A method for determining the Hamek constant between particles

Abstract

This invention relates to a method for determining the Hamek constant between particles, belonging to the field of microscopic interaction forces. The method includes: preparing a test sample; fixing a single particle to the tip of a microcantilever probe to fabricate a particle probe; using an atomic force microscope to test the interaction force between the probe and the particle, and the interaction force between the particle probe and the particle, respectively obtaining the force-distance curves between the probe and the particle, and between the particles, to obtain the adhesion force F between the probe and the particle. 12 Adhesion force between particles F 12 This method calculates the Hamek constant between the probe and the particle, as well as the Hamek constant between particles. It can be used to determine the Hamek constant between particles in both gaseous and liquid environments. The method is simple, reliable, and the results are less affected by the external environment, exhibiting high accuracy.

Description

Technical Field

[0001] This invention relates to a method for determining the Hamek constant between particles, belonging to the field of microscopic interaction forces. Background Technology

[0002] The Hamek constant is a parameter characterizing the magnitude of van der Waals attraction energy between substances, and therefore an important parameter for calculating interparticle van der Waals forces. Research on the Hamek constant between mineral material particles in a gaseous environment (such as air) can be used to improve the flowability of powder particles and optimize the storage and transportation of cementitious materials. Conversely, the Hamek constant between particles in a liquid environment (such as ultrapure water and water-reducing agent solutions) can lay a theoretical foundation for revealing the mechanism by which mineral admixtures and water-reducing agents affect the rheological behavior of cement paste.

[0003] Currently, testing methods based on microscopic or continuous medium theories, such as the extended DLVO equation and full-spectrum calculations based on Lifshitz theory, are widely used for the indirect calculation of the Hamek constant. However, these methods are mainly used for colloidal phases, and their accuracy largely depends on parameters such as refractive index, electronic polarizability, and dielectric constant, which are highly sensitive to testing conditions and difficult to obtain accurately in a liquid environment. Furthermore, in slurry suspensions, mineral admixtures and chemical additives significantly affect the properties of the slurry suspension, making the determination of these parameters even more challenging. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for determining the Hamek constant between particles in both gaseous and liquid environments. The method is simple, reliable, and the results are less affected by the external environment, with high accuracy.

[0005] The present invention adopts the following technical solution:

[0006] A method for determining the Hamek constant between particles includes the following steps:

[0007] (1) Prepare test samples;

[0008] (2) Fix a single particle to the tip of the microcantilever probe to make a particle probe;

[0009] (3) The interaction force between the probe and the particle, and the interaction force between the particle and the probe were tested using atomic force microscopy. The force-distance curves between the probe and the particle, and between the particles, were obtained respectively. The adhesion force F between the probe and the particle was obtained. 12 Adhesion force between particles F 12 ;

[0010] (4) Calculate the Hamek constant between probe and particle, and the Hamek constant between particles.

[0011] Preferably, when testing in a gas phase environment, the sample preparation process is as follows:

[0012] First, the granular material and transparent liquid light-curing resin are mixed evenly at a mass ratio of 1:2 to 1:3. After curing in a vacuum environment at room temperature (25°C) for 12 to 48 hours, the sample surface is polished with 600-grit, 1200-grit, and 2000-grit sandpaper, respectively. Then, diamond powder is used to polish the sample surface to minimize the impact of the roughness of the particle surface on the test results. Finally, the sample is cut into 10mm×10mm×5mm cubes, and loose particles and dust on the surface are removed using compressed air or nitrogen.

[0013] In step (1), when testing in a liquid phase environment, the sample preparation process is as follows:

[0014] Test samples were prepared using glass slides as the carrier. Due to the high light transmittance of glass slides, the resolution of particles in the liquid environment can be significantly improved under external light source irradiation. First, an appropriate amount of UV-curable adhesive was dropped onto a clean glass slide, and then spread evenly on the slide surface using a spatula. Next, the clean spatula was pressed firmly and used to thin the adhesive layer along one end of the slide, repeating this process 3-5 times until the adhesive layer thickness was less than 1 / 3 of the average particle size of the material being tested. Then, the particles were loaded into a 1ml syringe and sprayed from a distance of 20-30cm directly above the glass slide in a clean, dust-free environment, allowing the particles to disperse in the air and fall freely onto the slide surface. Afterward, the glass slide was placed in a UV environment, and removed after the UV adhesive cured. Finally, loose particles on the surface were removed using compressed air or nitrogen.

[0015] Preferably, during the preparation of the test sample in a gas phase environment, the transparent liquid photocurable resin is preferably a high-transmittance epoxy resin, the mass ratio of the particulate material to the high-transmittance epoxy resin is preferably 1:2.5, and the curing time is preferably 24 hours.

[0016] Preferably, the particles include, but are not limited to, reference cement, grade I fly ash, granulated blast furnace slag powder, limestone powder, and silica fume;

[0017] The gas phase includes air, vacuum, etc., and the liquid phase includes ultrapure water, water-reducing agent solution, etc.

[0018] Preferably, fixing a single cementitious material particle to the tip of a microcantilever probe instead of the probe tip itself to contact different cementitious material particles can obtain the interaction force between particles. For particle-particle interaction force testing, the key is to fix a single cementitious material particle to the tip of the microcantilever probe and ensure that it does not fall off during the test, thereby replacing the probe tip itself to contact the particle to be tested and test the interaction force between them. Step (2) is the process of making the particle probe as follows:

[0019] 2.1 Disperse the particles on a clean glass slide, and prepare a curing adhesive and apply it to the glass slide;

[0020] 2.2. In an atomic force microscope, gently touch the cured adhesive with a needle-less probe, and then move the probe over the pre-selected particles;

[0021] 2.3 After adjusting the position of the probe and the particle several times, insert the needle to make the probe contact the particle;

[0022] 2.4 After the adhesive has cured, lift the probe and observe the bonding effect between the probe and the particle. If the particle is covered by more than half of its volume by the cured adhesive or if there are foreign objects stuck to the top of the particle, repeat the above steps to make a new particle probe.

[0023] The probe used in this invention is preferably a commercially available silicon nitride probe, model DNP-10, manufactured by Bruker, with an elastic modulus between 0.06 and 0.35 N / m, suitable for contact modes in air and liquid environments, tapping modes in liquid environments, and force measurements. The probe tip is parabolic in shape with a radius of curvature of 20 nm.

[0024] Preferably, in step (3), when testing the force, the elastic coefficient of the probe is first calibrated using a standard sample to accurately convert the deflection deformation of the probe during the test into force;

[0025] When testing the interaction force between the probe and the particle, the positions of the probe and the particle are adjusted to ensure that the probe is in direct contact with the particle. Then, multiple measurement points are selected on the particle within a range of 1μm×1μm to 20μm×20μm, preferably within a range of 5μm×5μm, such as 256 (16×16) measurement points. Subsequently, multiple force-distance curves are obtained on a single particle by the contact and separation of the probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, when the probe separates from the particle, the probe quickly "bounces back" to its undeflected position. The change in force during this process is the adhesion force between the probe and the particle. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average value of multiple adhesion forces is the final adhesion force F between the probe and the particle. 12 ;

[0026] When testing the interaction force between the particle probe and the particles, the positions of the particles on the probe and the particles on the sample are adjusted to ensure that the particles on the probe are in direct contact with the particles on the sample. Then, multiple measurement points are selected on the sample particles within a range of 1μm×1μm to 20μm×20μm, preferably within a range of 5μm×5μm, such as 256 (16×16) measurement points. Subsequently, multiple force-distance curves are obtained on a single particle by observing the contact and separation of the particle probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, when the particle probe separates from the particle, the probe quickly "bounces back" to its undeflected position. The change in force during this process is the adhesion force between the particles. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average value of multiple adhesion forces is the final adhesion force F between the particles. 12 .

[0027] Atomic force microscopy (AFM) involves intermittently contacting a probe with a surface to directly measure the force-distance curve between the probe and the contact surface, thereby determining the attractive force between the probe and the contact surface and calculating the Hamek constant. This method is direct and efficient. This invention utilizes a Bioscope Resolve atomic force microscope manufactured by Bruker AG, Germany, to test the microscopic interaction forces between cementitious material particles. This instrument features a high-speed scanning triaxial closed-loop scanner with a scanning range of 0-100 μm in the XY direction and 0-15 μm in the Z direction. It can achieve rapid scanning at a frequency of at least 70 Hz and offers multiple measurement modes, including contact, tapping, and peak force tapping. It can measure the morphology, height, force curves, and modulus of samples in gas or liquid phase environments.

[0028] Atomic force microscopy (AFM) uses a piezoelectric crystal scanner to move the test sample closer to and away from the probe tip, measuring the normal surface interaction force between the probe and the sample. Specifically, the positional change of a laser beam emitted from a laser emitter, reflected from the probe cantilever to a photodiode detector, is recorded as a displacement function in the Z-direction of the probe cantilever. Using a pre-calibrated probe elastic coefficient, the deflection is converted into a force, thus obtaining the interaction force curve as a function of the surface separation distance. AFM can measure attractive and repulsive forces, corresponding to negative and positive deflection of the microcantilever probe, respectively.

[0029] Down Figure 4This is a typical force-distance curve between a probe and a particle. As the probe gradually approaches the test particle (i.e., the Extend process), the attractive gradient between the probe and the particle gradually exceeds the probe's elastic coefficient, causing the probe to deflect beyond the "zero force" position (point B). As the probe continues to approach (BC), the force will linearly increase to a preset maximum value, ensuring complete contact between the probe and the particle. Afterward, the probe will begin to move away from the particle (i.e., the Retract process). Near the separation position (point D), the probe's elastic coefficient will overcome the particle's attractive force. Therefore, the probe "bounces back" to its undeflected position (point E), where the force is essentially zero.

[0030] Preferably, in step (3), when testing in a liquid environment, 1 ml of ultrapure water is dropped onto the surface of the test sample to ensure that the test material particles and the probe are completely immersed in the liquid;

[0031] When testing in a water-reducing agent solution environment, the probe and particles were fully immersed in the solution for 3 minutes before the test began to ensure that the water-reducing agent molecules were adsorbed on the particle surface. Lomboy compared the surface roughness of cement particles before and after immersion in the aqueous solution for 45 minutes, and the results showed that the change was less than ±10%, which means that the effect of particle surface changes on the contact area and test results is negligible. Therefore, in this invention, the force-distance curves on a single particle were obtained within 40 minutes. For each material, at least 3 particles were selected from the prepared sample for testing. Therefore, at least 768 measurements were performed on the test materials under different environmental conditions to reduce random errors in the experiment.

[0032] Preferably, in step (4), the adhesion force is closely related to the adhesion work of the interface and the probe tip radius, as shown in the following formula (1). The adhesion work includes the following components, with the first three representing the work of van der Waals forces.

[0033] W = W d +W p +W i +W h W π +W da +W e (1)

[0034] In the formula: W is the adhesion work; W d The adhesion work generated by the London dispersion; W P The adhesion work generated by dipole-dipole (orientation) interaction; W i The adhesion work generated by the induction effect; W h The adhesion work generated by hydrogen bonding; W π The work done by the π bond; W da The adhesion work generated by the donor-acceptor bond; We The adhesion work generated by electrostatic interaction;

[0035] Based on the stiffness of the material, the JKR model (Johnson, Kendall, Roberts, 1964-1971) and the DMT model (Derjagin, Muller, Toropov, 1975) for adhesion forces of spherical particles in contact with a plane are proposed, as shown in equations (2) and (3), where the adhesion work W 12 The Hamek constant A between two contacting objects 12 Related to the interfacial spacing, or cutoff distance D0, it has been reported that the cutoff distance (D0) varies for different materials, but mainly falls between 0.13 and 0.20 nm. Following the suggestions of scholars such as Bhattacharya and Israelachvilli, this study uses an average D0 of 0.165 nm for calculating the surface energy of the interface and the Hamek constant of the material.

[0036] F 12 =cπRW 12 (2)

[0037]

[0038] In the formula: F 12 The adhesive force between two contacting objects includes the adhesive force between the probe and the particle, and the adhesive force between particles. In formula (4), F 12 This represents the adhesion force between the probe and the particle; c is a constant, taken as 1.5 in the JKR model and 2 in the DMT model; R is the probe tip radius; W 12 The adhesion work at the interface between the two contacting objects is W in formula (1); A 12 D0 is the Hamek constant between the probe and the test particle; D0 is the cutoff distance.

[0039] Combining formulas (2) and (3), the Hamelin constant between the probe and the test particle is derived as follows:

[0040]

[0041] Preferably, the key to determining the Hamek constant between particles lies in determining the tip curvature radius of the particle probe, which directly affects the calculation of the contact area between particles. For ease of analysis, it is assumed that all particles adhering to the probe are spherical, so the equivalent radius of the particles is calculated based on the principle of equivalent cross-sectional area.

[0042] To determine the tip curvature radius of the particle probe, the present invention makes the following assumptions:

[0043] 1) The material is homogeneous and isotropic;

[0044] 2) The size of the contact area is much smaller than the size of the test material particles;

[0045] 3) The force is perpendicular to the contact surface, and there is no friction on the surface of the contact area;

[0046] 4) The deformation is within the elastic limit of the material.

[0047] According to Hertz contact theory, when two spheres with radii R1 and R2 come into contact under the action of an external force F, a circular contact surface will be formed near the contact point due to local deformation. Equations (5) to (7) are used to calculate the contact surface radius r, the relative displacement δ between the centers of the two spheres, and the maximum contact compressive stress q0, respectively.

[0048]

[0049]

[0050]

[0051] in,

[0052] In the formula, v1 is the Poisson's ratio of the particle on the probe; E1 is the elastic modulus of the particle on the probe; v2 is the Poisson's ratio of the particle being tested in the sample; E2 is the elastic modulus of the particle being tested in the sample; and F represents the external force, i.e. the peak force in the force-distance curve.

[0053] In particle-particle interaction force testing, the size of the particles on the probe can be determined based on the captured SEM image, but the diameter of the tested particle is difficult to measure accurately. However, in the research process, to accurately identify the test material particles under atomic force microscopy and ensure good contact between the particle probe and the test particles, the diameter of the test material particles is chosen to be approximately 10-20 times the diameter of the particles adhered to the probe. Therefore, the Hertz contact problem between particles can be simplified to a particle-plane contact problem, hence in the above formula, R1 = R0, R2 approaches ∞, and R0 represents the radius of the particle adhered to the probe, yielding:

[0054]

[0055]

[0056]

[0057] Substituting the solution of formula (8) into formula (4), where the contact surface radius r in formula (8) is the same as the probe tip radius R in formula (4), the formula for calculating the Hamek constant between particles is shown in formula (11), where F in formula (11) 12This indicates the adhesion force between particles:

[0058]

[0059] Where this invention is not detailed, existing technologies may be used.

[0060] The beneficial effects of this invention are as follows:

[0061] (1) This invention provides a method for directly and quickly determining the Hamel constant between mineral material particles. The method is simple, has few test parameters, has small random errors in the experiment, and the results are accurate and reliable.

[0062] (2) Based on Hertz contact theory, this invention proposes for the first time a method for directly testing and calculating the Hamek constant between particles using atomic force microscopy, filling the technological gap in this area and providing the possibility for accurately calculating the interaction forces between particles of various mineral materials in different environments.

[0063] (3) The Hamek constant between mineral material particles in the air determined by this invention can be used to improve the flowability of powder particles and optimize the storage and transportation schemes of cementitious materials; while the Hamek constant between particles in the liquid phase environment lays a theoretical foundation for the study of the mechanism of action of mineral admixtures and water-reducing agents on the rheological behavior of cement paste. Attached Figure Description

[0064] Figure 1 A scanning electron microscope (SEM) schematic diagram of cement based on granular materials;

[0065] Figure 2 Photographs of samples prepared using granular cement as a reference material under an optical microscope;

[0066] Figure 3 SEM images of the fabricated primary fly ash particle probe;

[0067] Figure 4 This is a typical force-distance curve between the probe and the particle;

[0068] Figure 5 A schematic diagram of Hertz contact between particles;

[0069] Figure 6 This is a schematic diagram of the contact between a particle and a plane Hertz. Detailed Implementation

[0070] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments. However, this description is not limited thereto. All aspects not described in detail in the present invention are based on conventional techniques in the field.

[0071] Example 1

[0072] A method for determining the Hamek constant between particles includes the following steps:

[0073] (1) Prepare test samples;

[0074] (2) Fix a single particle to the tip of the microcantilever probe to make a particle probe;

[0075] (3) The interaction force between the probe and the particle, and the interaction force between the particle and the probe were tested using atomic force microscopy. The force-distance curves between the probe and the particle, and between the particles, were obtained respectively. The adhesion force F between the probe and the particle was obtained. 12 Adhesion force between particles F 12 ;

[0076] (4) Calculate the Hamek constant between probe and particle, and the Hamek constant between particles.

[0077] Example 2

[0078] A method for determining the Hamek constant between particles, as described in Example 1, except that the sample preparation process is as follows when testing in a gas phase environment:

[0079] First, the granular material and high-transmittance epoxy resin were mixed evenly at a mass ratio of 1:2.5. After curing in a vacuum environment at room temperature (25℃) for 24 hours, the sample surface was polished with 600-grit, 1200-grit, and 2000-grit sandpaper respectively. Then, diamond powder was used to polish the sample surface to minimize the impact of the roughness of the particle surface on the test results. Finally, the sample was cut into 10mm×10mm×5mm cubes, and loose particles and dust on the surface were removed with compressed air or nitrogen.

[0080] The surface morphology of the sample was observed using environmental scanning electron microscopy (ESEM), as follows: Figure 1 This is a scanning electron microscope (SEM) diagram of cement based on granular materials. It clearly shows that because the elastic modulus of the cementitious material particles is higher than that of the epoxy resin, the particles of the test material are fully exposed on the sample surface after grinding. Although some larger particles peel off during grinding, leaving pits on the surface, most particles remain encapsulated by epoxy resin, avoiding the adverse effects of particle movement or deflection on the results during testing. Furthermore, it can be seen that the contrast between the epoxy resin matrix and the cementitious material particles is low, and the color distinction is not obvious. Therefore, this method is only suitable for sample preparation for gas-phase environment testing.

[0081] In step (1), when testing in a liquid phase environment, the sample preparation process is as follows:

[0082] Test samples were prepared using glass slides as the carrier. Due to the high light transmittance of glass slides, the resolution of particles in the liquid environment can be significantly improved under external light source irradiation. First, an appropriate amount of UV-curable adhesive was dropped onto a clean glass slide, and then spread evenly on the slide surface using a spatula. Next, the clean spatula was pressed firmly and used to thin the adhesive layer along one end of the slide, repeating this process 3-5 times until the adhesive layer thickness was less than 1 / 3 of the average particle size of the material being tested. Then, the particles were loaded into a 1ml syringe and sprayed from a distance of 20-30cm directly above the glass slide in a clean, dust-free environment, allowing the particles to disperse in the air and fall freely onto the slide surface. Afterward, the glass slide was placed in a UV environment, and removed after the UV adhesive cured. Finally, loose particles on the surface were removed using compressed air or nitrogen. Figure 2 The images show samples prepared under an optical microscope using cement as a reference material. The test particles are well dispersed and highly recognizable on the glass slide, with clear individual particle outlines and strong contrast with the matrix. This demonstrates that the samples prepared using this method can meet the requirements for testing interparticle forces using atomic force microscopy in a liquid-phase environment.

[0083] Example 3

[0084] A method for determining the Hameke constant between particles, as described in Example 2, except that the particles include, but are not limited to, reference cement, grade I fly ash, granulated blast furnace slag powder, limestone powder, and silica fume.

[0085] The gas phase includes air, vacuum, etc., and the liquid phase includes ultrapure water, water-reducing agent solution, etc.

[0086] Example 4

[0087] A method for determining the Hamek constant between particles, as described in Example 3, differs in that a single cementitious material particle is fixed to the tip of a microcantilever probe instead of the probe tip itself to contact different cementitious material particles for testing. This allows the interaction force between particles to be obtained. For particle-particle interaction force testing, the key is to fix a single cementitious material particle to the tip of the microcantilever probe and ensure that it does not fall off during the test, thereby replacing the probe tip itself to contact the particle to be tested for interaction force. Step (2) involves the process of making the particle probe as follows:

[0088] 2.1 Disperse the particles on a clean glass slide, and prepare a curing adhesive and apply it to the glass slide;

[0089] 2.2. In an atomic force microscope, gently touch the cured adhesive with a needle-less probe, and then move the probe over the pre-selected particles;

[0090] 2.3 After adjusting the position of the probe and the particle several times, insert the needle to make the probe contact the particle;

[0091] 2.4 After the adhesive has cured, lift the probe and observe the bonding effect between the probe and the particle. If the particle is covered by more than half of its volume by the cured adhesive or if there are foreign objects stuck to the top of the particle, repeat the above steps to make a new particle probe.

[0092] as follows Figure 3 The image shown is an SEM image of the fabricated primary fly ash particle probe. It can be seen that the primary fly ash particles are firmly adhered to the probe tip. The selected primary fly ash particles are regularly shaped with relatively flat surfaces. Although smaller particles adhere to the sides of the primary particles, their relatively posterior position does not affect the contact between the primary fly ash particles on the probe and the particles of the test material. It should be noted that the particles selected for adhesion to the probe tip should not be too large. Firstly, large particles are difficult to solidify, have poor stability, and are prone to falling off. Secondly, particles extending beyond the sides of the probe tip will affect the adjustment of the relative position between the probe and the test material particles during subsequent testing, increasing the difficulty of the test. Furthermore, the amount of adhesive used when fixing the particles should not be excessive. If the particle is encapsulated by more than half its volume or if foreign matter adheres to the tip of the particle, the above steps should be repeated to fabricate a new particle probe.

[0093] The probe used in this invention is preferably a commercially available silicon nitride probe, model DNP-10, manufactured by Bruker, with an elastic modulus between 0.06 and 0.35 N / m, suitable for contact modes in air and liquid environments, tapping modes in liquid environments, and force measurements. The probe tip is parabolic in shape with a radius of curvature of 20 nm.

[0094] Example 5

[0095] A method for determining the Hamek constant between particles, as described in Example 4, except that in step (3), when testing the force, the elastic coefficient of the probe used is first calibrated by a standard sample to accurately convert the deflection deformation of the probe during the test into force;

[0096] When testing the interaction force between the probe and the particle, the positions of the probe and the particle are adjusted to ensure that the probe is in direct contact with the particle. Then, multiple measurement points are selected within a 5μm×5μm range on the particle, such as 256 (16×16) measurement points. Subsequently, multiple force-distance curves are obtained on a single particle by observing the contact and separation of the probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, when the probe separates from the particle, the probe quickly "bounces back" to its undeflected position. The change in force during this process is the adhesion force between the probe and the particle. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average of multiple adhesion forces is the final adhesion force F between the probe and the particle. 12 ;

[0097] When testing the interaction force between the particle probe and the particles, the positions of the particles on the probe and the particles on the sample are adjusted to ensure that the particles on the probe are in direct contact with the particles on the sample. Then, multiple measurement points are selected within a 5μm × 5μm range on the sample particles, such as 256 (16 × 16) measurement points. Subsequently, multiple force-distance curves are obtained on a single particle by observing the contact and separation of the particle probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, when the particle probe separates from the particle, the probe quickly "bounces back" to its undeflected position. The change in force during this process is the adhesion force between the particles. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average of multiple adhesion forces is the final adhesion force F between the particles. 12 .

[0098] Atomic force microscopy (AFM) involves intermittently contacting a probe with a surface to directly measure the force-distance curve between the probe and the contact surface, thereby determining the attractive force between the probe and the contact surface and calculating the Hamek constant. This method is direct and efficient. This invention utilizes a Bioscope Resolve atomic force microscope manufactured by Bruker AG, Germany, to test the microscopic interaction forces between cementitious material particles. This instrument features a high-speed scanning triaxial closed-loop scanner with a scanning range of 0-100 μm in the XY direction and 0-15 μm in the Z direction. It can achieve rapid scanning at a frequency of at least 70 Hz and offers multiple measurement modes, including contact, tapping, and peak force tapping. It can measure the morphology, height, force curves, and modulus of samples in gas or liquid phase environments.

[0099] Atomic force microscopy (AFM) uses a piezoelectric crystal scanner to move the test sample closer to and away from the probe tip, measuring the normal surface interaction force between the probe and the sample. Specifically, the positional change of a laser beam emitted from a laser emitter, reflected from the probe cantilever to a photodiode detector, is recorded as a displacement function in the Z-direction of the probe cantilever. Using a pre-calibrated probe elastic coefficient, the deflection is converted into a force, thus obtaining the interaction force curve as a function of the surface separation distance. AFM can measure attractive and repulsive forces, corresponding to negative and positive deflection of the microcantilever probe, respectively.

[0100] Down Figure 4This is a typical force-distance curve between a probe and a particle. As the probe gradually approaches the test particle (i.e., the Extend process), the attractive gradient between the probe and the particle gradually exceeds the probe's elastic coefficient, causing the probe to deflect beyond the "zero force" position (point B). As the probe continues to approach (BC), the force will linearly increase to a preset maximum value, ensuring complete contact between the probe and the particle. Afterward, the probe will begin to move away from the particle (i.e., the Retract process). Near the separation position (point D), the probe's elastic coefficient will overcome the particle's attractive force. Therefore, the probe "bounces back" to its undeflected position (point E), where the force is essentially zero, and the adhesion force F... 12 That is, the absolute value of the difference between the DE forces.

[0101] Example 6

[0102] A method for determining the Hamek constant between particles, as described in Example 5, except that in step (3), when testing in a liquid phase environment, 1 ml of ultrapure water is dropped onto the surface of the test sample to ensure that the test material particles and the probe are completely immersed in the liquid;

[0103] When testing in a water-reducing agent solution environment, the probe and particles were fully immersed in the solution for 3 minutes before the test began to ensure that the water-reducing agent molecules were adsorbed on the particle surface. Lomboy compared the surface roughness of cement particles before and after immersion in the aqueous solution for 45 minutes, and the results showed that the change was less than ±10%, which means that the effect of particle surface changes on the contact area and test results is negligible. Therefore, in this invention, the force-distance curves on a single particle were obtained within 40 minutes. For each material, at least 3 particles were selected from the prepared sample for testing. Therefore, at least 768 measurements were performed on the test materials under different environmental conditions to reduce random errors in the experiment.

[0104] Example 7

[0105] A method for determining the Hamek constant between particles, as described in Example 6, except that in step (4), the adhesion force is closely related to the adhesion work of the interface and the probe tip radius, as shown in the following formula (1). The adhesion work includes the following components, the first three of which represent the work of van der Waals forces.

[0106] W = W d +W p +W i +W h W π +W da +W e (1)

[0107] In the formula: W is the adhesion work; W d The adhesion work generated by the London dispersion; WP The adhesion work generated by dipole-dipole (orientation) interaction; W i The adhesion work generated by the induction effect; W h The adhesion work generated by hydrogen bonding; W π The work done by the π bond; W da The adhesion work generated by the donor-acceptor bond; W e The adhesion work generated by electrostatic interaction;

[0108] Based on the stiffness of the material, the JKR model (Johnson, Kendall, Roberts, 1964-1971) and the DMT model (Derjagin, Muller, Toropov, 1975) for adhesion forces of spherical particles in contact with a plane are proposed, as shown in equations (2) and (3), where the adhesion work W 12 The Hamek constant A between two contacting objects 12 Related to the interfacial spacing, or cutoff distance D0, it has been reported that the cutoff distance (D0) varies for different materials, but mainly falls between 0.13 and 0.20 nm. Following the suggestions of scholars such as Bhattacharya and Israelachvilli, this study uses an average D0 of 0.165 nm for calculating the surface energy of the interface and the Hamek constant of the material.

[0109] F 12 =cπRW 12 (2)

[0110]

[0111] In the formula: F 12 The adhesive force between two contacting objects includes the adhesive force between the probe and the particle, and the adhesive force between particles. In formula (4), F 12 This represents the adhesion force between the probe and the particle; c is a constant, taken as 1.5 in the JKR model and 2 in the DMT model; R is the probe tip radius; W 12 The adhesion work at the interface between the two contacting objects is W in formula (1); A 12 D0 is the Hamek constant between the probe and the test particle; D0 is the cutoff distance.

[0112] Combining formulas (2) and (3), the Hamelin constant between the probe and the test particle is derived as follows:

[0113]

[0114] Example 8

[0115] A method for determining the Hamek constant between particles, as described in Example 7, differs in that, in step (4), the key to determining the Hamek constant between particles lies in determining the tip curvature radius of the particle probe, which directly affects the calculation of the contact area between particles. For ease of analysis, it is assumed that all particles stuck on the probe are spherical, so the equivalent radius of the particles is calculated based on the principle of equivalent cross-sectional area.

[0116] To determine the tip curvature radius of the particle probe, the present invention makes the following assumptions:

[0117] 1) The material is homogeneous and isotropic;

[0118] 2) The size of the contact area is much smaller than the size of the test material particles;

[0119] 3) The force is perpendicular to the contact surface, and there is no friction on the surface of the contact area;

[0120] 4) The deformation is within the elastic limit of the material.

[0121] According to Hertz's contact theory, when two spheres with radii R1 and R2 come into contact under the action of an external force F, the following occurs: Figure 5 As shown, a circular contact surface will be formed near the contact point due to local deformation. Equations (5) to (7) are used to calculate the contact surface radius r, the relative displacement δ between the two sphere centers, and the maximum contact compressive stress q0, respectively.

[0122]

[0123]

[0124]

[0125] in,

[0126] In the formula, v1 is the Poisson's ratio of the particle on the probe; E1 is the elastic modulus of the particle on the probe; v2 is the Poisson's ratio of the particle being tested in the sample; E2 is the elastic modulus of the particle being tested in the sample; and F represents the external force, i.e., the peak force in the force-distance curve. Figure 4 The force corresponding to point C;

[0127] In particle-particle interaction force testing, the size of the particles on the probe can be determined based on the captured SEM image, but the diameter of the tested particle is difficult to measure accurately. However, in the research process, to accurately identify the test material particles under atomic force microscopy and ensure good contact between the particle probe and the test particles, the diameter of the test material particles is chosen to be approximately 10-20 times the diameter of the particles adhered to the probe. Therefore, the Hertz contact problem between particles can be simplified to a particle-plane contact problem, such as... Figure 6 As shown, in the above formula, R1 = R0, R2 approaches ∞, and R0 represents the radius of the particle adhering to the probe. Therefore:

[0128]

[0129]

[0130]

[0131] Substituting the solution of formula (8) into formula (4), where the contact surface radius r in formula (8) is the same as the probe tip radius R in formula (4), the formula for calculating the Hamek constant between particles is shown in formula (11), where F in formula (11) 12 This indicates the adhesion force between particles:

[0132]

[0133] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the Hamek constant between particles, characterized in that, Includes the following steps: (1) Prepare test samples; (2) Fix a single particle to the tip of the microcantilever probe to make a particle probe; (3) The interaction force between the probe and the particle, and the interaction force between the particle and the probe were tested using atomic force microscopy. The force-distance curves between the probe and the particle, and between the particles, were obtained respectively. The adhesion force F between the probe and the particle was obtained. 12 Adhesion force between particles F 12 ; (4) Calculate the Hamek constant between the probe and the particle, and the Hamek constant between particles; In step (1), when testing in a gas phase environment, the sample preparation process is as follows: First, the granular material and transparent liquid light-curing resin are mixed evenly at a mass ratio of 1:2 to 1:

3. After curing in a vacuum environment at room temperature for 12 to 48 hours, the sample surface is polished with 600-grit, 1200-grit, and 2000-grit sandpaper, respectively. Then, diamond powder is used to polish the sample surface to minimize the impact of the roughness of the particle surface on the test results. Finally, the sample is cut into 10mm×10mm×5mm cubes, and loose particles and dust on the surface are removed with compressed air or nitrogen. In step (1), when testing in a liquid phase environment, the sample preparation process is as follows: Test samples were prepared using a glass slide as a carrier. First, UV-curable adhesive was dropped onto a clean glass slide and spread evenly on the slide surface using a spatula. Then, the clean spatula was pressed firmly and the adhesive layer was thinned along one end of the glass slide, repeated 3-5 times until the adhesive layer thickness was less than 1 / 3 of the average particle size of the material to be tested. Next, the particles were loaded into a 1ml syringe and sprayed from 20-30cm directly above the glass slide in a clean, dust-free environment, allowing the particles to disperse in the air and fall freely onto the surface of the glass slide. After that, the glass slide was placed in a UV environment and removed after the UV adhesive cured. Finally, loose particles on the surface were removed using compressed air or nitrogen. Step (2) involves the following process for fabricating the particle probe: 2.1 Disperse the particles on a clean glass slide, and prepare a curing adhesive and apply it to the glass slide; 2.

2. In an atomic force microscope, gently touch the cured adhesive with a needle-less probe, and then move the probe over the pre-selected particles; 2.3 After adjusting the position of the probe and the particle several times, insert the needle to make the probe contact the particle; 2.4 After the adhesive has cured, lift the probe and observe the bonding effect between the probe and the particle. If the particle is covered by more than half of its volume by the cured adhesive or if there are foreign objects stuck to the top of the particle, repeat the above steps to make a new particle probe. In step (3), when testing the force, the elastic coefficient of the probe is first calibrated using a standard sample to accurately convert the deflection deformation of the probe during the test into force. When testing the interaction force between the probe and the particle, the positions of the probe and the particle are adjusted to ensure that the probe is in direct contact with the particle. Then, multiple measurement points are selected within a 5μm × 5μm range on the particle. Subsequently, multiple force-distance curves are obtained on a single particle by observing the contact and separation of the probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, the probe quickly "bounces back" to its undeflected position when it separates from the particle. The change in force during this process is the adhesion force between the probe and the particle. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average of multiple adhesion forces is the final adhesion force F between the probe and the particle. 12 ; When testing the interaction force between the particle probe and the particles, the positions of the particles on the probe and the particles on the sample are adjusted to ensure that the particles on the probe are in direct contact with the particles on the sample. Then, multiple measurement points are selected within a 5μm × 5μm range on the sample particles. Subsequently, multiple force-distance curves are obtained on a single particle by observing the contact and separation of the particle probe and the particle at different positions. Based on the interaction force-distance curve obtained by atomic force microscopy, in each interaction force-distance curve, when the particle probe separates from the particle, the probe quickly "bounces back" to its undeflected position. The change in force during this process is the adhesion force between the particles. This adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average of multiple adhesion forces is taken as the final adhesion force F between the particles. 12 ; In step (3), when testing in a liquid environment, 1 ml of ultrapure water is dropped onto the surface of the test sample to ensure that the test material particles and the probe are completely immersed in the liquid; When testing in a water-reducing agent solution environment, the probe and particles are completely immersed in the solution for 3 minutes before the test begins to ensure that the water-reducing agent molecules are adsorbed on the particle surface. In step (4), the adhesion force is closely related to the adhesion work of the interface and the probe tip radius, as shown in the following formula (1). The adhesion work includes the following components, with the first three representing the work of van der Waals forces. W=W d +W p +W i +W h +W p +W da +W e (1) In the formula: W is the adhesion work; W d The adhesion work generated by the London dispersion; W P The adhesion work generated by the dipole-dipole interaction; W i The adhesion work generated by the induction effect; W h The adhesion work generated by hydrogen bonding; W π The work done by the π bond; W da The adhesion work generated by the donor-acceptor bond; W e The adhesion work generated by electrostatic interaction; Based on the stiffness of the material, the JKR model and DMT model for adhesion force of spherical particles in contact with a plane are proposed, as shown in equations (2) and (3), where the adhesion work W 12 The Hamek constant A between two contacting objects 12 It is related to the interface spacing or cutoff distance D0, with an average value of 0.165nm; F 12 =cπRW 12 (2) In the formula: F 12 For the adhesive force between two contacting objects, F in formula (4) 12 This represents the adhesion force between the probe and the particle; c is a constant, taken as 1.5 in the JKR model and 2 in the DMT model; R is the probe tip radius; W 12 The adhesion work at the interface between two contacting objects; A 12 D0 is the Hamek constant between the probe and the test particle; D0 is the cutoff distance. Combining formulas (2) and (3), the Hamelin constant between the probe and the test particle is derived as follows: Assuming all particles adhering to the probe are spherical, the equivalent radius of the particles can be calculated based on the principle of equivalent cross-sectional area. According to Hertz contact theory, when two spheres with radii R1 and R2 come into contact under the action of an external force F, a circular contact surface will be formed near the contact point due to local deformation. Equations (5) to (7) are used to calculate the contact surface radius r, the relative displacement d between the centers of the two spheres, and the maximum contact compressive stress q0, respectively. in, In the formula, v1 is the Poisson's ratio of the particle on the probe; E1 is the elastic modulus of the particle on the probe; v2 is the Poisson's ratio of the particle being tested in the sample; E2 is the elastic modulus of the particle being tested in the sample; and F represents the external force, i.e. the peak force in the force-distance curve. By increasing the radius ratio of the test particle to the particles on the probe, with the diameter of the test particle being 10-20 times the diameter of the particles adhered to the probe, the Hertz contact problem between particles is simplified to a Hertz contact problem between a particle and a plane. Therefore, R1 = R0, R2 approaches ∞, and R0 represents the radius of the particle adhered to the probe. Substituting the solution of formula (8) into formula (4), where the contact surface radius r in formula (8) is the same as the probe tip radius R in formula (4), the formula for calculating the Hamek constant between particles is shown in formula (11), where F in formula (11) 12 This indicates the adhesion force between particles:

2. The method for determining the Hamek constant between particles according to claim 1, characterized in that, During the preparation of the test sample in a gas phase environment, the transparent liquid photocurable resin was a high-transmittance epoxy resin, and the mass ratio of the particulate material to the high-transmittance epoxy resin was 1:2.5; the curing time was 24 hours.

3. The method for determining the Hamek constant between particles according to claim 2, characterized in that, The granules are based on cement, grade 1 fly ash, granulated blast furnace slag powder, limestone powder or silica fume; The gas phase is air or vacuum, and the liquid phase is ultrapure water or water-reducing agent solution.

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