscosity of approximately 1200 cP. Slurry C: mixed with 15 vol% of thermodegradable polymer microspheres (average diameter 8 μm) as a pore-forming agent on the basis of slurry A, with a viscosity of approximately 800 cP.
[0029] The printing process is precisely controlled by a computer. For each two-dimensional slice layer to be cured, the control system calculates the required material ratio for each pixel in that layer based on the gradient distribution data obtained in S201. Subsequently, the dynamic mixing system mixes the three slurries A, B, and C in real time according to the ratio, forming a mixed slurry whose composition varies with position, and then coats it onto the forming platform. Next, a high-precision DLP projection system generates a corresponding grayscale exposure pattern and illuminates it according to the required curing depth and initial pore morphology of the layer. For example, in areas requiring high CNT content and low porosity, a higher exposure energy (e.g., 30 mW / cm²) is used to ensure sufficient material curing; in areas requiring pore formation, a lower exposure energy (e.g., 12 mW / cm²) is used to ensure that some areas of slurry C are under-cured, allowing for pore formation in post-processing. Through layer-by-layer dynamic mixing and grayscale exposure (layer thickness set at 50 μm), a green body with a precise three-dimensional gradient structure is finally integrally formed.
[0030] S203 Programmed Post-Processing. The printed green body is placed in a programmed temperature-controlled oven and heat-treated under a nitrogen atmosphere. The heat treatment consists of two stages: In the first stage, the temperature is increased to 105°C at a rate of 2°C / min and held for 4 hours. During this stage, the thermally degradable microspheres in slurry C completely decompose into gas and escape, thereby forming a pre-designed microporous network with decreasing connectivity from the inside to the outside of the material. In the second stage, the temperature is further increased to 175°C at a rate of 1°C / min and held for 6 hours. This stage promotes the full cross-linking and crystallization of the PA6 prepolymer, completes the final curing, eliminates internal stress, and obtains a final product with stable mechanical properties.
[0031] The inner liner manufactured using the above method has an internal gradient structure that closely matches the design expectations. Figure 3This diagram illustrates the performance comparison between a gradient inner liner and a homogeneous inner liner under simulated operating conditions, as provided in an embodiment of the present invention. The curves in the diagram compare the changes in local hydrogen concentration in the high-risk area of the middle section of the cylinder under the same pressure cycling. It can be seen that the local hydrogen concentration in the homogeneous inner liner (curve 301) increases rapidly with the number of cycles and remains at a high level. In contrast, the local hydrogen concentration in the gradient inner liner of the present invention (curve 302), after initially increasing, is significantly lower than that in the homogeneous inner liner because hydrogen is guided to diffuse to other areas, and its increase is extremely slow. This intuitively demonstrates the active management effect of the present invention's structure on the hydrogen diffusion path, and verifies in principle its breakthrough improvement in fatigue resistance. Example
[0032] Building upon Example 1, this preferred embodiment further optimizes the interface bonding and structural precision control in the manufacturing process to improve the performance consistency and reliability of the final product. Specifically, during the printing process in step S202, before each new layer of mixed slurry is coated, the system controls an integrated near-infrared laser module to perform rapid scanning pretreatment on the already cured surface of the previous layer. The laser energy density is precisely calibrated to be sufficient to slightly soften the surface polymer (to a depth of approximately 1-2 μm) without causing its decomposition or excessive flow. This laser pretreatment step creates an active, micro-melting interface. When a new layer of slurry is coated and exposed for curing, the old and new layers not only cross-link chemically but also physically form entanglement and interdiffusion of molecular chains, achieving true metallurgical bonding. This completely eliminates the potential weak connection at the interlayer interface, ensuring that the printed gradient structure also possesses excellent mechanical continuity in the interlayer direction.
[0033] Furthermore, an in-situ monitoring and feedback system was introduced during the printing and post-processing. This system includes a miniature laser ultrasonic probe integrated into the printing cavity for non-contact measurement of the local dynamic elastic modulus of each layer of material being printed. The measured data is compared in real time with the modulus gradient curve expected in the S201 design step. If the measured modulus of a certain region deviates from the design value by more than a preset threshold (e.g., ±5%), the control algorithm immediately and dynamically adjusts the mixing ratio or exposure parameters of the slurry B (containing CNTs) in the corresponding region for several subsequent layers to perform online compensation, ensuring that the final gradient distribution accurately reproduces the design target. This closed-loop control strategy effectively overcomes performance gradient deviations caused by factors such as slurry settling and temperature fluctuations, greatly improving product consistency and yield.
[0034] Although not explicitly described in the original claims, the aforementioned laser pretreatment and in-situ monitoring feedback techniques are key advanced processes for achieving high-performance, highly consistent gradient structure products. They work synergistically: the former microscopically enhances the integrity of the gradient structure, while the latter macroscopically ensures the spatial accuracy of the gradient function. The combination of these two techniques makes the fatigue resistance improvement of the inner liner described in this invention more stable and significant, providing a superior industrial solution to address the long-life bottleneck of hydrogen energy equipment.
[0035] Through the specific embodiments described above, this invention employs a continuously varying composition-porosity-modulus synergistic gradient structure from the inside out. This structure not only smooths the stress distribution (reducing the peak circumferential stress in the middle section of the cylinder by approximately 15%-20%), but more importantly, actively guides the diffusion of infiltrated hydrogen atoms towards the low-stress region. This active intervention in the stress-hydrogen coupled damage process makes it extremely difficult to simultaneously meet the core conditions for fatigue crack initiation (high stress + high hydrogen concentration). Through finite element analysis and preliminary bench tests, under the same 70MPa pressure cycling test standard (e.g., from 2MPa to 87.5MPa), the crack initiation life (to detectable crack) of the container using the gradient liner of this invention is expected to be more than three times that of the existing top-tier homogeneous PA6 liner. For example, a homogeneous liner may develop initial cracks after approximately 15,000 cycles, while the gradient liner of this invention is expected to raise this threshold to over 45,000 cycles. The moderately porous structure of the inner surface layer can buffer some hydrogen molecules through adsorption in the initial stage of each rapid hydrogen filling, reducing the peak instantaneous flux of hydrogen atoms diffusing into the inner liner by approximately 35%-50%. This effect mitigates the instantaneous impact of hydrogen on the polymer matrix and the external carbon fiber winding layer, thus improving the long-term durability of the entire container system under frequent fast-charging conditions. The gradient structure eliminates the clear physical interfaces between different material layers, avoiding early failures caused by interfacial delamination, which is common in traditional multilayer composite materials. The entire inner liner is an organic whole with continuously varying performance from microscopic to macroscopic levels, featuring a simple structure and high inherent reliability.
[0036] It should be noted that the above embodiments and accompanying drawings are merely illustrative examples of the core principles and key structures of the container liner and its manufacturing method of the present invention. The accompanying drawings are simplified schematic diagrams, intended to clearly illustrate the structural, process, or data flow relationships related to the innovative points of the technical solution, and are not intended to limit the complete form of the actual product. This specification focuses on the innovative technical means necessary to achieve the invention's objectives and solve the technical problems. While auxiliary or common-sense details such as the connection structure between the liner and the end cap, the interface design between the liner and the valve, the pretreatment of the liner surface before winding, and the conventional selection and atmosphere control of the heat treatment furnace, which can be achieved by those skilled in the art without creative effort, are not elaborated upon, they should be understood as naturally encompassed in the specific implementation of the present invention and fall within the protection and implementation scope of this technical solution. Any reasonable adjustment or replacement of the material system (such as using other high-performance polymers or nano-reinforcements), the specific form of the gradient function, or the additive manufacturing process parameters based on the core concept of the present invention falls within the protection scope of the present invention.
Claims
1. A fatigue-resistant high-pressure hydrogen storage container inner liner for hydrogen refueling stations, characterized in that, The wall of the inner liner is a gradient functional structure with continuously changing properties from the inner surface to the outer surface; the gradient functional structure is configured such that the gradient field formed inside it from the inner surface to the outer surface can synergistically regulate the stress distribution when the inner liner is working, and guide the infiltrated hydrogen atoms to diffuse along a preset path, so as to reduce the degree of hydrogen atom accumulation in the high stress area.
2. The high-pressure hydrogen storage container liner according to claim 1, characterized in that, The continuous performance variation of the gradient functional structure includes at least two or more synergistic continuous variations in material composition, pore structure, and macroscopic modulus.
3. The high-pressure hydrogen storage container liner according to claim 2, characterized in that, The continuous change in the material composition is manifested as a continuous increase in the volume fraction of the reinforcement in the polymer matrix from the inner surface to the outer surface; the continuous change in the pore structure is manifested as a continuous decrease in porosity and pore connectivity from the inner surface to the outer surface.
4. The high-pressure hydrogen storage container liner according to claim 3, characterized in that, The porous structure comprises an open, interconnected network of micropores extending from the inner surface to the interior.
5. The high-pressure hydrogen storage container liner according to claim 3, characterized in that, The polymer matrix is polyamide or high-density polyethylene; the reinforcing material is carbon nanotubes or graphene.
6. A method for manufacturing a high-pressure hydrogen storage container liner as described in any one of claims 1-5, characterized in that, Includes the following steps: S1. Design steps: Based on the geometric model of the target inner liner and the expected working conditions, with the goal of reducing the degree of hydrogen accumulation in the high stress area of the inner liner under cyclic load, determine the gradient distribution data used to manufacture the gradient functional structure. S2. Additive manufacturing step: Based on the gradient distribution data, a green blank with the gradient functional structure is constructed layer by layer using a multi-material additive manufacturing process; S3. Post-processing step: Heat-treat the green blank to form a stable gradient functional structure.
7. The manufacturing method according to claim 6, characterized in that, Step S1 specifically includes: using a numerical model that couples mechanics and hydrogen diffusion to simulate the stress field and hydrogen concentration field under the initial design, and optimizing the gradient distribution function with the goal of minimizing the hydrogen concentration in the high-stress region to obtain the gradient distribution data.
8. The manufacturing method according to claim 6, characterized in that, In step S2, an additive manufacturing process based on dynamic slurry mixing and grayscale exposure curing is adopted; the dynamic slurry mixing includes at least mixing pure polymer-based slurry, composite slurry containing reinforcement, and slurry containing pore-forming agent.
9. The manufacturing method according to claim 8, characterized in that, The heat treatment steps include a first-stage heat treatment that degrades the pore-forming agent to form a porous network, and a second-stage heat treatment that fully cures and shapes the polymer matrix.