A method for measuring Young's modulus and bending stiffness of two-dimensional nanomaterials

Abstract

The present invention discloses a method for measuring the Young's modulus and bending stiffness of a two-dimensional nanomaterial, comprising: forming a micron rectangular micropore array on a substrate, transferring a two-dimensional material to the micropore array, covering the rectangular micropores to form a suspended system film and performing a bubbling experiment, applying a uniformly distributed load perpendicular to the film to the film on the suspended rectangular micropores to achieve uniaxial stretching along the short axis; analyzing the morphology of the two-dimensional material, obtaining the internal and external pressure difference, and performing a force analysis, using thin film theory to solve the thin layer material, and combining the Poisson's ratio to obtain the Young's modulus of the material; using classical plate theory to solve the thick layer material to obtain the bending stiffness of the material. The present invention realizes the experimental measurement of the Young's modulus and bending stiffness of two-dimensional materials, especially anisotropic two-dimensional materials, overcoming the dependence of traditional methods on the substrate when performing uniaxial stretching on two-dimensional materials and the difficulty of measuring the mechanical parameters of anisotropic two-dimensional materials, while performing high-throughput uniaxial stretching of two-dimensional materials.

Description

Technical Field

[0001] The present invention relates to the field of measurement of intrinsic mechanical parameters of two-dimensional materials and strain engineering technology, and specifically to a controllable uniaxial loading technology for two-dimensional nanomaterials and a method for measuring the Young's modulus and bending stiffness of the material. Background Art

[0002] Two-dimensional materials such as graphene, boron nitride, black phosphorus, and transition metal chalcogenides, due to their unique atomic-level thickness and layered structure, exhibit extraordinary physical, mechanical, and chemical properties, leading to their extensive research by researchers both domestically and internationally. These two-dimensional materials show great potential for application in nanocomposites, electrode materials, flexible nanomaterials, and optoelectronic devices. Understanding the mechanical response of these two-dimensional materials plays a crucial role in device fabrication, device stability, and service life.

[0003] Due to the atomic-level thickness and small size of two-dimensional materials, traditional material mechanical property testing methods cannot be used directly. How to efficiently, quickly and accurately measure the intrinsic mechanical parameters of two-dimensional materials has always been the focus of research in the field of two-dimensional materials. In addition, the physical properties of semiconductor two-dimensional materials rely on strain regulation, such as the band gap regulation of black phosphorus can be achieved through uniaxial / biaxial loading. However, the strain loading of two-dimensional materials is often carried out through flexible substrate materials (such as thermoplastic PMMA, PET, elastomer PDMS, etc.). With the help of traditional mechanical loading methods, such as direct stretching, single cantilever beam, compression, two-point bending, three-point bending, four-point bending experiments on flexible substrates, uniaxial tension / compression deformation of two-dimensional materials can be achieved. It should be pointed out that when the flexible substrate is used to strain the two-dimensional material, interfacial shear slip will occur between the flexible substrate and the two-dimensional material while the strain is applied, resulting in a very limited deformation of the two-dimensional material itself and an uneven strain distribution. In addition, the roughness of the flexible substrate and the out-of-plane deformation introduced during the transfer of the two-dimensional material, such as wrinkles, bubbles, buckling and other microstructures, will affect the intrinsic physical properties of the two-dimensional material, and are also not conducive to the accurate measurement of mechanical parameters. For anisotropic two-dimensional materials, such as black phosphorus and rhenium disulfide, uniaxial loading is a prerequisite for measuring their intrinsic mechanical parameters. Therefore, how to simply and easily apply controllable uniaxial deformation loading to suspended two-dimensional materials is one of the urgent problems to be solved.

[0004] Common methods for testing the mechanical properties of two-dimensional materials include atomic force probe nanoindentation, in-situ stretching using microelectromechanical systems (MEMS), and micro- and nanoscale bubbling. Nanoindentation, based on an atomic force microscope (AFM), applies single-point loading to a two-dimensional material suspended on a circular hole substrate using a probe. The force-displacement curve is then acquired, allowing the Young's modulus and fracture strength of the material to be determined. This method has been widely used to test the mechanical properties of two-dimensional materials such as graphene and molybdenum disulfide. However, nanoindentation is a localized point loading technique, applying a concentrated force to the material through the tip, which can lead to stress concentration. Using a microelectromechanical system (MEMS) to perform in-situ stretching on a two-dimensional material under an electron microscope (EMS) can reveal the material's intrinsic mechanical parameters. However, this method relies on the microscope's operating system and suffers from cumbersome sample fabrication, poor controllability, and high device cost, making high-throughput mechanical parameter measurement difficult. The circular hole bubbling method applies controlled gas loading to a two-dimensional material suspended on a circular hole array. In situ atomic force microscopy is used to characterize the bubble morphology at different pressures, and mechanical models are used to determine the resulting mechanical parameters. Unlike nanoindentation technology, the bubbling method evenly distributes gas loading, which can not only monitor the mechanical response of two-dimensional materials under different pressures in situ, but also regulate the strain of two-dimensional materials with high throughput.

[0005] Bubbling methods are categorized into blind-hole (constant molecular number) bubbling and through-hole (gas loading) bubbling (Li Yuantong et al., ZL 20191 0332515.4). Bubbling experiments are currently the best method for achieving bidirectional deformation loading and measuring intrinsic and interfacial mechanical parameters of two-dimensional materials (Wang Guorui et al., ZL 2017 1 0237043.5). In the blind-hole bubbling method, the two-dimensional material is peeled off or transferred onto a blind-hole array substrate to form a test specimen. The specimen is then placed in an autoclave at a constant pressure for several days before being removed, facilitating discontinuous loading at a specific pressure differential. Through-hole bubbling, on the other hand, involves positioning the two-dimensional material onto a through-hole substrate to form a test specimen, which is then fixed to a through-hole bubbling test system and subjected to controlled pressure loading using gas. In comparison, blind-hole bubbling offers advantages such as simple sample preparation and high throughput. Through-hole bubbling requires precise positioning and transfer technology, but its testing process is relatively rapid. It should be pointed out that the sites selected for the bubbling experiments were all cylindrical porous substrates, on which biaxial tensile loading was achieved for the two-dimensional materials, and uniaxial stretching could not be achieved.

[0006] In summary, the current methods for achieving uniaxial stretching of suspended two-dimensional nanomaterials are still very scarce and very important. There are technical challenges in measuring the mechanical parameters of anisotropic two-dimensional materials. At the same time, more high-throughput testing methods are also needed to obtain the intrinsic mechanical properties of two-dimensional materials, enrich the mechanical property testing methods and strain control methods of two-dimensional nanomaterials. Summary of the Invention

[0007] The purpose of the present invention is to develop a uniaxial controllable loading deformation experimental technology for suspended two-dimensional material systems, to achieve accurate measurement of the Young's modulus and bending stiffness of two-dimensional materials, especially new methods and technologies for measuring the Young's modulus and bending stiffness of anisotropic two-dimensional materials.

[0008] To solve the above technical problems, the present invention specifically provides the following technical solution: a method for measuring the Young's modulus and bending stiffness of a two-dimensional nanomaterial, comprising the following steps:

[0009] Step 100: Design and process micrometer-scale rectangular micropores on a substrate material to form an array. Optimize the aspect ratio of the rectangular micropores through finite element analysis. For a film suspended on the rectangular micropores, when the aspect ratio of the rectangle is greater than 5:1, a uniformly distributed load perpendicular to the film is applied to the film, and the force on the film can be approximated as uniaxial tension along the minor axis.

[0010] Step 200: transferring the two-dimensional nanomaterial to be tested to the surface of a substrate material having a rectangular micropore array, and covering the rectangular micropores of the substrate material to form a suspension system film to form a sample to be tested;

[0011] Wherein, the thickness of the two-dimensional nanomaterial to be tested is 0.34 to 50 nm;

[0012] Step 300: performing a bubbling experiment on the sample to be tested to form cylindrical bubbles;

[0013] Step 400: using an atomic force microscope to obtain the morphology of the two-dimensional nanomaterial forming the cylindrical bubble, and simultaneously obtain the internal and external pressure difference Δp of the cylindrical bubble;

[0014] Step 500: Perform a force analysis on a quasi-cylindrical bubble. For a quasi-cylindrical bubble formed by a thin layer of two-dimensional nanomaterial with a thickness of 0.34 to 20 nm, use thin film theory to solve the problem. Combined with the Poisson's ratio ν of the two-dimensional nanomaterial to be tested, the Young's modulus of the thin layer of two-dimensional nanomaterial is obtained.

[0015] For cylindrical bubbles formed by thick layers of two-dimensional nanomaterials with a thickness of 20 to 50 nm, thin plate theory is used to solve the bending stiffness of the thick layer of two-dimensional nanomaterials along the short axis direction.

[0016] As a preferred solution of the present invention, the method for testing the Young's modulus of the thin-layer two-dimensional nanomaterial in step 500 includes:

[0017] A mechanical analysis of the thin-layer two-dimensional nanomaterial with a cylindrical bubble was performed. The morphology of the cylindrical directrix parallel to the short axis was analyzed. The thin film theory was used to solve the problem. Combined with the boundary conditions at the edge of the rectangular micropore, the following relationship was obtained:

[0018]

[0019] Wherein, Δp is the pressure difference between the inside and outside of the cylindrical bubble, β is a coefficient related to the boundary condition. For the solid / simply supported boundary condition, β=1, ν is the Poisson's ratio of the material, E is the Young's modulus of the thin layer of two-dimensional nanomaterial, t is the thickness of the material, a is the radius of the minor axis of the bubble, and h is the height of the center point of the minor axis of the bubble.

[0020] As a preferred solution of the present invention, for orthotropic thin-layer two-dimensional nanomaterials, the Young's modulus along the short axis direction at different lattice angles of the material is solved, and then the Young's modulus distribution is solved using the following formula:

[0021]

[0022] Among them, E1 and E2 are Young's modulus along the two main axes, G 12 is the shear modulus, ν 12 is the Poisson's ratio corresponding to the direction of the main axis E1, and θ is the angle between the short axis direction and the main axis E2 direction.

[0023] As a preferred solution of the present invention, the method for obtaining the internal and external pressure difference Δp of the cylindrical bubble is:

[0024] The surface morphology of the cylindrical bubble is obtained by atomic force microscopy, and the radius a of the bubble along the short axis and the height h of the bubble center are obtained. At the same time, the thickness t of the measured sample is obtained by characterizing the edge morphology of the material. The pressure difference △p inside and outside the bubble is obtained by calculating the bubble morphology or directly reading the pressure difference △p measured by the pressure gauge.

[0025] As a preferred solution of the present invention, the method for testing the bending stiffness of the thick layer two-dimensional nanomaterial in step 500 includes:

[0026] Mechanical analysis of cylindrical bubbles formed by thick-layer two-dimensional nanomaterials was performed using the following morphology formula and fitting:

[0027]

[0028] Where ω is the bubble profile function, x is the position variable, is a constant, F Tx is the in-plane force of the cylindrical bubble; Δp is the pressure difference between the inside and outside of the cylindrical bubble, a is the radius of the bubble's minor axis, and h is the height of the center point of the bubble's minor axis;

[0029] The bending stiffness D of thick-layer two-dimensional nanomaterials is obtained by fitting.

[0030] As a preferred solution of the present invention, for anisotropic thick-layer two-dimensional nanomaterials, the bending stiffness along the short axis at different angles is solved, and the anisotropic bending stiffness of the material is obtained by measuring samples in different directions.

[0031] As a preferred solution of the present invention, the aspect ratio of the rectangular micropores meets the following requirements:

[0032] The aspect ratio of the rectangular micropores is ≥5 to achieve uniform uniaxial stretching and simultaneously solve the Young's modulus;

[0033] Preferably, the aspect ratio of the rectangular micropore is 5.

[0034] As a preferred solution of the present invention, the base material is a flat, hard inorganic substrate;

[0035] Preferably, the inorganic substrate is a silicon wafer;

[0036] Preferably, the surface of the silicon wafer has a silicon dioxide / silicon nitride layer.

[0037] As a preferred solution of the present invention, the minor axis length of the rectangular micropore is 0.5 to 5 μm, preferably 1 to 2 μm, and the rectangular size of the rectangular micropore is 1×5 to 2×10 μm.

[0038] As a preferred solution of the present invention, the two-dimensional nanomaterial is a lamellar material or a two-dimensional thin film material with a thickness of nanometers;

[0039] Preferably, the two-dimensional nanomaterials include graphene, hexagonal boron nitride, black phosphorus, silicene, transition metal sulfide selenide compounds, two-dimensional layered metal carbon / nitride and various polymer films.

[0040] As a preferred solution of the present invention, the two-dimensional nanomaterial is prepared on a substrate having rectangular micropores by micromechanical exfoliation, chemical vapor deposition or epitaxial growth.

[0041] As a preferred solution of the present invention, the array of rectangular micropores is: a plurality of rectangular micropores are simultaneously covered with a two-dimensional nanomaterial of the same layer to achieve high-throughput parameter measurement;

[0042] Preferably, the array center spacing is 1 to 3 times the length of the major axis of the rectangular microwells, preferably 1.5 to 2.5 times;

[0043] The long axes of adjacent rectangular microwells on the array are rotated at the same or different angles, preferably at angles of 0°, ±10°, ±20°, ±30°, ±45°, and ±90°.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention adopts a rectangular substrate bubbling experiment to achieve stable, uniformly strained uniaxial tensile loading along the short axis direction on the two-dimensional material suspended on the rectangular hole, forming a cylindrical bubble. The atomic force microscope is used to continuously monitor its morphology changes under different pressures. For thin-layer two-dimensional materials, the Young's modulus of the two-dimensional material is calculated in combination with thin film theory. For thick-layer two-dimensional materials, the bending stiffness of the two-dimensional material is calculated in combination with thin plate theory. The present invention can realize the measurement of Young's modulus and bending stiffness of anisotropic two-dimensional materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0047] Figure 1 Schematic diagram of the three-dimensional principle of uniaxial tensile loading of the two-dimensional material of the present invention;

[0048] Figure 2 is the finite element simulation result described in Example 1 of the present invention;

[0049] Figure 3 a is a schematic diagram of the principle of blind hole bubbling (across section along the minor axis of a rectangle, inside a high-pressure autoclave) in Example 1 of the present invention;

[0050] Figure 3 b is a schematic diagram of the principle of blind hole bubbling in Example 1 of the present invention (a cross section along the minor axis of the rectangle, after taking out the high-pressure autoclave);

[0051] Figure 4 a is a design diagram of the single-layer graphene / silicon dioxide substrate array for blind hole bubbling in Example 1 of the present invention;

[0052] Figure 4 b is an optical image of the single-layer graphene / silicon dioxide substrate (sample system to be tested) described in the blind hole bubbling in Example 1 of the present invention;

[0053] Figure 5 : This is a profile height diagram along the short axis direction of the single-layer graphene bubbled with blind holes in Example 1 of the present invention at different pressures (the inset is a three-dimensional AFM topography diagram);

[0054] Figure 6 The h-Δp curve of the single-layer graphene experimentally measured in Example 1 of the present invention and the thin film theoretical fitting result are shown;

[0055] Figure 7Schematic diagram of the principle of through-hole bubbling (a cross section along the minor axis of a rectangle) described in Example 2 of the present invention;

[0056] Figure 8 : is a distribution diagram of the anisotropic Young's modulus of few-layer black phosphorus measured in the experiment in Example 2 of the present invention;

[0057] Figure 9 This is a graph showing the change in Raman peak position at the center of the suspended monolayer graphene with pressure in Example 3 of the present invention. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0059] The present invention provides a method for measuring the Young's modulus and bending stiffness of a two-dimensional nanomaterial, comprising the following steps:

[0060] Step 100: Design and process micrometer-scale rectangular micropores on a substrate material to form an array. Optimize the aspect ratio of the rectangular micropores through finite element analysis. For a film suspended on the rectangular micropores, when the aspect ratio of the rectangle is greater than 5:1, a uniformly distributed load perpendicular to the film is applied to the film, and the force on the film can be approximated as uniaxial tension along the minor axis.

[0061] Step 200: transferring the two-dimensional nanomaterial to be tested to the surface of a substrate material having a rectangular micropore array, and covering the rectangular micropores of the substrate material to form a suspension system film to form a sample to be tested;

[0062] Wherein, the thickness of the two-dimensional nanomaterial to be tested is 0.34 to 50 nm;

[0063] Step 300: performing a bubbling experiment on the sample to be tested to form cylindrical bubbles;

[0064] Step 400: using an atomic force microscope to obtain the morphology of the two-dimensional nanomaterial forming the cylindrical bubble, and simultaneously obtain the internal and external pressure difference Δp of the cylindrical bubble;

[0065] Step 500: Perform a force analysis on a quasi-cylindrical bubble. For a quasi-cylindrical bubble formed by a thin layer of two-dimensional nanomaterial with a thickness of 0.34 to 20 nm, use thin film theory to solve the problem. Combined with the Poisson's ratio ν of the two-dimensional nanomaterial to be tested, the Young's modulus of the thin layer of two-dimensional nanomaterial is obtained.

[0066] For cylindrical bubbles formed by thick layers of two-dimensional nanomaterials with a thickness of 20 to 50 nm, thin plate theory is used to solve the bending stiffness of the thick layer of two-dimensional nanomaterials along the short axis direction.

[0067] The method for testing the Young's modulus of the thin-layer two-dimensional nanomaterial in step 500 includes:

[0068] A mechanical analysis of the thin-layer two-dimensional nanomaterial with a cylindrical bubble was performed. The morphology of the cylindrical directrix parallel to the short axis was analyzed. The thin film theory was used to solve the problem. Combined with the boundary conditions at the edge of the rectangular micropore, the following relationship was obtained:

[0069]

[0070] Wherein, Δp is the pressure difference between the inside and outside of the cylindrical bubble, β is a coefficient related to the boundary condition. For the solid / simply supported boundary condition, β=1, ν is the Poisson's ratio of the material, E is the Young's modulus of the thin layer of two-dimensional nanomaterial, t is the thickness of the material, a is the radius of the minor axis of the bubble, and h is the height of the center point of the minor axis of the bubble.

[0071] For orthotropic thin-layer two-dimensional nanomaterials, the Young's modulus along the short axis at different lattice angles of the material is solved, and then the Young's modulus distribution is solved using the following formula:

[0072]

[0073] Among them, E1 and E2 are Young's modulus along the two main axes, G 12 is the shear modulus, ν 12 is the Poisson's ratio corresponding to the direction of the main axis E1, and θ is the angle between the short axis direction and the main axis E2 direction.

[0074] In this embodiment, the method for obtaining the internal and external pressure difference Δp of the cylindrical bubble is:

[0075] The surface morphology of the cylindrical bubble is obtained by atomic force microscopy, and the radius a of the bubble along the short axis and the height h of the bubble center are obtained. At the same time, the thickness t of the measured sample is obtained by characterizing the edge morphology of the material. The pressure difference △p inside and outside the bubble is obtained by calculating the bubble morphology or directly reading the pressure difference △p measured by the pressure gauge.

[0076] The method for testing the bending stiffness of the thick-layer two-dimensional nanomaterial in step 500 includes:

[0077] Mechanical analysis of cylindrical bubbles formed by thick-layer two-dimensional nanomaterials was performed using the following morphology formula and fitting:

[0078]

[0079] Where ω is the bubble profile function, x is the position variable, is a constant, F Tx is the in-plane force of the cylindrical bubble; Δp is the pressure difference between the inside and outside of the cylindrical bubble, a is the radius of the bubble's minor axis, and h is the height of the center point of the bubble's minor axis;

[0080] The bending stiffness D of thick-layer two-dimensional nanomaterials is obtained by fitting.

[0081] For anisotropic thick-layer two-dimensional nanomaterials, the bending stiffness along the short axis at different angles is calculated, and the anisotropic bending stiffness of the material is obtained by measuring samples in different directions.

[0082] The bubbling experiment adopts a blind hole bubbling test or a through hole bubbling test. For blind hole bubbling, the rectangular hole is required to be a blind hole and not pass through the substrate. It can be formed in an array. The two-dimensional material layer can cover multiple micropores at the same time and be loaded by micropore bubbling. For through hole bubbling, the rectangular micropores are required to pass through the substrate. The number of rectangular micropores is limited, preferably 1-2. All rectangular holes need to be covered with two-dimensional materials and loaded using an in-situ through hole bubbling device.

[0083] The blind hole bubbling experiment directly forms a closed measurement system between the two-dimensional material film to be measured and the substrate, including the following steps:

[0084] (a) placing the two-dimensional nanomaterial to be tested in a high-pressure gas autoclave, and gradually increasing the pressure by introducing gas into the autoclave to reach a target pressure and maintain it for a period of time;

[0085] The preferred pressure increase range is 0.10-1.00 MPa, with step-by-step loading, such as 0.10 MPa, 0.20 MPa, 0.30 MPa, 0.40 MPa, 0.50 MPa, 0.60 MPa, 0.70 MPa, 0.80 MPa, 0.90 MPa, and 1.00 MPa; however, the values ​​listed are not limited thereto, and other values ​​not listed within the range are also applicable.

[0086] (b) After the target pressure of the two-dimensional nanomaterial to be tested is maintained for a preset time, the sample covering the rectangular hole is removed to form a cylindrical bubble;

[0087] The preset maintenance time is preferably 2 to 7 days, more preferably 4 to 5 days;

[0088] (c) Using an atomic force microscope, the morphology of the cylindrical bubble described in step (b) is characterized to obtain the contour morphology along the short axis under different pressure differences and calculate the internal and external pressure difference Δp.

[0089] The through-hole bubbling experiment forms a closed test system by integrating the two-dimensional material film to be tested, the substrate, and the through-hole bubbling system equipment, including the following steps:

[0090] (a) bonding the sample to be tested described in step (1) to a through-hole bubbling device and sealing the air path to form a through-hole bubbling test system;

[0091] (b) using a high-pressure gas cylinder and a pressure control valve to apply a specific gas pressure to the sample described in step (a) so that the sample film to be tested forms a cylindrical bubble, and monitoring the pressure in the gas line with a high-precision barometer;

[0092] (c) Using an atomic force microscope, the cylindrical bubble described in (b) was morphologically characterized to obtain the contour morphology along the short axis under different pressures. The through-hole bubble experiment directly read the pressure difference Δp measured by the pressure gauge.

[0093] The pressurized gas used in the bubbling experiment is optional, preferably any one of nitrogen, inert gas, hydrogen, or carbon dioxide, but is not limited to the listed gases, and other gases are also applicable.

[0094] In this embodiment, the aspect ratio of the rectangular micropores meets the following requirements:

[0095] The aspect ratio of the rectangular micropores is ≥5 to achieve uniform uniaxial stretching and simultaneously solve the Young's modulus;

[0096] Preferably, the aspect ratio of the rectangular micropore is 5.

[0097] The base material is a flat, hard inorganic substrate; preferably, the inorganic substrate is a silicon wafer; further, the surface of the silicon wafer may have a silicon dioxide / silicon nitride layer.

[0098] The short axis length of the rectangular micropore is 0.5 to 5 μm, preferably 1 to 2 μm, and the rectangular size of the rectangular micropore is 1×5 to 2×10 μm.

[0099] 10. The method for measuring the Young's modulus and bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 6, characterized in that:

[0100] The two-dimensional nanomaterial is a sheet-like material or a thin film material with a two-dimensional nanometer thickness;

[0101] Preferably, two-dimensional nanomaterials include isotropic material systems such as graphene, hexagonal boron nitride, silicene, transition metal sulfide selenide compounds, two-dimensional layered metal carbon / nitrides and various polymer films; anisotropic two-dimensional material systems such as black phosphorus, rhenium disulfide, molybdenum trioxide, etc.

[0102] The two-dimensional nanomaterials are prepared on a substrate with rectangular micropores by micromechanical exfoliation, chemical vapor deposition or epitaxial growth.

[0103] The rectangular microwell array is: the same layer of two-dimensional nanomaterials covers multiple rectangular microwells at the same time to achieve high-throughput parameter measurement;

[0104] Preferably, the array center spacing is 1 to 3 times the length of the major axis of the rectangular microwells, preferably 1.5 to 2.5 times;

[0105] The long axes of adjacent rectangular microwells on the array are rotated at the same or different angles, preferably at angles of 0°, ±10°, ±20°, ±30°, ±45°, and ±90°.

[0106] The present invention mainly forms a sample system to be tested by forming a two-dimensional nanomaterial to be tested and a base material with a rectangular hole, and then conducts a bubbling experiment. Due to the pressure difference, the two-dimensional nanomaterial suspended on the rectangular hole undergoes out-of-plane deformation to form a cylindrical bubble, thereby achieving uniform uniaxial stretching of the suspended two-dimensional material along the short axis direction. The bubble height is adjusted by changing the differential pressure to achieve uniaxial strain loading of different sizes along the short axis direction. The bubble morphology and material thickness are characterized by an atomic force microscope. For the cylindrical bubble formed by a thin layer of two-dimensional material (0.34-20 nm), the thin film theory is used to solve it, and the Poisson's ratio ν of the two-dimensional nanomaterial to be tested is combined to obtain the elastic modulus E of the material. For the cylindrical bubble formed by a thick layer of two-dimensional material (20-50 nm), the thin plate theory is used to solve it, and the bending stiffness of the material along the short axis direction is obtained.

[0107] The following is further described with reference to specific embodiments:

[0108] Example 1:

[0109] This example is a single-layer graphene blind hole bubbling experiment. The two-dimensional nanomaterial used is natural graphite (Taizhou Juna New Energy Company) with a purity of >99% and a size of about 2 mm. The substrate material is a 4-inch P100 single-polished silicon wafer (Guangzhou Tuoxu Electronic Technology Co., Ltd.), and the surface is covered with a 300 nm thick silicon dioxide coating.

[0110] The method for uniaxially stretching the two-dimensional nanomaterial (specifically single-layer graphene) and measuring the Young's modulus of the two-dimensional nanomaterial specifically comprises the following steps:

[0111] (1) Design of aspect ratio of rectangular hole: Figure 2 The finite element simulation results shown in the figure show that when the aspect ratio of the rectangular micropore is greater than or equal to 5, the film on it can be subjected to uniaxial tension along the short axis when a uniformly distributed load is applied;

[0112] (2) Rectangular microwell array design: To achieve high-throughput mechanical parameter measurement, the rectangular holes on the substrate are patterned and arrayed, such as Figure 3 As shown in (a). Rectangular hole arrays of different orientations, the same depth, and the same size were machined on a silicon wafer. The rectangular holes were 10 μm long, 2 μm wide, and machined to a depth of 300 nm, forming a substrate material having a rectangular hole array. The center spacing of the rectangular holes in the rectangular hole array was 15 μm, and the rotation angles were 0°, 30°, 60°, 90°, 120°, and 150°.

[0113] (3) A graphene layer is prepared on the silicon wafer with the rectangular hole array in step (2) by using a micromechanical exfoliation method. The graphene covers the rectangular holes to form a closed environment, thereby forming a sample system to be tested, such as Figure 3 As shown in (a), the prepared sample was confirmed to be a single layer by combining Raman spectroscopy characterization;

[0114] (4) Using the sample to be tested described in step (3) to conduct a rectangular micropore bubbling experiment, specifically: placing the sample described in step (3) in an autoclave, using high-pressure nitrogen and a booster pump to introduce nitrogen into the autoclave, adjusting the pressure in the autoclave, and maintaining it until the pressure in the rectangular pore of the sample to be tested reaches equilibrium with the pressure in the autoclave, such as Figure 4 As shown in (a), the sample to be tested is taken out. Since the pressure in the cavity formed by the rectangular hole and the single-layer graphene is higher than the atmospheric pressure, the graphene will form cylindrical bubbles, as shown in Figure 4 (b) Atomic force microscopy was used to characterize the graphene monolayer suspended on the rectangular microwell. The bubble morphology parameters were measured and the pressure difference △p inside and outside the bubble was calculated. The bubble center height h and the bubble short axis radius a were recorded.

[0115] (4) Adjust the pressure in the autoclave and repeat step (4) to obtain the contour morphology of the same sample along the short axis direction under different pressure differences, such as Figure 5 As shown;

[0116] (5) Using formula (1), the in-plane tensile modulus of single-layer graphene is Et = 335.7 N / m, as Figure 6 As shown, combined with the thickness of single-layer graphene t=0.34nm, the Young's modulus of single-layer graphene is 987.4GPa.

[0117] In Example 1, using blind hole bubbling loading, the graphene suspended on the rectangular micropores forms cylindrical bubbles, which are in a uniform uniaxial stretching state along the short axis direction.

[0118] Example 2:

[0119] This example is a few-layer black phosphorus through-hole bubbling experiment. The two-dimensional nanomaterial used is black phosphorus crystal with a purity of >99.99%; the substrate material is a silicon nitride window pane prepared by micro-nano processing technology, with a silicon nitride film layer of 800nm, an outer window size of 5×5mm, and an inner window size of 50×50μm.

[0120] This embodiment provides a method for performing uniaxial stretching and anisotropic Young's modulus measurement on a suspended two-dimensional material (specifically, few-layer black phosphorus) using through-hole bubbling;

[0121] (1) machining a rectangular through hole in the center of the silicon nitride window pane, wherein the rectangular hole is 9 μm long and 1.8 μm wide;

[0122] (2) A thin layer of black phosphorus is peeled off from the dimethylsiloxane elastomer (PMDS) by mechanical stripping, and then positioned and transferred to the central rectangular hole of the window pane in step (1) to form a sample system to be tested, such as Figure 7 As shown;

[0123] (3) A rectangular micropore bubbling experiment is performed using the sample to be tested described in step (2), specifically: the sample shown in step (2) is bonded to a through-hole bubbling device so that the sample system to be tested and the through-hole bubbling device form a closed gas path, the suspended sample is loaded using a high-pressure gas cylinder and a pressure control valve, the pressure is recorded using a high-precision pressure gauge, and the morphology of the black phosphorus suspended on the rectangular micropore is characterized using an atomic force microscope, and the bubble center height h and the bubble short axis radius a are recorded.

[0124] (4) By applying pressure, the suspended few-layer black phosphorus material can be subjected to uniaxial tensile loading along the short axis direction. The Young's modulus of the material along the short axis direction can be calculated using the same method as described in Example 1. By measuring the Young's modulus of black phosphorus in different directions, the Young's modulus distribution of black phosphorus can be solved using formula (2). Figure 8 As shown, where E1 = 173 GPa, E2 = 54 GPa.

[0125] Example 3:

[0126] This embodiment provides a technology for strain control of monolayer graphene using the method of the present invention. The substrate design, sample preparation and loading process of the technology are the same as those in Example 1. Raman spectroscopy is used to monitor the peak position changes of the Raman G peak and 2D peak of monolayer graphene under different pressures. Figure 9 As shown in the figure, as the pressure increases, the G peak and 2D peak red-shift, realizing the strain regulation of single-layer graphene.

[0127] From the above three embodiments, it can be seen that the present invention uses a rectangular substrate bubbling experiment to perform uniaxial stretching on two-dimensional nanomaterials along the short axis direction, and solves it through film / thin plate theory to obtain the isotropic / anisotropic two-dimensional material mechanical parameters. The present invention provides a new method for realizing uniaxial stretching of two-dimensional materials, and at the same time provides a method for measuring the mechanical parameters of anisotropic two-dimensional materials, enriching the two-dimensional material mechanical experimental measurement means and two-dimensional material strain control method.

[0128] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.

Claims

1. A method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial, characterized in that: The steps include: Step 100: Design and process micrometer-scale rectangular micropores on a substrate material to form an array. Optimize the aspect ratio of the rectangular micropores through finite element analysis. For a film suspended on the rectangular micropores, the aspect ratio of the rectangular micropores is ≥5. Apply a uniformly distributed load perpendicular to the film to the film. Step 200: transferring the two-dimensional nanomaterial to be tested to the surface of a substrate material having a rectangular micropore array, and covering the rectangular micropores of the substrate material to form a suspension system film to form a sample to be tested; Wherein, the thickness of the two-dimensional nanomaterial to be tested is 0.34 to 50 nm; Step 300: performing a bubbling experiment on the sample to be tested to form cylindrical bubbles; Step 400: using an atomic force microscope to obtain the morphology of the two-dimensional nanomaterial forming the cylindrical bubble, and simultaneously obtain the internal and external pressure difference Δp of the cylindrical bubble; Step 500: Perform a force analysis on a quasi-cylindrical bubble. For a quasi-cylindrical bubble formed by a thin layer of two-dimensional nanomaterial with a thickness of 0.34 to 20 nm, use thin film theory to solve the problem. Combined with the Poisson's ratio ν of the two-dimensional nanomaterial to be tested, the Young's modulus of the thin layer of two-dimensional nanomaterial is obtained. For cylindrical bubbles formed by thick layers of two-dimensional nanomaterials with a thickness of 20 to 50 nm, the thin plate theory is used to solve the bending stiffness of the thick layer of two-dimensional nanomaterials along the minor axis. The method for measuring the Young's modulus of the thin-layer two-dimensional nanomaterial comprises: A mechanical analysis of the thin-layer two-dimensional nanomaterial with a cylindrical bubble was performed. The morphology of the cylindrical directrix parallel to the short axis was analyzed. The thin film theory was used to solve the problem. Combined with the boundary conditions at the edge of the rectangular micropore, the following relationship was obtained: Wherein, Δp is the pressure difference between the inside and outside of the cylindrical bubble, β is a coefficient related to the boundary conditions. For the solid / simply supported boundary conditions, β=1, ν is the Poisson's ratio of the material, E is the Young's modulus of the thin layer of two-dimensional nanomaterial, t is the thickness of the material, a is the radius of the minor axis of the bubble, and h is the height of the center point of the minor axis of the bubble; For orthotropic thin-layer two-dimensional nanomaterials, the Young's modulus along the short axis at different lattice angles of the material is solved, and then the Young's modulus distribution is solved using the following formula: Among them, E1 and E2 are Young's modulus along the two main axes, G 12 is the shear modulus, ν 12 is the Poisson's ratio corresponding to the direction of the main axis E1, and θ is the angle between the minor axis and the direction of the main axis E2; The method for measuring the bending stiffness of the thick layer two-dimensional nanomaterial includes: Mechanical analysis of cylindrical bubbles formed by thick-layer two-dimensional nanomaterials was performed using the following morphology formula and fitting: Where ω is the bubble profile function, x is the position variable, is a constant, F Tx is the surface force of the cylindrical bubble; Δp is the pressure difference between the inside and outside of the cylindrical bubble, a is the radius of the bubble's minor axis, and h is the height of the center point of the bubble's minor axis; The bending stiffness D of thick-layer two-dimensional nanomaterials is obtained by fitting.

2. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to claim 1, characterized in that: The aspect ratio of the rectangular micropores meets the following requirements: The aspect ratio of the rectangular micropore is 5.

3. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to claim 1, characterized in that: The method for obtaining the internal and external pressure difference △p of a cylindrical bubble is: The surface morphology of the cylindrical bubble is obtained by atomic force microscopy, and the radius a of the bubble along the short axis and the height h of the bubble center are obtained. At the same time, the thickness t of the measured sample is obtained by characterizing the edge morphology of the material. The pressure difference △p inside and outside the bubble is obtained by calculating the bubble morphology or directly reading the pressure difference △p measured by the pressure gauge.

4. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to claim 1, characterized in that: For anisotropic thick-layer two-dimensional nanomaterials, the bending stiffness along the short axis at different angles is calculated, and the anisotropic bending stiffness of the material is obtained by measuring samples in different directions.

5. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 4, characterized in that: The base material is a flat and hard inorganic substrate; The inorganic substrate is a silicon wafer; The surface of the silicon wafer has a silicon dioxide layer or a silicon nitride layer.

6. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 4, characterized in that: The short axis length of the rectangular micropore is 0.5 to 5 μm, and the rectangular size of the rectangular micropore is 1×5 to 2×10 μm.

7. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 4, characterized in that: The two-dimensional nanomaterial is a sheet-like material or a thin film material with a two-dimensional nanometer thickness; Two-dimensional nanomaterials include graphene, hexagonal boron nitride, silicene, transition metal sulfide selenides, two-dimensional layered metal carbides, two-dimensional layered metal nitrides, various polymer films, black phosphorus, rhenium disulfide or molybdenum trioxide.

8. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 4, characterized in that: The two-dimensional nanomaterial is prepared on a substrate with rectangular micropores by a micromechanical peeling method, a chemical vapor deposition method or an epitaxial growth method.

9. The method for measuring the Young's modulus or bending stiffness of a two-dimensional nanomaterial according to any one of claims 1 to 4, characterized in that: The rectangular microwell array is: a plurality of rectangular microwells are covered with a two-dimensional nanomaterial of the same layer at the same time to achieve high-throughput parameter measurement; The center spacing of the array is 1 to 3 times the length of the major axis of the rectangular microwells; The long axes of adjacent rectangular microwells on the array are rotated at the same or different angles, and the rotation angles are 0°, ±10°, ±20°, ±30°, ±45° or ±90°.

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