Quantitative analysis method and system for nanomaterial re-agglomeration phenomenon

Abstract

This invention relates to the field of nanomaterial analysis technology, specifically disclosing a method and system for quantitative analysis of nanomaterial re-agglomeration phenomena. The method includes: continuously acquiring multimodal particle size distribution data at multiple time points to obtain a multimodal particle size distribution time series; mapping the multimodal particle size distribution data at each time point to a pre-constructed agglomeration feature space to obtain feature points and form feature point trajectories; calculating a displacement vector sequence based on the feature point trajectories, and then calculating the re-agglomeration rate; calculating the spatial distance between the current feature point and the initial feature point, and then calculating the re-agglomeration rate; calculating the agglomeration structure characteristic index based on the orientation region of the current feature point in the agglomeration feature space; and outputting the re-agglomeration rate, re-agglomeration rate, and agglomeration structure characteristic index as quantitative analysis results. This invention achieves simultaneous quantitative characterization of the degree, rate, and structural type of re-agglomeration, providing a comprehensive quantitative basis for the stability assessment of nanomaterials.

Description

Technical Field

[0001] This invention relates to the field of nanomaterial analysis technology, and in particular to a method and system for quantitative analysis of nanomaterial re-agglomeration phenomena. Background Technology

[0002] Nanomaterials, due to their high specific surface area and surface energy, are prone to re-aggregation in dispersed systems, directly affecting their performance in catalysis, medicine, energy, and other fields. Accurately quantifying the degree, rate, and structural type of re-aggregation is crucial for the stability assessment and application optimization of nanomaterials. Current technologies mainly employ single detection methods such as dynamic light scattering and laser particle size analysis, assessing the degree of aggregation by measuring particle size changes, or determining the aggregation type by observing the microstructure using transmission electron microscopy.

[0003] However, existing methods have fundamental flaws: particle size data obtained from different detection principles cannot be compared and integrated at a unified scale, making it difficult to distinguish between false positive signals caused by environmental factors and real aggregation behavior; at the same time, existing technologies can only output a single indicator of the degree of aggregation, and cannot simultaneously quantify the rate change of re-aggregation and the evolution of structural types, let alone predict the development trend of the re-aggregation process. This makes the stability assessment of nanomaterials remain at a static and one-sided level, which is difficult to meet the needs of comprehensive, dynamic and quantitative characterization of re-aggregation behavior in practical applications.

[0004] Therefore, this invention proposes a quantitative analysis method and system for the re-agglomeration phenomenon of nanomaterials. Summary of the Invention

[0005] This invention provides a quantitative analysis method and system for the re-agglomeration phenomenon of nanomaterials, overcoming the fundamental defect of existing technologies that cannot simultaneously and dynamically quantitatively characterize the degree, rate and structure type of re-agglomeration. It achieves the coordinated quantitative output of re-agglomeration rate, re-agglomeration rate and agglomeration structure characteristic index, providing a comprehensive, dynamic and multidimensional quantitative analysis basis for the stability assessment of nanomaterials.

[0006] This invention provides a method for quantitative analysis of the re-agglomeration phenomenon of nanomaterials, comprising the following steps: Multimodal particle size distribution data were continuously collected at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The multimodal particle size distribution data at each time point is mapped to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space, forming the feature point trajectory; Calculate the displacement vector between adjacent time points based on the feature point trajectory to obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. Calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and calculate the re-aggregation rate based on the spatial distance; Calculate the clustering structure characteristic index based on the location region of the feature point at the current time in the clustering feature space; The reagglomeration rate, reagglomeration speed, and agglomeration structure characteristic index are output as quantitative analysis results of the reagglomeration phenomenon of nanomaterials.

[0007] Furthermore, the multimodal particle size distribution data includes dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data. The dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data are aligned according to the acquisition time points to form a multimodal particle size distribution time series.

[0008] Furthermore, dynamic light scattering particle size distribution data is continuously acquired at preset time intervals by an in-situ detection probe embedded in the nanoparticle dispersion system. The in-situ detection probe integrates a dynamic light scattering sensor, a focused beam reflection measurement sensor, a temperature sensor, a pH sensor, a viscosity sensor, and an ionic strength sensor. The in-situ detection probe simultaneously acquires the temperature, pH, viscosity, and ionic strength parameters of the nanoparticle dispersion system as an environmental parameter sequence.

[0009] Furthermore, prior to the step of mapping the multimodal particle size distribution data at each time point to the pre-constructed clustering feature space, the following steps are also included: The viscosity parameters at each time point are input into a pre-constructed viscosity shift correction function, which outputs a viscosity drift correction coefficient. The viscosity drift correction coefficient is then multiplied by the dynamic light scattering particle size distribution data at the corresponding time point to obtain the viscosity-corrected dynamic light scattering particle size distribution data. The ion intensity parameter at each time point is input into a pre-constructed ion intensity refractive index correction function, and the refractive index fluctuation correction coefficient is output. The refractive index fluctuation correction coefficient is multiplied with the dynamic light scattering particle size distribution data at the corresponding time point to obtain the dynamic light scattering particle size distribution data after ion intensity correction. The nanoparticle concentration parameters at each time point are input into a pre-constructed concentration multiple scattering correction function, which outputs a multiple scattering attenuation correction coefficient. The multiple scattering attenuation correction coefficient is then multiplied by the laser particle size distribution data at the corresponding time point to obtain the concentration-corrected laser particle size distribution data.

[0010] Furthermore, the clustering feature space is pre-constructed through the following steps: Multimodal particle size distribution data and corresponding transmission electron microscopy (TEM) morphology data of multiple nanoparticle samples were collected at different time points. Image segmentation and feature extraction were performed on each transmission electron microscope microstructure data to obtain the porosity parameter, pore connectivity parameter, and particle boundary clarity parameter of each nanoparticle sample at each time point. Based on the comprehensive evaluation of porosity parameters, pore connectivity parameters, and particle boundary clarity parameters, the true aggregation state category of each nanoparticle sample at each time point is determined. The true aggregation state categories include unaggregated state, soft aggregation state, and hard aggregation state. A deep neural network was trained using multimodal particle size distribution data at each time point as input features and the corresponding real aggregation state category as output label. The output space of the last hidden layer of the deep neural network is used as the clustering feature space.

[0011] Furthermore, the step of mapping the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space includes: The peak particle size, average particle size, and particle size distribution width are extracted from the dynamic light scattering particle size distribution data at each time point as three components of the dynamic light scattering feature vector, and combined to form the dynamic light scattering feature vector. The peak particle size, average particle size, and particle size distribution width are extracted from the laser particle size analysis particle size distribution data at each time point as three components of the laser particle size analysis feature vector, and combined to form the laser particle size analysis feature vector. The peak chord length, average chord length, and chord length distribution width are extracted from the focused beam reflection measurement chord length distribution data at each time point as three components of the focused beam reflection measurement feature vector, and combined to form the focused beam reflection measurement feature vector. The dynamic light scattering feature vector, the laser particle size analysis feature vector, and the focused beam reflection measurement feature vector are sequentially spliced ​​together to form a multimodal feature vector; The multimodal feature vector is input into a deep neural network. After transformation through multiple hidden layers, the coordinates of the feature point in the clustering feature space at that time point are output from the last hidden layer of the deep neural network. Connect the coordinates of all feature points at all time points in chronological order to form the feature point trajectory.

[0012] Further, the displacement vectors between feature points at adjacent time points are calculated based on the feature point trajectories to obtain a displacement vector sequence. The re-aggregation rate is then calculated based on the displacement vector sequence, including: Calculate the displacement vectors between adjacent time points in the feature point trajectory. Each displacement vector contains the displacement magnitude and displacement direction. The average value of all displacements in the displacement vector sequence is used as the re-agglomeration rate, and the unit of the re-agglomeration rate is matched with the unit of the acquisition time interval.

[0013] Further, the step of calculating the spatial distance between the feature point at the current time point and the feature point at the initial time point, and calculating the re-aggregation rate based on the spatial distance, includes: The time point corresponding to the initial stable state of the nanoparticle dispersion system is taken as the initial time point, and the coordinates of the initial feature point in the aggregation feature space are obtained. Calculate the Euclidean distance between the feature point coordinates at the current time point and the feature point coordinates at the initial time point, and use it as the current state deviation value; The current state deviation value is compared with the preset fully dispersed state deviation benchmark value, and the re-agglomeration rate is calculated. The re-agglomeration rate is calculated by dividing the current state deviation value by the preset fully dispersed state deviation benchmark value and then multiplying by 100%.

[0014] Furthermore, it also includes: The absolute value of the difference between the displacement magnitude at the current time point and the displacement magnitude at the previous time point is taken as the fluctuation amplitude of the displacement magnitude in the displacement vector sequence. When the fluctuation range of the displacement exceeds the preset fluctuation threshold, the sampling time interval will be shortened to half of the original interval. When the fluctuation amplitude of the displacement is less than the preset fluctuation threshold for three consecutive time points, the sampling time interval will be extended to twice the original interval. When the re-agglomeration rate is greater than or equal to the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, a hard agglomeration risk warning signal is generated. When the re-agglomeration rate is greater than or equal to the preset moderate threshold but less than the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, an intervention suggestion signal is generated.

[0015] This invention provides a quantitative analysis system for the re-agglomeration phenomenon of nanomaterials, comprising: The multimodal data acquisition module is used to continuously acquire multimodal particle size distribution data at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The feature space mapping module is used to map the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space, obtain the feature points at each time point in the clustering feature space, and form the feature point trajectory. The evolution trend quantification module is used to calculate the displacement vector between feature points at adjacent time points based on the feature point trajectory, obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. The state deviation quantization module is used to calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and to calculate the re-aggregation rate based on the spatial distance; The structural feature quantification module is used to calculate the clustering structural feature index based on the location region of the feature point at the current time point in the clustering feature space. The quantitative index output module is used to output the re-agglomeration rate, re-agglomeration speed, and agglomeration structure characteristic index as quantitative analysis results of the re-agglomeration phenomenon of nanomaterials.

[0016] The beneficial effects of this invention compared to existing technologies are as follows: This invention overcomes the fundamental shortcomings of existing technologies, such as the inability to compare and integrate particle size data obtained from different detection principles at a unified scale, the difficulty in distinguishing between environmental interference and actual aggregation behavior, the inability to output only a single aggregation degree index without simultaneously quantifying re-aggregation rate and structural type evolution, and the inability to dynamically predict the re-aggregation process. By constructing an aggregation feature space to uniformly map multimodal particle size distribution data, and calculating based on the displacement vector, spatial distance, and orientation region of feature point trajectories, this invention achieves simultaneous quantitative output of re-aggregation rate, re-aggregation speed, and aggregation structure characteristic index. This elevates the evaluation of nanomaterial re-aggregation phenomena from static, one-sided single-index measurement to dynamic, multi-dimensional, and comprehensive quantitative characterization, providing complete data support for the stability assessment and application optimization of nanomaterials.

[0017] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained through the structures particularly pointed out in this application.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is an overall flowchart of the quantitative analysis method for the re-agglomeration phenomenon of nanomaterials in the embodiments of the present invention; Figure 2 This is a flowchart illustrating the construction of the clustering feature space and data mapping in an embodiment of the present invention. Detailed Implementation

[0020] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0021] like Figure 1 and Figure 2 As shown, this invention provides an embodiment of a method for quantitative analysis of the re-agglomeration phenomenon of nanomaterials, comprising the following steps: Multimodal particle size distribution data were continuously collected at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The multimodal particle size distribution data at each time point is mapped to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space, forming the feature point trajectory; Calculate the displacement vector between adjacent time points based on the feature point trajectory to obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. Calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and calculate the re-aggregation rate based on the spatial distance; Calculate the clustering structure characteristic index based on the location region of the feature point at the current time in the clustering feature space; The reagglomeration rate, reagglomeration speed, and agglomeration structure characteristic index are output as quantitative analysis results of the reagglomeration phenomenon of nanomaterials.

[0022] In this embodiment, the nanoparticle dispersion system refers to a suspension system formed by uniformly distributing nanoparticles in a liquid medium. The nanoparticles remain dispersed in the liquid medium, which can be water, organic solvent, or buffer solution. The concentration of the nanoparticles is determined according to the specific application scenario.

[0023] In this embodiment, multimodal particle size distribution data refers to various particle size distribution data obtained through different detection principles, including hydrodynamic diameter distribution data measured by dynamic light scattering technology, volume diameter distribution data measured by laser particle size analysis technology, and chord length distribution data measured by focused beam reflection measurement technology. These data reflect the size characteristics of nanoparticles from different dimensions.

[0024] In this embodiment, multimodal particle size distribution data at multiple time points are continuously collected in the nanoparticle dispersion system to obtain a multimodal particle size distribution time series. This means repeatedly collecting dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data of the nanoparticle dispersion system at preset time intervals, and taking the three types of data collected at the same time point as a multimodal particle size distribution data at one time point. All the data at all time points are arranged in chronological order to form a data sequence that includes the time dimension and the multimodal particle size distribution dimension.

[0025] In this embodiment, the pre-constructed aggregation feature space is a multi-dimensional vector space, obtained through training a deep neural network. During construction, a large amount of multimodal particle size distribution data and corresponding transmission electron microscopy (TEM) images of nanoparticle samples at different time points are first collected. Image segmentation and feature extraction are performed on the TEM images to obtain porosity parameters, pore connectivity parameters, and particle boundary clarity parameters for each sample. Based on a comprehensive evaluation of these parameters, the true aggregation state category of each sample at each time point is determined. The true aggregation state categories include unaggregated state, soft aggregation state, and hard aggregation state. Then, using the multimodal particle size distribution data at each time point as input features and the corresponding true aggregation state category as output labels, a multi-layer deep neural network is trained. After training, the output space of the last hidden layer of the deep neural network is used as the aggregation feature space, where points in different regions correspond to different true aggregation state categories.

[0026] In this embodiment, the multimodal particle size distribution data at each time point is mapped to a pre-constructed aggregation feature space to obtain the feature points at each time point in the aggregation feature space, forming a feature point trajectory. This means that the dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data at each time point are input into a trained deep neural network. After transformation through multiple hidden layers of the network, the coordinate values ​​of the time point in the aggregation feature space are output from the last hidden layer of the network as feature point coordinates. The feature point coordinates of all time points are connected sequentially in chronological order to form a continuous trajectory characterizing the re-aggregation evolution process of nanoparticles.

[0027] In this embodiment, the displacement vector between adjacent time points is calculated based on the feature point trajectory to obtain the displacement vector sequence. This means taking the feature point coordinates of each pair of adjacent time points from the feature point trajectory in sequence, calculating the difference between the feature point coordinates of the next time point and the feature point coordinates of the previous time point, and the difference includes two attributes: magnitude and direction. All the differences between adjacent time points are arranged in chronological order to form the displacement vector sequence.

[0028] In this embodiment, calculating the reagglomeration rate based on the displacement vector sequence means taking the arithmetic mean of the magnitudes of all displacement vectors in the displacement vector sequence and using the average value as the reagglomeration rate. The unit of this value matches the unit of the acquisition time interval, reflecting the average distance the nanoparticles move per unit time in the agglomeration characteristic space and characterizing the speed at which the reagglomeration phenomenon occurs.

[0029] In this embodiment, the current time point feature point refers to the feature point coordinates corresponding to the latest acquisition time point in the aggregation feature space, representing the aggregation state of the nanoparticle dispersion system at the current moment.

[0030] In this embodiment, the initial time point feature point refers to the coordinates of the feature point in the aggregation feature space corresponding to the time point of the initial stable state of the nanoparticle dispersion system. It represents the aggregation state of the nanoparticle dispersion system when it has just been prepared and reached a stable dispersion state, and serves as a benchmark point for comparing the degree of subsequent re-aggregation.

[0031] In this embodiment, calculating the spatial distance between the feature point at the current time point and the feature point at the initial time point refers to calculating the Euclidean distance between the coordinates of the feature point at the current time point and the coordinates of the feature point at the initial time point in the clustering feature space. This distance value quantifies the degree of deviation of the current clustering state from the initial dispersion state.

[0032] In this embodiment, calculating the reagglomeration rate based on spatial distance means dividing the Euclidean distance between the current time point feature point and the initial time point feature point by a preset deviation benchmark value of the completely dispersed state, and then multiplying by 100% to obtain a percentage value as the reagglomeration rate. This value reflects the percentage of the current agglomeration degree of nanoparticles relative to the completely dispersed state.

[0033] In this embodiment, the directional region of the current time point feature point in the clustering feature space refers to the directional relationship of the current time point feature point coordinates relative to the preset center coordinates of each feature region in the clustering feature space. The feature regions include non-clustered region, soft clustered region, and hard clustered region, and each feature region has a region center coordinate.

[0034] In this embodiment, the clustering structure characteristic index is calculated based on the location region of the feature point at the current time point in the clustering feature space. The specific calculation method is as follows: First, determine the centers of the soft-cluster and hard-cluster feature regions in the clustering feature space. The centers of the soft-cluster feature regions are determined as follows: extract the coordinates of all feature points labeled as soft-clustered samples from the training sample set in the clustering feature space, calculate the arithmetic mean of these coordinates, and obtain the coordinates of the soft-cluster feature region centers. The centers of the hard-cluster feature regions are determined similarly: extract the coordinates of all feature points labeled as hard-clustered samples from the training sample set in the clustering feature space, calculate their arithmetic mean, and obtain the coordinates of the hard-cluster feature region centers.

[0035] Secondly, calculate the Euclidean distance between the coordinates of the feature point at the current time point and the center coordinates of the feature region in the soft agglomeration state, as the first distance; calculate the Euclidean distance between the coordinates of the feature point at the current time point and the center coordinates of the feature region in the hard agglomeration state, as the second distance.

[0036] Then, the first distance is divided by the sum of the first and second distances, and the quotient is used as the clustering structure characteristic index. The value of this index ranges from 0 to 1. When the feature point is infinitely close to the center of the feature region of the soft clustering state, the first distance approaches 0, and the index approaches 0, indicating that the current clustering type tends to be soft clustering; when the feature point is infinitely close to the center of the feature region of the hard clustering state, the second distance approaches 0, and the index approaches 1, indicating that the current clustering type tends to be hard clustering; when the feature point is located in the transition region between soft and hard clustering, the index value is between 0 and 1, reflecting the degree of mixing or transition state of soft and hard clustering.

[0037] It should be noted that the rationale for this calculation formula lies in the normalization comparison of the distance between the feature point and the two reference centers, so that the index value can intuitively reflect the relative position of the feature point with respect to the two reference centers, thereby quantitatively characterizing the type of cluster structure.

[0038] The index ranges from zero to one. The closer the value is to zero, the more likely the current reunification type is to be soft reunification. The closer the value is to one, the more likely the current reunification type is to be hard reunification.

[0039] In this embodiment, the reagglomeration rate refers to the average distance the nanoparticles move per unit time in the agglomeration characteristic space, reflecting the speed at which the reagglomeration phenomenon occurs. It is calculated from the average value of all displacements in the displacement vector sequence.

[0040] In this embodiment, the reagglomeration rate refers to the percentage of deviation of the current agglomeration state from the initial dispersion state. It is calculated by dividing the spatial distance between the feature point at the current time point and the feature point at the initial time point by a preset deviation benchmark value for the completely dispersed state and then multiplying by 100%.

[0041] In this embodiment, the aggregation structure characteristic index is a numerical indicator that quantifies whether the current aggregation type tends to be soft or hard. It is calculated by dividing the first distance between the feature point at the current time and the center of the soft aggregation feature region by the sum of the first distance and the second distance. An index value close to zero indicates a tendency towards soft aggregation, and a value close to one indicates a tendency towards hard aggregation.

[0042] Furthermore, the multimodal particle size distribution data includes dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data. The dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data are aligned according to the acquisition time points to form a multimodal particle size distribution time series.

[0043] In this embodiment, dynamic light scattering particle size distribution data refers to the hydrodynamic diameter distribution data of nanoparticles obtained by measuring the Brownian motion velocity of nanoparticles in a liquid medium using dynamic light scattering technology and converting it according to the Stokes-Einstein equation. This data reflects the equivalent spherical diameter distribution of nanoparticles during diffusion in the liquid medium. Laser particle size analysis particle size distribution data refers to the volumetric diameter distribution data of nanoparticles obtained by measuring the scattering angle and intensity distribution of laser light by nanoparticles using laser particle size analysis technology and converting it according to Mie scattering theory. This data reflects the volumetric equivalent diameter distribution of nanoparticles under dry or wet dispersion conditions. Focused beam reflection measurement chord length distribution data refers to the chord length distribution data of nanoparticles obtained by scanning the nanoparticle dispersion system with a focused laser beam using focused beam reflection measurement technology, detecting the reflected pulse signal generated by the laser beam being blocked by particles, and converting it according to the pulse duration. This data reflects the actual size distribution of nanoparticles in the concentrated slurry system and is not limited by the system concentration.

[0044] In this embodiment, the dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data are aligned according to the acquisition time points to form a multimodal particle size distribution time series. This means that after acquiring the three types of data simultaneously at the same time point or separately at the same time interval, the dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data at all time points are grouped according to the corresponding time points. The three types of data at the same time point constitute the multimodal particle size distribution data at that time point. The multimodal particle size distribution data at all time points are arranged in chronological order to form a data sequence that simultaneously includes the time dimension and the multimodal particle size distribution dimension.

[0045] Furthermore, dynamic light scattering particle size distribution data is continuously acquired at preset time intervals by an in-situ detection probe embedded in the nanoparticle dispersion system. The in-situ detection probe integrates a dynamic light scattering sensor, a focused beam reflection measurement sensor, a temperature sensor, a pH sensor, a viscosity sensor, and an ionic strength sensor. The in-situ detection probe simultaneously acquires the temperature, pH, viscosity, and ionic strength parameters of the nanoparticle dispersion system as an environmental parameter sequence.

[0046] In this embodiment, embedding the nanoparticle dispersion system means immersing the sensing part of the detection probe directly into the liquid medium containing nanoparticles, so that the probe is in direct contact with the nanoparticle dispersion system, thereby realizing real-time in-situ measurement of the internal state of the dispersion system and avoiding disturbance and damage to the dispersion system caused by the sampling process.

[0047] In this embodiment, the in-situ detection probe refers to a composite detection device that integrates multiple sensors. The outer shell of the probe is encapsulated with corrosion-resistant material. The front end is the sensing area that can be directly immersed in the nanoparticle dispersion system. The rear end is connected to the data acquisition and processing unit through a cable to realize synchronous, real-time and continuous measurement of multiple parameters inside the dispersion system.

[0048] In this embodiment, the preset time interval refers to the time length between two adjacent acquisition operations that is preset according to the detection requirements. The time interval can be a fixed constant or can be dynamically adjusted according to the actual situation. The value of the time interval determines the sampling frequency.

[0049] In this embodiment, dynamic light scattering particle size distribution data is continuously collected by an in-situ detection probe embedded in the nanoparticle dispersion system at preset time intervals. This means that the in-situ detection probe, which integrates a dynamic light scattering sensor, is immersed in the nanoparticle dispersion system. The dynamic light scattering sensor repeatedly emits laser light and receives the scattering signals from the nanoparticles at preset fixed or variable time intervals. Each collection yields a set of dynamic light scattering particle size distribution data, and multiple time points of dynamic light scattering particle size distribution data are continuously collected.

[0050] In this embodiment, the in-situ detection probe integrates a dynamic light scattering sensor, a focused beam reflection measurement sensor, a temperature sensor, a pH sensor, a viscosity sensor, and an ion strength sensor. This means that a dynamic light scattering sensor, a focused beam reflection measurement sensor, a temperature sensor, a pH sensor, a viscosity sensor, and an ion strength sensor are all encapsulated in a single probe housing. The detection ends of each sensor are exposed at the front end of the probe and are in direct contact with the nanoparticle dispersion system. All sensors work synchronously and output multiple detection data at the same time.

[0051] In this embodiment, the dynamic light scattering sensor is a sensor that measures the particle size of nanoparticles based on the principle of dynamic light scattering. The sensor contains a laser, a photodetector, and a signal processing unit. The laser emits laser light into the nanoparticle dispersion system, the photodetector receives the intensity fluctuation signal of scattered light caused by the Brownian motion of the nanoparticles, and the signal processing unit performs correlation function analysis on the fluctuation signal and calculates the hydrodynamic diameter distribution data of the nanoparticles according to the Stokes-Einstein equation.

[0052] In this embodiment, the focused beam reflection measurement sensor is a sensor that measures the chord length of particles based on the principle of focused beam reflection. The sensor contains a high-power laser, a high-speed rotating optical scanning mechanism, and a photodetector. After being focused by the scanning mechanism, the laser beam rotates and scans at high speed in the nanoparticle dispersion system. When the laser beam sweeps across the surface of the nanoparticles, it generates a reflection pulse. The photodetector receives the reflection pulse and records the pulse duration. The chord length of the particles is calculated based on the scanning speed and the pulse duration. The chord lengths of a large number of particles are statistically analyzed to form chord length distribution data.

[0053] In this embodiment, the viscosity sensor is a sensor that measures the viscosity of a liquid based on the principle of vibration or the principle of pressure difference. The sensor contains a vibration element or a microchannel structure and a pressure sensor. By measuring the damping change of the vibration element in the liquid or measuring the pressure difference change of the liquid passing through the microchannel, the viscosity parameters of the nanoparticle dispersion system are calculated.

[0054] In this embodiment, the ion strength sensor is a sensor that measures the ion strength in a solution based on the principle of conductivity measurement or the principle of ion selective electrode. The sensor contains a conductivity electrode or ion selective electrode and a reference electrode. By measuring the conductivity of the solution or the electrode potential of a specific ion, the ion strength parameters of the nanoparticle dispersion system are calculated.

[0055] In this embodiment, the in-situ detection probe simultaneously collects temperature, pH, viscosity, and ionic strength parameters of the nanoparticle dispersion system as an environmental parameter sequence. This means that the temperature sensor, pH sensor, viscosity sensor, and ionic strength sensor integrated in the in-situ detection probe work synchronously at each acquisition time point to measure the temperature, pH, viscosity, and ionic strength values ​​of the nanoparticle dispersion system at the current moment. The temperature values ​​measured at all time points are arranged in chronological order to form a temperature parameter sequence. Similarly, the pH parameter sequence, viscosity parameter sequence, and ionic strength parameter sequence are obtained. These sequences together constitute the environmental parameter sequence.

[0056] Furthermore, prior to the step of mapping the multimodal particle size distribution data at each time point to the pre-constructed clustering feature space, the following steps are also included: The viscosity parameter at each time point is input into a pre-constructed viscosity shift correction function, which outputs a viscosity drift correction coefficient. This coefficient is then multiplied by the dynamic light scattering particle size distribution data at the corresponding time point to obtain the viscosity-corrected dynamic light scattering particle size distribution data. The viscosity shift correction function is constructed as follows: multiple standard nanoparticle dispersion systems with gradient viscosity values ​​are prepared, each system containing nanoparticles of the same true particle size. The particle size data of each system is measured using a dynamic light scattering sensor. The ratio of the measured particle size to the true particle size is used as the viscosity drift correction coefficient. A quadratic polynomial fitting is employed with the viscosity parameter as the independent variable and the viscosity drift correction coefficient as the dependent variable to obtain the viscosity shift correction function. The phrase "multiplying the viscosity drift correction coefficient by the dynamic light scattering particle size distribution data" refers to using this coefficient as a multiplier factor, multiplying it by the intensity percentage value corresponding to each particle size interval in the particle size distribution data to obtain the corrected intensity percentage distribution.

[0057] The ion intensity parameter at each time point is input into a pre-constructed ion intensity refractive index correction function, which outputs a refractive index fluctuation correction coefficient. This coefficient is then multiplied by the dynamic light scattering particle size distribution data at the corresponding time point to obtain the ion intensity-corrected dynamic light scattering particle size distribution data. The ion intensity refractive index correction function is constructed as follows: multiple standard nanoparticle dispersion systems with gradient ion intensity values ​​are prepared, each system containing nanoparticles of the same actual particle size. The particle size data of each system is measured using a dynamic light scattering sensor. The ratio of the measured particle size to the actual particle size is used as the refractive index fluctuation correction coefficient. A linear function is used to fit the ion intensity refractive index correction function, with the ion intensity parameter as the independent variable and the refractive index fluctuation correction coefficient as the dependent variable. Multiplying the refractive index fluctuation correction coefficient by the dynamic light scattering particle size distribution data means using this coefficient as a multiplier factor and multiplying it by the intensity percentage value corresponding to each particle size interval in the particle size distribution data to obtain the corrected intensity percentage distribution.

[0058] The nanoparticle concentration parameters at each time point are input into a pre-constructed concentration multiple scattering correction function, which outputs a multiple scattering attenuation correction coefficient. This coefficient is then multiplied by the corresponding laser particle size analysis (LDA) particle size distribution data to obtain the concentration-corrected LDA particle size distribution data. The concentration multiple scattering correction function is constructed as follows: multiple standard nanoparticle dispersion systems with gradient concentration values ​​are prepared, each system containing nanoparticles of the same true particle size. The particle size of each system is measured using a laser particle size analyzer. The ratio of the measured particle size to the true particle size is used as the multiple scattering attenuation correction coefficient. A negative exponential function is used to fit the concentration multiple scattering correction function, with the concentration parameter as the independent variable and the coefficient as the dependent variable. Multiplying the multiple scattering attenuation correction coefficient by the LDA particle size distribution data means using this coefficient as a multiplier factor and multiplying it by the volume percentage value corresponding to each particle size interval in the particle size distribution data to obtain the corrected volume percentage distribution.

[0059] In this embodiment, the pre-constructed viscosity shift correction function refers to the mapping relationship between the viscosity parameter established through experimental calibration and the dynamic light scattering particle size measurement shift. During construction, multiple standard nanoparticle dispersion systems with different viscosity values ​​are prepared. The actual particle size of the nanoparticles in each standard system is the same, but the viscosity is different. The particle size data of each standard system is measured using a dynamic light scattering sensor. The ratio of the measured value to the actual value is used as the viscosity shift correction coefficient. Data fitting is performed with the viscosity parameter as the independent variable and the viscosity shift correction coefficient as the dependent variable to obtain the viscosity shift correction function. This function can be in the form of a polynomial function or an exponential function.

[0060] In this embodiment, the viscosity drift correction coefficient is a numerical factor used to correct the influence of viscosity on the dynamic light scattering particle size measurement results. Multiplying this coefficient by the original measurement data can eliminate the particle size measurement deviation caused by viscosity changes, making the corrected data equivalent to the measurement value under standard viscosity conditions.

[0061] In this embodiment, the viscosity parameter at each time point is input into a pre-constructed viscosity shift correction function, and the viscosity drift correction coefficient is output. This means that the viscosity value measured by the viscosity sensor at the current acquisition time point is substituted into the pre-fitted viscosity shift correction function, and the viscosity drift correction coefficient value corresponding to the viscosity value is obtained through function calculation.

[0062] In this embodiment, the dynamic light scattering particle size distribution data at the corresponding time point refers to the dynamic light scattering particle size distribution data obtained by the dynamic light scattering sensor at the same acquisition time point. This data is the corresponding data acquired at the same time as the viscosity parameter, ionic strength parameter, and nanoparticle concentration parameter at that time point.

[0063] In this embodiment, multiplying the viscosity drift correction coefficient with the dynamic light scattering particle size distribution data at the corresponding time point to obtain the viscosity-corrected dynamic light scattering particle size distribution data means using the viscosity drift correction coefficient calculated at the same time point as a multiplier factor and multiplying it with each particle size value in the original dynamic light scattering particle size distribution data at that time point to obtain a new set of particle size distribution data. This new set of data is the viscosity-corrected dynamic light scattering particle size distribution data.

[0064] In this embodiment, the viscosity-corrected dynamic light scattering particle size distribution data refers to the particle size distribution data after eliminating the influence of viscosity changes on the dynamic light scattering measurement results. This data can be regarded as the equivalent particle size distribution data measured under standard viscosity conditions, which is convenient for comparison and analysis with data measured under different viscosity conditions.

[0065] In this embodiment, the pre-constructed ion intensity refractive index correction function refers to the mapping relationship function between the ion intensity parameter and the refractive index fluctuation of the dispersion system, established through experimental calibration. During construction, multiple standard nanoparticle dispersion systems with different ion intensities are prepared, and the refractive index value of each standard system is measured. Data fitting is performed with the ion intensity parameter as the independent variable and the refractive index fluctuation correction coefficient as the dependent variable to obtain the ion intensity refractive index correction function. This function can be in the form of a linear function or a polynomial function.

[0066] In this embodiment, the ion intensity parameter at each time point is input into a pre-constructed ion intensity refractive index correction function, and the refractive index fluctuation correction coefficient is output. This means that the ion intensity value measured by the ion intensity sensor at the current acquisition time point is substituted into the pre-fitted ion intensity refractive index correction function, and the refractive index fluctuation correction coefficient value corresponding to the ion intensity value is obtained through function calculation.

[0067] In this embodiment, the refractive index fluctuation correction coefficient is a numerical factor used to correct the influence of the refractive index change of the dispersion system on the dynamic light scattering measurement results. Multiplying this factor by the original measurement data can eliminate the particle size measurement deviation caused by the refractive index fluctuation due to the change in ion strength.

[0068] In this embodiment, multiplying the refractive index fluctuation correction coefficient with the dynamic light scattering particle size distribution data at the corresponding time point to obtain the ion intensity corrected dynamic light scattering particle size distribution data means using the refractive index fluctuation correction coefficient calculated at the same time point as a multiplier factor and multiplying it with each particle size value in the original dynamic light scattering particle size distribution data at that time point to obtain a new set of particle size distribution data. This new set of data is the dynamic light scattering particle size distribution data after ion intensity correction.

[0069] In this embodiment, the dynamic light scattering particle size distribution data after ion strength correction refers to the particle size distribution data after eliminating the influence of refractive index fluctuations caused by changes in ion strength on the dynamic light scattering measurement results. This data can be regarded as the equivalent particle size distribution data measured under standard ion strength conditions.

[0070] In this embodiment, the nanoparticle concentration parameter refers to the mass or number of nanoparticles contained per unit volume in the nanoparticle dispersion system, typically expressed in milligrams per milliliter or numbers per milliliter. This parameter can be measured using methods such as gravimetric analysis, UV-Vis spectrophotometry, or particle counters. Furthermore, in-situ synchronous data acquisition is achieved through a laser concentration sensor integrated with the in-situ detection probe, or offline gravimetric measurement followed by alignment with in-situ multimodal data at the acquisition time point ensures that the concentration correction matches the laser particle size analysis data at the corresponding time point.

[0071] In this embodiment, the pre-constructed concentration multiple scattering correction function refers to the mapping relationship between the nanoparticle concentration parameter and the laser particle size analysis multiple scattering attenuation established through experimental calibration. During construction, multiple standard nanoparticle dispersion systems with different concentrations are prepared. Each standard system has the same actual nanoparticle size but different concentrations. The particle size data of each standard system is measured using a laser particle size analyzer. The ratio of the measured value to the actual value is used as the multiple scattering attenuation correction coefficient. Data fitting is performed with the concentration parameter as the independent variable and the multiple scattering attenuation correction coefficient as the dependent variable to obtain the concentration multiple scattering correction function. This function can be in the form of a negative exponential function or a power function.

[0072] In this embodiment, the nanoparticle concentration parameter at each time point is input into a pre-constructed concentration multiple scattering correction function, and the multiple scattering attenuation correction coefficient is output. This means that the nanoparticle concentration value obtained at the current acquisition time point is substituted into the pre-fitted concentration multiple scattering correction function, and the multiple scattering attenuation correction coefficient value corresponding to the concentration value is obtained through function calculation.

[0073] In this embodiment, the multiple scattering attenuation correction coefficient is a numerical factor used to correct the influence of multiple scattering effect caused by excessively high nanoparticle concentration on the laser particle size analysis measurement results. Multiplying this factor by the original measurement data can eliminate the particle size measurement deviation caused by multiple scattering attenuation due to excessively high concentration.

[0074] In this embodiment, the laser particle size distribution data at the corresponding time point refers to the laser particle size distribution data obtained by the laser particle size analyzer at the same acquisition time point. This data and the nanoparticle concentration parameter at that time point are corresponding data acquired at the same time.

[0075] In this embodiment, multiplying the multiple scattering attenuation correction coefficient with the laser particle size distribution data at the corresponding time point to obtain the concentration-corrected laser particle size distribution data means using the multiple scattering attenuation correction coefficient calculated at the same time point as a multiplier factor and multiplying it with each particle size value in the original laser particle size distribution data at that time point to obtain a new set of particle size distribution data. This new set of data is the concentration-corrected laser particle size distribution data.

[0076] In this embodiment, the concentration-corrected laser particle size distribution data refers to the particle size distribution data after eliminating the influence of multiple scattering effects caused by excessively high nanoparticle concentration on the laser particle size analysis measurement results. This data can be regarded as the equivalent particle size distribution data measured under standard concentration conditions.

[0077] Furthermore, the clustering feature space is pre-constructed through the following steps: Multimodal particle size distribution data and corresponding transmission electron microscopy (TEM) morphology data of multiple nanoparticle samples were collected at different time points. During acquisition, strict synchronization between multimodal particle size distribution data acquisition and TEM sampling was ensured. Specifically, at each acquisition time point, in-situ measurement of multimodal particle size distribution data was completed first, followed immediately by TEM sample preparation and imaging from the dispersion system, ensuring that the aggregation state reflected in the TEM image corresponds to the particle size distribution data at that time point.

[0078] Image segmentation and feature extraction were performed on each transmission electron microscope (TEM) microstructure data to obtain the porosity parameter, pore connectivity parameter, and particle boundary clarity parameter of each nanoparticle sample at each time point.

[0079] Based on a comprehensive evaluation of porosity, pore connectivity, and particle boundary clarity parameters, the true aggregation state category of each nanoparticle sample at each time point is determined. The specific rules for the comprehensive evaluation are as follows: when the porosity parameter is less than a first preset threshold, the pore connectivity parameter is less than a second preset threshold, and the particle boundary clarity parameter is greater than a third preset threshold, it is determined to be in a non-aggregated state; when the porosity parameter is between the first and fourth preset thresholds, the pore connectivity parameter is between the second and fifth preset thresholds, and the particle boundary clarity parameter is between the third and sixth preset thresholds, it is determined to be in a soft aggregated state; when the porosity parameter is greater than the fourth preset threshold, the pore connectivity parameter is greater than the fifth preset threshold, and the particle boundary clarity parameter is less than the sixth preset threshold, it is determined to be in a hard aggregated state.

[0080] The above-mentioned preset thresholds are determined as follows: at least 50 transmission electron microscopy images of known aggregate states are acquired, and the porosity parameter, pore connectivity parameter, and particle boundary sharpness parameter of each image are calculated. For the three categories of unaggregated state, soft aggregated state, and hard aggregated state, the numerical distribution range of each parameter is statistically analyzed. The upper limit of the parameter distribution of the unaggregated state is used as the first preset threshold, the second preset threshold, and the third preset threshold. The lower limit and upper limit of the parameter distribution of the soft aggregated state are used as the fourth preset threshold, the fifth preset threshold, and the sixth preset threshold, respectively. The fourth preset threshold corresponds to the lower limit of porosity of the soft aggregated state, the fifth preset threshold corresponds to the lower limit of pore connectivity of the soft aggregated state, and the sixth preset threshold corresponds to the upper limit of particle boundary sharpness of the soft aggregated state.

[0081] A deep neural network was trained using multimodal particle size distribution data at each time point as input features and the corresponding true clustering state category as the output label. This deep neural network employed a metric learning strategy for training, aiming to map samples of the same clustering state category as closely spaced feature points in the last hidden layer, and samples of different clustering state categories as far apart feature points, rather than simply pursuing classification accuracy. Specifically, a triplet loss function was used during network training. In each training batch, one anchor sample, one positive sample of the same class as the anchor, and one negative sample of a different class were randomly selected. Optimization was performed to ensure that the distance between the anchor and the positive sample was less than the distance between the anchor and the negative sample. The network structure was a five-layer fully connected network with 9 nodes in the input layer (corresponding to a 9-dimensional multimodal feature vector), 128, 64, and 32 nodes in the first three hidden layers, 2 nodes in the last hidden layer, and 3 nodes in the output layer. Training was stopped when the classification accuracy on the validation set reached above 95% and the triplet loss function converged.

[0082] The output space of the last hidden layer of the trained deep neural network is used as the clustering feature space. This output space is a two-dimensional space, where the coordinates of each feature point are the two output values ​​of the last hidden layer of the network. Since the network is trained using a metric learning strategy, this two-dimensional space has the following properties: samples of the same clustering state category form clusters in this space, and samples of different clustering state categories are separated from each other in this space, thus making the clustering states highly distinguishable in the feature space.

[0083] In this embodiment, multiple nanoparticle samples refer to multiple independent nanoparticle dispersion system samples obtained from different batches, different formulations or different processing conditions. These samples have diversity in terms of particle size distribution, surface properties, dispersion medium, etc., and are used to cover various aggregation states that may occur during the re-aggregation process of nanomaterials.

[0084] In this embodiment, collecting multimodal particle size distribution data and corresponding transmission electron microscopy (TEM) microstructure data of multiple nanoparticle samples at different time points means that for each nanoparticle sample, starting from its initial stable state after preparation, dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data are collected multiple times at preset time intervals. At each acquisition time point, a small amount of sample is simultaneously taken for TEM sample preparation and imaging to obtain the TEM microstructure image corresponding to that time point. Finally, each sample has a set of multimodal particle size distribution data and a corresponding TEM microstructure image at each time point.

[0085] In this embodiment, the transmission electron microscope (TEM) micromorphology data refers to the high-resolution image data of nanoparticles obtained by taking a TEM image. The image can clearly show the morphology, size, dispersion state and connection mode between nanoparticles. The image can show whether the particles are dispersed individually or adhered to each other, whether the adhesion is a simple contact or has fused and grown, and whether there is a porous structure inside the particles.

[0086] In this embodiment, image segmentation and feature extraction are performed on each transmission electron microscope (TEM) microstructure data to obtain the porosity parameter, pore connectivity parameter, and particle boundary sharpness parameter for each nanoparticle sample at each time point. This involves inputting each TEM image into image processing software, first performing image segmentation to distinguish between particle regions and pore regions in the image, then calculating the percentage of the total area of ​​pore regions to the total area of ​​the image as the porosity parameter, calculating the ratio of the number of interconnected pore regions to the total number of pore regions as the pore connectivity parameter, and calculating the gradient intensity and continuity of particle boundaries as the particle boundary sharpness parameter. These three parameters together quantify and characterize the microstructure features of the aggregates at that time point.

[0087] In this embodiment, the porosity parameter refers to the percentage of the pore area in the transmission electron microscope image to the total image area, reflecting the abundance of pores inside the aggregate; the pore connectivity parameter refers to the ratio of the number of interconnected pore areas to the total number of pore areas, reflecting the degree of connectivity of pores inside the aggregate; the particle boundary clarity parameter refers to the comprehensive quantitative value of the gradient intensity and continuity of the particle boundary, reflecting whether the particles are in simple contact or have fused and grown. Clear boundaries indicate that the particles maintain an independent morphology, while blurred boundaries indicate that material diffusion and fusion have occurred between the particles.

[0088] In this embodiment, based on a comprehensive evaluation of porosity parameters, pore connectivity parameters, and particle boundary clarity parameters, the true aggregation state category of each nanoparticle sample at each time point is determined. The true aggregation state category includes non-aggregated state, soft aggregation state, and hard aggregation state. This means comparing the three parameter values ​​extracted at each time point with preset classification rules. When the porosity parameter is lower than a first threshold, the pore connectivity parameter is lower than a second threshold, and the particle boundary clarity parameter is higher than a third threshold, the aggregation state at that time point is determined to be non-aggregated state. When the porosity parameter is between the first and second thresholds, the pore connectivity parameter is between the second and third thresholds, and the particle boundary clarity parameter is between the third and fourth thresholds, it is determined to be soft aggregation state. When the porosity parameter is higher than the second threshold, the pore connectivity parameter is higher than the third threshold, and the particle boundary clarity parameter is lower than the fourth threshold, it is determined to be hard aggregation state.

[0089] In this embodiment, multimodal particle size distribution data at each time point is used as input features, and the corresponding true aggregation state category is used as output label. Training a deep neural network involves combining dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data at each acquisition time point into an input vector. The true aggregation state category determined by transmission electron microscopy image analysis at that time point is converted into a classification label value. The input vectors of all samples at all time points and the corresponding classification label values ​​constitute a training dataset. A multi-layer deep neural network is trained using this dataset. The number of nodes in the network's input layer matches the dimension of the input vector, and the number of nodes in the output layer matches the number of classification categories. The network continuously adjusts the internal connection weights through the backpropagation algorithm to minimize the error between the network's classification output of the input vector and the true label.

[0090] In this embodiment, the output space of the last hidden layer of the deep neural network is used as the clustering feature space. This means that in the trained deep neural network, after the input layer and before the output layer, multiple hidden layers are used for feature transformation. The output vector of the last hidden layer represents the high-order features extracted by the network from the original multimodal particle size distribution data. The multidimensional space in which these feature vectors are located is the clustering feature space. This space has the following properties: after the multimodal particle size distribution data with the same input clustering state category are transformed by the network, the feature points in this space are close to each other, and the feature points of multimodal particle size distribution data with different input clustering state categories are far apart from each other, so that the clustering state categories are distinguishable in this space.

[0091] Furthermore, the step of mapping the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space includes: The peak particle size, average particle size, and particle size distribution width are extracted from the dynamic light scattering particle size distribution data at each time point as three components of the dynamic light scattering feature vector, and combined to form the dynamic light scattering feature vector. The peak particle size, average particle size, and particle size distribution width are extracted from the laser particle size analysis particle size distribution data at each time point as three components of the laser particle size analysis feature vector, and combined to form the laser particle size analysis feature vector. The peak chord length, average chord length, and chord length distribution width are extracted from the focused beam reflection measurement chord length distribution data at each time point as three components of the focused beam reflection measurement feature vector, and combined to form the focused beam reflection measurement feature vector. The dynamic light scattering feature vector, laser particle size analysis feature vector, and focused beam reflection measurement feature vector are normalized separately and then concatenated in sequence to form a multimodal feature vector. The normalization process is as follows: for each of the three components (peak particle size, average particle size, and particle size distribution width) in the dynamic light scattering feature vector, the mean and standard deviation of that component across all training samples are calculated. The normalized component value is then obtained by subtracting the mean from the normalized value for each sample and dividing by the standard deviation. The normalization process for the laser particle size analysis feature vector and the focused beam reflection measurement feature vector is similar. This normalization ensures that the three features, which have different sources and dimensions, have similar numerical ranges, preventing any one type of feature from dominating network training due to excessively large values.

[0092] It should be noted that simplifying the complete particle size distribution curve into three statistical features—peak size, average size, and distribution width—is based on the following considerations: peak size reflects the most probable particle size, average size reflects the overall particle size level, and distribution width reflects the dispersion of the particle size distribution. These three statistical features can characterize the main information of the particle size distribution with a lower dimension, reducing the feature dimensionality while ensuring sufficient information, thus reducing the computational burden of network training. For possible bimodal or multimodal distributions, the feature representation ability can be enhanced by increasing the number of extracted peaks (e.g., extracting the first and second peaks). In specific implementation, the number of extracted peaks can be determined according to the sample characteristics.

[0093] The multimodal feature vector is input into a deep neural network. After transformation through multiple hidden layers, the coordinates of the feature point in the clustering feature space at that time point are output from the last hidden layer of the deep neural network. Connect the coordinates of all feature points at all time points in chronological order to form the feature point trajectory.

[0094] In this embodiment, peak particle size, average particle size, and particle size distribution width refer to three statistical features extracted from particle size distribution data. Peak particle size is the particle size value corresponding to the highest point in the particle size distribution curve, representing the particle size that appears most frequently in the dispersion system; average particle size is the arithmetic mean or weighted average of all particle sizes, representing the overall size level of the dispersion system; particle size distribution width is the span or variance of the particle size distribution, usually expressed as the difference between the particle size at which the cumulative distribution reaches 10% and the particle size at which the cumulative distribution reaches 90%, reflecting the uniformity of particle size.

[0095] In this embodiment, the peak particle size, average particle size, and particle size distribution width are extracted from the dynamic light scattering particle size distribution data at each time point as three components of the dynamic light scattering feature vector. These components are then combined to form the dynamic light scattering feature vector. This involves statistically analyzing the dynamic light scattering particle size distribution data obtained at each acquisition time point, identifying the particle size value corresponding to the peak of the distribution curve as the peak particle size, calculating the weighted average of all particle sizes as the average particle size, and calculating the difference between the cumulative 10% and 90% particle sizes as the particle size distribution width. These three values ​​are then arranged into a three-dimensional vector in the order of peak particle size, average particle size, and particle size distribution width. This vector is the dynamic light scattering feature vector at that time point.

[0096] In this embodiment, the peak particle size, average particle size, and particle size distribution width are extracted from the laser particle size analysis particle size distribution data at each time point as three components of the laser particle size analysis feature vector. These components are then combined to form the laser particle size analysis feature vector. This involves statistically analyzing the laser particle size distribution data obtained at each acquisition time point, identifying the particle size value corresponding to the peak of the distribution curve as the peak particle size, calculating the volume-weighted average of all particle sizes as the average particle size, and calculating the difference between the cumulative 10% and 90% particle sizes as the particle size distribution width. These three values ​​are then arranged into a three-dimensional vector in the order of peak particle size, average particle size, and particle size distribution width. This vector is the laser particle size analysis feature vector for that time point.

[0097] In this embodiment, peak chord length, average chord length, and chord length distribution width refer to three statistical features extracted from the chord length distribution data. Peak chord length is the chord length value corresponding to the highest point in the chord length distribution curve, representing the chord length of the particles with the highest frequency in the dispersion system; average chord length is the arithmetic mean or weighted average of all particle chord lengths, representing the overall chord length level of the dispersion system; chord length distribution width is the span or variance of the chord length distribution, usually expressed as the difference between the chord length when the cumulative distribution reaches 10% and the chord length when the cumulative distribution reaches 90%, reflecting the uniformity of the particle chord length distribution.

[0098] In this embodiment, the peak chord length, average chord length, and chord length distribution width are extracted from the focused beam reflection measurement chord length distribution data at each time point as three components of the focused beam reflection measurement feature vector. These components are then combined to form the focused beam reflection measurement feature vector. This involves statistically analyzing the focused beam reflection measurement chord length distribution data obtained at each acquisition time point, identifying the chord length value corresponding to the peak of the distribution curve as the peak chord length, calculating the arithmetic mean of all chord lengths as the average chord length, and calculating the difference between the cumulative 10% and 90% chord lengths as the chord length distribution width. These three values ​​are then arranged into a three-dimensional vector in the order of peak chord length, average chord length, and chord length distribution width. This vector is the focused beam reflection measurement feature vector at that time point.

[0099] In this embodiment, the dynamic light scattering feature vector, the laser particle size analysis feature vector, and the focused beam reflection measurement feature vector are sequentially spliced ​​into a multimodal feature vector. This means that the dynamic light scattering feature vector, the laser particle size analysis feature vector, and the focused beam reflection measurement feature vector obtained at the same time point are sequentially connected end to end to form a nine-dimensional vector. The first three components of this vector come from the dynamic light scattering feature vector, the middle three components come from the laser particle size analysis feature vector, and the last three components come from the focused beam reflection measurement feature vector. This nine-dimensional vector is the multimodal feature vector at that time point.

[0100] In this embodiment, a deep neural network refers to an artificial neural network model consisting of an input layer, multiple hidden layers, and an output layer. Each layer contains multiple neurons, and neurons in adjacent layers are connected by weights. Specifically, the deep neural network used in this embodiment is a multilayer perceptron network with three to five hidden layers and sixty-four to two hundred and fifty-six neurons per layer. The activation function is a linear rectified function, and the output layer uses a normalized exponential function for multi-class classification tasks. The network is trained using a stochastic gradient descent optimization algorithm, and the loss function is the cross-entropy loss function.

[0101] In this embodiment, the multimodal feature vector is input into the deep neural network. After transformation through multiple hidden layers, the feature point coordinates in the clustering feature space at that time point are output from the last hidden layer of the deep neural network. This means that the nine-dimensional multimodal feature vector at each time point is passed as input data to the trained deep neural network. The vector passes through the network's input layer, first hidden layer, second hidden layer and so on until the last hidden layer. Each layer performs linear transformation and nonlinear activation processing on the input data. A two-dimensional vector is output from the last hidden layer, and this two-dimensional vector is used as the coordinate value of that time point in the clustering feature space, i.e., the feature point coordinates.

[0102] In this embodiment, the feature point coordinates of all time points are connected sequentially in chronological order to form a feature point trajectory. This means that the feature point coordinates of the first acquisition time point are taken as the starting point, the feature point coordinates of the second acquisition time point are taken as the second point, and so on. In the aggregation feature space, the feature points of adjacent time points are connected by straight line segments to form a continuous broken line that reflects the movement of the feature point coordinates over time. This broken line is the feature point trajectory, which intuitively shows the evolution path of the nanoparticle aggregation state in the feature space.

[0103] Further, the displacement vectors between feature points at adjacent time points are calculated based on the feature point trajectories to obtain a displacement vector sequence. The re-aggregation rate is then calculated based on the displacement vector sequence, including: Calculate the displacement vectors between adjacent time points in the feature point trajectory. Each displacement vector contains the displacement magnitude and displacement direction. The average value of all displacements in the displacement vector sequence is used as the re-agglomeration rate, and the unit of the re-agglomeration rate is matched with the unit of the acquisition time interval.

[0104] In this embodiment, the displacement vector between adjacent time points in the feature point trajectory is calculated. Each displacement vector includes displacement magnitude and displacement direction. This means that the coordinates of each pair of adjacent time points are extracted from the feature point trajectory in sequence, and the coordinates of the feature point at the previous time point are subtracted from the coordinates of the feature point at the later time point to obtain a difference vector in a multi-dimensional space. The length of this vector is obtained by calculating the Euclidean norm as the displacement magnitude, and the pointing angle of this vector in space is the displacement direction. The displacement magnitude reflects the intensity of the change in the clustering state within the time period, and the displacement direction reflects the type tendency of the clustering state evolution.

[0105] In this embodiment, the displacement vector sequence refers to the sequence formed by arranging the displacement vectors between all adjacent time points in the feature point trajectory in chronological order. The first displacement vector in the sequence corresponds to the displacement from the first time point to the second time point, the second displacement vector corresponds to the displacement from the second time point to the third time point, and so on. The length of the entire sequence is equal to the total number of acquisition time points minus one.

[0106] In this embodiment, the average value of all displacement magnitudes in the displacement vector sequence is used as the re-agglomeration rate. The unit of the re-agglomeration rate matches the unit of the acquisition time interval. This means that the displacement magnitude of each displacement vector in the displacement vector sequence is first calculated, then all displacement magnitudes are added together to obtain a sum, and the sum is divided by the number of displacement vectors to obtain the arithmetic mean. This average value is the re-agglomeration rate. If the acquisition time interval is in seconds, the unit of the re-agglomeration rate is the characteristic space unit per second; if the acquisition time interval is in minutes, the unit of the re-agglomeration rate is the characteristic space unit per minute. This value characterizes the average change in the agglomeration state of nanoparticles per unit time.

[0107] Further, the step of calculating the spatial distance between the feature point at the current time point and the feature point at the initial time point, and calculating the re-aggregation rate based on the spatial distance, includes: The time point corresponding to the initial stable state of the nanoparticle dispersion system is taken as the initial time point, and the coordinates of the initial feature point in the aggregation feature space are obtained. Calculate the Euclidean distance between the feature point coordinates at the current time point and the feature point coordinates at the initial time point, and use it as the current state deviation value; The current state deviation value is compared with the preset fully dispersed state deviation benchmark value, and the re-agglomeration rate is calculated. The re-agglomeration rate is calculated by dividing the current state deviation value by the preset fully dispersed state deviation benchmark value and then multiplying by 100%.

[0108] In this embodiment, the initial stable state of the nanoparticle dispersion system refers to the state in which the nanoparticle dispersion system reaches a state of uniform particle distribution, stable particle size distribution, and no significant agglomeration after it has just been prepared and fully dispersed. In this state, the nanoparticles remain independently dispersed in the dispersion medium, and the particle size distribution data obtained by dynamic light scattering, laser particle size analysis, and focused beam reflection measurement fluctuate very little over time. Usually, the state corresponding to the first time point after preparation or the average value of the first few time points is taken as the initial stable state.

[0109] In this embodiment, the time point corresponding to the initial stable state of the nanoparticle dispersion system is taken as the initial time point. This means that in the multimodal particle size distribution time series, the time point that represents the initial stable state of the nanoparticle dispersion system is selected. This time point is usually the first time point in the time series, or the first time point after the dispersion system has been verified to have reached stability, and is used as the reference time for all subsequent comparisons.

[0110] In this embodiment, obtaining the initial feature point coordinates in the aggregation feature space at the initial time point means inputting the multimodal particle size distribution data at the initial time point into a trained deep neural network. After transformation through multiple hidden layers of the network, the coordinate value of the time point in the aggregation feature space is output from the last hidden layer. This coordinate value is saved as the initial feature point coordinates, representing the feature position of the nanoparticle dispersion system in the initial stable state.

[0111] In this embodiment, the feature point coordinates at the current time point refer to the coordinate values ​​of the time point for which re-agglomeration analysis needs to be performed in the agglomeration feature space. These coordinate values ​​are obtained by inputting the multimodal particle size distribution data at the current time point into a deep neural network and outputting it from the last hidden layer. They represent the agglomeration state feature position of the nanoparticle dispersion system at the current moment.

[0112] In this embodiment, the initial time point feature point coordinates refer to the coordinate values ​​of the initial time point in the aggregation feature space. These coordinate values ​​serve as a benchmark reference point for measuring changes in the degree of aggregation and represent the characteristic positions of the nanoparticle dispersion system in the initial stable state.

[0113] In this embodiment, the Euclidean distance between the feature point coordinates at the current time point and the feature point coordinates at the initial time point is calculated as the current state deviation value. This refers to the straight-line distance between the feature point coordinates at the current time point and the feature point coordinates at the initial time point in the clustering feature space. Specifically, the calculation method is to add the squares of the differences in each dimension of the two coordinate values ​​and then take the square root. The resulting distance value is the current state deviation value, which quantifies the degree of deviation of the current clustering state from the initial stable state.

[0114] In this embodiment, the preset deviation benchmark value for complete dispersion is a reference distance value pre-set through experimental calibration. This value represents the maximum permissible deviation between the characteristic points and the initial characteristic points when the nanoparticle dispersion system is in a completely ideal dispersion state. The benchmark value is determined as follows: multiple nanoparticle samples prepared under optimal dispersion conditions and verified to be free of any agglomeration are collected, the current state deviation value of each sample is calculated, and the statistical upper limit or average value of these deviation values ​​is multiplied by a safety factor to obtain the preset deviation benchmark value for complete dispersion.

[0115] For example, when using the method of multiplying the statistical upper limit by a safety factor, the statistical upper limit is taken as the 95th quantile of all sample state deviation values, and the safety factor is taken as 1.2. The product is used as the benchmark value for complete dispersion state deviation. For example, if the 95th quantile of the state deviation value of a certain type of nanoparticle sample is 0.42 characteristic space units, then the benchmark value for complete dispersion state deviation is taken as 0.5 characteristic space units. When using the method of multiplying the average value by a safety factor, the safety factor is taken as 1.5, and the product is used as the benchmark value for complete dispersion state deviation. For example, if the average value of the state deviation value of a certain type of nanoparticle sample is 0.28 characteristic space units, then the benchmark value for complete dispersion state deviation is taken as 0.42 characteristic space units. The specific values ​​can be adjusted according to the dispersion stability of the sample and the detection accuracy requirements.

[0116] Furthermore, it also includes: The absolute value of the difference between the displacement magnitude at the current time point and the displacement magnitude at the previous time point is taken as the fluctuation amplitude of the displacement magnitude in the displacement vector sequence. When the fluctuation range of the displacement exceeds the preset fluctuation threshold, the subsequent acquisition time interval will be shortened to half of the initial acquisition time interval, and the shortest acquisition time interval will not be less than 10 seconds. When the fluctuation range of the displacement is less than the preset fluctuation threshold for three consecutive time points, the subsequent collection time interval will be extended to twice the initial collection time interval, and the longest collection time interval shall not exceed 1 hour. When calculating the reaggregation rate, the magnitude of each displacement vector is divided by the length of its corresponding time interval to obtain the displacement rate per unit time. The arithmetic mean of all displacement rates per unit time is then used as the reaggregation rate.

[0117] When the re-agglomeration rate is greater than or equal to the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, a hard agglomeration risk warning signal is generated. When the re-agglomeration rate is greater than or equal to the preset moderate threshold but less than the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, an intervention suggestion signal is generated.

[0118] In this embodiment, the previous time point refers to the previous collection time point before the current time point, excluding the case where the initial time point is used as the previous time point.

[0119] In this embodiment, the preset fluctuation threshold refers to a critical value for the magnitude of displacement fluctuation, pre-defined through experimental calibration. This critical value is used to determine whether the drastic change in the agglomeration state of nanoparticles reaches a level requiring adjustment of the sampling frequency. The threshold is determined by collecting multiple nanoparticle samples that slowly agglomerate under stable conditions, calculating the statistical distribution of the differences between adjacent displacement magnitudes in their displacement vector sequence, and using the 95th percentile of this statistical distribution as the preset fluctuation threshold. When the fluctuation amplitude of the displacement magnitude exceeds this threshold, it indicates a drastic change in the agglomeration state, requiring an increase in the sampling density.

[0120] In this embodiment, the preset heavy re-agglomeration threshold refers to a pre-set critical value for re-agglomeration rate determined experimentally, such as 80%. This critical value is used to determine whether the degree of re-agglomeration of nanoparticles has reached a heavy level. The threshold is determined as follows: multiple nanoparticle samples that have been verified by transmission electron microscopy to have undergone severe agglomeration are collected, and the re-agglomeration rate values ​​of these samples in the heavy agglomeration state are calculated. The lower limit or average value of these values ​​is multiplied by a safety factor to obtain the preset heavy re-agglomeration threshold. When the re-agglomeration rate is greater than or equal to this threshold, it is determined to be heavy re-agglomeration.

[0121] In this embodiment, the preset soft and hard thresholds refer to a pre-defined critical value for the aggregation structure characteristic index, determined experimentally. This critical value is used to distinguish between soft and hard aggregation types. The threshold is determined as follows: multiple nanoparticle samples, verified by transmission electron microscopy to belong to soft and hard aggregation respectively, are collected. The distribution ranges of the aggregation structure characteristic index for soft aggregation samples and hard aggregation samples are calculated. The boundary point between these two distribution ranges is used as the preset soft and hard thresholds. When the aggregation structure characteristic index is less than this threshold, it is determined to be a soft aggregation tendency; when the aggregation structure characteristic index is greater than or equal to this threshold, it is determined to be a hard aggregation tendency. An exemplary value for the preset soft and hard thresholds is 0.6. When the aggregation structure characteristic index is greater than or equal to 0.6, it is determined to be a hard aggregation tendency; when it is less than 0.6, it is determined to be a soft aggregation tendency.

[0122] In this embodiment, the preset moderate threshold refers to a pre-defined re-agglomeration rate critical value determined experimentally. This critical value is used to determine whether the degree of re-agglomeration of nanoparticles has reached a moderate level. The threshold is determined as follows: multiple nanoparticle samples that have been verified by transmission electron microscopy to have undergone significant agglomeration but have not yet reached a severe level are collected. The re-agglomeration rate range of these samples in a moderate agglomeration state is calculated. The lower limit of this range is used as the preset moderate threshold, and the upper limit is used as a reference for a severe threshold. When the re-agglomeration rate is greater than or equal to the preset moderate threshold and less than the preset severe threshold, it is determined to be moderate re-agglomeration. An exemplary value for the preset moderate threshold is 50%.

[0123] In this embodiment, when the fluctuation range of the displacement magnitude exceeds a preset fluctuation threshold, the subsequent acquisition time interval is shortened to half of the initial acquisition time interval, but the shortest acquisition time interval is not less than 10 seconds; when the fluctuation range of the displacement magnitude is less than the preset fluctuation threshold for three consecutive time points, the subsequent acquisition time interval is extended to twice the initial acquisition time interval, but the longest acquisition time interval does not exceed 1 hour. The initial acquisition time interval refers to the time interval set during the first acquisition, serving as the benchmark for all adjustments. It should be noted that when calculating the re-aggregation rate, since the acquisition time interval may change, the arithmetic mean of the displacement magnitudes cannot be simply taken. The specific processing method is as follows: the magnitude of each displacement vector is divided by its corresponding time interval length to obtain the displacement rate per unit time within that time interval, and the arithmetic mean of all displacement rates per unit time is taken as the re-aggregation rate. This processing method ensures that the unit of the re-aggregation rate is uniformly set to the feature space unit per second, eliminating the influence of time interval changes on the rate calculation.

[0124] The preset fluctuation threshold is determined by collecting multiple nanoparticle samples that slowly aggregate under stable conditions, calculating the absolute value of the difference between adjacent displacements in their displacement vector sequence, and using the 95th percentile value of the statistical distribution of these differences as the preset fluctuation threshold.

[0125] This invention provides an embodiment of a quantitative analysis system for the re-agglomeration phenomenon of nanomaterials, comprising: The multimodal data acquisition module is used to continuously acquire multimodal particle size distribution data at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The feature space mapping module is used to map the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space, obtain the feature points at each time point in the clustering feature space, and form the feature point trajectory. The evolution trend quantification module is used to calculate the displacement vector between feature points at adjacent time points based on the feature point trajectory, obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. The state deviation quantization module is used to calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and to calculate the re-aggregation rate based on the spatial distance; The structural feature quantification module is used to calculate the clustering structural feature index based on the location region of the feature point at the current time point in the clustering feature space. The quantitative index output module is used to output the re-agglomeration rate, re-agglomeration speed, and agglomeration structure characteristic index as quantitative analysis results of the re-agglomeration phenomenon of nanomaterials.

[0126] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of this invention and its equivalents, this invention also intends to include these modifications and variations.

Claims

1. A quantitative analysis method for the re-agglomeration phenomenon of nanomaterials, characterized in that, Includes the following steps: Multimodal particle size distribution data were continuously collected at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The multimodal particle size distribution data at each time point is mapped to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space, forming the feature point trajectory; Calculate the displacement vector between adjacent time points based on the feature point trajectory to obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. Calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and calculate the re-aggregation rate based on the spatial distance; Calculate the clustering structure characteristic index based on the location region of the feature point at the current time in the clustering feature space; The reagglomeration rate, reagglomeration speed, and agglomeration structure characteristic index are output as quantitative analysis results of the reagglomeration phenomenon of nanomaterials.

2. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 1, characterized in that, The multimodal particle size distribution data includes dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data. The dynamic light scattering particle size distribution data, laser particle size analysis particle size distribution data, and focused beam reflection measurement chord length distribution data are aligned according to the acquisition time points to form a multimodal particle size distribution time series.

3. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 2, characterized in that, Dynamic light scattering particle size distribution data is continuously acquired at preset time intervals by an in-situ detection probe embedded in the nanoparticle dispersion system. The in-situ detection probe integrates a dynamic light scattering sensor, a focused beam reflection measurement sensor, a temperature sensor, a pH sensor, a viscosity sensor, and an ionic strength sensor. The in-situ detection probe simultaneously acquires the temperature, pH, viscosity, and ionic strength parameters of the nanoparticle dispersion system as an environmental parameter sequence.

4. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 3, characterized in that, Before the step of mapping the multimodal particle size distribution data at each time point to the pre-constructed clustering feature space, the following steps are also included: The viscosity parameters at each time point are input into a pre-constructed viscosity shift correction function, which outputs a viscosity drift correction coefficient. The viscosity drift correction coefficient is then multiplied by the dynamic light scattering particle size distribution data at the corresponding time point to obtain the viscosity-corrected dynamic light scattering particle size distribution data. The ion intensity parameter at each time point is input into a pre-constructed ion intensity refractive index correction function, and the refractive index fluctuation correction coefficient is output. The refractive index fluctuation correction coefficient is multiplied with the dynamic light scattering particle size distribution data at the corresponding time point to obtain the dynamic light scattering particle size distribution data after ion intensity correction. The nanoparticle concentration parameters at each time point are input into a pre-constructed concentration multiple scattering correction function, which outputs a multiple scattering attenuation correction coefficient. The multiple scattering attenuation correction coefficient is then multiplied by the laser particle size distribution data at the corresponding time point to obtain the concentration-corrected laser particle size distribution data.

5. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 1, characterized in that, The clustering feature space is pre-constructed through the following steps: Multimodal particle size distribution data and corresponding transmission electron microscopy (TEM) morphology data of multiple nanoparticle samples were collected at different time points. Image segmentation and feature extraction were performed on each transmission electron microscope microstructure data to obtain the porosity parameter, pore connectivity parameter, and particle boundary clarity parameter of each nanoparticle sample at each time point. Based on the comprehensive evaluation of porosity parameters, pore connectivity parameters, and particle boundary clarity parameters, the true aggregation state category of each nanoparticle sample at each time point is determined. The true aggregation state categories include unaggregated state, soft aggregation state, and hard aggregation state. A deep neural network was trained using multimodal particle size distribution data at each time point as input features and the corresponding real aggregation state category as output label. The output space of the last hidden layer of the deep neural network is used as the clustering feature space.

6. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 5, characterized in that, The steps of mapping the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space to obtain the feature points at each time point in the clustering feature space include: The peak particle size, average particle size, and particle size distribution width are extracted from the dynamic light scattering particle size distribution data at each time point as three components of the dynamic light scattering feature vector, and combined to form the dynamic light scattering feature vector. The peak particle size, average particle size, and particle size distribution width are extracted from the laser particle size analysis particle size distribution data at each time point as three components of the laser particle size analysis feature vector, and combined to form the laser particle size analysis feature vector. The peak chord length, average chord length, and chord length distribution width are extracted from the focused beam reflection measurement chord length distribution data at each time point as three components of the focused beam reflection measurement feature vector, and combined to form the focused beam reflection measurement feature vector. The dynamic light scattering feature vector, the laser particle size analysis feature vector, and the focused beam reflection measurement feature vector are sequentially spliced ​​together to form a multimodal feature vector; The multimodal feature vector is input into a deep neural network. After transformation through multiple hidden layers, the coordinates of the feature point in the clustering feature space at that time point are output from the last hidden layer of the deep neural network. Connect the coordinates of all feature points at all time points in chronological order to form the feature point trajectory.

7. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 1, characterized in that, The displacement vector between adjacent time points is calculated based on the feature point trajectory to obtain a displacement vector sequence. The re-aggregation rate is then calculated based on the displacement vector sequence, including: Calculate the displacement vectors between adjacent time points in the feature point trajectory. Each displacement vector contains the displacement magnitude and displacement direction. The average value of all displacements in the displacement vector sequence is used as the re-agglomeration rate, and the unit of the re-agglomeration rate is matched with the unit of the acquisition time interval.

8. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 1, characterized in that, The steps for calculating the spatial distance between the feature point at the current time point and the feature point at the initial time point, and then calculating the re-aggregation rate based on the spatial distance, include: The time point corresponding to the initial stable state of the nanoparticle dispersion system is taken as the initial time point, and the coordinates of the initial feature point in the aggregation feature space are obtained. Calculate the Euclidean distance between the feature point coordinates at the current time point and the feature point coordinates at the initial time point, and use it as the current state deviation value; The current state deviation value is compared with the preset fully dispersed state deviation benchmark value, and the re-agglomeration rate is calculated. The re-agglomeration rate is calculated by dividing the current state deviation value by the preset fully dispersed state deviation benchmark value and then multiplying by 100%.

9. The method for quantitative analysis of nanomaterial re-agglomeration phenomenon according to claim 7, characterized in that, Also includes: The absolute value of the difference between the displacement magnitude at the current time point and the displacement magnitude at the previous time point is taken as the fluctuation amplitude of the displacement magnitude in the displacement vector sequence. When the fluctuation range of the displacement exceeds the preset fluctuation threshold, the sampling time interval will be shortened to half of the original interval. When the fluctuation amplitude of the displacement is less than the preset fluctuation threshold for three consecutive time points, the sampling time interval will be extended to twice the original interval. When the re-agglomeration rate is greater than or equal to the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, a hard agglomeration risk warning signal is generated. When the re-agglomeration rate is greater than or equal to the preset moderate threshold but less than the preset severe threshold and the agglomeration structure characteristic index is greater than or equal to the preset soft and hard thresholds, an intervention suggestion signal is generated.

10. A quantitative analysis system for the re-agglomeration phenomenon of nanomaterials, characterized in that, include: The multimodal data acquisition module is used to continuously acquire multimodal particle size distribution data at multiple time points in a nanoparticle dispersion system to obtain a multimodal particle size distribution time series. The feature space mapping module is used to map the multimodal particle size distribution data at each time point to a pre-constructed clustering feature space, obtain the feature points at each time point in the clustering feature space, and form the feature point trajectory. The evolution trend quantification module is used to calculate the displacement vector between feature points at adjacent time points based on the feature point trajectory, obtain the displacement vector sequence, and calculate the re-aggregation rate based on the displacement vector sequence. The state deviation quantization module is used to calculate the spatial distance between the feature point at the current time point and the feature point at the initial time point, and to calculate the re-aggregation rate based on the spatial distance; The structural feature quantification module is used to calculate the clustering structural feature index based on the location region of the feature point at the current time point in the clustering feature space. The quantitative index output module is used to output the re-agglomeration rate, re-agglomeration speed, and agglomeration structure characteristic index as quantitative analysis results of the re-agglomeration phenomenon of nanomaterials.

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