A multi-angle dynamic light scattering particle measurement method and analysis system

Abstract

The application belongs to the technical field of optical measurement, and particularly relates to a multi-angle dynamic light scattering particle measurement method and an analysis system. The method comprises the following steps: S1, loading a sample to be measured and completing system initialization, and configuring space-time scanning basic parameters; S2, collecting scattering light intensity signals and light intensity autocorrelation functions corresponding to each space-time micro area to obtain original measurement data; S3, performing noise reduction and baseline correction preprocessing on the original measurement data, and analyzing to obtain apparent fluid dynamic particle diameters and average scattering light intensities of each space-time micro area, and constructing a data matrix in the space-time dimension; S4, taking dynamic light scattering theory and a sedimentation kinetics equation as double physical constraints, performing global fitting on full space-time dimension data to obtain a true particle size distribution and a sedimentation coefficient distribution after correction of sedimentation deviation; and S5, based on the true particle size and the sedimentation coefficient, and in combination with viscosity and density parameters of a dispersion medium, calculating to obtain particle effective density and a sample sedimentation stability index.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, specifically relating to a multi-angle dynamic light scattering particle measurement method and analysis system. Background Technology

[0002] Dynamic light scattering (DLS) is a mainstream technique for characterizing the size of nano- and submicron-sized particles. It is based on the principle of scattered light intensity fluctuations caused by Brownian motion of particles, and obtains the hydrodynamic particle size distribution by analyzing the light intensity autocorrelation function. However, with the expansion of application scenarios, existing DLS techniques have revealed three significant shortcomings in the measurement of complex systems:

[0003] In actual measurements, when the sample particles are large, have a high concentration, or have a density that differs significantly from the dispersion medium, the particles will settle significantly under the influence of gravity. This causes the sample concentration in the measurement area to change dynamically over time and space, which undermines the traditional DLS measurement premise of "uniform and stable system". Ultimately, this results in distorted particle size measurement results and poor data repeatability.

[0004] To address this issue, existing solutions mainly fall into two categories: one is to reduce the concentration by diluting the sample or to maintain the uniformity of the system by mechanical stirring, thereby avoiding the sedimentation effect. However, dilution will change the original aggregation state of the sample, and stirring will introduce external interference, neither of which can reflect the intrinsic characteristics of the sample. The other category is to use analytical centrifugation to measure sedimentation characteristics separately. However, such equipment is complex in structure, expensive, and cannot obtain accurate particle size distribution parameters at the same time, making it difficult to achieve correlation analysis between particle size and sedimentation characteristics. Summary of the Invention

[0005] To address the aforementioned shortcomings in the existing technology, this invention provides a multi-angle dynamic light scattering particle measurement method and analysis system to solve the problems mentioned in the background technology.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for measuring dynamic light scattering particles from multiple angles includes the following steps;

[0008] S1 loads the sample to be tested and completes system initialization, configuring the basic parameters for spatiotemporal scanning;

[0009] S2 performs dynamic light scattering measurements on micro-regions at different heights within the sample cell at different time points, collects the scattered light intensity signal and light intensity autocorrelation function corresponding to each spatiotemporal micro-region, and obtains the raw measurement data in the two-dimensional time-space dimension.

[0010] S3 performs noise reduction and baseline correction preprocessing on the raw measurement data, analyzes the apparent hydrodynamic particle size and average scattered light intensity of each spatiotemporal micro-region, and constructs a spatiotemporal data matrix.

[0011] S4 uses dynamic light scattering theory and sedimentation dynamics equation as dual physical constraints to establish a coupled mathematical model of particle size-sedimentation coefficient-light intensity distribution. It then performs global fitting and solution on data in all time and space dimensions to obtain the true particle size distribution and sedimentation coefficient distribution after correcting for sedimentation deviation.

[0012] S5 calculates the effective particle density and sample sedimentation stability index based on the actual particle size and sedimentation coefficient, combined with the viscosity and density parameters of the dispersion medium.

[0013] S6 outputs and stores all measurement results.

[0014] Further, step S2 includes;

[0015] S21 generates displacement control timing based on the selected scanning mode, and establishes a synchronous triggering association between the displacement stage movement and the digital correlator acquisition.

[0016] When the S22 adopts step scanning, the control displacement stage steps sequentially to each preset measurement height. After the displacement stabilizes, the digital correlator is triggered to complete the acquisition of the scattered light intensity signal and the calculation of the autocorrelation function of a single point. After all height points are measured, the next scanning cycle begins.

[0017] When S23 uses continuous scanning, the control displacement stage moves at a preset constant speed along the vertical direction at a uniform speed, and synchronously triggers the digital correlator to continuously collect data in segments at fixed time intervals. Each segment of collected data corresponds to a measurement micro-area in a height range.

[0018] S24 labels each set of collected data with the corresponding measurement height coordinates and measurement timestamp, and stores them according to the height dimension and time dimension to form a two-dimensional original dataset in time and space.

[0019] Further, step S3 includes;

[0020] S31 performs noise reduction on the original photon counting timing signal, performs baseline correction on the light intensity autocorrelation function, and takes the mean value of the autocorrelation function in the long delay interval as the baseline value for normalization correction.

[0021] S32 performs inversion analysis on the corrected light intensity autocorrelation function to obtain the apparent hydrodynamic particle size distribution of the corresponding spatiotemporal micro-region, and statistically analyzes the average scattered light intensity value during the measurement period.

[0022] Furthermore, step S3 also includes;

[0023] The apparent hydrodynamic particle size and average scattered light intensity of each spatiotemporal microregion are associated with their corresponding height coordinates and timestamps, and arranged in rows by height and columns by time to construct a spatiotemporal data matrix.

[0024] Further, step S4 includes;

[0025] S41 is based on dynamic light scattering theory and establishes the correspondence between real fluid dynamics particle size and particle diffusion coefficient through the Stokes-Einstein equation;

[0026] The relationship between particle settling velocity and particle size and effective particle density is established based on Stokes' law of settling.

[0027] The evolution of particle concentration with height and time is described based on the Mason-Weaver sedimentation-diffusion equation. At the same time, the scattered light intensity is set to be linearly positively correlated with the local particle concentration, thus constructing a closed-loop coupled physical model of "true particle size-diffusion coefficient-sedimentation velocity-concentration distribution-light intensity distribution".

[0028] Furthermore, the expression for Stokes' law of settling is: In the formula, Let g be the particle settling velocity, and g be the acceleration due to gravity. The effective density of the particles, Let d be the density of the dispersion medium and d be the actual hydrodynamic particle size. To determine the viscosity of the dispersing medium;

[0029] The Mason-Weaver sedimentation-diffusion equation is expressed as follows: In the formula, Let be the particle concentration at height z at time t, and D be the particle diffusion coefficient; the scattered light intensity and concentration satisfy... , where k is the light intensity proportionality coefficient.

[0030] Furthermore, step S4 also includes;

[0031] S42 constructs a global fitting objective function: taking the true particle size distribution function and effective particle density as the core parameters to be optimized, the measured data of all points in the spatiotemporal data matrix are used as the fitting benchmark, the particle size residual and light intensity residual are calculated respectively, and the total residual sum of squares objective function is constructed by weighted summation.

[0032] Furthermore, the objective function expression for the sum of squared residuals is: In the formula, These represent the theoretical apparent particle size and theoretical scattered light intensity at height m and time point n, respectively. The measured apparent particle size and measured light intensity at the corresponding points are respectively. These are the weighting coefficients for particle size residual and light intensity residual, respectively.

[0033] Further, step S5 includes;

[0034] Based on the actual hydrodynamic particle size and corresponding settling velocity obtained by iterative solution, and combined with the known viscosity and density parameters of the dispersion medium, S51 modifies Stokes' sedimentation law and reverse-derives the effective density of the particles. For monodisperse systems, the average effective density is calculated by directly substituting the average particle size and average settling velocity. For polydisperse systems, the effective density of particles in each particle size range is obtained by substituting the corresponding settling velocity, thus forming an effective density distribution.

[0035] The calculation formula is derived from a modification of Stokes' law of settlement: In the formula, The effective density of the particles, Here, d represents the particle settling velocity corresponding to the particle size, d is the actual hydrodynamic particle size, and g is the acceleration due to gravity. To disperse the viscosity of the medium, The density of the dispersion medium.

[0036] Furthermore, step S5 also includes;

[0037] S52 calculates the sample sedimentation stability index: based on the spatial distribution of scattered light intensity at each moment in the spatiotemporal data matrix, the suspension stability of the sample is characterized by quantifying the degree of stratification of light intensity in the sample cell.

[0038] Light intensity distribution data at the initial time and the set measurement endpoint are selected. The relative standard deviation of light intensity within the effective measurement height of the sample cell at both times is calculated. The ratio of these two values ​​is used as the settling stability index. The calculation formula is as follows: In the formula, SI is the settlement stability index. The values ​​represent the standard deviations of the scattered light intensity within the effective measurement height at the initial time and time t, respectively. The values ​​represent the average scattered light intensity within the effective measurement height at the initial time and time t, respectively.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. This solution acquires two-dimensional light scattering measurement data in time and space through vertical scanning. The dynamic light scattering theory and sedimentation dynamics equations form a coupled model with dual physical constraints. The decoupling of sedimentation motion and Brownian motion is achieved through global fitting solution. This can correct the apparent particle size distortion caused by sedimentation effect and obtain the true hydrodynamic particle size distribution of particles. This solves the industry pain point of traditional dynamic light scattering technology for measuring easily sedimentable particles with overly large and inaccurate results.

[0041] 2. This method eliminates the need for pretreatment operations such as dilution and stirring of the sample to be tested. It can directly measure the sample at its original concentration, completely preserving the original dispersion state and sedimentation behavior of the sample. The measurement process does not disrupt the physicochemical equilibrium of the sample system, and the measured particle size and sedimentation characteristics are more consistent with the actual application state of the sample. It avoids the problems of particle agglomeration and sedimentation characteristic distortion caused by pretreatment steps such as dilution and ultrasonication in traditional methods.

[0042] 3. Based on spatiotemporal two-dimensional data and global coupled calculation, this scheme can distinguish the sedimentation coefficients and sedimentation behaviors of different particle size components in polydisperse systems, breaking through the limitation of traditional sedimentation analysis methods that can only obtain the overall average sedimentation rate of the system; it can accurately characterize the stratified sedimentation process of complex polydisperse samples, providing more refined data support for the stability assessment of colloidal and suspension systems. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating a multi-angle dynamic light scattering particle measurement method according to the present invention.

[0044] Figure 2 This is a schematic diagram illustrating the process of forming the original measurement data in this invention;

[0045] Figure 3 This is a schematic diagram of the process for constructing the data matrix in this invention;

[0046] Figure 4 This is a flowchart illustrating step S4 of the present invention. Detailed Implementation

[0047] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0048] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual images. They should not be construed as limiting the scope of this application. To better illustrate the embodiments of the present invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0049] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "inner," and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present application. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0050] In the description of this invention, unless otherwise explicitly specified and limited, the term "connection" or similar designation indicating a connection between components should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0051] In practical measurements, when sample particles are large, have high concentrations, or their density differs significantly from that of the dispersion medium, the particles will settle noticeably under gravity. This causes the sample concentration within the measurement area to dynamically change over time and space, violating the traditional DLS measurement premise of "uniform and stable system." Ultimately, this results in distorted particle size measurement results and poor data repeatability. To address this, we offer the following solution.

[0052] Example 1:

[0053] like Figures 1-4 As shown, specifically, this invention provides a method for measuring multi-angle dynamic light scattering particles, comprising the following steps:

[0054] S1 loads the sample to be tested and completes system initialization, configures the basic parameters for spatiotemporal scanning, and completes optical path alignment and hardware parameter settings before measurement.

[0055] Specifically, this includes: S11 injecting the sample to be tested into the sample cell and placing it at the loading position of the vertical electric displacement stage;

[0056] S12 sets the measurement temperature and completes the configuration of operating parameters for the laser source and digital correlator;

[0057] The configuration of laser source operating parameters refers to the preset settings for laser output state and stability conditions. Example configurations include: Output wavelength: Select a fixed output wavelength of 633nm (helium-neon laser) or 532nm (solid-state laser) to match the scattering characteristics of the sample under test; Output power: Set the laser output power to 10mW; Preheating and temperature control: Set the laser source preheating time to 15min and turn on the built-in temperature control module to ensure stable output wavelength and power.

[0058] The configuration of operating parameters for a digital correlator refers to the preset settings for correlation operation rules and sampling acquisition modes. Example configurations include: correlation channels and delay range, sampling clock and counting mode, and single accumulation duration.

[0059] S13 adjusts the relative positions of the incident light path and the scattered light detection light path to complete the initial light path alignment of the scattering center;

[0060] S14 sets the number of measurement height points, single-point measurement duration, and scan cycle count. The standard setting for the number of measurement height points is based on the effective measurement height of the sample cell, the resolution requirements of the sedimentation concentration gradient, and the intensity of spatial changes in particle sedimentation. Specific requirements are as follows: Boundary constraints: The measurement height range should avoid the liquid surface tension zone and the bottom wall effect zone. Generally, an invalid interval of 2-3 mm is reserved at the top and bottom, and points are only placed within the effective measurement height in the middle of the sample cell; Spacing constraints: The spacing between adjacent measurement heights should ensure that the difference in scattered light intensity between the two points can be significantly distinguished. The standard setting is 2-5 mm. For samples with faster sedimentation rates and wider particle size distributions, the height spacing should be smaller and the number of points should be more; Quantification reference: For a conventional sample cell with an effective measurement height of 20 mm, 3-8 measurement height points are generally set. For samples with severe sedimentation and obvious concentration stratification, the number of measurement height points can be increased to 8-12 to ensure the accuracy of concentration gradient fitting in the spatial dimension.

[0061] The standard setting for single-site measurement duration is based on the signal-to-noise ratio (SNR) requirement of the DLS autocorrelation function, the Brownian motion rate of particles, and the tolerance for concentration changes within a single site. Specific requirements are as follows: SNR constraint: Sufficient photons must be available during the measurement period, the autocorrelation function baseline must be stable, and statistical noise must be below 1% to ensure the reliability of particle size resolution. Larger particle sizes and weaker scattered light require longer measurement durations. Sedimentation interference constraint: Within the single-site measurement duration, the concentration change caused by particle sedimentation in the micro-region must be controlled within 5% to avoid significant sedimentation during the single-site measurement process, which could lead to apparent particle size distortion. Quantization reference: For nanoscale particles of 10–100 nm, the single-site measurement duration is typically set to 10–30 s; for submicron particles of 100 nm–1 μm, it is typically set to 30–60 s. For large-diameter samples that are prone to sedimentation, the single-site duration should be shortened as much as possible while ensuring the SNR. The overall SNR can be improved through multiple cycles of accumulation.

[0062] The standard for setting the number of scanning cycles is based on the sample sedimentation rate, the fitting accuracy requirements of the sedimentation kinetics process, and the upper limit of the total measurement time. Specific requirements are as follows: Process coverage constraint: The total measurement time (single cycle time × number of cycles) must cover the observable sedimentation changes, ensuring that the difference in light intensity between the first and last samples at the end of the measurement is ≥10%, ensuring that sedimentation kinetic characteristics can be effectively captured; Fitting accuracy constraint: The number of sampling points in the time dimension must meet the fitting degrees of freedom requirements of the Mason-Weaver equation. Too few cycles will lead to excessively large fitting errors in the sedimentation coefficient; Quantification reference: For micron-sized particle samples with fast sedimentation rates, 5-10 cycles are typically set, with a total measurement time controlled between 10-30 minutes; for submicron-sized colloidal systems with slow sedimentation rates, 10-20 cycles are typically set, with a total measurement time between 30-120 minutes; for samples with extremely high stability, the number of cycles can be appropriately increased to accumulate a higher amount of time dimension data.

[0063] The S2-driven high-precision vertical electric displacement stage scans along the vertical direction in a preset mode, performing dynamic light scattering measurements on micro-regions at different heights within the sample cell at different time points. It collects the scattered light intensity signal and light intensity autocorrelation function corresponding to each spatiotemporal micro-region, obtaining the original measurement data in the two-dimensional time-space dimension.

[0064] The scattered light intensity signal refers to the time-domain photon count signal output by the photomultiplier tube in the scattered light detection module after photoelectric conversion of the scattered light from particles in the measurement micro-region. It reflects the instantaneous intensity change of the scattered light from particles in the micro-region at a specific time and height. By statistically analyzing the signal during the measurement period, the average scattered light intensity of the micro-region can be obtained, which is used to characterize the particle concentration change at the corresponding location.

[0065] The light intensity autocorrelation function refers to the normalized function obtained by performing a second-order autocorrelation operation on the scattered light intensity signal using a digital correlator. ,in The delay time is denoted by ; this function characterizes the time correlation of scattered light intensity fluctuations, and its decay rate is directly related to the diffusion coefficient of the Brownian motion of the particles.

[0066] The original measurement data specifically refers to multiple sets of basic measurement data marked in a one-to-one correspondence between measurement time and measurement height, including: original photon counting time-series data output by the photomultiplier tube, second-order normalized light intensity autocorrelation function data generated by the digital correlator, vertical height coordinate data corresponding to each measurement point, and sample temperature data at the measurement time. After the high-precision vertical electric displacement stage moves to the target measurement height and stabilizes, the scattered light detection module receives the scattered light from the particles in the corresponding micro-region, performs photoelectric conversion by the photomultiplier tube, and outputs the original photon counting time-series signal corresponding to the scattered light intensity; the digital correlator receives this time-series signal and generates a second-order light intensity autocorrelation function through multi-channel delay correlation operation; the position code of the displacement stage is read simultaneously to obtain the current measurement height coordinates, and the temperature sensor data is collected to obtain the current sample temperature; the above data are associated and marked with the corresponding measurement timestamps, and after the collection of all spatiotemporal points is completed, a two-dimensional original measurement dataset in time and space is formed.

[0067] Specifically, this includes: S21 generating displacement control timing based on the selected scanning mode, and establishing a synchronous triggering association between the displacement stage movement and the digital correlator acquisition;

[0068] Example of synchronous triggering in step-scan mode: Timing generation: Based on the preset number of measurement height points, the spacing between adjacent heights, the movement speed of the displacement stage, and the measurement duration per point, a periodic timing sequence of "displacement movement—position stabilization—data acquisition—next displacement" is generated, with each height point corresponding to an independent timing unit. Trigger association: The host computer sends a target height command to the controller of the vertical electric displacement stage. After the displacement stage moves to the target height and the vibration is eliminated, the controller outputs a "ready in position" level signal. This level signal is directly connected to the external trigger port of the digital correlator as a data acquisition start signal, triggering the digital correlator to start counting the scattered light intensity and calculating the autocorrelation function at that point. After the single-point acquisition duration ends, the digital correlator outputs a "acquisition completed" feedback signal to the displacement stage controller, triggering the displacement stage to move to the next height point.

[0069] Example of synchronous triggering in continuous scan mode

[0070] Timing generation: Based on the preset uniform motion speed of the displacement stage and the single-segment data acquisition duration, a continuous segmented acquisition timing sequence with equal time intervals is generated, with each time segment corresponding to a height interval within the sample cell.

[0071] Triggering association: The host computer sends a uniform motion command to the displacement stage. After the displacement stage reaches the set speed, it outputs a "uniform speed start" synchronization pulse to the digital correlator. The digital correlator takes this pulse as the time zero point and automatically triggers segmented acquisition at preset time intervals. After each segment acquisition is completed, it automatically calculates the autocorrelation function of that segment and converts the corresponding measurement height according to the motion speed and time difference, thus completing the binding of data with spatial position.

[0072] When the S22 adopts step scanning, the control displacement stage steps sequentially to each preset measurement height. After the displacement stabilizes, the digital correlator is triggered to complete the acquisition of the scattered light intensity signal and the calculation of the autocorrelation function of a single point. After all height points are measured, the next scanning cycle begins.

[0073] When S23 uses continuous scanning, the control displacement stage moves at a preset constant speed along the vertical direction at a uniform speed, and synchronously triggers the digital correlator to continuously collect data in segments at fixed time intervals. Each segment of collected data corresponds to a measurement micro-area in a height range.

[0074] S24 labels each set of collected data with the corresponding measurement height coordinates and measurement timestamp, and stores them according to the height dimension and time dimension to form a two-dimensional original dataset in time and space.

[0075] S3 performs noise reduction and baseline correction preprocessing on the raw measurement data, analyzes the apparent hydrodynamic particle size and average scattered light intensity of each spatiotemporal micro-region, and constructs a spatiotemporal data matrix.

[0076] Specifically, this includes: S31 performs noise reduction processing on the original photon counting timing signal, eliminating dark counting noise and abnormal pulse spikes, while performing baseline correction on the light intensity autocorrelation function, taking the mean value of the autocorrelation function in the long delay interval as the baseline value for normalization correction, and eliminating DC offset interference.

[0077] First, noise reduction is performed on the original photon counting time-series signal: Background signals from the photomultiplier tube are pre-collected under no-light-incident conditions, the dark count rate is statistically obtained, and a dark count threshold is set. Basis noise components below the threshold in the time-series signal are removed. A sliding window with a width of 50-200 sampling points is used to traverse the entire time-series signal. The arithmetic mean of the photon counts within each window is calculated. Abnormal pulse spikes with count amplitudes exceeding three standard deviations of the window's average are replaced with the mean of adjacent valid data within the window, completing the time-domain signal noise reduction. Next, baseline correction is performed on the light intensity autocorrelation function: A long-delay channel interval with a delay time greater than 10 times the Brownian relaxation time of the particles is selected, typically from the last 20% of the channels in the autocorrelation function. The arithmetic mean of the autocorrelation function within this interval is calculated as the baseline value. The normalization correction for the entire delay interval is performed using the following formula: In the formula, This is the original second-order autocorrelation function of light intensity. The corrected normalized autocorrelation function is shown below. The autocorrelation function value at the long delay converges to 1 after correction, eliminating the baseline deviation caused by the system's DC offset and light intensity drift.

[0078] S32 performs inversion analysis on the corrected light intensity autocorrelation function to obtain the apparent hydrodynamic particle size distribution of the corresponding spatiotemporal micro-region, and at the same time, it statistically analyzes the average scattered light intensity value during the measurement period.

[0079] An example is given of establishing the relationship between diffusion coefficient and hydrodynamic particle size based on the Stokes-Einstein equations. The cumulant method or the CONTIN regularization algorithm is then used to invert and analyze the corrected autocorrelation function. The fundamental physical relationships of dynamic light scattering are as follows: the second-order light intensity autocorrelation function and the first-order electric field autocorrelation function... Satisfying the Siegert relation: In the formula The coherence coefficient is determined by the optical path coherence and the area of ​​the detector spot; the attenuation linewidth... The particle diffusion coefficient D satisfies: The formula for calculating the scattering vector q is: In the formula, n is the refractive index of the dispersion medium. Laser wavelength in vacuum To detect the scattering angle; the particle diffusion coefficient and the hydrodynamic particle size satisfy the Stokes-Einstein equation: In the formula Where is Boltzmann's constant, and T is the thermodynamic temperature. To disperse the viscosity of the medium, The particle size is determined by fluid dynamics.

[0080] When using the cumulant method for analysis, the logarithm of the first-order autocorrelation function is taken and then expanded into a polynomial: The first-order cumulant is solved by fitting. The average attenuation linewidth is obtained, and substituted into the above formula to calculate the Z-mean apparent hydrodynamic particle size; the second-order cumulant is then used to calculate the average attenuation linewidth. Calculate the multi-dispersion index When using the CONTIN algorithm for analysis, the regularization coefficient is set to 0.01~0.1. Under non-negative constraints, the first kind of Fredholm integral equation is solved through regularized inversion to obtain a continuous attenuation linewidth distribution. After particle size conversion, the apparent particle size distribution is output, including intensity distribution, number distribution, and volume distribution. Simultaneously, the arithmetic mean of the denoised photon counting time-series signal is performed to obtain the average photon count rate within the measurement period, which is used as the average scattered light intensity value of the corresponding micro-region. In the formula Let N be the photon count at the i-th sampling time, and N be the total number of sampling points. The average scattered light intensity of this micro-region is given.

[0081] S33 associates the apparent hydrodynamic particle size, average scattered light intensity, and corresponding height coordinates and timestamps of each spatiotemporal micro-region, arranging them as rows of height and columns of time to construct a spatiotemporal data matrix.

[0082] For example, rows are arranged in ascending order of height value, with the measured height as the row dimension. The total number of rows equals the preset number of measured height points M. Columns are arranged in chronological order of measurement time, with the total number of columns equal to the number of scan loops N. A two-dimensional spatiotemporal data matrix is ​​constructed. Its expression is:

[0083] The apparent hydrodynamic particle size parameters and average scattered light intensity values ​​of each spatiotemporal microregion are matched one by one with the corresponding height coordinates and timestamps, and then filled into the corresponding positions in the matrix; each element in the matrix The structured data at the m-th height and n-th time point are stored, including the average scattered light intensity, Z-mean apparent particle size, polydispersity index, apparent particle size distribution array, measured temperature, and single-point measurement duration. The resulting M-row × N-column two-dimensional spatiotemporal data matrix serves as the input dataset for subsequent collaborative solution.

[0084] S4 uses dynamic light scattering theory and sedimentation dynamics equation as dual physical constraints to establish a coupled mathematical model of particle size-sedimentation coefficient-light intensity distribution. It performs global fitting and solution on data in all time and space dimensions to obtain the true particle size distribution and sedimentation coefficient distribution after correcting sedimentation deviation, thus eliminating particle size measurement distortion caused by sedimentation effect.

[0085] Specifically, it includes;

[0086] S41 constructs a coupled mathematical model with dual physical constraints: Based on dynamic light scattering theory, the correspondence between real hydrodynamic particle size and particle diffusion coefficient is established through the Stokes-Einstein equation; the correspondence between particle settling velocity and particle size and effective particle density is established based on Stokes' sedimentation law; the evolution of particle concentration with height and time is described based on the Mason-Weaver settling-diffusion equation, while setting a linear positive correlation between scattered light intensity and local particle concentration, ultimately constructing a closed-loop coupled physical model of "real particle size - diffusion coefficient - settling velocity - concentration distribution - light intensity distribution"; the expression of Stokes' sedimentation law is: In the formula, Let g be the particle settling velocity, and g be the acceleration due to gravity. The effective density of the particles, Let d be the density of the dispersion medium and d be the actual hydrodynamic particle size. Let be the viscosity of the dispersion medium; the Mason-Weaver sedimentation-diffusion equation is expressed as: In the formula, Let be the particle concentration at height z at time t, and D be the particle diffusion coefficient; the scattered light intensity and concentration satisfy... , where k is the light intensity proportionality coefficient.

[0087] S42 constructs the objective function for global fitting: using the true particle size distribution function and effective particle density as the core parameters to be optimized, and taking the measured data of all points in the spatiotemporal data matrix as the fitting benchmark, the particle size residual and light intensity residual are calculated respectively. A weighted summation is then used to construct the objective function of the total residual sum of squares, expressed as: In the formula, These represent the theoretical apparent particle size and theoretical scattered light intensity at height m and time point n, respectively. The measured apparent particle size and measured light intensity at the corresponding points are respectively. These are the weighting coefficients for particle size residual and light intensity residual, respectively.

[0088] S43 employs a nonlinear iterative algorithm for global solution: inputting initial estimates of particle size distribution and initial density values, and using the Levenberg-Marquardt nonlinear least squares algorithm for iterative optimization; in each iteration, updating the calculation results of the coupled model based on the current parameters to be optimized, simultaneously calculating the total residual and parameter update step size, and continuously correcting the true particle size distribution and effective density parameters; when the total residual is less than the preset convergence threshold or the number of iterations reaches the preset upper limit, the iteration stops.

[0089] S44 outputs the corrected parameter distribution: After iterative convergence, it outputs the true hydrodynamic particle size distribution that eliminates sedimentation interference, as well as the sedimentation coefficient distribution that corresponds one-to-one with each particle size interval, thus completing the correction of particle size measurement deviation caused by sedimentation effect.

[0090] S5 calculates the effective particle density and sample sedimentation stability index based on the actual particle size and sedimentation coefficient, combined with the viscosity and density parameters of the dispersion medium. It can simultaneously achieve multi-parameter characterization of particle size and sedimentation characteristics without diluting or stirring the sample; specifically including:

[0091] S51 Calculation of Effective Particle Density: Based on the actual hydrodynamic particle size and corresponding settling velocity obtained through iterative solutions, combined with the known viscosity and density parameters of the dispersion medium, Stokes' sedimentation law is modified, and the effective particle density is calculated by reverse derivation. For monodisperse systems, the average particle size and average settling velocity are directly substituted to calculate the average effective density. For polydisperse systems, the corresponding settling velocities are substituted for each particle size interval to obtain the effective particle density for each interval, forming an effective density distribution. The calculation formula is derived from a modification of Stokes' sedimentation law. In the formula, The effective density of the particles, Here, d represents the particle settling velocity corresponding to the particle size, d is the actual hydrodynamic particle size, and g is the acceleration due to gravity. To disperse the viscosity of the medium, The density of the dispersion medium.

[0092] S52 calculates the sample sedimentation stability index: Based on the spatial distribution of scattered light intensity at each moment in the spatiotemporal data matrix, the suspension stability of the sample is characterized by quantifying the stratification of light intensity within the sample cell; light intensity distribution data at the initial moment and the set measurement endpoint are selected, and the relative standard deviation of light intensity within the effective measurement height of the sample cell at the two moments is calculated. The ratio of the two is used as the sedimentation stability index. The calculation formula is as follows: In the formula, SI is the settlement stability index. The values ​​represent the standard deviations of the scattered light intensity within the effective measurement height at the initial time and time t, respectively. The values ​​represent the average scattered light intensity within the effective measurement height at the initial time and time t, respectively. The larger the sedimentation stability index value, the more significant the sample concentration stratification, the faster the sedimentation rate, and the worse the suspension stability.

[0093] S6 outputs and stores all measurement results.

[0094] Specifically, the system visualizes the measurement results through a host computer interface, automatically generating standardized test reports. The output includes: the true hydrodynamic particle size distribution after sedimentation correction, covering intensity distribution, quantity distribution, and volume distribution, as well as core characteristic parameters such as Z-mean particle size, peak particle size, and polydispersity index; sedimentation coefficient distribution curves and characteristic sedimentation coefficient values; effective particle density values ​​or effective density distribution across different particle size ranges; and sedimentation stability index. Simultaneously, it displays the global fitting residual, measurement environment temperature, dispersion medium parameters, and scan configuration parameters. The report supports exporting to common formats such as PDF and Excel, and can be directly used for sample analysis and quality recording.

[0095] On the other hand, it completes the archiving and storage of data throughout the entire process. The stored content includes: the original scattered light intensity time series signal and the original light intensity autocorrelation function data of each spatiotemporal microregion, the preprocessed spatiotemporal data matrix, the iterative parameters and intermediate results of the collaborative solution process, and all characterization parameters of the final output; the stored data is saved in a structured format, supporting historical data backtracking, retrieval, and secondary analysis.

[0096] This invention also provides a multi-angle dynamic light scattering particle measurement and analysis system for implementing the above-mentioned measurement method. The system includes a laser source, an incident light path module, a sample cell, a scattered light detection module, a digital correlator, and a host computer processing unit. It also includes a vertical scanning drive unit and a collaborative solution unit. The vertical scanning drive unit includes a high-precision vertical electric displacement stage, which carries the sample cell or the scattered light detection module and moves in a stepping or continuous manner along the vertical direction to perform dynamic light scattering measurements on micro-regions at different heights within the sample cell, acquiring raw measurement data in a two-dimensional time-space dimension. The collaborative solution unit, embedded in the host computer processing unit, is configured to: analyze the autocorrelation function of light intensity in each spatiotemporal micro-region to obtain the apparent hydrodynamic particle size; combine the spatiotemporal evolution law of scattered light intensity; establish a coupled model using dynamic light scattering theory and sedimentation dynamics equations as dual physical constraints; obtain the true particle size distribution after correcting sedimentation deviation through global fitting; and simultaneously output the sedimentation coefficient distribution, effective particle density, and sample sedimentation stability index.

[0097] The above are merely embodiments of the present invention. The circuits, electronic components, and modules involved are all prior art, fully achievable by those skilled in the art, and require no further explanation. The scope of protection in this application does not involve improvements to the software and methods. Commonly known structures and characteristics in the solutions are not described in detail here. Those skilled in the art are aware of all common technical knowledge in the field prior to the application date or priority date, are aware of all prior art in that field, and have the ability to apply conventional experimental methods prior to that date. Those skilled in the art can, under the guidance of this application, improve and implement this solution in combination with their own capabilities. Some typical known structures or methods should not be obstacles for those skilled in the art to implement this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the structure of the present invention. These should also be considered within the scope of protection of the present invention, and will not affect the effectiveness of the implementation of the present invention or the practicality of the application.

Claims

1. A method for measuring multi-angle dynamic light scattering particles, characterized in that... Includes the following steps: S1 loads the sample to be tested and completes system initialization, configuring the basic parameters for spatiotemporal scanning; S2 performs dynamic light scattering measurements on micro-regions at different heights within the sample cell at different time points, collects the scattered light intensity signal and light intensity autocorrelation function corresponding to each spatiotemporal micro-region, and obtains the raw measurement data in the two-dimensional time-space dimension. S3 performs noise reduction and baseline correction preprocessing on the raw measurement data, analyzes the apparent hydrodynamic particle size and average scattered light intensity of each spatiotemporal micro-region, and constructs a spatiotemporal data matrix. S4 uses dynamic light scattering theory and sedimentation dynamics equation as dual physical constraints to establish a coupled mathematical model of particle size-sedimentation coefficient-light intensity distribution. It then performs global fitting and solution on data in all time and space dimensions to obtain the true particle size distribution and sedimentation coefficient distribution after correcting for sedimentation deviation. S5 calculates the effective particle density and sample sedimentation stability index based on the actual particle size and sedimentation coefficient, combined with the viscosity and density parameters of the dispersion medium. S6 outputs and stores all measurement results.

2. The method for measuring multi-angle dynamic light scattering particles as described in claim 1, characterized in that... Step S2 includes: S21 generates displacement control timing based on the selected scanning mode, and establishes a synchronous triggering association between the displacement stage movement and the digital correlator acquisition. When the S22 adopts step scanning, the control displacement stage steps sequentially to each preset measurement height. After the displacement stabilizes, the digital correlator is triggered to complete the acquisition of the scattered light intensity signal and the calculation of the autocorrelation function of a single point. After all height points are measured, the next scanning cycle begins. When S23 uses continuous scanning, the control displacement stage moves at a preset constant speed along the vertical direction at a uniform speed, and synchronously triggers the digital correlator to continuously collect data in segments at fixed time intervals. Each segment of collected data corresponds to a measurement micro-area in a height range. S24 labels each set of collected data with the corresponding measurement height coordinates and measurement timestamp, and stores them according to the height dimension and time dimension to form a two-dimensional original dataset in time and space.

3. The method for measuring multi-angle dynamic light scattering particles as described in claim 2, characterized in that... Step S3 includes: S31 performs noise reduction on the original photon counting timing signal, performs baseline correction on the light intensity autocorrelation function, and takes the mean value of the autocorrelation function in the long delay interval as the baseline value for normalization correction. S32 performs inversion analysis on the corrected light intensity autocorrelation function to obtain the apparent hydrodynamic particle size distribution of the corresponding spatiotemporal micro-region, and statistically analyzes the average scattered light intensity value during the measurement period.

4. The method for measuring multi-angle dynamic light scattering particles as described in claim 3, characterized in that... Step S3 further includes: S33 associates the apparent hydrodynamic particle size, average scattered light intensity, and corresponding height coordinates and timestamps of each spatiotemporal micro-region, arranging them as rows of height and columns of time to construct a spatiotemporal data matrix.

5. The method for measuring multi-angle dynamic light scattering particles as described in claim 1, characterized in that... Step S4 includes: S41 is based on dynamic light scattering theory and establishes the correspondence between real fluid dynamics particle size and particle diffusion coefficient through the Stokes-Einstein equation; The relationship between particle settling velocity and particle size and effective particle density is established based on Stokes' law of settling. The evolution of particle concentration with height and time is described based on the Mason-Weaver sedimentation-diffusion equation. At the same time, the intensity of scattered light is linearly positively correlated with the local particle concentration, and a shape-coupled physical model is constructed.

6. The method for measuring multi-angle dynamic light scattering particles as described in claim 5, characterized in that... The expression for Stokes' law of settling is: In the formula, Let g be the particle settling velocity, and g be the acceleration due to gravity. The effective density of the particles, Let d be the density of the dispersion medium and d be the actual hydrodynamic particle size. To determine the viscosity of the dispersing medium; The Mason-Weaver sedimentation-diffusion equation is expressed as follows: In the formula, Let be the particle concentration at height z at time t, and D be the particle diffusion coefficient; the scattered light intensity and concentration satisfy... , where k is the light intensity proportionality coefficient.

7. The method for measuring multi-angle dynamic light scattering particles as described in claim 5, characterized in that... Step S4 further includes: S42 constructs a global fitting objective function: taking the true particle size distribution function and effective particle density as the core parameters to be optimized, the measured data of all points in the spatiotemporal data matrix are used as the fitting benchmark, the particle size residual and light intensity residual are calculated respectively, and the total residual sum of squares objective function is constructed by weighted summation.

8. The method for measuring multi-angle dynamic light scattering particles as described in claim 7, characterized in that... The objective function expression for the sum of squared residuals is: In the formula, These represent the theoretical apparent particle size and theoretical scattered light intensity at height m and time point n, respectively. The measured apparent particle size and measured light intensity at the corresponding points are respectively. These are the weighting coefficients for particle size residual and light intensity residual, respectively.

9. The method for measuring multi-angle dynamic light scattering particles as described in claim 1, characterized in that... Step S5 includes: Based on the actual hydrodynamic particle size and corresponding settling velocity obtained by iterative solution, and combined with the known viscosity and density parameters of the dispersion medium, S51 modifies Stokes' sedimentation law and reverse-derives the effective density of the particles. For monodisperse systems, the average effective density is calculated by directly substituting the average particle size and average settling velocity. For polydisperse systems, the effective density of particles in each particle size range is obtained by substituting the corresponding settling velocity, thus forming an effective density distribution. The calculation formula is derived from a modification of Stokes' law of settlement: In the formula, The effective density of the particles, Here, d represents the particle settling velocity corresponding to the particle size, d is the actual hydrodynamic particle size, and g is the acceleration due to gravity. To disperse the viscosity of the medium, The density of the dispersion medium.

10. The method for measuring multi-angle dynamic light scattering particles as described in claim 9, characterized in that... Step S5 further includes: S52 calculates the sample sedimentation stability index: based on the spatial distribution of scattered light intensity at each moment in the spatiotemporal data matrix, the suspension stability of the sample is characterized by quantifying the degree of stratification of light intensity in the sample cell. Light intensity distribution data at the initial time and the set measurement endpoint are selected. The relative standard deviation of light intensity within the effective measurement height of the sample cell at both times is calculated. The ratio of these two values ​​is used as the settling stability index. The calculation formula is as follows: In the formula, SI is the settlement stability index. The values ​​represent the standard deviations of the scattered light intensity within the effective measurement height at the initial time and time t, respectively. The values ​​represent the average scattered light intensity within the effective measurement height at the initial time and time t, respectively.

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