Non-spherical particle size inversion method and system based on dynamic light scattering method

Abstract

The application discloses a non-spherical particle size inversion method and system based on a dynamic light scattering method, relates to the field of nanoparticle detection, and is used for high-precision and high-noise-resistance inversion of non-spherical nanoparticle size and morphology distribution. A non-spherical particle light scattering model is established; vertical-vertical, vertical-horizontal polarization direction scattering light signals of the non-spherical particle are collected, and an electric field autocorrelation function is obtained through pretreatment; the electric field autocorrelation function is taken as input, and a particle swarm algorithm is used to obtain the Stokes radius distribution and the aspect ratio distribution of the non-spherical particle; wherein, the particle swarm algorithm is improved by combining Latin hypercube sampling initialization, stage dynamic learning factor adjustment, elite strategy inertia weight distribution, adaptive boundary shrinkage, population mutation and Tikhonov regularization. The application effectively solves the coupling problem of size and morphology parameters, improves the global optimization ability and noise resistance robustness of the algorithm, and realizes high-precision and high-stability inversion of non-spherical particle size and morphology parameters.

Description

Technical Field

[0001] This invention relates to the field of nanoparticle detection technology, and in particular to a method and system for particle size inversion of non-spherical particles based on dynamic light scattering. Background Technology

[0002] The particle size distribution and morphological parameters (such as aspect ratio) of particles are key indicators determining their physical, chemical, and biological properties, and have significant application value in materials science, biomedicine, nanoelectronics, and chemical engineering. Dynamic light scattering (DLS) technology has become one of the mainstream technologies for nanoparticle size measurement due to its advantages such as non-contact, non-destructive, rapid measurement, and applicability to nanoscale particles. Its core principle is to detect the intensity fluctuations of scattered light caused by the Brownian motion of particles, and combine this with the relationship between the diffusion coefficient and particle size to invert the particle size distribution.

[0003] However, traditional DLS technology is mainly designed for spherical particles, while in practical applications, a large number of nanoparticles (such as nanorods, columnar nanocrystals, and biomacromolecules) are non-spherical. The light scattering characteristics of non-spherical particles are affected by both size (characterized by Stokes radius) and morphology (characterized by aspect ratio). The intensity fluctuations of scattered light are strongly coupled with these two parameters, making it difficult for traditional inversion methods to accurately obtain both parameters simultaneously. Furthermore, the Stokes radius and aspect ratio are not single values ​​in actual particle systems, but follow a certain distribution, further increasing the difficulty and complexity of the inversion. Summary of the Invention

[0004] The purpose of this invention is to provide a non-spherical particle size inversion method and system based on dynamic light scattering, which addresses all or part of the problems mentioned above, and enables high-precision and high-noise-resistance inversion of the size and morphological distribution of non-spherical nanoparticles.

[0005] The technical solution adopted in this invention is as follows: In a first aspect, this application provides a non-spherical particle size inversion method based on dynamic light scattering, comprising: Establish a light scattering model for non-spherical particles; Scattered light signals from non-spherical particles in vertical-vertical and vertical-horizontal polarization directions were collected and preprocessed to obtain the electric field autocorrelation function. Using the electric field autocorrelation function as input, the Stokes radius distribution and aspect ratio distribution of non-spherical particles are obtained by inversion using the particle swarm optimization algorithm. The particle swarm optimization algorithm initializes particles based on Latin hypercube sampling. During iterative optimization, the learning factor is adjusted in stages, and the particle boundaries are adjusted based on the iteration progress and population distribution. A mutation mechanism is used to maintain population diversity at or above a set diversity threshold, and out-of-bounds particles are smoothed out. In each iteration, the Tikhonov regularized fitness function is used to calculate particle fitness, and elite particles with optimal individual fitness are dynamically assigned inertial weights.

[0006] Optionally, a light scattering model for non-spherical particles is established, including: Define key parameters, including Stokes radius, translational diffusion coefficient, polarizability, shape parameter, and rotational diffusion coefficient; The polarizability is separated into isotropic polarizability and anisotropic polarizability; The translational relaxation rate is calculated based on the translational diffusion coefficient, and the mixed relaxation rate is calculated based on the translational diffusion coefficient and the rotational diffusion coefficient. The bidispersion of size and morphology of non-spherical particles was jointly characterized based on Stokes radius, shape parameters, translational relaxation rate, mixed relaxation rate, isotropic polarizability, and anisotropic polarizability.

[0007] Optionally, when splitting the polarizability, an ellipsoidal equivalent model is used to calculate the isotropic and anisotropic polarizability of the non-spherical particles.

[0008] Optionally, the electric field autocorrelation function includes a vertical-vertical polarization double exponential form and a vertical-horizontal polarization single exponential form.

[0009] Optional, phased adjustment of learning factors, including: The individual learning factor decreases linearly from the first set value with each iteration. The social learning factor increases linearly from the second set value onwards with the number of iterations, and the second set value is less than the first set value.

[0010] Optionally, the particle boundaries can be adjusted based on the iteration progress and population distribution, including: Particle boundary adjustment is triggered based on the set boundary contraction interval; Each time the particle boundary is adjusted, the current global optimal position is used as the center, and the current boundary range is reduced according to the set shrinkage rate while ensuring that the particle boundary is not lower than the set minimum boundary range.

[0011] Optionally, population diversity can be maintained at or above a set diversity threshold through mutation mechanisms, including: Population diversity is detected at predetermined intervals or when the stall counter reaches a stall threshold. Determine whether the population diversity is below the diversity threshold; If the population diversity is lower than the diversity threshold, a mutation operation is triggered, and particles with a set mutation ratio are randomly selected for mutation. After mutation, the particle position is bounded and the stagnation counter is reset.

[0012] Optionally, smooth out out-of-bounds particles, including: For out-of-bounds particles, within the particle boundary, the particle position is randomly reset, and the velocity direction of the out-of-bounds particles is adjusted to be towards the inside of the particle boundary based on the reset particle position.

[0013] Optionally, the inertial weights are dynamically assigned to elite particles that select individuals with optimal fitness, including: A predetermined number or proportion of elite particles with high fitness are assigned a first inertial weight, and the remaining non-elite particles are assigned a second inertial weight, wherein the first inertial weight is less than the second inertial weight.

[0014] In a second aspect, this application provides a non-spherical particle size inversion system based on a dynamic light scattering method, comprising: Lasers provide visible light laser sources; A polarizer is placed in the optical path of the laser to give the laser source a polarization direction. A transparent sample container is placed in the optical path of the laser to hold the non-spherical particle sample to be tested; A laser trap is placed in the optical path of the laser to absorb unscattered direct laser light. A bias camera is aimed at the sample container to simultaneously obtain scattered light signals in multiple polarization directions; A computer is connected to the bias camera to acquire the scattered light signal obtained by the polarization camera, and runs a non-spherical particle size inversion method based on dynamic light scattering to invert the Stokes radius distribution and aspect ratio distribution of the non-spherical particles.

[0015] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: Compared to traditional DLS technology, this application has the following advantages: First, it overcomes the parameter coupling challenge, achieving simultaneous and accurate detection of multiple parameters. Traditional DLS, by only capturing the translational diffusion signal of particles, cannot distinguish the coupled influence of size and morphology on the intensity fluctuations of scattered light, making it difficult to simultaneously and accurately obtain the Stokes radius and aspect ratio. This application, however, simultaneously captures both translational and rotational diffusion signals, establishing independent correlations between size, aspect ratio, and both translational and rotational diffusion coefficients. It can simultaneously invert the two key parameters of size and morphology, completely solving the core bottleneck of traditional technology. Furthermore, it can accurately adapt to polydisperse particle systems where both the Stokes radius and aspect ratio follow a normal distribution, effectively reducing the difficulty and complexity of the inversion and improving the accuracy of the detection results.

[0016] Secondly, it offers greater adaptability and covers a wider range of application scenarios. Traditional DLS is only suitable for detecting spherical particles. When detecting non-spherical particles such as rods, it is necessary to assume that the particles are spherical, resulting in large detection errors and failing to reflect the true morphology and size characteristics of the particles. This application does not require the assumption of sphericality and can accurately adapt to nanoscale rod-shaped particles (detectable down to a few nanometers). It can truly reflect the inherent physical properties of rod-shaped particles and is suitable for the detection needs of various rod-shaped nanoparticles (such as nanorods and columnar nanocrystals) in materials science, biomedicine, and other fields, thus overcoming the application limitations of traditional DLS.

[0017] Third, it inherits core advantages and improves detection accuracy. This application fully inherits the core advantages of traditional DLS: non-contact, non-destructive, rapid measurement, and strong statistical representativeness. It does not require complex sample preparation and can be directly detected in liquid suspensions. It can also detect multiple orders of magnitude of particles simultaneously, ensuring the statistical reliability of the detection results. At the same time, the Tikhonov optimization method is used in the fitness function to effectively reduce errors caused by noise and signal fluctuations, and the inversion results are superior to those of traditional DLS technology. Attached Figure Description

[0018] The present invention will be described by way of example and with reference to the accompanying drawings, wherein: Figure 1 This is a structural diagram of a particle size inversion device.

[0019] Figure 2 This is a flowchart of the non-spherical particle size inversion method.

[0020] Figure 3 This is a flowchart of a non-spherical particle size inversion method based on an improved PSO algorithm.

[0021] Figure 4 The first aspect ratio under 0% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0022] Figure 5 The second aspect ratio under 0% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0023] Figure 6 The third aspect ratio under 0% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0024] Figure 7 The first aspect ratio under 1% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0025] Figure 8 The second aspect ratio under 1% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0026] Figure 9 The third aspect ratio under 1% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0027] Figure 10 First aspect ratio under 3% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0028] Figure 11 The second aspect ratio under 3% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0029] Figure 12 The third aspect ratio under 3% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0030] Figure 13 The first aspect ratio under 5% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0031] Figure 14 The second aspect ratio under 5% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve.

[0032] Figure 15 The third aspect ratio under 5% noise intensity and Stokes radius A comparison of the theoretical and inversion distribution curves, where subplot (a) shows the aspect ratio. Distribution curve, subplot (b) shows the Stokes radius. Distribution curve. Detailed Implementation

[0033] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0034] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0035] To address the difficulty of traditional DLS technology in retrieving the size and morphology parameters of non-spherical particles, this application proposes a non-spherical particle size inversion method based on dynamic light scattering. This method utilizes depolarized dynamic light scattering (DDLS) technology and is specifically designed for the detection needs of non-spherical particles (for ease of explanation, rod-shaped particles will be used as an example in the following embodiments). The core principle is: based on the traditional DLS detection of scattered light intensity fluctuations, polarization state resolution technology is introduced to capture the simultaneous translational and rotational diffusion behaviors in the Brownian motion of rod-shaped particles. By acquiring scattered light signals in two polarization directions (vertical-vertical (VV) and vertical-horizontal (VH), the translational diffusion coefficient and rotational diffusion coefficient are extracted respectively. Then, combined with a quantitative correlation model between the rod-shaped particle size, aspect ratio, and the two diffusion coefficients, the decoupled inversion of the two key parameters of size and morphology is achieved.

[0036] Furthermore, in terms of inversion methods, the Particle Swarm Optimization (PSO) algorithm is widely used due to its simple principle and high optimization efficiency. However, the traditional PSO algorithm has significant limitations when processing the inversion of multiple parameters (double normal distribution parameters) of non-spherical nanoparticles such as rods: ① Insufficient initial particle swarm diversity, which easily gets trapped in local optima, resulting in low inversion accuracy; ② Fixed position update strategy, lacking adaptability to multi-parameter coupling relationships, and weak ability to coordinate optimization for Stokes radius and aspect ratio; ③ Poor noise resistance, the DDLS measurement signal is easily affected by environmental noise and electrical noise, and the inversion error of traditional PSO increases significantly in noisy environments; ④ The objective function is not optimized for the light scattering characteristics of rod-shaped particles, making it difficult to accurately describe the mapping relationship between the scattering signal and the double normal distribution parameters.

[0037] In response, this application, in addition to using DDLS technology, also specifically optimizes the inversion methods involved in the inversion process. By improving the PSO algorithm, high-precision and highly noise-resistant inversion of Stokes radius (normal distribution) and aspect ratio (normal distribution) is achieved.

[0038] In one optional implementation, the non-spherical particle size inversion method based on dynamic light scattering includes the following steps: S1. Establish a light scattering model for rod-shaped particles.

[0039] In traditional DLS technology, modeling spherical particles is based on the following core assumptions: the particles are isotropic, exhibit only translational Brownian motion, and their size distribution can be described by monodisperse or polydisperse probability density functions (PDFs). Key parameters include: Stokes radius (Equivalent spherical radius, reflecting diffusion characteristics); Translational diffusion coefficient It satisfies the Stokes-Einstein equation: ;in Boltzmann's constant, For temperature, Solvent viscosity; polarizability Due to its isotropic nature, it has only a single polarizability parameter. Scattering vector ; The solvent refractive index, λ The incident light wavelength, θ The scattering angle; Translational relaxation rate .

[0040] Under vertical-vertical (VV) polarization and homogeneous detection conditions, the normalized EACF (Electric Autocorrelation Coefficient function) of monodisperse spherical particles is in a single exponential form: ;in, For the correlation time; sp is the identifier for spherical particles; the superscript (1) indicates the first-order electric field autocorrelation function EACF. Under the same particle shape and polarization, sp and VV can be omitted.

[0041] For polydisperse spherical particles, the normalized EACF is generalized by weighting and summing the EACF of particles of different sizes according to their size distribution as follows: ; in For the first The weight of the particle-like structure (determined by the size distribution PDF and polarizability). For the first Stokes radius of particle-like particles.

[0042] Intensity Autocorrelation Function (IACF) and EACF (by...) (This indicates a connection via Siegert relations) ; Wherein, the superscript (2) denotes the second-order intensity autocorrelation function IACF; and These are instrument constants, both of which can be determined experimentally. Neither depends on the concentration or particle size of the sample being tested; they are determined solely by the optical path geometry and the electrical characteristics of the photodetector. (Constant) A is the gain scaling factor for the photoelectric instrument, a baseline constant representing the DC baseline gain corresponding to the average scattered light intensity received by the detector. Due to the dark current of the photodetector, residual interference from ambient stray light, or the inherent DC bias of the signal acquisition card, the actual baseline value may be higher or lower than 1. For example, in scenarios with dilute samples, low laser power, and low detector strength, A≈0.2-1; in scenarios with high-concentration suspensions, high laser power, and high amplification gain, A≈1-10. These are core instrument constants for DLS, characterizing the spatial coherence of the detection system, describing the spatial coherence contrast of the optical field, quantifying the maximum modulation depth of intensity fluctuations caused by interference intensity of scattered light from different particles, and theoretically constrained within a certain range. In this application, precision measuring instruments Standard benchtop dynamic light scattering instrument Optical path misalignment, high stray light, wide aperture detection The intensity of the scattered light is proportional to the square of the particle polarizability, and the scattering angle and detection distance of the particles are approximately the same within the measurement volume.

[0043] The modeling of non-spherical (e.g. rod-shaped) particles addressed in this application is more complex and requires solving the following three key problems: polarizability splitting caused by anisotropy, introduction of rotational diffusion, and joint characterization of size and shape polydispersity.

[0044] Based on the parameters for spherical particles, add parameters related to the shape and rotation of rod-shaped particles: Shape parameters: diameter ,length Aspect Ratio ; Rotational diffusion coefficient: Rotational diffusion coefficient perpendicular to the rod axis Its expression is: ; in The interpolation function (obtained from the bead shell model, applicable to...) ).

[0045] Polarizability decomposition: Due to the anisotropy of rod-shaped particles, polarizability is divided into: isotropic polarizability ( The polarizability is parallel to the rod axis. (Polarization perpendicular to the rod axis), anisotropic polarization .

[0046] Mixed relaxation rate: includes contributions from both translational and rotational diffusion. .

[0047] Next, we will derive the EACF of monodisperse rod-shaped particles, distinguishing between two cases: VV polarization (which includes both translational and mixed relaxation modes) and VH polarization (which only includes mixed relaxation modes).

[0048] In VV polarization, based on the anisotropic polarizability-dependent framework, the nonnormalized EACF of monodisperse rod-shaped particles is in a double-exponential form (superposition of two relaxation modes): ; In the formula, the subscript rd indicates rod-shaped particles, which is used to distinguish them from the spherical particle identifier sp; <n>This represents the ensemble statistical average, indicating the average number of nanorod-shaped particles within the measured laser volume. It is only related to the sample concentration and the laser irradiation volume, and does not change with time or particle diffusion behavior.

[0049] After normalization, it becomes: ; Among them, the weighting coefficient , Translation relaxation rate Consistent with spherical particles (by Stokes radius) (derived from the Stokes-Stein equation) Length of rod-shaped particles With Stokes radius Relationship: ( For interpolation functions, and (Determined jointly by the bead shell model).

[0050] In VH polarization, only the horizontal component of the scattered light is detected, and the normalized EACF of the monodisperse rod-shaped particles is in a single exponential form (mixed relaxation modes only): .

[0051] Consider the Stokes radius of rod-shaped particles and length-to-diameter ratio Both exhibit polydispersity, and a bivariate probability density function is used. Describe its joint distribution and generalize EACF by weighted summation: 1. Only Stokes radius polydispersity (aspect ratio monodispersity).

[0052] The rod-shaped particles are divided into boxes according to their Stokes radius (box spacing). , i (For Stokes radius binning index), the normalized EACF under VV polarization is: ; in (Translation relaxation mode weights) (Hybrid relaxation mode weights), normalized coefficients . These represent the simultaneous existence of Stokes radii. and length-to-diameter ratio When more dispersed, about and The form of a bivariate function.

[0053] 2. Only aspect ratio polydispersity (Stokes radius monodispersity).

[0054] The rod-shaped particles were divided into boxes according to their length and diameter (box spacing). , j (For the major axis section bin index), the normalized EACF under VV polarization is: .

[0055] 3. Stokes radius and aspect ratio are both highly variable (generally speaking).

[0056] Joint bivariate distribution The normalized EACF under VV polarization is in the form of a double summation: ; 4. Multi-distribution promotion of VH polarization.

[0057] Under VH polarization, only mixed relaxation modes are present, and the multidispersed EACF is: ; in Normalization coefficient .

[0058] In this application, a model adaptation for polarizability calculation is also performed. Since the polarizability of rod-shaped particles is difficult to calculate directly, an ellipsoidal equivalent model is used for adaptation in this application. 1. Assuming an ellipsoidal particle with the same aspect ratio and dielectric constant as the rod-shaped particle, its isotropic polarizability per unit volume is... and anisotropic polarization It can be calculated using classical electromagnetic theory; Physical Applicability Conditions: Rayleigh Scattering Limit: All geometric dimensions (diameter d, length L) of the rod-shaped particle are much smaller than the incident light wavelength λ. Taking λ=647nm as an example, the size of the gold rod-shaped particle is only tens to hundreds of nanometers. This condition is met, and the vande Hulst long ellipsoid polarizability theory can be used for calculation.

[0059] 2. The overall polarizability of rod-shaped particles is the unit volume polarizability multiplied by the particle volume. ,Right now: ; ; 3. Verification basis: The unit volume dynamics of ellipsoidal particles and cylindrical particles (rod-shaped) with the same aspect ratio are highly consistent with the results calculated by the method of moments, ensuring the accuracy of model adaptation.

[0060] This concludes the entire process of extending the modeling from spherical particles to rod-shaped particles, and the theoretical model has been established. The core of this extension is to broaden the modeling from spherical to rod-shaped particles by expanding parameters (introducing shape and rotational diffusion parameters), splitting polarizability (adapting to anisotropy), and enhancing the polydispersity dimension (joint distribution of size and shape). This transforms the single-exponential, single-dimensional EACF of spherical particles into a double-exponential, double-dimensional EACF of rod-shaped particles. This extension process retains the core framework of spherical particle modeling (such as Siegert relations and the weighted summation concept), while simultaneously solving the problem of calculating the polarizability of rod-shaped particles through an ellipsoidal equivalent model. Ultimately, it achieves accurate characterization of the polydispersity of rod-shaped nanoparticles, providing a theoretical foundation for DDLS analysis of anisotropic nanomaterials.

[0061] S2. Based on the DDLS measurement system, collect the scattered light signal (scattered light intensity fluctuation signal).

[0062] DDLS (Dispersive Radiation Scattering) technology is based on the principle of light scattering. It obtains particle size distribution information by performing correlation calculations on the intensity of scattered light from nanoparticles. Its core logic is that nanoparticles undergo Brownian motion in a solvent, causing the intensity of scattered light to fluctuate over time. By analyzing the temporal correlation of this fluctuation signal, the diffusion coefficient of the particles can be derived, and then the particle size and distribution can be calculated using the Stokes-Einstein equation.

[0063] Autocorrelation function of electric field of nanoparticles It is the core analysis object of DDLS technology, and its continuous form is expressed as: ; in, It is a normalized attenuation linewidth distribution function that satisfies the normalization condition. ; It is the attenuation linewidth, defined as ( Let be the translational diffusion coefficient of the particles. (This is the scattering vector; the two parameters remain consistent with those in the previous text).

[0064] Under actual measurement conditions, the discrete form of the electric field autocorrelation function should be used to adapt to experimental data processing. Its discrete form is expressed as: ; in, The relevant time The One measurement value, It is the number of channels in the correlator or spectrum analyzer. It is the number of particle size categories to be measured.

[0065] In actual measurements, noise will be present. Therefore, Gaussian white noise needs to be added during the preprocessing stage. The corrected electric field autocorrelation function is: ; in Is Gaussian white noise at the specified time point It refers to the noise level.

[0066] The hardware structure of the DDLS system for measuring particle size distribution is as follows: Figure 1 As shown, its structure and the functions of each component are as follows: 1. Laser, providing a visible light laser source to provide incident light for experiments; 2. A polarizer, placed in the optical path of the laser, gives the laser source a polarization direction; 3. Sample container: A transparent cuvette is placed in the laser optical path to hold the nanoparticle sample to be tested; 4. Laser trap, placed in the laser's optical path to absorb unscattered direct laser light and avoid interference; 5. A polarization camera is aimed at the sample container to simultaneously obtain scattered light signals from multiple polarization directions; 6. A computer connected to a polarization camera acquires the scattered light signal obtained by the camera and converts it into an electrical signal. It processes the time-varying electrical signal to obtain the light intensity autocorrelation function of the scattered light signal. The computer performs data processing, result display, saving, and output. Refractive index and photodetector parameters can be set. The computer includes a light scattering signal data preprocessing module to process the scattered light signal and obtain the electric field autocorrelation function. It also includes a built-in non-spherical particle size inversion method based on dynamic light scattering for inverting particle size distribution (i.e., the Stokes radius and aspect ratio distribution of rod-shaped particles).

[0067] The granularity inversion process includes: 1. Sample preparation and data acquisition: Place the nanoparticle sample to be tested into the sample container and collect data on the change of light scattering intensity over time using the above-mentioned device.

[0068] 2. Data preprocessing: The collected raw data is preprocessed to obtain the electric field autocorrelation function, i.e., EACF data.

[0069] 3. Input the obtained EACF data into the granularity inversion algorithm program to perform parameter inversion.

[0070] The experiment used gold nanorods in water as a simulation object, based on the unimodal Gaussian bivariate probability density function (PDF). To describe the polydispersity of nanorods, the PDF is defined by four core parameters: Mean Stokes radius (Unit: nm) Stokes radius relative standard deviation (Range: 10%~20%) for Standard deviation; Average length-to-diameter ratio ( For length, (Diameter; range: 2~12). Relative standard deviation of aspect ratio (Range: 1%~10%) for The standard deviation.

[0071] S3. Perform parameter inversion using the improved PSO algorithm.

[0072] The process of the particle size inversion method based on the improved PSO algorithm is as follows: Figure 2 As shown.

[0073] To address the shortcomings of the original PSO algorithm in inverting non-spherical particle size, such as susceptibility to local optima, insufficient convergence accuracy, and poor robustness to ill-posed inversion problems, this application proposes an improved PSO algorithm that integrates regularization techniques and a multi-dimensional dynamic optimization mechanism, taking into account the parameter space characteristics of the EACF inversion problem. This algorithm is designed with the core principle of "global exploration in the early stage, local development in the later stage, and maintaining diversity throughout the process." Through key technological improvements such as initialization optimization, dynamic parameter adjustment, boundary adaptation, and diversity maintenance, it achieves the four core parameters of rod-shaped particle size (mean Stokes radius, mean ... Stokes radius relative standard deviation Average length-to-diameter ratio Length-to-diameter ratio relative standard deviation High-precision and robust inversion.

[0074] Specific improvements to the granularity inversion algorithm include: 1. Improved particle initialization based on [previous technology / method].

[0075] Existing technical defects: The original PSO algorithm usually uses random uniform sampling to initialize particle positions, which can easily lead to uneven distribution of particles in the parameter space and some key areas not being covered. Especially in the 4-dimensional parameter space of EACF inversion, the initial population may be concentrated in a local area, affecting the algorithm's global search capability and increasing the risk of getting trapped in local optima.

[0076] The improvement measures in this application are as follows: The initial particle population is generated using the Latin hypercube sampling (LHS) method, specifically implemented as follows: The boundary intervals of each parameter to be inverted are uniformly layered to ensure that each dimension of the parameter space is equally covered; An initial particle set satisfying both uniformity and randomness is generated by randomly pairing the layered nodes of each dimension, as expressed by the formula: ; in, The number of particles, i.e., the size of the particle swarm; For parameter dimensions (inversion mean Stokes radius in this application) Stokes radius relative standard deviation Average length-to-diameter ratio Length-to-diameter ratio relative standard deviation Four parameters, therefore ); The function guarantees that the initial particles are uniformly distributed in the 4-dimensional parameter space, with no overlap and complete coverage; These represent the upper and lower boundaries of the parameter, respectively.

[0077] Technical effects: The initial population can uniformly cover the entire feasible parameter domain, avoiding search blind spots caused by particle aggregation, laying the foundation for subsequent global optimal search, and improving the algorithm's adaptability to the multi-peak parameter space in EACF inversion.

[0078] 2. A phased dynamic learning factor adjustment mechanism.

[0079] Existing technical limitations: Individual learning factor in the original PSO algorithm Social learning factors It is usually set to a fixed value (e.g.) Unable to achieve a dynamic balance between "global exploration" and "local development": fixed and This can easily lead to insufficient exploration in the early stages (particles have difficulty escaping local regions) or slow convergence in the later stages (particle oscillations do not converge). Especially in EACF inversion, the parameters are strongly coupled, requiring extensive searching in the early stages and accurate convergence in the later stages.

[0080] The improvement measure in this application is to design a staged dynamic learning factor adjustment strategy, which adjusts linearly according to the number of iterations. and The possible values ​​of: Individual learning factors (Guiding particles to move closer to their optimal position): This decreases linearly from 2.0 to 0.5 with each iteration, as shown in the formula: ; Social learning factors (Guiding particles to approach the global optimum): The value increases linearly from 0.5 to 2.5 with the number of iterations, as shown in the formula: ; in, This represents the current iteration number. This represents the maximum number of iterations.

[0081] Technical effect: Early stage of iteration ( big, Smaller particles tend to explore their surroundings, enhancing their global search capabilities and avoiding premature entrapment in local optima; in the later stages of iteration ( Small, Larger particles tend to converge toward the global optimum, improving local development accuracy, accelerating algorithm convergence, and ensuring the accuracy of inversion parameters.

[0082] 3. Dynamic inertia weight allocation driven by elite strategy.

[0083] Existing technical limitations: Inertial weights in the original PSO algorithm Typically, a fixed value or linear decreasing strategy is used, without considering the fitness differences of individual particles: excellent particles (high fitness) and ordinary particles are given the same weight, which cannot fully utilize the local development potential of elite particles, and it is also difficult to maintain global exploration capability through ordinary particles, resulting in low search efficiency of the algorithm.

[0084] The improvement measures in this application are as follows: a dynamic inertia weight allocation mechanism is designed by combining an elite strategy, and the specific steps are as follows: After each iteration, the individual optimal fitness of all particles ( Sort the results and filter out those with a percentage of [percentage missing]. (In this application) Elite particles (configurable), the rest are non-elite / ordinary particles.

[0085] Differentiated inertial weights are assigned to elite and non-elite particles: Elite particles (top 20% of fitness): assigned a smaller first inertial weight. Strengthen local development capabilities and guide them to search precisely near the optimal region; Non-elite particles (bottom 80% of fitness ranking): Assign a larger second inertial weight. This strengthens the global exploration capability and encourages it to look beyond the current area for better solutions. The weight allocation formula is expressed as follows (example):

[0086] `sorted_fit` represents the sorted fitness; `sorted_idx` represents the sorted particle index; the `sort()` function sorts the best fitness values ​​`pbest_fit` in descending order; `elite_ratio` is the elite particle ratio parameter, set to 0.2 during operation, meaning elite particles account for 20%; `n_particles` is the PSO algorithm particle count parameter set to 100; `elite_idx` represents the elite particle index; `round()` is the rounding function to retain integer values; `w(elite_idx)` is the elite particle weight, with a smaller weight of 0.4 for local exploration; `non_elite_idx` represents the non-elite particle index; `end` represents the sequence number of the last particle; `w(non_elite_idx)` is the non-elite particle weight, with a larger weight of 0.9 for global exploration.

[0087] The first and second inertia weights assigned above are example values, and can be configured / adjusted in practice, as long as the first inertia weight is less than the second inertia weight; and, as a preferred implementation, the first inertia weight is not higher than 0.5 and the second inertia weight is not lower than 0.5.

[0088] Technical effect: By differentiating weight allocation, a collaborative search mode of "precise development of elite particles and extensive exploration of ordinary particles" is achieved, which not only ensures the accuracy of the algorithm in finding the optimal solution, but also maintains the global search capability and improves the search efficiency of complex parameter space in EACF inversion.

[0089] 4. Adaptive dynamic boundary adjustment mechanism.

[0090] Existing technical limitations: The parameter boundaries of the original PSO algorithm remain fixed. In the later stages of iteration, particles gradually gather towards the global optimum, but the fixed boundaries still cause some particles to search in invalid regions, wasting computational resources. At the same time, the fixed boundaries cannot adapt to the dynamic changes in the parameter space, which may limit the further convergence of particles towards the optimal solution and affect the inversion accuracy.

[0091] The improvement measures in this application are as follows: an adaptive boundary adjustment mechanism based on iteration progress and population distribution is designed, and the specific implementation is as follows: Set the boundary contraction interval ( (Configurable), triggers a particle boundary adjustment once every 50 generations (except for the last generation, to avoid convergence oscillation); At the current global optimal position ( Centered on ), and considering the current distribution range of the particle population, based on the initial boundary contraction rate ( (Configurable) Shrink the current boundary range, the formula is:

[0092] These represent the updated lower and upper bounds of the parameters, respectively, which will replace the lower and upper bounds in subsequent calculations. Set the minimum boundary ratio ( (Configurable) to ensure that the boundary does not shrink excessively (the minimum boundary range is not less than 50% of the initial range), thus avoiding the loss of the optimal solution; Synchronous update speed boundary ( , ), to match the parameter boundaries:

[0093] Technical effects: In the later stages of iteration, the parameter search range is gradually reduced, guiding particles to concentrate in the global optimal region, reducing invalid searches and improving computational efficiency; the boundary adjustment is centered on the global optimal position, ensuring that the search range always revolves around the potential optimal solution, while avoiding excessive shrinkage through minimum boundary constraints, thus balancing convergence accuracy and search completeness.

[0094] 5. Mechanisms for maintaining and varying population diversity.

[0095] Existing technical defects: The original PSO algorithm is prone to a decrease in population diversity during the iteration process, and particles tend to converge to local optima, resulting in "premature convergence" of the algorithm. Especially in EACF inversion, the parameter space has multi-peak characteristics, and insufficient population diversity will prevent the algorithm from finding the global optimum.

[0096] The improvement measures in this application are as follows: a population variation mechanism based on diversity detection and stagnation counting is designed, with the specific steps as follows: Every 5 generations (configurable) or when the stall counter ( Used to record the global optimal position gbest When the number of iterations without significant change reaches a stagnation threshold (e.g., 10, configurable), calculate population diversity (measured by the standard deviation of particle positions): ; In the formula, The matrix form representing particles, abbreviated as ,in This indicates the row index (particle index) and column index (parameter index) of the matrix, with ":" representing all elements in the row / column; This represents the standard deviation parameter.

[0097] If diversity is below the threshold ( Trigger mutation operation: Set mutation ratio ( (or 0.2, configurable), randomly select 10% of the particles for mutation; add a small perturbation to the position of the selected particles (the perturbation amplitude is 10% of the parameter boundary range):

[0098] Indicates the number of mutated particles; The row index indicating where the mutation occurred; Indicates random generation OK, A matrix of columns, where the element values ​​are in the range of columns. Interval.

[0099] After mutation, the particle position is bounded ( ), ensuring it is within the feasible region; reset the stall counter after mutation ( ), to avoid continued stagnation.

[0100] Technical effects: Actively maintains population diversity, effectively avoids premature convergence of the algorithm, and ensures that particles can continuously explore the parameter space. It is especially suitable for multi-peak, strongly coupled parameter spaces in EACF inversion, and increases the probability of the algorithm finding the global optimal solution.

[0101] 6. Optimized out-of-bounds handling mechanism.

[0102] Existing technical defects: The original PSO algorithm usually handles out-of-bounds particles by "directly trunculating to the boundary value", which can easily lead to sudden changes in particle velocity, disrupt the search continuity of the population, and even cause algorithm oscillations, affecting convergence stability.

[0103] The improvement measures in this application are as follows: A smoothing out-of-bounds handling strategy is designed, changing "direct truncation to the boundary value" to randomly resetting the position of out-of-bounds particles to within the boundary, and adjusting the velocity direction of the out-of-bounds particles based on the reset particle positions to guide them to move inwards towards the boundary. The specific implementation process is as follows: in, These represent the upper and lower bounds of the element in the d-th column of the particle matrix, respectively. Indicates calculation Random numbers within a range; This represents the velocity of the element in the i-th row and d-th column of the particle matrix.

[0104] Technical effects: It avoids mutations caused by direct truncation of particle positions, maintaining the continuity of population search; velocity adjustment guides particles to move within the feasible region, reducing the recurrence of boundary crossing phenomena and improving the convergence stability of the algorithm.

[0105] 7. Design of a fitness function incorporating Tikhonov regularization.

[0106] Existing technical shortcomings: The fitness function of the original PSO algorithm usually only considers the residual between the predicted value and the observed value (such as mean square error). However, the EACF inversion problem is an ill-posed problem (the observed data contains noise and the parameter space has high dimensionality). A fitness function based solely on the residual is prone to overfitting noise in the inversion results and parameter distortion (such as exceeding the physical constraints).

[0107] The improvement measures in this application are as follows: a zero-order Tikhonov regularization term is incorporated into the fitness function to balance residual minimization with solution smoothness. The specific design is as follows: First, the Tikhonov regularization algorithm is used ( Solve for the optimal regularization parameter ( , ):

[0108] and There are two sets of regularization parameters, where These represent the aspect ratio-dominated regularization parameter, solution vector norm, and residual norm, respectively. Let represent the Stokes radius-dominated regularization parameter, solution vector norm, and residual norm, respectively; This represents the EACF after adding Gaussian noise in the simulation.

[0109] fitness function It consists of the residual term res and the regularization term reg:

[0110] in, The function is the inversion EACF corresponding to the current particle parameters, and norm() is the matrix norm solving function. For noisy observations of EACF, The solution vector.

[0111] Technical effects: The regularization term effectively suppresses the influence of noise on the inversion results, avoids overfitting, and improves the robustness of the algorithm to observation noise; it balances the "inversion accuracy" and "reasonableness of the solution", ensuring that the inversion parameters meet physical constraints (such as EACF∈[0,1]), and improves the reliability of the inversion results.

[0112] Based on the above explanation of the improved PSO algorithm, see [link to relevant documentation]. Figure 3 The following describes the steps for parameter inversion based on this improved PSO algorithm.

[0113] 1. Parameter initialization: Set physical constants, experimental parameters (see Table 1), and inversion parameter boundaries (in one specific embodiment, ...). Algorithm parameters (number of particles, maximum number of iterations, etc.) are used to generate the initial particle population and initial velocity based on Latin hypercube sampling.

[0114] 2. Observation data generation: The noise-free theoretical EACF is calculated based on the real parameters. Gaussian noise is added to obtain the noisy observation EACF, and the optimal regularization parameter is solved by the Tikhonov algorithm.

[0115] 3. Iterative optimization: a. Phased adjustment of learning factors and ; b. Calculate the fitness of each particle (residual term res + regularization term reg); c. Update the individual optimal position of the particle ( ) and global optimal position ( Record the stall counter; d. Trigger dynamic boundary adjustments based on iteration progress, and update the velocity boundary synchronously; e. Assign dynamic inertia weights based on an elite strategy; f. Update particle velocity and position, using smoothing outbound behavior handling; g. Detect population diversity and trigger mutation operation when a threshold condition is reached, resetting the stall counter.

[0116] 4. Convergence judgment: Stop iterating after reaching the convergence accuracy or the maximum number of iterations, and output the global optimal position as the inversion parameter.

[0117] 5. Result verification: The robustness of the algorithm is verified by calculating the average relative error of the inversion parameters through multiple random sampling tests.

[0118] It is worth noting that although this application has described each improvement point in detail above, these improvements are not isolated but rather interconnected and synergistic, exhibiting strong coupling. For example, Latin hypercube sampling provides a uniform initial population for the dynamic adjustment mechanism; dynamic learning factors and elite weight allocation work together to achieve an "exploration-development" balance; dynamic boundary adjustment and population mutation mechanisms jointly maintain search efficiency and diversity; and regularized fitness functions and out-of-bounds handling mechanisms ensure the rationality and stability of the inversion results.

[0119] Table 1 shows a list of parameters used in the simulation environment, which includes the physical parameters and algorithm parameters used.

[0120] Table 1 Parameter List

[0121] Table 2 shows the parameter inversion results of the two-parameter normal distribution under different noise conditions. The theoretical parameters used are the aspect ratio and relative standard deviation. Stokes radius relative standard deviation Average length-to-diameter ratio Mean Stokes radius (Unit: nm); e.g. Figures 4-15 As shown, a comparison graph of the theoretical normal distribution curve and the inverted normal distribution curve with two parameters is presented. Figures 4-6 This is a comparison chart of the theoretical normal distribution curve and the inverted normal distribution curve when the noise intensity is 0%. Figure 4 Subgraphs (a) and (b) in the figure represent the results of the first simulation experiment. Figure 5 Subgraphs (a) and (b) in the figure represent the results of the second simulation experiment. Figure 6 Subgraphs (a) and (b) in the figure represent the results of the third simulation experiment (the same applies below). Figures 7-9 This is a comparison chart of the theoretical normal distribution curve and the inverted normal distribution curve under a noise intensity of 1%. Figures 10-12 This is a comparison chart of the theoretical normal distribution curve and the inverted normal distribution curve under a noise intensity of 3%. Figures 13-15 This is a comparison of the theoretical normal distribution curve and the inverted normal distribution curve under a noise intensity of 5%. It can be seen that noise intensity has a certain impact on the accuracy of the inversion. The main impact on the inversion parameters is evident in the significant effect on the standard deviation of the aspect ratio normal distribution, while the impact on the other three parameters is not significant.

[0122] Table 2. Parameter inversion results of the two-parameter normal distribution under different noise conditions.

[0123] As can be seen from the data in Table 2, the inversion accuracy decreases with increasing noise intensity, mainly due to the accuracy of the relative standard deviation of the aspect ratio. , , The inversion results for these three parameters are all quite good, and their stability is also high under repeated experiments.

[0124] For particle size inversion algorithms, through the above-mentioned multi-dimensional improvements, the improved PSO algorithm proposed in this application effectively solves the problems of local optima and poor robustness of the original PSO in EACF four-parameter inversion, and achieves high-precision and stable parameter inversion, providing certain algorithmic support for the accurate characterization of nanoparticle properties (such as aspect ratio and Stokes radius).

[0125] This application is not limited to the specific embodiments described above. This application extends to any new features or combinations disclosed in this specification, as well as any new steps or combinations of any new methods or processes disclosed.< / n>

Claims

1. A method for inverting the particle size of non-spherical particles based on dynamic light scattering, characterized in that, include: Establish a light scattering model for non-spherical particles; Scattered light signals from non-spherical particles in vertical-vertical and vertical-horizontal polarization directions were collected and preprocessed to obtain the electric field autocorrelation function. Using the electric field autocorrelation function as input, the Stokes radius distribution and aspect ratio distribution of non-spherical particles are obtained by inversion using the particle swarm optimization algorithm. The particle swarm optimization algorithm initializes particles based on Latin hypercube sampling. During iterative optimization, the learning factor is adjusted in stages, and the particle boundaries are adjusted based on the iteration progress and population distribution. A mutation mechanism is used to maintain population diversity at or above a set diversity threshold, and out-of-bounds particles are smoothed out. In each iteration, the Tikhonov regularized fitness function is used to calculate particle fitness, and elite particles with optimal individual fitness are dynamically assigned inertial weights.

2. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, Establish a light scattering model for non-spherical particles, including: Define key parameters, including Stokes radius, translational diffusion coefficient, polarizability, shape parameter, and rotational diffusion coefficient; The polarizability is separated into isotropic polarizability and anisotropic polarizability; The translational relaxation rate is calculated based on the translational diffusion coefficient, and the mixed relaxation rate is calculated based on the translational diffusion coefficient and the rotational diffusion coefficient. The bidispersion of size and morphology of non-spherical particles was jointly characterized based on Stokes radius, shape parameters, translational relaxation rate, mixed relaxation rate, isotropic polarizability, and anisotropic polarizability.

3. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 2, characterized in that, When splitting the polarizability, the isotropic and anisotropic polarizability of non-spherical particles are calculated using an ellipsoidal equivalent model.

4. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, The electric field autocorrelation function includes a vertical-vertical polarization double exponential form and a vertical-horizontal polarization single exponential form.

5. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, The learning factors are adjusted in stages, including: The individual learning factor decreases linearly from the first set value with each iteration. The social learning factor increases linearly from the second set value onwards with the number of iterations, and the second set value is less than the first set value.

6. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, Adjusting particle boundaries based on iteration progress and population distribution includes: Particle boundary adjustment is triggered based on the set boundary contraction interval; Each time the particle boundary is adjusted, the current global optimal position is used as the center, and the current boundary range is reduced according to the set shrinkage rate while ensuring that the particle boundary is not lower than the set minimum boundary range.

7. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, Maintaining population diversity above a set diversity threshold through mutation mechanisms includes: Population diversity is detected at predetermined intervals or when the stall counter reaches a stall threshold. Determine whether the population diversity is below the diversity threshold; If the population diversity is lower than the diversity threshold, a mutation operation is triggered, and particles with a set mutation ratio are randomly selected for mutation. After mutation, the particle position is bounded and the stagnation counter is reset.

8. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, Smoothing out-of-bounds particles includes: For out-of-bounds particles, within the particle boundary, the particle position is randomly reset, and the velocity direction of the out-of-bounds particles is adjusted to be towards the inside of the particle boundary based on the reset particle position.

9. The non-spherical particle size inversion method based on dynamic light scattering as described in claim 1, characterized in that, Dynamically assign inertial weights to elite particles with optimal individual fitness, including: A predetermined number or proportion of elite particles with high fitness are assigned a first inertial weight, and the remaining non-elite particles are assigned a second inertial weight, wherein the first inertial weight is less than the second inertial weight.

10. A non-spherical particle size inversion system based on dynamic light scattering method, characterized in that, include: Lasers provide visible light laser sources; A polarizer is placed in the optical path of the laser to give the laser source a polarization direction. A transparent sample container is placed in the optical path of the laser to hold the non-spherical particle sample to be tested; A laser trap is placed in the optical path of the laser to absorb unscattered direct laser light. A bias camera is aimed at the sample container to simultaneously obtain scattered light signals in multiple polarization directions; A computer is connected to the bias camera, acquires the scattered light signal obtained by the polarization camera, and runs the non-spherical particle size inversion method based on dynamic light scattering as described in any one of claims 1-9 to invert the Stokes radius distribution and aspect ratio distribution of the non-spherical particles.

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