Surface modification process of ultra-fine quartz sand based on particle size distribution model

Abstract

The present application relates to quartz sand surface modification process technical field, especially in a kind of superfine quartz sand surface modification process based on particle size distribution model, comprising: constructing initial particle size distribution model and dividing three particle size intervals;Dry pretreatment forms dry material;Specific surface area correction model and redetermine the mass proportion of each interval;To the first interval suspension join modifier, real-time monitoring viscosity to adjust the rate of addition, obtain the first modification characteristic curve;Based on the first curve correction second interval modifier dosage, third interval modifier dosage and obtain corresponding curve;For each curve time lag analysis and weighted fusion, obtain granularity-modification parameter;When reaching preset threshold, terminate reaction, after treatment product is obtained.The present application improves quartz sand modification uniformity by zoning processing, viscosity feedback, time lag analysis and intelligent determination.

Description

Technical Field

[0001] This invention relates to the field of quartz sand surface modification technology, and in particular to an ultrafine quartz sand surface modification process based on a particle size distribution model. Background Technology

[0002] Ultrafine silica sand is widely used in electronic packaging materials, high-performance composite materials, precision casting, high-grade coatings, and fillers due to its high hardness, high chemical stability, excellent insulation, and low coefficient of thermal expansion. In these applications, the surface properties of silica sand, such as hydrophilicity / hydrophobicity, surface energy, and interfacial bonding strength with the organic matrix, are often more critical than its bulk properties, directly determining the final performance of the composite material.

[0003] To improve the compatibility and dispersibility of quartz sand with organic phases, surface modification technology is widely used in industry, among which the chemical grafting method with silane coupling agents is the most mature and effective. A typical process involves mixing and stirring quartz sand powder with a solution or hydrolysate of a silane coupling agent at a certain temperature, causing the coupling agent to undergo chemical adsorption and condensation reactions on the particle surface, forming an organic monolayer, thereby achieving the property transformation from an inorganic surface to an organic surface.

[0004] Although the technology has been used for many years, it still faces a series of long-standing technical bottlenecks in large-scale, high-quality production, which restrict its application in high-end fields.

[0005] Chinese Patent Publication No. CN120681762A discloses an ultrafine active silicon powder and its preparation method. The preparation method of the ultrafine active silicon powder of this invention includes the following steps: mixing silicon powder, a portion of a surface modifier, and water, then grinding to obtain an ultrafine silicon powder slurry; drying the ultrafine silicon powder slurry, mixing and modifying it with the remaining surface modifier, and then cooling to obtain the ultrafine active silicon powder. Therefore, the ultrafine active silicon powder and its preparation method have the following problems: First, this process treats all silicon microparticles as a uniform whole, failing to consider the inherent particle size distribution differences in the raw materials. Ultrafine silicon microparticles typically have a wide particle size distribution range, with significant differences in specific surface area, surface energy, and surface hydroxyl density between particles of different sizes. This results in varying adsorption capacities and reactivity of the modifiers. However, this process treats all particles with a uniform modifier dosage and uniform process conditions. This inevitably leads to insufficient coating or complete depletion of the modifier in fine particles due to their large specific surface area, while excessive modifier residue remains in coarse particles due to their small specific surface area. Ultimately, this results in uneven modifier coating and unstable product performance.

[0006] Secondly, the process employs a two-stage modifier addition method of "wet grinding followed by dry modification." However, the modifier dosage calculation is based on an empirical mass percentage (0.6–1.2:100) rather than on the actual specific surface area requirements of the particles. Furthermore, the distribution ratio (2:1–2) is a pre-set fixed value, lacking scientific basis and dynamic adjustment capability. When the properties of raw materials fluctuate between different batches, the fixed dosage and fixed ratio cannot adapt, leading to waste or insufficient dosage of modifier and significant batch-to-batch differences in product quality.

[0007] Third, the entire process lacks real-time monitoring and feedback control of the reaction state. Neither the wet grinding stage nor the dry modification stage employs any process monitoring methods; the reaction endpoint is determined solely by fixed time intervals (e.g., 60 minutes for grinding, 15-30 minutes for modification). Since the reactivity of different batches of raw materials may vary, this fixed-time treatment often leads to either undertreatment or overtreatment. The former affects the modification effect, while the latter results in energy waste.

[0008] Fourth, this process cannot effectively control the uniformity of modification of particles with different sizes. Since the particle group is not partitioned and no index is established to evaluate the uniformity of modification, although the activation degree of the final product (93.4% to 95.3% in the examples) meets general requirements, this level of uniformity is still insufficient for high-end fields such as electronic packaging and high-performance composite materials, and it is difficult to ensure the performance consistency of the material at the microscale. Summary of the Invention

[0009] Therefore, this invention provides a surface modification process for ultrafine quartz sand based on a particle size distribution model, which overcomes the problems in the prior art, such as uneven coating of modifier, inaccurate dosage of modifier, lack of real-time feedback control of reaction process, and poor product stability caused by ignoring the differences in particle size distribution.

[0010] To achieve the above objectives, this invention provides a surface modification process for ultrafine quartz sand based on a particle size distribution model, comprising: Step S1: Obtain the particle size data of the ultrafine quartz sand to be modified, and divide the quartz sand particle group into three different particle size ranges. Step S2: Perform activation pretreatment on particles in each particle size range to form dry materials corresponding to each particle size range; Step S3: Obtain the measured specific surface area value of particles in each particle size range, and correct the mass ratio of each particle size range based on the measured specific surface area value and the theoretical specific surface area value to determine the specific surface area characteristics of each range. Step S4: Determine the first liquid-solid ratio based on the specific surface area characteristics of the particles in the first particle size range, and continuously add liquid medium to the dry material in the first particle size range to obtain a uniform suspension in the first range. Step S5: Based on the mass ratio and specific surface area characteristics of the particles in the first particle size range, determine the theoretical dosage of the first dose modifier to obtain the first range modified slurry by dripping. In this step, the addition rate of the modifier is dynamically adjusted according to the viscosity of the reaction system during the dripping process, and the first modification characteristic curve is determined based on the surface coating rate monitored during the reaction process. Step S6: Based on the first modification characteristic curve and the mass ratio and specific surface area characteristics of particles in each particle size range, determine the dosage of modifier added for particles in the second and third particle size ranges to obtain the second and third modification characteristic curves. Step S7: Perform time-delay analysis on the modified characteristic curves based on the specific surface area characteristics of each interval to obtain the relevant functions for calculating the comprehensive performance index. Step S8: After merging the modified slurries from each zone, the slurries are matured, and the comprehensive modification index value is calculated in real time. The timing of terminating the reaction is determined based on the comprehensive modification index value to obtain the final modified slurry. After post-processing, the surface-modified ultrafine quartz sand product is obtained.

[0011] Further, step S1 includes: Step S11: Obtain the original particle size analysis data of the ultrafine quartz sand to be modified using a laser particle size analyzer; Step S12: Verify and standardize the original particle size analysis data to obtain an effective particle size dataset; Step S13: Based on the effective particle size dataset, a preset continuous probability distribution function is selected, and an initial particle size distribution model is established by fitting the model using the least squares method, and the characteristic parameters of the model are obtained. The characteristic parameters include at least the D10 value, the D50 value, and the D90 value. Step S14: Based on the characteristic parameters of the initial particle size distribution model, the quartz sand particle group is sequentially divided into a first particle size interval, a second particle size interval, and a third particle size interval.

[0012] Further, in step S3, correcting the initial particle size distribution model includes: Step S31: Calculate the relative deviation between the theoretical specific surface area and the measured specific surface area value of particles in each particle size range; Step S32: Based on the direction and magnitude of the relative deviation, iteratively correct the initial particle size distribution model until the relative deviation between the theoretical specific surface area value and the measured specific surface area value is within a preset deviation threshold range.

[0013] Further, in step S5, real-time monitoring of the system viscosity to dynamically adjust the addition rate of the modifier includes: Step S51: Obtain the viscosity change rate of the reaction system in real time; Step S52: Compare the viscosity change rate with a preset threshold range, and dynamically adjust the dropping rate of the first dose modifier based on the comparison result; If the viscosity change rate is lower than the lower limit of the preset threshold range, then the addition rate of the first dose modifier is increased; If the viscosity change rate is within a preset threshold range, then the current addition rate of the first dose of modifier is maintained. If the viscosity change rate is higher than the upper limit of the preset threshold range, the addition rate of the first dose modifier is reduced.

[0014] Further, in step S5, the first modified characteristic curve is determined based on the coating rate-time curve formed by the measured surface coating rate and the corresponding sampling time, wherein the surface coating rate is determined by intermittent sampling at preset time intervals during the reaction process of particles in the first particle size range.

[0015] Further, step S6 includes: Step S61: Extract the actual amount of modifier consumed when the coating rate of particles in the first particle size range reaches the preset target threshold from the first modification characteristic curve. Step S62: Calculate the ratio of the actual amount of modifier consumed to the theoretical amount of the first dose modifier to obtain the correction coefficient; Step S63: Based on the mass ratio and specific surface area characteristics of particles in the second and third particle size ranges, determine the corresponding theoretical amount of modifier. Step S64: Based on the correction coefficient and the corresponding theoretically calculated dose, obtain the corrected dosage of the second dose modifier and the dosage of the third dose modifier; In step S65, the corrected dosage of the second and third doses of modifier are added to the corresponding systems, and the reaction state of each system is monitored to obtain the second and third modification characteristic curves.

[0016] Further, in step S7, the time delay analysis includes: Step S71: Based on the first modification characteristic curve, the second modification characteristic curve and the third modification characteristic curve, determine the time required for each particle size range to reach the same coating rate threshold, and determine the corresponding time difference. Step S72: Based on the magnitude of the time difference, determine the reaction rate weighting coefficient of the particles in each interval; Step S73: Determine the comprehensive weight based on the product of the mass ratio of each interval and the reaction rate weight coefficient, and perform a weighted summation of the real-time coverage rates of each interval to obtain the corrected weighted average coverage rate. Step S74: Calculate the uniformity of coverage in each interval based on the real-time coverage rate of each interval; Step S75: The product of the corrected weighted average coating rate and the interval coating uniformity is used as the particle size modification parameter.

[0017] Further, in step S8, the comprehensive modification index value is determined by substituting the real-time coating rate of each interval into the particle size-modification parameter calculation; If the comprehensive performance index value is greater than or equal to the preset threshold within the preset maximum ripening time, it is determined that the reaction has reached the termination time. If the comprehensive performance index value is always less than the preset threshold within the preset maximum maturation time, the amount of modifier to be added is determined based on the difference between the comprehensive modification index value at the end of the maximum maturation time and the preset threshold. After adding the modifier, maturation continues until the comprehensive performance index value is greater than or equal to the preset threshold.

[0018] Furthermore, in step S4, the liquid medium is a mixed solvent prepared by water and alcohol solvent in a preset ratio.

[0019] On the other hand, the present invention also provides a surface-modified ultrafine quartz sand obtained by applying the ultrafine quartz sand surface modification process based on the particle size distribution model described above, wherein the ultrafine quartz sand surface is grafted with a silane coupling agent layer.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention divides the quartz sand into three particle size intervals for separate processing by establishing a particle size distribution model, extracts the actual consumption from the first interval to correct the dosage of subsequent intervals, monitors the viscosity in real time to dynamically adjust the dropping acceleration rate, and uses time delay analysis and multi-parameter fusion to determine the endpoint. This solves the problems of uneven coating, waste of dosage, uncontrollable process and poor product stability caused by ignoring the differences in particle size distribution in traditional processes, and achieves a modifier utilization rate of 98.2% and a product activation index of 98.5%.

[0021] Furthermore, this invention divides quartz sand into three particle size ranges by establishing a particle size distribution model and calculates the amount of modifier used in each range. This solves the problems of insufficient coating of fine particles and residual modifier in coarse particles caused by ignoring differences in particle size distribution in traditional processes. Through precise division of particle size, particles in the same particle size range have the same reaction probability during the modification process. This avoids the problem of uneven coating reaction caused by inconsistent reaction rates between particles due to different reaction capabilities of particles of different sizes in the same reaction process. This results in a highly consistent coating rate in the three ranges, with a coating uniformity of over 0.98, laying the foundation for the subsequent maturation of the overall slurry.

[0022] Furthermore, this invention calculates a correction coefficient by extracting the actual modifier consumption from the modification characteristic curve of the first interval, and applies it to the dosage determination of particles in the second and third intervals. This allows the modifier dosage to be based on the actual specific surface area requirement rather than an empirical percentage, solving the problem that fixed dosage and fixed distribution ratio cannot adapt to raw material fluctuations. The modifier utilization rate reaches 98.2%, effectively reducing production costs.

[0023] Furthermore, by monitoring the viscosity change rate of the system in real time and comparing it with a preset threshold range, and dynamically adjusting the droplet acceleration rate of the modifier, the present invention ensures that the reaction is always in the optimal kinetic range, and the particle size after modification is basically the same as that before modification. This solves the problem of under-treatment or over-treatment caused by fixed-time treatment and provides a stable slurry state for the subsequent maturation process.

[0024] Furthermore, this invention determines the reaction rate weighting coefficient for each interval through time delay analysis, calculates the corrected weighted average coating rate by multiplying the mass ratio by the rate weight as the comprehensive weight, and uses the product of this weighting and the coating uniformity of the interval as the particle size-modification parameter. This parameter is calculated in real time during the curing process to determine the endpoint, which solves the problems of traditional processes being unable to evaluate the modification uniformity of particles of different sizes and the endpoint determination relying on a fixed time. The product activation index reaches 98.5% and the contact angle reaches 125°, which can meet the application requirements of high-end fields such as electronic packaging and high-performance composite materials. Attached Figure Description

[0025] Figure 1 This is a flowchart of the surface modification process for ultrafine quartz sand based on a particle size distribution model according to the present invention. Figure 2 This is a flowchart of step S1 of the ultrafine quartz sand surface modification process based on a particle size distribution model of the present invention. Figure 3 This is a flowchart of step S3 of the ultrafine quartz sand surface modification process based on a particle size distribution model of the present invention. Figure 4 This is a flowchart of step S5 of the ultrafine quartz sand surface modification process based on the particle size distribution model of the present invention. Figure 5 This is a flowchart of step S6 of the ultrafine quartz sand surface modification process based on a particle size distribution model of the present invention. Figure 6 This is a flowchart of step S7 of the ultrafine quartz sand surface modification process based on the particle size distribution model of the present invention. Detailed Implementation

[0026] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0027] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0028] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances. Example

[0029] Please see Figure 1 The diagram shows a flowchart of the ultrafine quartz sand surface modification process based on a particle size distribution model according to the present invention. This embodiment of the ultrafine quartz sand surface modification process based on a particle size distribution model includes: Step S1: Obtain the particle size data of the ultrafine quartz sand to be modified, and construct an initial particle size distribution model based on the particle size data to divide the quartz sand particle group into a first particle size interval, a second particle size interval, and a third particle size interval. Step S1 includes: Step S11: Obtain the original particle size analysis data of the ultrafine quartz sand to be modified using a laser particle size analyzer; Step S12: Verify and standardize the original particle size analysis data to obtain an effective particle size dataset; Step S13: Based on the effective particle size dataset, a preset continuous probability distribution function is selected, and an initial particle size distribution model is established by fitting the model using the least squares method, and the characteristic parameters of the model are obtained. The characteristic parameters include at least the D10 value, the D50 value, and the D90 value. Step S14: Based on the characteristic parameters of the initial particle size distribution model, the quartz sand particle group is sequentially divided into a first particle size interval, a second particle size interval, and a third particle size interval.

[0030] Specifically, 1000g of the ultrafine quartz sand sample to be modified was taken, and its particle size distribution was determined using a Malvern Mastersizer 3000 laser particle size analyzer. Before measurement, the sample was thoroughly mixed, and approximately 2g of sample was added to the dispersion cell using a sampling spoon. Measurement conditions: the dispersion medium was deionized water, the refractive index was set to 1.52 (quartz refractive index), and sodium hexametaphosphate (concentration 0.1%) was used as the dispersant. Ultrasonic dispersion for 5 minutes was performed to fully disperse agglomerated particles, and the shading rate was controlled at 10%–15% to ensure test accuracy. The pump speed was 2500 rpm, and each sample was measured three times, with the average value taken. The instrument automatically recorded the volume percentage of each particle size channel, generating raw particle size analysis data.

[0031] The raw particle size analysis data underwent verification and standardization. First, the data integrity was checked, and outliers caused by bubbles, impurities, or instrument fluctuations (such as a sudden change in the volume percentage of a channel to 0 or an abnormally high value) were removed. Then, the data was standardized so that the sum of the volume percentages for all particle size channels was 100%. Finally, the data was organized into a standard format: particle size sequence (unit: μm) and its corresponding cumulative volume percentage, forming a valid particle size dataset. In this embodiment, a total of 64 valid data points were measured, with particle sizes ranging from 0.1 μm to 200 μm.

[0032] The log-normal distribution function was chosen as the preset continuous probability distribution function. The effective particle size dataset was fitted using the least squares method to establish an initial particle size distribution model. The expression for the log-normal distribution function is: ; Where d is the particle size (μm), μ is the mean of ln(d) (μm), and σ is the standard deviation of ln(d) (μm); The Levenberg-Marquardt algorithm was used for nonlinear least-squares fitting, with the objective function being to minimize the sum of squared residuals between the measured and theoretical cumulative distributions. After the fitting converged, the characteristic parameters of the model were obtained: μ = 2.01, σ = 0.52. The particle size distribution characteristic values ​​were calculated based on the fitting results. Substituting the values ​​into the calculation, we get D10 = 3.82 μm, D50 = 7.47 μm, and D90 = 14.6 μm. After correction by the instrument's built-in software, the final characteristic parameters are determined as follows: D10 = 1.5 μm, D50 = 8.0 μm, and D90 = 18.0 μm. The distribution width Span = (D90 - D10) / D50 = (18.0 - 1.5) / 8.0 = 16.5 / 8.0 = 2.06. This distribution width is relatively large (preferably set to Span > 2 for a wide distribution), indicating that there are significant differences in particle size within the particle group. The specific surface area difference between fine and coarse particles can be several times, making it necessary to perform zoning to avoid uneven coating.

[0033] Using the obtained feature parameters D10, D50, and D90 as thresholds, the quartz sand particle group is divided into three particle size ranges: The first particle size range includes particles with a diameter ≤ D10, i.e., ultrafine particles with a diameter ≤ 1.5 μm. These particles have a large specific surface area (>10 m² / g), high surface energy, and the strongest reactivity, making them extremely prone to aggregation and requiring priority treatment and key control.

[0034] The second particle size range: particles with a diameter between D10 and D90, i.e., the main particles with a diameter between 1.5μm and 18.0μm (excluding the two ends of the range). This particle size range accounts for the largest proportion of the mass and determines the overall modification effect of the product, so it is necessary to ensure that it is fully and uniformly coated.

[0035] The third particle size range: particles with a diameter ≥ D90, i.e., coarse particles with a diameter ≥ 18.0 μm. These particles have a small specific surface area (< 2.5 m² / g), require a small amount of modifier, and react relatively slowly. It is necessary to prevent excessive residue of modifier.

[0036] Based on the particle size distribution model, calculate the mass proportion of each interval in the overall particle group. Integrate the cumulative distribution curve: The mass ratio of the first particle size interval is W1 = F(D10) - F(0), where F(d) is the cumulative distribution function. From the cumulative distribution curve, the cumulative percentage corresponding to particle size ≤ 1.5 μm is approximately 19.2%, and D10 in the above measurement is 1.5 μm.

[0037] The mass ratio of the second particle size range, W2 = F(D90) - F(D10), corresponds to a cumulative percentage of approximately 62.5% for particle sizes ranging from 1.5 μm to 18.0 μm.

[0038] The mass ratio of the third particle size range is W3 = F(∞) - F(D90), and the cumulative percentage corresponding to the particle size > 18.0 μm is approximately 18.3%.

[0039] The results of this division will be used for sampling of the measured specific surface area and model calibration in the subsequent step S3.

[0040] Step S2: Within a preset first temperature range, the particles in each particle size range are mechanically dispersed and preheated to form pre-activated dry materials corresponding to each particle size range. Specifically, samples of ultrafine quartz sand to be modified, from three different particle size ranges, were fed into an SHR-200A high-speed mixer. This equipment features heating and shearing functions, a 200L inner tank, and high-speed stirring blades. The first temperature range was set to 70℃, and the heating system was activated. After the temperature reached the set value, it was maintained at a constant temperature of 70℃. Under this constant temperature condition, the stirring blades were activated at a speed of 1000 rpm to mechanically disperse and preheat the quartz sand. The treatment time was 15 minutes. During this process, the high-speed rotating blades applied strong shearing force to the particles, breaking down soft agglomerates between them; simultaneously, heat transfer caused the moisture adsorbed on the particle surface to evaporate. After treatment, heating and stirring were turned off, yielding a pre-activated dry material. This material was a loose powder with no obvious lumps, and its temperature was approximately 65℃~70℃. It was then set aside for later use. Testing showed that the moisture content of the treated material decreased from 0.35% before treatment to 0.12%, indicating that the surface adsorbed water had been largely removed.

[0041] Step S3: Obtain the measured specific surface area value of particles in each particle size range, correct the mass ratio of each particle size range based on the measured specific surface area value and the theoretical specific surface area value, and use the measured specific surface area value as the specific surface area characteristic of each range. In step S3, the correction of the initial particle size distribution model includes: Step S31: Calculate the relative deviation between the theoretical specific surface area and the measured specific surface area value of particles in each particle size range; Step S32: Based on the direction and magnitude of the relative deviation, iteratively correct the initial particle size distribution model until the relative deviation between the theoretical specific surface area value and the measured specific surface area value is within a preset deviation threshold range.

[0042] Specifically, a Micron ASAP2460 surface area analyzer was used to determine the specific surface area of ​​particles in the first, second, and third particle size ranges via nitrogen adsorption-desorption (BET) method. Before measurement, the samples were degassed at 150°C for 4 hours to remove adsorbed moisture and gas. Approximately 2g of each sample was weighed and placed in a sample tube, and nitrogen adsorption-desorption testing was performed at liquid nitrogen temperature (-196°C). The specific surface area was calculated using the multi-point BET method. The results are as follows: The measured specific surface area of ​​the first particle size range, S1, is 3.2 m² / g. The measured specific surface area of ​​the second particle size range is S2 = 0.41 m² / g; The measured specific surface area of ​​the third particle size range, S3, is 0.14 m² / g. Based on the initial particle size distribution model established in step S1, the initial model parameters are: μ0 = 2.01, σ0 = 0.52. The theoretical specific surface area of ​​particles in each size range is calculated using an integral method. For each range, its volume average particle size is first calculated. (Unit: μm), the calculation formula is: ; Where d is the particle size (μm), and f(d) is the probability density function of the particle size distribution (dimensionless). i,min and d i,max These are the lower and upper limits (μm) of the particle size in the i-th interval, respectively. In this embodiment, the calculation is as follows: First particle size range (0μm~1.5μm): Volume average particle size =0.8μm; Second particle size range (1.5–18.0 μm): Volume average particle size =6.5μm; Third particle size range (18.0–200 μm): Volume average particle size =22.0μm; The formula for calculating the theoretical specific surface area Si0 is: ; Where ρ is the density of the quartz sand. Taken as 2.65 g / cm³. 3 , Given the volume average particle size (μm), the following was calculated: Theoretical specific surface area of ​​the first particle size range ; Theoretical specific surface area of ​​the second particle size range ; Theoretical specific surface area of ​​the third particle size range ; Calculate the relative deviation ki between the measured specific surface area and the theoretical specific surface area for each interval: ; Substituting the values ​​into the calculation, we get: δ1 = 13.1% for the first particle size range, δ2 = 17.8% for the second particle size range, and δ3 = 35.9% for the third particle size range. In this embodiment, a preset deviation threshold of ±10% is preferred. Within this threshold range, the particle size distribution can be characterized by consistency between the particle size range and the specific surface area, meaning that the theoretical specific surface area predicted by the model matches the measured value well, indicating that the particle size distribution model can accurately reflect the surface characteristics of the particles. When the deviation exceeds the threshold, it indicates a significant difference between the model and the actual situation, requiring iterative correction of the initial particle size distribution model.

[0043] It is understandable that the mechanism of particle size model correction lies in the fact that the theoretical specific surface area is inversely proportional to the volume average particle size, i.e. When the measured specific surface area is greater than the theoretical value, it indicates that the actual particles are finer than the model predicts, because smaller particle sizes result in larger specific surface areas. In this case, the distribution parameters need to be adjusted towards smaller particle sizes, shifting the overall particle size distribution predicted by the model to the left, thereby increasing the theoretical specific surface area to approximate the measured value. Conversely, when the measured specific surface area is less than the theoretical value, it indicates that the actual particles are coarser than the model predicts. The distribution parameters need to be adjusted towards larger particle sizes, shifting the overall particle size distribution predicted by the model to the right, thereby decreasing the theoretical specific surface area to approximate the measured value. By iteratively correcting the distribution parameters μ and σ based on the direction and magnitude of the relative deviation, the theoretical specific surface area gradually approaches the measured value, ultimately obtaining a calibration model that truly reflects the particle size distribution characteristics of the particle group, ensuring the accuracy and reliability of subsequent mass ratio calculations for each interval.

[0044] At this point, the deviations in the first, second, and third particle size intervals all exceed the threshold, requiring iterative correction of the initial particle size distribution model. Based on the direction and magnitude of the relative deviations, the model distribution parameters are adjusted. Since the measured values ​​are greater than the theoretical values, it indicates that the actual particles are finer or have rougher surfaces than the model predicts, and the distribution parameters need to be adjusted towards finer particles, i.e., smaller particle sizes. If the measured values ​​are less than the theoretical values, the distribution parameters are adjusted towards coarser particles, i.e., larger particle sizes.

[0045] First iteration: Calculate the weighted average of the relative deviations of each interval as the basis for overall adjustment. ; Substitution ; Based on the inverse relationship between volume average particle size and theoretical specific surface area, the adjustment range and relative deviation of volume average particle size satisfy the following: ; in, This represents the change in volume average particle size (μm). The volume average particle size (μm) before adjustment is given, and Δμ is the change in the distribution parameter μ.

[0046] Meanwhile, the relationship between the volume average particle size and the distribution parameters is as follows: ; Assuming σ remains constant during the adjustment process, then , Adjust μ from 2.01 to 2.01−0.241=1.769, keep σ at 0.52, and recalculate the theoretical specific surface area for each interval: Theoretical specific surface area for the first particle size range: S10' = 3.28 m² 2 / g, relative deviation δ1'=(3.2−3.28) / 3.28×100%=−2.4%; The theoretical specific surface area of ​​the second particle size range is S20' = 0.403 m². 2 / g, relative deviation δ2'=(0.41−0.403) / 0.403×100%=1.7%; The theoretical specific surface area of ​​the third particle size range is S30' = 0.119 m². 2 / g, relative deviation δ3'=(0.14−0.119) / 0.119×100%=17.6%=(0.14−0.119) / 0.119×100%=17.6%; Among them, 3.2m 2 / g, 0.41 m 2 / g, 0.14 m 2 / g represents the measured specific surface area values ​​of particles in the first, second, and third particle size ranges obtained by the BET method in step S3.

[0047] The deviations in the first and second granularity intervals are within the threshold range, but the deviation in the third granularity interval still exceeds the threshold and is relatively large (17.6%), requiring further adjustment.

[0048] The second iteration adjusts σ to change the distribution width based on the deviation in the third granularity interval. The relationship between the relative deviation of the third interval and the change in σ is as follows: ; Where λ is the adjustment coefficient, which is a verification value obtained by inverse operation based on several historical trials, and is set to 0.5. The calculation yields: Δσ=−0.176×0.52×0.5=−0.0458; Adjust σ from 0.52 to 0.52−0.0458=0.474, keep μ at 1.769, and recalculate: The theoretical specific surface area of ​​the third particle size range is S30 = 0.128 m². 2 / g, relative deviation k3=(0.14−0.128) / 0.128×100%=9.4%; At this point, the relative deviations of each interval are -2.4%, 1.7%, and 9.4%, respectively, all within the preset ±10% deviation threshold range, and the iterative correction is complete.

[0049] The corrected model parameters are: μ = 1.769, σ = 0.474. The mass ratios for each particle size range are then redefined using the corrected model. The mass ratio of the first particle size range, W1, is 17.8%. The mass ratio of the second particle size range, W2, is 65.0%. The mass ratio of the third particle size range, W3, is 17.2%. The measured specific surface area value is used as the specific surface area characteristic for each particle size range: S10 = 3.2 m 2 / g, S20=0.41m 2 / g, S30=0.14m 2 / g.

[0050] Recalculate the volume average particle size for each particle size range: First particle size range (0μm~1.5μm): Volume average particle size =0.65μm; Second particle size range (1.5–18.0 μm): Volume average particle size =5.8μm; Third particle size range (18.0–200 μm): Volume average particle size =19.5μm; Step S4: Determine the first liquid-solid ratio based on the specific surface area characteristics of the particles in the first particle size range, continuously add liquid medium to the dry material in the first particle size range, apply shear and stirring with the initial dispersion intensity, adjust the system temperature to the initial reaction temperature, and transform the system into a uniform suspension in the first particle size range. Specifically, the first liquid-to-solid ratio is determined based on the specific surface area characteristics of particles in the first particle size range. In this invention, to ensure sufficient surface modification, high specific surface area particles require a thicker slurry to maintain the collision frequency. Therefore, the larger the specific surface area, the smaller the liquid-to-solid ratio. The formula for calculating the first liquid-to-solid ratio is set as follows: ; Where R1 is the first liquid-to-solid ratio, R0 is the reference liquid-to-solid ratio (taken as R0 = 4.0), and S1 is the specific surface area (m²) of the first particle size range. 2 / g), S0 is the baseline specific surface area, taken as S0=5.0m². 2 / g; β is an adjustment coefficient, taken as β=0.1.

[0051] Understandably, based on industrial experience, a liquid-to-solid ratio of 1:4 is sufficient to ensure good dispersibility and mass transfer efficiency for quartz sand with a typical specific surface area (approximately 5 m² / g), while also considering the volume utilization rate of the reactor. The reference specific surface area is the median specific surface area of ​​typical ultrafine quartz sand, which can be calibrated through several experiments. When S1=S0, R1=R0=4.0, and a standard liquid-to-solid ratio is used. β determines the sensitivity of the liquid-to-solid ratio to changes in specific surface area. Preferably, when β is 0.1, the liquid-to-solid ratio decreases by approximately 10% for every 1 m² / g increase in specific surface area, which aligns with engineering experience.

[0052] Substituting the values, we get R1 = 4.9; Based on the mass ratio W1 = 0.178 for the first particle size range, take the corresponding mass of material m1 = 178g from the 1000g dry material obtained in step S2. According to the first liquid-to-solid ratio R1 = 4.9, add a liquid medium to the taken m1 = 178g material. The liquid medium is a mixed solvent of water and ethanol at a volume ratio of 3:1, with a density of approximately 0.95g / mL. The amount of liquid medium added, L1, is: L1 = m1 × R1 = 872.2g; Converted to volume, it is approximately V1 = 918 mL; The material and liquid medium are added to a 1L glass reactor and stirred at a speed n corresponding to the initial dispersion intensity. 初始 Apply shear and stirring at 400 rpm to adjust the system temperature to the initial reaction temperature T. 初始 At 65℃, the system was gradually transformed from a dry state into a homogeneous suspension in the first zone, with a total volume of: ; Where, ρ 石英 =2.65g / cm 3， Let V be the density of the quartz sand. Substituting this into the equation, we get V. 总 =985.2mL.

[0053] Step S5: Based on the mass ratio and specific surface area characteristics of particles in the first particle size range, determine the theoretical dosage of the first dose modifier. Add the first dose modifier dropwise into the uniform suspension in the first range. Adjust the addition rate of the modifier dynamically according to the viscosity of the reaction system. During the reaction, take intermittent samples offline to measure the surface coating rate to obtain the coating rate-time curve of particles in the first particle size range as the first modification characteristic curve. After the dropwise addition is completed, obtain the modified slurry of the first range. Specifically, in step S5, the viscosity of the system is monitored in real time to dynamically adjust the addition rate of the modifier, including: Step S51: Obtain the viscosity change rate of the reaction system in real time; Step S52: Compare the viscosity change rate with a preset threshold range, and dynamically adjust the dropping rate of the first dose modifier based on the comparison result; If the viscosity change rate is lower than the lower limit of the preset threshold range, then the addition rate of the first dose modifier is increased; If the viscosity change rate is within a preset threshold range, then the current addition rate of the first dose of modifier is maintained. If the viscosity change rate is higher than the upper limit of the preset threshold range, the addition rate of the first dose modifier is reduced.

[0054] Calculation of the theoretical dosage of the first dose modifier: The first dose modifier is selected as KH-550 silane coupling agent, specifically γ-aminopropyltriethoxysilane, with a molecular weight M. w =221.37 g / mol, density ρ=0.946g / mL.

[0055] It is understandable that the KH-550 silane coupling agent molecule contains a hydrolyzable alkoxy group (-OCH2CH3) at one end, which generates a silanol group (Si-OH) under hydrolysis conditions; and an amino group (-NH2) at the other end, which can react with organic polymers. The silanol group generated by hydrolysis undergoes a dehydration condensation reaction with the silanol group on the surface of the quartz sand particles to form a Si-O-Si covalent bond, thereby allowing KH-550 to be firmly coated on the surface of the quartz sand particles by chemical bonding. The exposed amino group (-NH2) at the other end can impart hydrophobicity and reactivity to the surface of the quartz sand particles. During the modification process, the viscosity of the system changes regularly with the addition of the modifier: the viscosity rises slowly in the early stage of the reaction, as the modifier begins to combine with the particle surface; the viscosity rises rapidly in the middle stage of the reaction, as the coating layer gradually forms and the interaction between particles is enhanced; the viscosity tends to stabilize in the later stage of the reaction, indicating that the surface active sites are gradually saturated and the modification reaction is basically completed; before modification, the quartz sand settles rapidly in water, while after modification, the particles form a stable suspension in water; Thermogravimetric analysis can detect the characteristic weight loss peaks (300℃~600℃) of organic matter (i.e. KH-550 molecules grafted onto the particle surface), which can confirm that the modifier has been grafted onto the particle surface.

[0056] Based on the reaction mechanism between silane coupling agents and silanol groups, the theoretical amount of modifier required for monolayer coating can be calculated using specific surface area. The required modifier is q0 = 0.01 g / m². 2 Based on empirical calculations, the theoretical modification dose required per unit mass of particles in the first interval is: q10 = S1 × q0 = 3.2m 2 / g×0.01g / m 2 =0.032g / g; The mass of the material in the first interval is m1 = 192g. Calculate the theoretical dosage of the first dose of modifier: M10=m1×q10=178g×0.032g / g=5.7g; Converted to volume: V10 = M10 / ρ = 5.7g / 0.946g / mL ≈ 6.03mL.

[0057] Set the initial addition rate: based on the particle size characteristics (volume average particle size) of the particles in the first particle size range. =0.65μm), set the initial addition rate r10 = 0.4mL / min. The smaller the particle size, the larger the specific surface area and the higher the reactivity. The initial addition rate should be appropriately reduced to prevent local overconcentration.

[0058] The first dose of modifier was added dropwise to the homogeneous suspension in the first interval at an initial addition rate of 0.4 mL / min. The viscosity of the system was monitored in real time using an NDJ-5S digital viscometer, with the viscosity value η (mPa·s) recorded every 10 seconds. The viscosity change rate η(t) (mPa·s / min) was calculated in real time. The preset viscosity change rate threshold range was: lower limit η min =0.5 mPa·s / min, upper limit η max =2.0 mPa·s / min.

[0059] Understandably, this threshold range was determined through preliminary experiments: below the lower limit indicates a slow reaction rate, which can be accelerated; above the upper limit indicates an overly vigorous reaction or a risk of aggregation, which requires slowing down the addition. The reaction process record is shown in Table 1. Table 1. Viscosity changes during the reaction process

[0060] The total addition time was approximately 35 minutes, and the first dose of modifier was completely added.

[0061] During the reaction, sampling time points were determined as follows for intermittent sampling: (1) Sampling was performed at 5-minute intervals to obtain uniformly distributed data points; (2) Sampling was intensified at 12 min and 18 min when the viscosity change rate exceeded the threshold to capture information on the stage of drastic change in the reaction; (3) Sampling was triggered when the amount of modifier added reached 30%, 60%, and 90% to correlate the addition progress with the coating effect.

[0062] Fourteen samples were obtained, and the surface coating rate was determined using thermogravimetric analysis (TGA, Netzsch STA449F3, Germany). It is understood that uncoated silica powder experiences minimal weight loss during heating, while samples coated with organosilanes undergo organic decomposition and weight loss at 300℃–600℃; the weight loss rate is the coating rate. Test conditions: nitrogen atmosphere, heating rate 10℃ / min, from room temperature to 800℃. A coating rate-time curve C1=f1(t) was plotted with reaction time t (min) on the x-axis and coating rate C1 (%) on the y-axis for particles in the first particle size range. This curve reflects the modification reaction kinetics of particles in this range.

[0063] Step S6: Based on the first modification characteristic curve and the mass ratio and specific surface area characteristics of particles in each particle size range, determine the dosage of modifier added for particles in the second and third particle size ranges, and obtain the second and third modification characteristic curves accordingly. After the addition is completed, the modified slurry in the second and third ranges is obtained respectively. Step S61: Extract the actual amount of modifier consumed when the coating rate of particles in the first particle size range reaches the preset target threshold from the first modification characteristic curve. Step S62: Calculate the ratio of the actual amount of modifier consumed to the theoretical amount of the first dose modifier to obtain the correction coefficient; Step S63: Based on the mass ratio and specific surface area characteristics of particles in the second and third particle size ranges, determine the corresponding theoretical amount of modifier. Step S64: Based on the correction coefficient and the corresponding theoretically calculated dose, obtain the corrected dosage of the second dose modifier and the dosage of the third dose modifier; In step S65, the corrected dosage of the second and third doses of modifier are added to the corresponding systems, and the reaction state of each system is monitored to obtain the second and third modification characteristic curves.

[0064] Specifically, key information is extracted from the coverage-time curve C1: The time required for the coating rate to reach 50% is: t1,50 = 12.5 min; The time required for the coating rate to reach 80% is: t1,80 = 22.0 min; The time required for the coating rate to reach 95% is: t1,95 = 42.5 min; In this embodiment, the actual amount of modifier consumed when a 95% coating rate is achieved is M1 = 5.70g (all added). Calculate the ratio of actual modifier consumption to theoretical consumption in the first interval, and use it as the correction coefficient k for subsequent intervals: ; Where M1 is the actual amount (g) of the first dose modifier and M10 is the theoretical amount (g) of the first dose modifier. In this embodiment, the correction factor is 1.0, indicating that the theoretical calculation matches the actual requirements well. However, when the properties of raw materials fluctuate, the correction factor may deviate from 1.0. In this case, applying this correction factor can effectively eliminate the deviation.

[0065] Based on the specific surface area characteristics of particles in the second and third size ranges, the required modification dosage per unit mass is calculated: Second particle size range: q20 = S2 × q0 = 0.41 m 2 / g×0.01g / m2=0.0041g / g; Third particle size range: q30 = S3 × q0 = 0.14 m 2 / g×0.01g / m2=0.0014g / g; The mass of material in the second particle size range is m2 = 1000g × 0.65 = 650g; The mass of material in the third particle size range is m3 = 1000g × 0.172 = 172g; Theoretical dosage: M20=m2×q20=650g×0.0041g / g=2.665g; M30=m3×q30=172g×0.0014g / g=0.241g; Apply the correction factor k=1.0 to the theoretical dose: M2=M20×k=21.88g×1.0=2.665g; M3=M30×k=3.29g×1.0=0.241g; Convert to volume (KH-550 density ρ) k =0.946g / mL): LV2 = 2.665 / 0.946 = 2.82 mL; LV3 = 0.241 / 0.946 = 0.25 mL; Based on the mass ratio of the second particle size range, take 650g of the remaining material from the 1000g dry material obtained in step S2, and construct a homogeneous suspension of the second range according to the second liquid-to-solid ratio R2 = 4.0 (the specific surface area is small, so a baseline liquid-to-solid ratio is used) determined based on its specific surface area characteristics. Add a liquid medium. L² = m² × R² = 650g × 4.0 = 2600g Converted to volume, it is approximately V2 = 2737 mL; The material in the second particle size range and 2737 mL of liquid medium were added to a 5 L glass reactor and stirred at a speed n corresponding to the initial dispersion intensity. 初始 Apply shear and stirring at 400 rpm to adjust the system temperature to the initial reaction temperature T. 初始 =65℃, so that the system gradually transforms from a dry state into a uniform suspension in the second zone.

[0066] The corrected second dose of modifier M2 = 2.665 g was added dropwise to the suspension at an initial addition rate r20 = 0.2 mL / min. The system viscosity was monitored in real time to dynamically adjust the addition rate, following the same procedure as in step S5. Surface coating rate was measured intermittently, and the coating rate-time curve C2 = f2(t) for particles in the second particle size range was obtained. Results: The time required for the coating rate to reach 50% is: t2,50 = 18.5 min; The time required for the coating rate to reach 80% is: t2,80 = 32.0 min; The time required for the coating rate to reach 95% is: t2,95 = 58.0 min; Since the amount of modifier used in the third particle zone is extremely small, in order to facilitate precise control, the modifier is diluted with anhydrous ethanol to a concentration of 10%, and the volume after dilution is about 2.5 mL. The initial addition rate is set to 0.1 mL / min.

[0067] Take 172g of the dry material from the third region obtained in step S2, and construct a homogeneous suspension of the third region according to the liquid-to-solid ratio R3 = 4.5 (the liquid-to-solid ratio can be appropriately increased if the specific surface area is smaller). Add the liquid phase medium: L3 = m3 × R3 = 172g × 4.5 = 774g; Converted to volume, it is approximately V3 = 815 mL; The material and liquid medium are added to a 1L glass reactor and stirred at a speed n corresponding to the initial dispersion intensity. 初始 Apply shear and stirring at 400 rpm to adjust the system temperature to the initial reaction temperature T. 初始 =65℃, so that the system gradually transforms from a dry state into a uniform suspension in the second zone.

[0068] 2.5 mL of the diluted modifier was added dropwise to the suspension at an initial addition rate of r30 = 0.1 mL / min. The system viscosity was monitored in real time and samples were taken intermittently to determine the surface coating rate, obtaining the coating rate-time curve C3 = f3(t) for particles in the third particle size range. Results: The time required for the coating rate to reach 50% is: t3,50 = 8.5 min; Time required for 80% coverage: t3,80 = 15.0 min; The time required for the coating rate to reach 95% is: t3,95 = 32.0 min; Step S7: Combine the specific surface area characteristics of each interval to perform time delay analysis and weighted fusion on the modified characteristic curves to obtain the relevant function for calculating the comprehensive performance index; Step S8: Combine the modified slurries from each interval and continue maturing. Calculate the comprehensive modification index value in real time. If the comprehensive modification index value is greater than or equal to a preset threshold, terminate the reaction to obtain the final modified slurry. Perform solid-liquid separation, washing, and drying on the final modified slurry to obtain a surface-modified ultrafine quartz sand product.

[0069] In step S7, the time delay analysis includes: Step S71: Based on the first modification characteristic curve, the second modification characteristic curve and the third modification characteristic curve, determine the time required for each particle size range to reach the same coating rate threshold, and determine the corresponding time difference. Step S72: Based on the magnitude of the time difference, determine the reaction rate weighting coefficient of the particles in each interval; Step S73: Determine the comprehensive weight based on the product of the mass ratio of each interval and the reaction rate weight coefficient, and perform a weighted summation of the real-time coverage rates of each interval to obtain the corrected weighted average coverage rate. Step S74: Calculate the uniformity of coverage in each interval based on the real-time coverage rate of each interval; Step S75: The product of the corrected weighted average coating rate and the interval coating uniformity is used as the particle size modification parameter.

[0070] Specifically, the reaction time ti,95 (unit: min) corresponding to the particle coating rate reaching 95% in each interval was extracted from the three modified characteristic curves: The first interval t1,95 = 42.5 min; The second interval is t2,95 = 58.0 min; The third interval is t3,95 = 32.0 min; Calculate the time difference Δti1 (unit: min) with the first interval as the reference: Δt21=|t2,95−t1,95|=|58.0−42.5|=15.5min Δt31=|t3,95−t1,95|=|32.0−42.5|=10.5min Δt23=|t2,95−t3,95|=|58.0−32.0|=26.0min The time difference quantifies the difference in reaction rate between particles in different intervals: the first interval differs from the second interval by 15.5 min, the first interval differs from the third interval by 10.5 min, and the second interval differs from the third interval by 26.0 min, indicating that the second interval reacts the slowest, the third interval reacts the fastest, and the first interval is in the middle.

[0071] Using the average time difference across all intervals as a benchmark, calculate the reaction rate weighting coefficient αi for each interval. A benchmark time constant τ0 = 20 min is chosen (set empirically, equivalent to a typical reaction time). The reaction rate weighting coefficient is inversely proportional to the reaction time deviation of each interval relative to the benchmark. First, calculate the average reaction time for each interval: ; Deviation of each interval from the average time:

[0072] The formula for calculating the reaction rate weighting coefficient is: ; Substitute into the calculation: ; Constructing granularity-modification parameter functions: The product of the mass ratio Wi of each interval and the reaction rate weighting coefficient αi is used as the comprehensive weight ωi: ωi = Wi × αi; Corrected weighted average coverage (unit:%): ; The uniformity of coverage within each interval, U (dimensionless), characterizes the consistency of modification across intervals. The calculation formula is as follows: ; Among them, C max C represents the maximum (%) of the coating efficiency across the three particle size ranges. min The minimum value (%) is given. The closer the U value is to 1, the closer the coverage rates of each interval are, and the better the uniformity of modification.

[0073] ; After the addition is complete, the modified slurries from the first, second, and third particle size ranges are combined to obtain the overall reaction slurry, which is then further matured at a temperature of 65℃ and a stirring speed of 200 rpm. Based on product performance requirements, the preset comprehensive modification index threshold I0 = 0.85 and the preset maximum maturation time Tmax = 90 min are determined.

[0074] During the maturation process, based on the coating rate-time curves obtained in steps S5 and S6, the real-time coating rates C1(t), C2(t), and C3(t) corresponding to each interval of the current maturation time are read, and the comprehensive modification index value I(t) is calculated in real time in the particle size-modification parameter function.

[0075] When the reaction proceeded to t=60min (at which point all three curves had reached a stable state), the real-time coating rate Ci(t) of the particles in each interval was read (unit: %): The first interval C1(60) = 95.0%; The second interval C2(60) = 95.5%; The third interval C3(60) = 96.0%; Calculate the overall weight of each interval: ω1 = 0.192 × 0.923 = 0.177; ω² = 0.625 × 0.591 = 0.369; ω3 = 0.183 × 0.622 = 0.114; Sum of overall weights: Ω = 0.177 + 0.369 + 0.114 = 0.660; Substituting into the calculation, we get: ; The product of the corrected weighted average coating rate and the coating uniformity within each particle size range is used as the particle size modification parameter I. This parameter comprehensively reflects two core dimensions of the modification effect: the sufficiency of characterizing coating and surface modification, and the consistency of coating uniformity among particles in each particle size range. ; Substituting the values ​​into the calculation, we get I = 0.9445 ≥ I0, indicating that the reaction is complete and the final modified slurry is obtained. Stirring and heating are stopped, and the final modified slurry in the reactor is transferred to a storage container. The slurry undergoes solid-liquid separation, washing, and drying to remove unreacted modifiers and byproducts, yielding a dried quartz sand product. Example

[0076] Unlike Example 1, different batches of raw materials were used and the same processing method was adopted for modification. Due to the low activity of the raw materials or the fluctuation of process conditions, the comprehensive modification index value did not reach the preset threshold within the preset maximum ripening time, and modifiers needed to be added.

[0077] Specifically, the modified slurries from the first, second, and third particle size ranges are combined to obtain a complete reactive slurry, which is then further matured. The preset comprehensive modification index threshold I0 = 0.85, and the preset maximum maturation time Tmax = 90 min.

[0078] During the maturation process, based on the coating rate-time curves obtained in steps S5 and S6, the real-time coating rates C1(t), C2(t), and C3(t) corresponding to the current maturation time are read and substituted into the granularity-modification parameter function constructed in step S7 to calculate the comprehensive modification index value I(t) in real time.

[0079] When the maturation time reaches Tmax = 90 min, I(90) = 0.82 is calculated, which is still less than the preset threshold I0 = 0.85. Based on the difference between the comprehensive modification index value at the maximum maturation time endpoint and the preset threshold ΔI = I0 − I(90) = 0.03, the required additional modification dose is calculated according to the empirical formula: ; in, The amount of modification to be added (g), k m M is the supplementary coefficient. t Total modifier dosage (g); It is understandable that the added coefficient k m This is an empirical constant obtained through previous experiments, used to convert the deviation of the comprehensive modification index value into the modifier addition amount. Its physical meaning lies in reflecting the sensitivity of the modifier dosage to the comprehensive modification index value. In this embodiment, the value k is taken as...m =0.5. When ΔI=0.03, the replenishment amount is 1.5% of the total amount (0.5 × 0.03 × 100% = 1.5%), which is consistent with engineering practice experience. This coefficient can be adjusted within the range of 0.3 to 0.8 according to the characteristics of different quartz sand raw materials, or it can be adaptively optimized through historical batch data.

[0080] Substituting the data, we get ΔM = 0.5 × 0.03 × 8.606 = 0.129 g; The modifier was added to the overall reaction slurry, and maturation continued. After the addition, I(t) was calculated in real time. When t=105min, I=0.92≥I0, the reaction was determined to be at the right time to terminate the reaction, and the final modified slurry was obtained.

[0081] The final modified slurry was subjected to solid-liquid separation, washing, and drying to obtain surface-modified ultrafine quartz sand. Testing showed that the product had an activation index of 97.8% and a contact angle of 121°, with all indicators still meeting the requirements for high-end applications.

[0082] Comparative Example 1: The modifier was added dropwise at a fixed rate (0.4 mL / min) to the first, second, and third uniform suspensions in one continuous drop, and the remaining steps were the same as in Example 1.

[0083] Comparative Example 2: Without performing model correction in step S3, the mass ratio determined in step S1 is used directly, and the amount of modifier is determined based on the theoretical specific surface area calculated based on particle size (rather than the measured value). The remaining steps are exactly the same as in Example 1.

[0084] Comparative Example 3: Quartz sand was modified according to the method of Example 1 in Chinese Patent CN120681762A.

[0085] The performance of the quartz sand products obtained in Examples 1 and 2 and Comparative Examples 1, 2 and 3 was tested, and the results are as follows: Table 2. Performance test results of ultrafine quartz sand products prepared in each embodiment and comparative example.

[0086] As shown in the table above, firstly, regarding the modification effect, the activation index (≥98.2%) and contact angle (≥122°) of Examples 1 and 2 are significantly better than those of the comparative examples (≤86.%, ≤95°). This indicates that the present invention achieves uniform and complete coating of the modifier on the particle surface through zoned differential processing and real-time feedback control. Comparative Example 1 suffered from reaction runaway due to the lack of viscosity feedback control, Comparative Example 2 suffered from dosage deviation due to the lack of model correction, and Comparative Example 3 suffered from uneven coating due to the inability of traditional overall processes to solve the problem of wide particle size distribution.

[0087] Second, regarding modification efficiency, the modifier utilization rate of the embodiments (≥97.5%) is much higher than that of the comparative examples (≤86.1%), verifying the effectiveness of the present invention in correcting the dosage in subsequent intervals based on the actual reaction results of the first interval. That is, the correction coefficient is first calculated based on the ratio of the actual consumption to the theoretical dosage in the first interval, and then the correction coefficient is applied to the dosage calculation in the second and third intervals, so that the modifier dosage is accurately matched with the actual needs. Comparative Example 1 resulted in wasted modifier due to the lack of real-time feedback, Comparative Example 2 resulted in a deviation between the theoretical value and the actual needs due to the lack of model correction, and Comparative Example 3 could not adapt to the fluctuations in raw material characteristics due to the fixed dosage distribution.

[0088] Third, regarding the uniformity of modification, the uniformity of the coating in the embodiment (≥0.985) is close to the theoretical maximum value and much higher than that of Comparative Example 3 (0.83). This indicates that the present invention, through time delay analysis and weight coefficient correction, ensures a high degree of consistency in the degree of modification in each particle size range, and solves the prominent problems of insufficient coating of fine particles and residual modifier in coarse particles in traditional processes.

[0089] Fourth, regarding the inhibition of agglomeration, the particle size remained basically unchanged after modification in the examples, while the particle size of Comparative Examples 1 and 3 increased significantly (D50 increased from 8.0 μm to over 10.2 μm), indicating that the viscosity feedback control mechanism of the present invention effectively prevents local over-concentration and particle agglomeration.

[0090] Fifth, in terms of overall performance, the particle size-modification parameter I value (≥0.92) of the embodiment is much higher than the preset threshold of 0.85 and better than each comparative example (≤0.83), indicating that the product has achieved excellent levels in both modification sufficiency and uniformity, and can meet the requirements of high-end fields such as electronic packaging and high-performance composite materials.

[0091] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A surface modification process for ultrafine quartz sand based on a particle size distribution model, characterized in that, include: Step S1: Obtain the particle size data of the ultrafine quartz sand to be modified, and divide the quartz sand particle group into three different particle size ranges. Step S2: Perform activation pretreatment on particles in each particle size range to form dry materials corresponding to each particle size range; Step S3: Obtain the measured specific surface area value of particles in each particle size range, correct the mass ratio of each particle size range based on the measured specific surface area value and the theoretical specific surface area value, and use the measured specific surface area value as the specific surface area characteristic of each range. Step S4: Determine the first liquid-solid ratio based on the specific surface area characteristics of the particles in the first particle size range, and continuously add liquid medium to the dry material in the first particle size range to obtain a uniform suspension in the first range. Step S5: Based on the mass ratio and specific surface area characteristics of the particles in the first particle size range, determine the theoretical dosage of the first dose modifier to obtain the first range modified slurry by drop addition. The addition rate of the modifier is dynamically adjusted according to the viscosity of the reaction system during the drop addition process. The first modification characteristic curve is determined based on the surface coating rate monitored during the reaction process. The first modification characteristic curve is determined based on the coating rate-time curve formed by the measured surface coating rate and the corresponding sampling time. Step S6: Based on the first modification characteristic curve and the mass ratio and specific surface area characteristics of particles in each particle size range, determine the dosage of modifier added for particles in the second and third particle size ranges to obtain the second and third modification characteristic curves, including: Step S61: Extract the actual amount of modifier consumed when the coating rate of particles in the first particle size range reaches the preset target threshold from the first modification characteristic curve. Step S62: Calculate the ratio of the actual amount of modifier consumed to the theoretical amount of the first dose modifier to obtain the correction coefficient; Step S63: Based on the mass ratio and specific surface area characteristics of particles in the second and third particle size ranges, determine the corresponding theoretical amount of modifier. Step S64: Based on the correction coefficient and the corresponding theoretically calculated dose, obtain the corrected dosage of the second dose modifier and the dosage of the third dose modifier; Step S65: Add the corrected second dose of modifier and the third dose of modifier to the corresponding systems respectively, and monitor the reaction state of each system to obtain the second modification characteristic curve and the third modification characteristic curve. Step S7: Perform time-delay analysis on the modified characteristic curves based on the specific surface area characteristics of each interval to obtain the relevant function for calculating the comprehensive performance index. The time delay analysis includes: Step S71: Based on the first modification characteristic curve, the second modification characteristic curve and the third modification characteristic curve, determine the time required for each particle size range to reach the same coating rate threshold, and determine the deviation of the time for each range from the average time. Step S72: Based on the deviation of each interval time from the average time, determine the reaction rate weighting coefficient of the particles in each interval. Step S73: Determine the comprehensive weight based on the product of the mass ratio of each interval and the reaction rate weight coefficient, and perform a weighted summation of the real-time coverage rates of each interval to obtain the corrected weighted average coverage rate. Step S74: Calculate the uniformity of coverage in each interval based on the real-time coverage rate of each interval; Step S75: The product of the corrected weighted average coating rate and the interval coating uniformity is used as the particle size-modification parameter. Step S8: After merging the modified slurries from each interval, the mixture is matured, and the comprehensive modification index value is calculated in real time. The timing for terminating the reaction is determined based on the comprehensive modification index value to obtain the final modified slurry. After post-processing, a surface-modified ultrafine quartz sand product is obtained. The comprehensive modification index value is determined by substituting the real-time coating rate of each interval into the particle size-modification parameter calculation.

2. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 1, characterized in that, Step S1 includes: Step S11: Obtain the original particle size analysis data of the ultrafine quartz sand to be modified using a laser particle size analyzer; Step S12: Verify and standardize the original particle size analysis data to obtain an effective particle size dataset; Step S13: Based on the effective particle size dataset, a preset continuous probability distribution function is selected, and an initial particle size distribution model is established by fitting the model using the least squares method, and the characteristic parameters of the model are obtained. The characteristic parameters include at least the D10 value, the D50 value, and the D90 value. Step S14: Based on the characteristic parameters of the initial particle size distribution model, the quartz sand particle group is sequentially divided into a first particle size interval, a second particle size interval, and a third particle size interval.

3. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 1, characterized in that, In step S3, the initial particle size distribution model is corrected, including: Step S31: Calculate the relative deviation between the theoretical specific surface area and the measured specific surface area value of particles in each particle size range; Step S32: Based on the direction and magnitude of the relative deviation, iteratively correct the initial particle size distribution model until the relative deviation between the theoretical specific surface area value and the measured specific surface area value is within a preset deviation threshold range.

4. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 3, characterized in that, In step S5, the addition rate of the modifier is dynamically adjusted according to the viscosity of the reaction system during the dropping process, including: Step S51: Obtain the viscosity change rate of the reaction system in real time; Step S52: Compare the viscosity change rate with a preset threshold range, and dynamically adjust the dropping rate of the first dose modifier based on the comparison result. If the viscosity change rate is lower than the lower limit of a preset threshold range, then the addition rate of the first dose modifier is increased; If the viscosity change rate is within a preset threshold range, then the current addition rate of the first dose of modifier is maintained. If the viscosity change rate is higher than the upper limit of the preset threshold range, the addition rate of the first dose modifier is reduced.

5. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 1, characterized in that, In step S5, the surface coating rate is determined by intermittent sampling at preset time intervals during the reaction process of particles in the first particle size range.

6. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 1, characterized in that, In step S8, the comprehensive modification index value is determined by substituting the real-time coating rate of each interval into the particle size-modification parameter calculation. If the comprehensive modification index value is greater than or equal to the preset threshold within the preset maximum ripening time, it is determined that the reaction has reached the termination time. If the comprehensive modification index value is never less than the preset threshold within the preset maximum maturation time, the amount of modifier to be added is determined based on the difference between the comprehensive modification index value at the end of the maximum maturation time and the preset threshold. After adding the modifier, maturation continues until the comprehensive modification index value is greater than or equal to the preset threshold.

7. The surface modification process for ultrafine quartz sand based on a particle size distribution model according to claim 1, characterized in that, In step S4, the liquid medium is a mixed solvent prepared by water and alcohol solvent in a preset ratio.

8. A surface-modified ultrafine quartz sand obtained by applying the ultrafine quartz sand surface modification process based on the particle size distribution model according to any one of claims 1-7, characterized in that, The surface of the ultrafine quartz sand is grafted with a silane coupling agent layer.

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