Method for determining the equivalent hamaker constant of a cement paste suspension system

Abstract

The application relates to a method for determining the equivalent Hamaker constant of a cement paste suspension system, belonging to the field of micro interaction force, and comprising the following steps: preparing a test sample, respectively preparing a cement test sample and a mineral admixture test sample; preparing a particle probe: respectively fixing a single cement particle and a mineral admixture particle at the tip of a micro-cantilever probe to obtain a corresponding particle probe; using an atomic force microscope to test the interaction force between the probe and the particle and the interaction force between the particles, respectively obtaining the force-distance curve between the probe and the particle and the force-distance curve between the particles, and then obtaining the adhesion force between the probe and the particle and between the particles; and calculating the Hamaker constant and the equivalent Hamaker constant between the particles. The application can accurately describe the interaction force between the cementitious material particles in the paste, and further reveal the action mechanism of the mineral admixture on the rheological behavior of the cement paste, so that accurate prediction and optimization control of the rheological parameters of the cement paste can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for determining the equivalent Hamaker constant of a cement slurry suspension system, belonging to the field of micro-interaction forces. BACKGROUND

[0002] The Hamaker constant is a parameter representing the size of the van der Waals attractive energy between substances. As a high-concentration suspension system, the cement slurry suspension system has multiple micro-interaction forces inside, among which the van der Waals force is the main reason for the agglomeration of particles in the cement slurry suspension system and the reduction of flow performance. The van der Waals force between particles can be calculated by the Hamaker constant, so the Hamaker constant is an important parameter for describing the strength of van der Waals interaction.

[0003] At present, test methods based on micro or continuum medium theory, such as extended DLVO equation and full spectrum calculation based on Lifshitz theory, have been widely used for indirect calculation of the Hamaker constant. However, these methods are mainly used for colloidal phase, and their accuracy depends largely on parameters such as refractive index, electronic polarizability and dielectric constant, but these parameters are very sensitive to test conditions and are very difficult to accurately obtain in cement slurry suspension systems.

[0004] Studies have shown that the Hamaker constant between cement and different mineral admixture particles is significantly different. In order to calculate the overall Hamaker constant of the cement slurry suspension system to quantify the interaction force between particles in the cement-mineral admixture slurry, it is urgent to propose an effective Hamaker constant between different material particles that comprehensively considers the interaction force between particles in the cement-mineral admixture slurry. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a method for determining the equivalent Hamaker constant of a cement slurry suspension system, which can more representatively and accurately describe the interaction force between cementitious material particles in the slurry, and further reveal the action mechanism of mineral admixtures on the rheological behavior of cement slurry, and realize accurate prediction and optimization control of the rheological parameters of cement slurry.

[0006] The present application adopts the following technical solutions:

[0007] A method for determining the equivalent Hamaker constant of a cement slurry suspension system, the method for determining the equivalent Hamaker constant of the cement slurry suspension system, characterized in that it comprises the following steps:

[0008] (1) Preparing test samples: for a binary cement-mineral admixture cement slurry suspension system, there are three different types of inter-particle interactions, namely cement-cement, cement-mineral admixture and mineral admixture-mineral admixture, and cement test samples and mineral admixture test samples are prepared respectively;

[0009] (2) Fabrication of particle probes: Single cement particles and mineral admixture particles are fixed on the tip of the microcantilever probe to obtain cement particle probes and mineral admixture particle probes.

[0010] (3) The interaction force between the particle probe and the particles was tested using an atomic force microscope to obtain the force-distance curve between the particles, and then the adhesion force F between the particles was obtained. 12 ;

[0011] In this step, the adhesion between particles includes the adhesion between cement particles, the adhesion between cement particles and mineral admixture particles, and the adhesion between mineral admixture particles.

[0012] (4) Calculate the Hamek constant between particles;

[0013] (5) Calculate the equivalent Hamek constant of the cement slurry suspension system.

[0014] Preferably, in step (1), the preparation process of the test sample is as follows:

[0015] 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 scraped thinner 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 test material, which consisted of cement particles and mineral admixture particles. 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 them 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, compressed air or nitrogen was used to remove loose particles from the surface.

[0016] Preferably, the specific process for fabricating the particle probe in step (2) is as follows:

[0017] 2.1 Disperse the particles on a clean glass slide, and prepare a curing adhesive and apply it to the glass slide;

[0018] 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;

[0019] 2.3 After adjusting the position of the probe and the particle several times, insert the needle to make the probe contact the particle;

[0020] 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.

[0021] When the particles are cement particles, a cement particle probe is prepared; when the particles are mineral admixture particles, a mineral admixture particle probe is prepared.

[0022] The probe of this invention preferably uses a commercial 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 measurement.

[0023] 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;

[0024] 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 .

[0025] 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.

[0026] 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.

[0027] Down Figure 4 This 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.

[0028] Preferably, in step (3), during testing in an ultrapure water environment, 1 ml of ultrapure water is dropped onto the surface of the test sample to ensure that both the test material particles and the probe are completely immersed in the liquid. To reduce the impact of mineral material hydration on the test results, the test is completed within 40 minutes. Therefore, in this invention, the acquisition of the force-distance curve on a single particle is completed within 40 minutes. For each type of particulate material, at least three particles are selected on the prepared sample for testing to reduce random errors generated by the experiment.

[0029] In the 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.

[0030] Preferably, in step (4), the Hamek constant between the probe and the test particle is:

[0031]

[0032] Among them, A 12 D is the Hamek constant between the probe and the test particle; D0 is the cutoff distance; F 12 The adhesive force between the two contacting objects is the adhesive force between the probe and the test particle in this case; c is a constant, which is 1.5 in the JKR model and 2 in the DMT model; R is the probe tip radius.

[0033] 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.

[0034] To determine the tip curvature radius of the particle probe, the present invention makes the following assumptions:

[0035] 1) The material is homogeneous and isotropic;

[0036] 2) The size of the contact area is much smaller than the size of the test material particles;

[0037] 3) The force is perpendicular to the contact surface, and there is no friction on the surface of the contact area;

[0038] 4) The deformation is within the elastic limit of the material.

[0039] 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.

[0040]

[0041]

[0042]

[0043] in,

[0044] 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.

[0045] 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:

[0046]

[0047]

[0048]

[0049] 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). 12 This refers to the adhesive force between two contacting objects; in this case, it refers to the adhesive force between particles.

[0050]

[0051] Preferably, in step (5), to calculate the equivalent Hamek constant of the cement slurry suspension system of binary cement-mineral admixture, it is first necessary to determine the collision probability between various particles; it is assumed that the probability of any particle interacting with cement or mineral admixture particles is the probability of that particle contacting the surface of a certain type of material particle, that is, the collision probability between each particle is calculated by combining the ratio of the surface area of ​​cement and mineral admixture in the system to the total surface area with the probability model. The specific calculation method is as follows:

[0052] Let V be the volume percentage of cement in a unit volume of cement paste. c The volume percentage of mineral admixtures is V. m The surface areas of cement particles and mineral admixture particles are respectively:

[0053] M c =ρ c ·V c ·S c (12)

[0054] M m =ρ m ·V m ·S m (13)

[0055] Where: M c The total surface area of ​​the cement is in meters. 2 M m The total surface area of ​​the mineral admixture, in m 2 ;ρ c The density of cement (kg / m³) 3 ;ρ m The density of the mineral admixture is kg / m³ 3 V c Let m be the volume of cement in the slurry. 3 V mLet m be the volume of the mineral admixtures in the slurry. 3 S c The specific surface area of ​​cement (m) 2 / kg; S m The specific surface area (m²) of the mineral admixture 2 / kg;

[0056] If the total surface area of ​​all particles in the slurry is considered as unit 1, then the surface area ratios of cement particles and mineral admixture particles are represented by N, and are respectively:

[0057]

[0058]

[0059] N c N represents the surface area ratio of cement. m Indicates the surface area ratio of mineral admixtures;

[0060] Combining probability theory and mathematical statistics, the collision probability P of cement-cement, cement-mineral admixture, and mineral admixture-mineral admixture in cement paste is... c-c P c-m P m-m They are respectively:

[0061]

[0062]

[0063]

[0064] The total probability P of the above three types of inter-particle collisions is 1, that is:

[0065]

[0066] The equivalent Hamek constant of a cement slurry suspension system is defined as the sum of the products of the Hamek constants between any two material particles and the probability of their interaction, i.e.:

[0067]

[0068] In the formula: A is the equivalent Hamek constant for the cement slurry suspension system; A is the Hamek constant between particles in the liquid environment; A c-c A represents the Hamek constant between cement particles in a liquid environment; c-m A is the Hamelin constant between cement particles and mineral admixture particles in a liquid environment; m-m The Hamelcke constant is the inter-particle relationship between mineral admixtures in a liquid environment.

[0069] The liquid environment includes ultrapure water and water-reducing agent solution environments. When calculating the Hamek constant, F... 12 It should also refer to the adhesive force between two contacting objects in a corresponding liquid environment;

[0070] Based on the above analysis, for complex cement slurry suspension systems prepared from multi-component cementitious materials, the surface area of ​​all particles of any cementitious material per unit volume of slurry is:

[0071] M i =ρ i ·V i ·S i (twenty one)

[0072] M i ρ represents the total surface area of ​​the i-th type of particle. i This represents the density of the i-th type of particle (kg / m³). 3 V i S represents the volume percentage of the i-th type of particle. i m represents the specific surface area of ​​the i-th type of particle. 2 / kg;

[0073] The percentage of the surface area of ​​any material particle in the total surface area of ​​all materials is:

[0074]

[0075] In the formula: n represents the types of multi-component cementitious materials in the cement paste;

[0076] Then the probability P of interaction between any material particles within the system i-i and the probability P of its interaction with another type of material particle i-j They are respectively:

[0077]

[0078]

[0079] Similarly, the total probability of interactions between all types of particles in the slurry is 1, that is:

[0080]

[0081] Accordingly, the equivalent Hamek constant between material particles used in cement paste prepared from multi-component cementitious materials is:

[0082]

[0083] Where this invention is not detailed, existing technologies may be used.

[0084] The beneficial effects of this invention are as follows:

[0085] This invention proposes an equivalent Hamaker constant calculation method for cement slurry suspension systems, taking into account the spatial distribution and collision probability of particles in the slurry. Using the equivalent Hamaker constant allows for a more representative and accurate description of the interaction forces between cementitious material particles in the slurry, thereby revealing the mechanism by which mineral admixtures affect the rheological behavior of cement slurry and enabling accurate prediction and optimized control of cement slurry rheological parameters.

[0086] The method for calculating the Hamek constant proposed in this invention is simple, requires few test parameters, has small random errors in experiments, and yields accurate and reliable results.

[0087] This invention, based on Hertz contact theory, proposes for the first time a method for directly testing and calculating the Hamek constant between particles using atomic force microscopy, filling a technological gap in this field and providing the possibility for accurately calculating the interaction forces between particles of various mineral materials in different environments. Attached Figure Description

[0088] Figure 1 Photographs of samples prepared using cement as a granular material under an optical microscope;

[0089] Figure 2 SEM images of the fabricated particle probe;

[0090] Figure 3 This is a typical force-distance curve between the probe and the particle;

[0091] Figure 4 A schematic diagram of Hertz contact between particles;

[0092] Figure 5 This is a schematic diagram of the contact between a particle and a plane Hertz. Detailed Implementation

[0093] 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.

[0094] Example 1

[0095] A method for determining the equivalent Hamek constant of a cement slurry suspension system includes the following steps:

[0096] (1) Preparation of test samples: For the cement slurry suspension system of binary cement-mineral admixture, there are three different types of particle interactions, namely cement-cement, cement-mineral admixture, and mineral admixture-mineral admixture. Cement test samples and mineral admixture test samples were prepared respectively.

[0097] (2) Fabrication of particle probes: Single cement particles and mineral admixture particles are fixed on the tip of the microcantilever probe to obtain cement particle probes and mineral admixture particle probes.

[0098] (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 then obtained. 12 Adhesion force between particles F 12 ;

[0099] In this step, the adhesion forces obtained include the adhesion force between the probe and cement particles, the adhesion force between the probe and mineral admixture particles, the adhesion force between cement particles, the adhesion force between cement particles and mineral admixture particles, and the adhesion force between mineral admixture particles.

[0100] (4) Calculate the Hamek constant between particles;

[0101] (5) Calculate the equivalent Hamek constant of the cement slurry suspension system.

[0102] Example 2

[0103] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 1, except that in step (1), the preparation process of the test sample is as follows:

[0104] 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 scraped thinner 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 test material, which consisted of cement particles and mineral admixture particles. 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 them 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, compressed air or nitrogen was used to remove loose particles from the surface.

[0105] Figure 1The 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.

[0106] Example 3

[0107] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 2, differs in that a single cementitious material particle is fixed on the tip of a microcantilever probe instead of the probe tip itself to contact different cementitious material particles for testing, thereby obtaining the interaction force between particles. For particle-particle interaction force testing, the key is to fix a single cementitious material particle on the tip of the microcantilever probe and ensure that it does not fall off during the test, thus replacing the probe tip itself to contact the particle to be tested for the interaction force. The specific process of making the particle probe in step (2) is as follows:

[0108] 2.1 Disperse the particles on a clean glass slide, and prepare a curing adhesive and apply it to the glass slide;

[0109] 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;

[0110] 2.3 After adjusting the position of the probe and the particle several times, insert the needle to make the probe contact the particle;

[0111] 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.

[0112] When the particles are cement particles, a cement particle probe is prepared; when the particles are mineral admixture particles, a mineral admixture particle probe is prepared.

[0113] as follows Figure 2The image shown is an SEM image of a fabricated particle probe. It can be seen that the particles are firmly adhered to the probe tip. The selected particles are regularly shaped, and their surfaces are generally flat. Although smaller particles adhere to the sides of the probe, their relatively posterior position does not affect the contact between the particles on the probe and the test material particles. It should be noted that the particles selected for attachment 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 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 to fix 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.

[0114] The probe of this invention preferably uses a commercial 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 measurement.

[0115] Example 4

[0116] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 3, 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;

[0117] 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 ;

[0118] 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 .

[0119] 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.

[0120] 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.

[0121] Figure 3This 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.

[0122] Example 5

[0123] A method for determining the equivalent Hamek constant of a cement slurry suspension system is described in Example 4, except that in step (3), 1 ml of ultrapure water is added to the surface of the test sample during testing in an ultrapure water environment to ensure that the test material particles and the probe are completely immersed in the liquid. To reduce the influence of mineral hydration on the test results, the test is completed within 40 minutes. Therefore, in this invention, the force-distance curve of a single particle is obtained within 40 minutes. For each type of particulate material, at least three particles are selected on the prepared sample for testing to reduce random errors generated by the experiment.

[0124] In the 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.

[0125] Example 6

[0126] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 5, 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.

[0127] W = W d +W p +W i +W h +W π +W da +W e (1)

[0128] 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; Wπ 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;

[0129] 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.

[0130] F 12 =cπRW 12 (2)

[0131]

[0132] In the formula: F 12 The adhesive force between the two contacting objects includes the adhesive force between the probe and the particle, and the adhesive force between particles; here, it is the adhesive 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.

[0133] Combining formulas (2) and (3), the Hamelin constant between the probe and the test particle is derived as follows:

[0134]

[0135] Example 7

[0136] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 6, differs in that 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.

[0137] To determine the tip curvature radius of the particle probe, the present invention makes the following assumptions:

[0138] 1) The material is homogeneous and isotropic;

[0139] 2) The size of the contact area is much smaller than the size of the test material particles;

[0140] 3) The force is perpendicular to the contact surface, and there is no friction on the surface of the contact area;

[0141] 4) The deformation is within the elastic limit of the material.

[0142] 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, as follows: Figure 4 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.

[0143]

[0144]

[0145]

[0146] in,

[0147] 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 3 The force corresponding to point C;

[0148] 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 5 As shown, in the above formula, R1 = R0, R2 approaches ∞, and R0 represents the radius of the particle adhering to the probe. Therefore:

[0149]

[0150]

[0151]

[0152] 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). 12 This refers to the adhesive force between two contacting objects; in this case, it refers to the adhesive force between particles.

[0153]

[0154] Example 8

[0155] A method for determining the equivalent Hamek constant of a cement slurry suspension system, as described in Example 7, differs in that, in step (5), to calculate the equivalent Hamek constant of the cement slurry suspension system of binary cement-mineral admixture, it is first necessary to determine the collision probability between various particles; it is assumed that the probability of any particle interacting with cement or mineral admixture particles is the probability of that particle contacting the surface of a certain type of material particle, that is, the collision probability between each particle is calculated by combining the ratio of the surface area of ​​cement and mineral admixture in the system to the total surface area with a probability model, and the specific calculation method is as follows:

[0156] Let V be the volume percentage of cement in a unit volume of cement paste. c The volume percentage of mineral admixtures is V. m The surface areas of cement particles and mineral admixture particles are respectively:

[0157] M c =ρ c ·V c ·S c (12)

[0158] M m =ρ m ·V m ·S m (13)

[0159] Where: M c The total surface area of ​​the cement is in meters. 2 M m The total surface area of ​​the mineral admixture, in m 2 ;ρ c The density of cement (kg / m³) 3 ;ρ m The density of the mineral admixture is kg / m³ 3 V c Let m be the volume of cement in the slurry. 3 V m Let m be the volume of the mineral admixtures in the slurry.3 S c The specific surface area of ​​cement (m) 2 / kg; S m The specific surface area (m²) of the mineral admixture 2 / kg;

[0160] If the total surface area of ​​all particles in the slurry is considered as unit 1, then the surface area ratios of cement particles and mineral admixture particles are represented by N, and are respectively:

[0161]

[0162]

[0163] N c N represents the surface area ratio of cement. m Indicates the surface area ratio of mineral admixtures;

[0164] Combining probability theory and mathematical statistics, the collision probability P of cement-cement, cement-mineral admixture, and mineral admixture-mineral admixture in cement paste is... c-c P c-m P m-m They are respectively:

[0165]

[0166]

[0167]

[0168] The total probability P of the above three types of inter-particle collisions is 1, that is:

[0169]

[0170] The equivalent Hamek constant of a cement slurry suspension system is defined as the sum of the products of the Hamek constants between any two material particles and the probability of their interaction, i.e.:

[0171]

[0172] In the formula: A is the equivalent Hamek constant for the cement slurry suspension system; A is the Hamek constant between particles in the liquid environment; A c-c A represents the Hamek constant between cement particles in a liquid environment; c-m A is the Hamelin constant between cement particles and mineral admixture particles in a liquid environment; m-m The Hamelcke constant is the inter-particle relationship between mineral admixtures in a liquid environment.

[0173] The liquid environment includes ultrapure water and water-reducing agent solution environments. When calculating the Hamek constant, F... 12 It should also refer to the adhesive force between two contacting objects in a corresponding liquid environment;

[0174] Based on the above analysis, for complex cement slurry suspension systems prepared from multi-component cementitious materials, the surface area of ​​all particles of any cementitious material per unit volume of slurry is:

[0175] M i =ρ i ·V i ·S i (twenty one)

[0176] M i ρ represents the total surface area of ​​the i-th type of particle. i This represents the density of the i-th type of particle (kg / m³). 3 V i S represents the volume percentage of the i-th type of particle. i m represents the specific surface area of ​​the i-th type of particle. 2 / kg;

[0177] The percentage of the surface area of ​​any material particle in the total surface area of ​​all materials is:

[0178]

[0179] In the formula: n represents the types of multi-component cementitious materials in the cement paste;

[0180] Then the probability P of interaction between any material particles within the system i-i and the probability P of its interaction with another type of material particle i-j They are respectively:

[0181]

[0182]

[0183] Similarly, the total probability of interactions between all types of particles in the slurry is 1, that is:

[0184]

[0185] Accordingly, the equivalent Hamek constant between material particles used in cement paste prepared from multi-component cementitious materials is:

[0186]

[0187] 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 effective Hamek constant of a cement slurry suspension system, characterized in that, Comprising the following steps: (1) Preparation of test samples: for the cement paste suspension system of binary cement-mineral admixture, there are three different types of inter-particle interactions, namely cement-cement, cement-mineral admixture, and mineral admixture-mineral admixture, respectively, and the cement test sample and the mineral admixture test sample are prepared respectively; (2) Preparation of particle probes: a single cement particle and a mineral admixture particle are fixed respectively at the tip of a micro-cantilever probe to obtain a cement particle probe and a mineral admixture particle probe; (3) Atomic force microscope is used to test the interaction force between particle probe and particle, to obtain the force-distance curve between particles, and then to obtain the adhesion force F between particles 12 ; (4) Calculation of Hamaker constant between particles; (5) Calculation of the equivalent Hamaker constant of the cement paste suspension system; In step (5), to calculate the equivalent Hamaker constant of the cement paste suspension system of binary cement-mineral admixture, it is necessary to first determine the inter-particle collision probability of various particles; It is considered that the interaction probability of any particle with cement or mineral admixture particles is the probability of the particle contacting the surface of a certain type of material particle, that is, the inter-particle collision probability is calculated by combining the probability model with the ratio of the surface area of cement and mineral admixture in the system to the total surface area, and the specific calculation method is as follows: The volume ratio of cement in a unit volume of cement paste is V c The volume ratio of mineral admixtures is V m The surface area of the cement particles and mineral admixture particles are respectively: M c = p c · V c · S c (12) M m = p m · V m · S m (13) wherein: M c is the total surface area of the cement, m 2 ; M m S is the total surface area of the mineral admixture, m 2 ; p c Density of cement kg / m 3 ; ρ m Density of mineral admixture, kg / m 3 ; V c Volume of cement in the paste, m 3 ; V m Volume of mineral admixture in the paste, m 3 ; S c The specific surface area m of the cement 2 / kg; S m The specific surface area m of the mineral admixture 2 / kg; The total surface area of all particles in the paste is taken as a unit of 1, and the surface area ratio of cement particles and mineral admixture particles is represented by N, which is: N c N represents the surface area fraction of cement m N represents the surface area fraction of mineral admixture Combining probability theory and mathematical statistics, the collision probability P of cement-cement, cement-mineral admixture, and mineral admixture-mineral admixture in cement paste is... c-c P c-m P m-m They are respectively: The total probability P of the above-mentioned three types of inter-particle collisions is 1, that is: The equivalent Hamaker constant of the cement paste suspension system is defined as the sum of the product of the Hamaker constant between any two types of material particles and the interaction probability between them, that is: wherein: Aeffis the effective Hamaker constant of the cement paste suspension system; A c-c Acpw is the Hamaker constant between cement particles - water in the liquid environment; A c-m Acpm is the Hamaker constant between cement particles - mineral admixture particles in the liquid environment; A m-m Amm is the Hamaker constant between mineral admixture particles - mineral admixture particles in the liquid environment; The liquid environment includes an ultrapure water liquid environment and a water-reducing agent solution environment. In the calculation of the Hamaker constant, F 12 It should also be the adhesion between the two contact objects in the corresponding liquid environment; For a complex cement paste suspension system prepared by multi-component cementitious materials, the total surface area of all particles of any cementitious material in a unit volume of paste is: M i = p i · V i · S i (21) M i S represents the total surface area of the i-th particle, p i represents the density of the i-th particle kg / m 3 , V i represents the volume fraction of the i-th particle, S i represents the specific surface area of the i-th particle m 2 / kg; The proportion of the surface area of any material particle in the total surface area of all materials is: In the formula: n is the number of multi-component cementitious materials in the cement paste; The interaction probability P of any material in the system with itself i-i and with another material particle is respectively: i-j P = 1 - exp(-z) Similarly, the total probability of the interaction between all types of particles in the paste is 1, that is: Correspondingly, the equivalent Hamaker constant between the particles of the materials used in the cement paste prepared by multi-component cementitious materials is:

2. The method of determining the equivalent Hamec constant of a cement slurry suspension system of claim 1, wherein, In step (1), the preparation process of the test sample is: A glass slide is used as a carrier to prepare the test sample. First, drop UV ultraviolet curing glue on a clean glass slide, and evenly spread the glue on the surface of the glass slide with a spatula. Then, press the clean spatula tightly and scrape the surface glue layer along one end of the glass slide. Repeat 3-5 times until the glue layer is less than 1 / 3 of the average particle size of the material particles to be tested, that is, cement particles and mineral admixture particles. Then, load the particles into a 1ml syringe, and in a clean and dust-free environment, spray the particles 20-30cm above the glass slide to make them disperse in the air and freely fall onto the surface of the glass slide. Then, place the glass slide in a UV environment, and take it out after the UV glue is cured. Finally, use compressed air or nitrogen to remove the loose particles on the surface.

3. The method of determining the effective Hamec constant of a cement slurry suspension system of claim 1, wherein, The specific process of preparing the particle probe in step (2) is as follows: 2.1, disperse the particles on a clean glass slide, and prepare and spread the curing glue on the glass slide; 2.2, gently touch the curing glue with a needle-free probe in the atomic force microscope, and then move the probe above the pre-selected particle; 2.3, after adjusting the position of the probe and the particle several times, lower the probe to make the probe contact the particle; 2.4, after the curing glue is cured, lift the probe and observe the bonding effect of the probe and the particle, if the particle is wrapped by the curing glue more than half or the top of the particle is bonded with foreign matter, repeat the above steps to make new particle probes; When the particle is a cement particle, a cement particle probe is prepared; when the particle is a mineral admixture particle, a mineral admixture particle probe is prepared.

4. The method of claim 1, wherein the cement slurry suspension system is characterized by a Hamaker constant. In step (3), when testing the force, first calibrate the elastic coefficient of the probe used by the standard sample, which is used to accurately convert the deflection deformation of the probe during the test into force; When testing the interaction force between the particle probe and the particles, the position of the particles on the probe and the particles on the sample is adjusted to ensure that the particles on the probe are in contact with the particles on the sample, and then a plurality of measurement points are selected in the range of 1 μm x 1 μm to 20 μm x 20 μm on the particles on the sample. Thereafter, a plurality of force-distance curves are obtained on a single particle by contact and separation of the particle probe and the particles at different positions. In each interaction force-distance curve obtained by the atomic force microscope, the probe quickly "rebound" to its undeflected position when the particle probe and the particles are separated. The change in force during this process is the adhesion force between the particles and the particles. The adhesion force is the absolute value of the difference between the minimum value and 0 in the force-distance curve. The average of a plurality of adhesion forces is the final adhesion force F between the particles and the particles. 12 .

5. The method of determining the equivalent Hamec constant of a cement slurry suspension system of claim 4, wherein, In step (3), when testing in an ultrapure water environment, 1ml of ultrapure water liquid is added on the surface of the test sample to ensure that the test material particles and the probe are completely immersed in the liquid; In the water reducing agent solution environment, the probe and the particle are completely immersed in the solution for 3 minutes before testing, to ensure that the water reducing agent molecules are adsorbed on the surface of the particle.

6. The method of claim 4, wherein the cement slurry suspension system is characterized by a Hamaker constant equivalent to that of a sphere having a diameter of 0.1 μm. In step (4), the Hamaker constant between the probe and the test particle is: where A 12 is the Hamaker constant between the probe and the test particle; D0is the cutoff distance; F 12 is the adhesion between two contacting objects, here between the probe and the test particle; c is a constant, taken to be 1.5 in the JKR model and 2 in the DMT model; R is the probe tip radius; Assuming that all the particles adhering to the probe are spherical, the equivalent radius of the particle is obtained by conversion according to the cross-sectional area equivalence principle; According to the Hertz contact theory, when two spheres with radii R1 and R2 are in contact under the action of an external force F, a circular contact surface will be formed near the contact point due to local deformation. The contact surface radius r, the relative displacement δ of the two sphere centers and the maximum contact stress q0 are calculated by equations (5)-(7): wherein 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 measured particle in the sample; E2 is the elastic modulus of the measured particle 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 and the particle on the probe, the Hertz contact problem between the particles is simplified to the Hertz contact problem between the particle and the plane, so R1=R0 and R2 tends to ∞, R0 represents the radius of the particle adhering to the probe, and the following equation is obtained: Substitute the solution of formula (8) into formula (4), wherein the contact surface radius r in formula (8) is the probe tip radius R in formula (4), to obtain the formula (11) for calculating the Hamaker constant between particles-particles, F 12 is the adhesion between two contact objects, which is the adhesion between particles and particles here:

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