Method for preparing piezoelectric catalytic ceramic membrane at low temperature based on nano-particle modified rod-like barium titanate powder

By synthesizing rod-shaped BaTiO3 powder modified with nanoparticles under alkaline conditions and using sodium oleate to regulate crystal morphology and surface nanoparticle formation, the problem of preparing high-performance ceramic membranes was solved. This resulted in a piezoelectric catalytic ceramic membrane with high permeability flux and mechanical strength at low temperatures, exhibiting excellent separation and catalytic degradation functions.

CN120900434APending Publication Date: 2025-11-07JINGDEZHEN CERAMIC UNIV

Patent Information

Application Number
CN202511134336.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-08-14
Publication Date
2025-11-07

AI Technical Summary

Technical Problem

Existing technologies make it difficult to prepare high-performance ceramic membranes without increasing process flow and costs, especially the synthesis of rod-shaped BaTiO3 powder, which is difficult and traditional methods result in decreased porosity and weakened permeability.

Method used

Rod-shaped BaTiO3 powder modified with nanoparticles was synthesized in an alkaline environment using Bi4Ti3O12, BaCl·8H2O, sodium oleate and NaOH. Piezoelectric catalytic ceramic membrane was prepared by hydrothermal reaction and low-temperature calcination. The selective adsorption of sodium oleate was used to regulate the crystal morphology and surface nanoparticle generation, forming a serrated structure to improve permeation flux and mechanical strength.

Benefits of technology

A piezoelectric catalytic ceramic membrane with high permeability flux and mechanical strength was prepared at low temperature. It has good separation performance and catalytic degradation function, uniform pore size distribution, and surface structure that is conducive to liquid transport, thus reducing the preparation cost.

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Abstract

The invention discloses a method for preparing a piezoelectric catalytic ceramic membrane at low temperature based on nano-particle modified rod-like barium titanate powder, which comprises the following steps: preparing nano-particle modified rod-like BaTiO3 powder from Bi4Ti3O12, BaCl. 8H2O, sodium oleate, deionized water and a NaOH solution, granulating, pressing and calcining to obtain a ceramic membrane product, and further carrying out electric polarization to obtain the piezoelectric catalytic ceramic membrane. The rod-like BaTiO3 powder of the nanoparticles with high surface activity not only ensures the mechanical strength of the ceramic membrane, but also effectively reduces the firing temperature. Meanwhile, the surface of the prepared ceramic membrane is of a wormlike curved surface structure, the pore size distribution is uniform, the stable separation performance is achieved, and the catalytic degradation function is achieved after electric polarization. The method is green and energy-saving, and the product can be applied to the fields of solid / gas and liquid separation, water environment restoration and the like, and has good application value.
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Description

TECHNICAL FIELD

[0001] The application relates to the technical field of inorganic nonmetallic materials, in particular to a method for preparing a piezocatalytic ceramic membrane at low temperature based on nanoparticle-modified barium titanate powder. BACKGROUND

[0002] Separation is one of the most important units in modern industrial production process as a key link of process industry, in other words, the quality of separation determines the quality of downstream products. The membrane separation technology taking ceramic membranes as elements is gradually becoming the darling of the era in the separation field due to good environmental adaptability. In the separation process, the ceramic membrane needs to bear a certain transmembrane pressure difference and needs to maintain good separation efficiency, which undoubtedly puts forward requirements for the pore structure, connection strength and other properties of the ceramic membrane. However, since the performance of the ceramic membrane is directly related to the accumulation effect of the raw material powder and the neck connection formed in the sintering process, the connection sites of the conventional ceramic powder film are usually few and the formed neck strength is weak. Therefore, in order to improve the strength and permeation flux of the ceramic membrane, one performance is often sacrificed, for example, increasing the calcination temperature can form a strong connection neck to improve the strength of the ceramic membrane, but will lead to the decrease of porosity and the weakening of permeability. Although there are some ways to improve the membrane permeability at present, such as further modifying the membrane surface on the basis of obtaining a high-strength ceramic membrane to improve the permeability by improving the membrane pore and the diffusion rate of water in the membrane pore, the additional processing processes such as organic grafting and inorganic nanoparticle deposition increase the process flow and cost of membrane preparation. Therefore, on the basis of not performing secondary membrane modification, simple and efficient preparation of high-performance ceramic membranes has important significance for further exerting the inherent advantages of the ceramic membranes and the potential value of the ceramic membranes in the process industry field.

[0003] It is a reliable choice to prepare ceramic membranes with particles such as rods having high specific surface area to obtain high permeation flux. During the process of packing molding, the anisotropic shape of the rod-shaped particles is more likely to cross, bridge and arch, forming a more open and through three-dimensional network structure, thereby exhibiting higher permeation flux and smaller permeation resistance. Furthermore, the large amount of surface particles can effectively increase the specific surface area and surface energy of the rod-shaped particles, and the surface particles can act as "activation points" to effectively promote the mass transfer during the sintering process. BaTiO3 is a ceramic powder with wide raw material sources and simple synthesis. The ceramic membrane prepared with BaTiO3 as raw material will have significant economic advantages. More importantly, BaTiO3 also has piezoelectric properties. The prepared piezoelectric ceramic membrane can not only have physical separation function but also have catalytic degradation function, which can undoubtedly play an important role in environmental remediation. However, since BaTiO3 belongs to perovskite structure, it is easy to change to cubic structure during growth, which increases the difficulty of synthesizing rod-shaped structure. At present, the main methods for synthesizing rod-shaped BaTiO3 powder are hydrothermal / solvothermal method (CN102351238B, CN104909448A, CN105293584A, CN106517263A, CN108275799A, CN109574152A / CN104909448A, CN110563016A), molten salt method (CN103922348B), template method (CN106517263A) and the like. Specifically, the hydrothermal / solvothermal method usually needs to adjust the conditions such as alkali concentration, surfactant and temperature to realize directional growth, and then obtain rod-shaped structure. However, due to the closed high-pressure environment of hydrothermal method, which is conducive to the ordered arrangement of atoms, and the alkaline condition which promotes the "Oswald ripening" process, the rod-shaped BaTiO3 synthesized is usually smooth in surface. Moreover, in order to have nano-particles on the surface, secondary treatment is often used as a trade-off (such as CN105293584A). Therefore, simple and efficient synthesis of rod-shaped BaTiO3 powder with surface nano-particle modification and the ceramic membrane prepared therefrom is still a big problem in the field of high-performance ceramic membrane preparation. SUMMARY

[0004] The present application overcomes the problems of the prior art and provides a method for low-temperature preparation of piezoelectric catalytic ceramic membranes based on nanoparticle-modified rod-shaped barium titanate powder, which is low in cost, simple in process and suitable for large-scale production.

[0005] The technical scheme of the present application is: a method for low-temperature preparation of piezoelectric catalytic ceramic membranes based on nanoparticle-modified rod-shaped barium titanate powder, characterized by comprising the following steps: Step one: Bi4Ti3O 12 , BaCl·8H2O and sodium oleate are dissolved in deionized water, and after being uniformly dissolved and stirred, NaOH solution is added and stirred to obtain a light yellow suspension; Step two: the light yellow suspension prepared in step one is put into a hydrothermal reactor to obtain white wet powder by hydrothermal reaction; Step three: the white wet powder prepared in step two is washed to neutral, and is further filtered and dried to obtain rod-shaped BaTiO3 powder modified by nanoparticles; Step four: the rod-shaped BaTiO3 powder prepared in step three is subjected to spray-grinding granulation, and is put into a steel mold after standing for 36 h to obtain a green body by pressing; Step five: the green body prepared in step four is calcined in a muffle furnace and is cooled with the furnace to obtain a ceramic membrane product; Step six: the ceramic membrane product prepared in step five is coated with silver electrodes on both sides, and is calcined at 500 ℃ for 2 h. The ceramic membrane product with the back silver electrode is connected to a power supply and is immersed in insulating oil at 85 ℃ for electrode polarization. The ceramic membrane product after polarization is immersed in 60 ℃ anhydrous ethanol for 2 h until the water flux is restored. Finally, the ceramic membrane product is polished to remove the silver electrode, is washed by ultrasonic, and is dried after removing the surface particles. After cooling, a piezocatalytic ceramic membrane product is obtained.

[0006] The Bi4Ti3O 12 The mass ratio of BaCl2·8H2O, sodium oleate and deionized water is 0.9-1.4:2.3-3.5:0.1-0.2:50-70; the mass ratio of NaOH solution and deionized water is 4.5-5.2:100.

[0007] The hydrothermal reaction temperature in step two is 240 ℃, and the holding time is 20 h.

[0008] In step three, the washing step is to first wash with dilute hydrochloric acid with pH=1, and then wash with deionized water until neutral. The filtering and drying step is to filter with filter paper and then dry at 80-90 ℃ for 4-6 hours.

[0009] The spray solution in step four is a 1wt% PVA solution.

[0010] In the spray-grinding granulation process in step four, the mass ratio of the rod-shaped BaTiO3 powder and the spray solution is 2.5-5:1, and the grinding time is 1-2 h.

[0011] The pressure in the pressing process in step four is 4 MPa.

[0012] The green body in step four is in the shape of a round sheet.

[0013] The calcination temperature in step five is 1050-1150 ℃, and the holding time is 1-2 h.

[0014] The polarization condition in the step six is 4.5-5.5 kV / mm, and the polarization time is 20-40 min; the sandpaper used in the polishing process is 600 mesh, and the ultrasonic washing time is 0.5-1 h.

[0015] The performance of the piezocatalytic ceramic membrane product prepared in the step six is as follows: the mechanical strength is 20.3-25.3 Mpa, the pure water permeation flux is 168.6-225.3 L / (m 2 ·h·bar).

[0016] The piezocatalytic ceramic membrane product prepared in the step six is connected by multiple points between monomers, has a large neck connection area, has a uniform and smooth membrane surface and presents a worm-like curved surface structure, and has a narrow pore size distribution.

[0017] The present application has the following beneficial effects: (1) The present application uses sheet-shaped Bi4Ti3O 12 as a Ti source, and the bismuth layer structure Bi-O bond is opened in an alkaline environment to act as a morphology "customization agent", and the selective adsorption of sodium oleate induces directional growth to regulate the growth process of BaTiO3 to obtain a rod-shaped structure. At the same time, the adsorption of sodium oleate not only regulates the crystal morphology, but also provides more nucleation sites for the generation and attachment of new nanoparticles after being adsorbed on the surface of the rod-shaped BaTiO3, and the "steric hindrance effect" produced by the hydrophobic carbon chain effectively avoids the complete fusion of the nanoparticles, so that the finally synthesized BaTiO3 presents a sawtooth-shaped nanoparticle modified rod-shaped structure. Here, the obtained BaTiO3 powder not only has anisotropy, but also has high activity, effectively reducing the sintering temperature required for preparing a ceramic membrane based on it.

[0018] (2) The present application uses the rod-shaped body with nanoparticles on the surface as a ceramic membrane substrate, and the rod-shaped body is more likely to form a network structure of crossing and arching in the free stacking process due to its anisotropy, which ensures the permeation flux. During calcination, the nanoparticles on the surface have high activity and small size, and the diffusion rate is fast, so that a good neck connection area can be formed at a lower temperature, ensuring the mechanical strength of the ceramic membrane.

[0019] (3) The ceramic membrane prepared by the present application presents a worm-like curved surface structure, and the pore size distribution is uniform. The curved surface structure is beneficial to the infiltration and sliding of water molecules, and provides an important guarantee for the rapid transmission of liquid in the membrane pore channel. The uniform pore size distribution can avoid rapid membrane pollution caused by local concentration polarization difference, and lays a foundation for long-term stable operation of membrane separation.

[0020] (4) The piezocatalytic ceramic membrane prepared by the application has the catalytic degradation function in addition to the physical separation function of the traditional ceramic membrane, the technology utilizes the electrode polarization process to make the ferroelectric domain flip and generate piezoelectric polarization, the piezoelectric charge generated under the intermittent transmembrane pressure is induced to participate in the oxidation-reduction reaction, and the catalytic degradation function is realized. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is the SEM graph (x 10k times) of the powder obtained in the embodiment 1 of the application; Figure 2 is the SEM graph (x 30k times) of the powder obtained in the embodiment 1 of the application; Figure 3 is the X-ray diffraction spectrum of the powder obtained in the embodiment 1 of the application; Figure 4 is the surface SEM morphology graph of the separation membrane obtained in the embodiment 1 of the application; Figure 5 is the Congo red dye degradation performance graph of the separation membrane obtained in the embodiment 1 of the application; Figure 6 is the surface SEM morphology graph of the separation membrane obtained in the embodiment 2 of the application; Figure 7 is the Congo red dye degradation performance graph of the separation membrane obtained in the embodiment 2 of the application; Figure 8 is the cross-sectional SEM morphology graph of the separation membrane obtained in the embodiment 3 of the application; Figure 9 is the Congo red dye degradation performance graph of the separation membrane obtained in the embodiment 3 of the application. DETAILED DESCRIPTION

[0022] The application will be further described in detail below in combination with the drawings and specific embodiments. Embodiment 1

[0023] A method for preparing a piezocatalytic ceramic membrane at low temperature based on nanoparticle modified rod-shaped barium titanate powder, the specific operation steps are as follows: (1) 0.9g Bi4Ti3O12, 2.3g BaCl2·8H2O and 0.1g sodium oleate are weighed into 50g deionized water, and after being dissolved and stirred uniformly, 2.25g NaOH is added to further stir uniformly to obtain a light yellow suspension; 12 (2) The suspension is placed in a hydrothermal reactor, and hydrothermal reaction is carried out at 240℃ for 20h, and after the reaction is completed, a white wet powder is obtained; (3) The obtained powder is first washed with dilute hydrochloric acid with pH=1, and then washed with deionized water to neutral, and further filtered and dried at 80℃ for 6h to obtain a nanoparticle modified rod-shaped BaTiO3 powder; ​(4) 1 g of BaTiO3 powder was weighed, 0.4 g of PVA solution with a concentration of 1 wt% was measured, and the powder was spray milled and granulated, and the powder milled for 2 h was aged for 36 h, and a proper amount of powder was placed in a steel mold to press a disc-shaped green body, wherein the pressure was 4 MPa; (5) The green body was calcined in a muffle furnace at 1050°C for 2 h, and the ceramic membrane product was obtained by cooling in the furnace; (6) The obtained ceramic membrane product was further coated with silver electrodes on both sides, and calcined at 500°C for 2 h, then the membrane with silver electrodes on the back was connected to the power supply and immersed in 85°C insulating oil for electrode polarization, the polarization conditions were 5.5 kV / mm and the polarization time was 40 min; the membrane after polarization was immersed in 60°C anhydrous ethanol for 2 h until the water flux recovered, finally the membrane was polished with 600 mesh sandpaper to remove the silver electrode, ultrasonic washed for 1 h to remove the surface particles, and then dried, the sample was taken out after cooling for standby and performance test.

[0024] As shown in Figure 1 , the powder prepared in this embodiment has a rod-like structure as a whole, the surface is rich in nanoparticles and presents a jagged shape, and the rod-like bodies are interlocked during stacking to form an arch structure.

[0025] As shown in Figure 2 , the partial enlarged view of the powder prepared in this embodiment shows that the length and diameter of the rod-like body are about 4.5 um and 0.2 um respectively, and the particles on the surface are uniformly distributed on the surface of the rod-like structure, and the size is mainly concentrated at 30 nm.

[0026] As shown in Figure 3 , the powder prepared in this embodiment was analyzed by X-ray diffraction (XRD), and the characteristic peak position and intensity were consistent with those of barium titanate (PDF 05-0626), and no other crystal phase impurity peak existed, indicating that the product was barium titanate and had good crystalline properties.

[0027] As shown in Figure 4 , the surface structure of the ceramic membrane prepared in this embodiment is uniform and has a relatively narrow pore size distribution, and the surface particles of the membrane are worm-like curved structures. The connection between the monomers has a multi-point connection structure, which is tight and has high strength, and the neck connection area is large and the connection effect is good.

[0028] As shown in Figure 5 , the degradation performance of the piezocatalytic ceramic membrane prepared in this embodiment with 10 mg·L -1 of Congo red (CR) as the degradation object is shown in the graph of degradation performance and time, which shows that the material also has good catalytic degradation function in the separation process. Example 2

[0029] A method for preparing a piezoelectric catalytic ceramic membrane at low temperature based on nanoparticle modified barium titanate powder, the specific operation steps are as follows: (1) 1.4g Bi4Ti3O 12 , 3.5g BaCl·8H2O, 0.2g sodium oleate is dissolved in 70g deionized water, after dissolution and stirring, 3.64g NaOH is added and further stirred to obtain a light yellow suspension; (2) The suspension is placed in a hydrothermal reactor and heated at 240℃ for 20h to carry out hydrothermal reaction, and after the reaction is completed, a white wet powder is obtained; (3) The obtained powder is first washed with dilute hydrochloric acid with pH=1 and then washed with deionized water until neutral, and then filtered and dried at 90℃ for 4h to obtain nanoparticle modified barium titanate powder; (4) 1g BaTiO3 powder is weighed, 0.2g PVA solution with a concentration of 1wt% is measured, and the powder is sprayed and milled for granulation, and the milled powder is aged for 36h, and a proper amount of powder is placed in a steel mold to press a disc-shaped green body, wherein the pressure is 4MPa; (5) The green body is placed in a muffle furnace and calcined at 1100℃ for 1.5h, and then cooled in the furnace to obtain a ceramic membrane product; (6) Further, the obtained ceramic membrane product is coated with silver electrodes on both sides, and calcined at 500℃ for 2h, then the membrane with silver electrodes is connected to the power supply and immersed in 85℃ insulating oil for electrode polarization, the polarization conditions are 5.0kV / mm and the polarization time is 30min; the membrane after polarization is immersed in 60℃ anhydrous ethanol for 2h until the water flux is restored, finally the membrane is polished with 600 mesh sandpaper to remove the silver electrode, ultrasonic washing for 0.75h to remove the surface particles, and then dried, the sample is taken out after cooling for standby and performance test.

[0030] As shown in Figure 6 , the ceramic membrane prepared in this embodiment has uniform and complete surface structure, and the monomer particles are uniformly stacked to form a porous structure with a relatively narrow pore size distribution. The surface of the monomer has a good curved structure, and the mutual connection form is significantly multi-point, the neck connection area is large, and the fusion effect is significant.

[0031] As shown in Figure 7 , the piezoelectric catalytic ceramic membrane prepared in this embodiment has a degradation performance and time relationship graph when 10mg·L -1 of Congo red (CR) is used as the degradation object, which shows that the material has good catalytic degradation function in the separation process. Example 3

[0032] A method for preparing a piezoelectric catalytic ceramic membrane at low temperature based on nanoparticle modified barium titanate powder, the specific operation steps are as follows: (1) 1.2 g of Bi4Ti3O12, 2.9 g of BaCl2·8H2O, and 0.15 g of sodium oleate were dissolved in 60 g of deionized water, and after being uniformly dissolved and stirred, 2.91 g of NaOH was added and further stirred to obtain a light yellow suspension; 12 (2) The suspension was placed in a hydrothermal reactor and reacted at 240°C for 20 h, and after the reaction was completed, a white wet powder was obtained; (3) The obtained powder was first washed with dilute hydrochloric acid with pH = 1, and then washed with deionized water until neutral, and further filtered and dried at 85°C for 5 h to obtain a nanoparticle-modified rod-shaped BaTiO3 powder; (4) 1 g of the BaTiO3 powder was weighed, 0.3 g of a 1wt% PVA solution was measured, and the powder was spray-milled and granulated, and the powder milled for 1.5 h was aged for 36 h, and a proper amount of powder was placed in a steel mold to press to obtain a round disc-shaped green body, wherein the pressure was 4 MPa; (5) The green body was placed in a muffle furnace and calcined at 1150°C for 1 h, and then cooled in the furnace to obtain a ceramic membrane product; (6) The obtained ceramic membrane product was further coated with silver electrodes on both sides, and calcined at 500°C for 2 h, and then the membrane with silver electrodes on the back was connected to a power supply and immersed in 85°C insulating oil for electrode polarization, and the polarization conditions were 4.5 kV / mm and 20 min, and after polarization, the membrane was immersed in 60°C anhydrous ethanol for 2 h until the water flux recovered, and finally the membrane was polished with 600 mesh sandpaper to remove the silver electrode, and after ultrasonic washing for 0.5 h, the surface particles were removed and dried, and after the sample cooled, it was taken out for standby and performance testing.

[0033] As shown in Figure 8 , the ceramic membrane prepared in the embodiment has obvious fusion effect, the neck area is large, and the connection effect is significant. The surface of the monomer particles is smooth, the pore structure area of the monomer stacked together is reduced, the pore size is reduced, and the separation selectivity is improved.

[0034] As shown in Figure 9 , the piezocatalytic ceramic membrane prepared in the embodiment has a degradation performance and time relationship graph when 10 mg·L-1 of Congo red (CR) is taken as the degradation object, which shows that the material also has good catalytic degradation function in the separation process. -1

[0035] As shown in the following table, the ceramic membranes prepared in Examples 1-3 have high mechanical strength, permeation flux and catalytic degradation performance.

[0036]

[0037] ​​The above examples only illustrate the principles of the present application and its effects and advantages, and part of the applied embodiments, but are not used to limit the present application; it should be noted that, for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are all within the protection scope of the present application.

Claims

1. A method for low-temperature preparation of piezocatalytic ceramic membranes based on nanoparticle-modified barium titanate powder, characterized by The method comprises the following steps: Step one: Bi4Ti3O12, BaCl2·8H2O, and sodium oleate were dissolved in deionized water, and then NaOH solution was added to obtain a light yellow suspension after stirring and uniformity. 12 , BaCl2·8H2O, and sodium oleate were dissolved in deionized water, and then NaOH solution was added to obtain a light yellow suspension after stirring and uniformity. Step two: the light yellow suspension prepared in step one is placed in a hydrothermal reactor to obtain white wet powder through hydrothermal reaction; Step three: the white wet powder prepared in step two is washed to neutral, and then is further filtered and dried to obtain rod-like BaTiO3 powder modified by nanoparticles; Step four: the rod-like BaTiO3 powder prepared in step three is subjected to spray grinding and granulation, and is placed in a steel mold after standing for 36 hours to obtain a green body; Step five: the green body prepared in step four is calcined in a muffle furnace and is cooled with the furnace to obtain a ceramic membrane product; Step six: the ceramic membrane product prepared in step five is coated with silver electrodes on both sides, and is calcined at 500 DEG C for 2 hours; the ceramic membrane product with silver electrodes on the back is connected to a power supply and is immersed in insulating oil at 85 DEG C for electrode polarization; the ceramic membrane product after polarization is immersed in anhydrous ethanol at 60 DEG C for 2 hours until the water flux is restored; finally, the ceramic membrane product is polished to remove the silver electrodes, is ultrasonically washed to remove surface particles, and is dried to obtain a piezocatalytic ceramic membrane product after cooling.

2. The method of claim 1, wherein: The Bi4Ti3O 12 The mass ratio of BaCl·8H2O, sodium oleate and deionized water is 0.9-1.4:2.3-3.5:0.1-0.2:50-70; the mass ratio of NaOH solution and deionized water is 4.5-5.2:

100.

3. The method of claim 1, wherein: In step two, the hydrothermal reaction temperature is 240 DEG C, and the holding time is 20 hours.

4. The method of claim 1, wherein: In step three, the washing step is to first wash with dilute hydrochloric acid with pH=1, and then wash with deionized water until neutral; the filtering and drying step is to filter with filter paper and then dry at 80-90 DEG C for 4-6 hours.

5. The method of claim 1, wherein: In step four, the spray solution is a 1wt% PVA solution.

6. The method of claim 1, wherein: In the spray grinding and granulation process in step four, the mass ratio of the rod-like BaTiO3 powder to the spray solution is 2.5-5:1, and the grinding time is 1-2 hours.

7. The method of claim 1, wherein: In step four, the pressure in the pressing process is 4 MPa, and the green body is in the shape of a round sheet.

8. The method of claim 1, wherein: In step five, the calcination temperature is 1050-1150 DEG C, and the holding time is 1-2 hours.

9. The method of claim 1, wherein: In step six, the electrode polarization conditions are 4.5-5.5 kV / mm, and the electrode polarization time is 20-40 minutes; the polishing process uses 600-mesh sandpaper, and the ultrasonic washing time is 0.5-1 hour.

10. The method of claim 1, wherein: The piezocatalytic ceramic membrane product prepared in step six has the following properties: mechanical strength of 20.3-25.3 MPa, pure water permeation flux of 168.6-225.3 L / (m 2 ·h·bar).

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