A method and system for automated determination of nanoparticle hamaker constant based on dynamic light scattering data

Abstract

The application belongs to the field of colloid and interface science and nanoparticle characterization technology, and particularly relates to a nanoparticle Hamaker constant automatic determination method and system based on dynamic light scattering data, which comprises the following steps: data acquisition and ion recognition, obtaining time series data under multiple electrolyte concentrations and ion species in the electrolyte solution; ion-specific parameter automatic calling, automatically calling the effective charge coefficient of the ion from a preset ion-specific parameter database; total average coagulation rate automatic calculation, automatically calculating the total average coagulation rate for each concentration; scatter set construction, automatically identifying the turning point by using a piecewise linear fitting algorithm, and realizing automatic interpretation of the critical coagulation concentration; calculation model construction, automatically inverting the Hamaker constant; and outputting the critical coagulation concentration and the Hamaker constant. The application provides a complete automatic determination process, is simple and convenient to operate, is high in economic efficiency and mathematical stability, and is suitable for any ion system.

Description

Technical Field

[0002] This invention belongs to, but is not limited to, the fields of colloid and interface science and nanoparticle characterization technology, and particularly relates to an automated method and system for determining the Hamaker constant of nanoparticles based on dynamic light scattering data. Background Technology

[0003] The Hamaker constant is a key material parameter describing van der Waals interactions between colloidal particles and has wide applications in environmental engineering, nanomaterials, and biomedicine. Accurate determination of the Hamaker constant of nanoparticles is crucial for understanding colloidal stability, nanoparticle migration and aggregation behavior, and predicting and regulating the transport and fate of nanoparticles in the environment.

[0004] Currently, the main methods for determining the Hamaker constant include:

[0005] (1) Theoretical calculation method based on Lifshitz theory, but in general, for most materials, it is difficult to obtain the optical property parameters of the full spectrum of the material required for calculation (Faure et al., 2011; Pinchuk, 2012).

[0006] (2) Direct measurement using a surface force meter / atomic force microscope. However, both of these methods require high sample purity and are greatly affected by impurities.

[0007] (3) Critical coagulation concentration (CCC) method based on the classic DLVO (Derjaguin-Landau-Verwey-Overbeek) theory of colloidal interfaces.

[0008] In recent years, based on DLVO theory and dynamic light scattering (DLS) technology, researchers have developed methods to estimate the Hamaker constant by measuring particle aggregation kinetics. Guo et al. (2016) first proposed using DLS to determine the CCC of soil / clay colloids in the Li⁺ system and used a manual "stepwise approximation method" to invert the Hamaker constant. This method provides a new approach for the experimental determination of the Hamaker constant, but it still has the following shortcomings: 1) The determination of CCC depends on manually visually observing the inflection point from the graph of total average aggregation rate (TAA) versus electrolyte concentration, which is highly subjective and inefficient; 2) The inversion of the Hamaker constant depends on repeated manual calculations, lacks an automated process, and the results have poor repeatability. Luo et al. (2018) further found that the classical DLVO theory ignores the ion-specific effect (Hofmeister effect), which leads to the same material being affected by different ions (such as Li⁺). + K + Cs +The Hamaker constants measured in the DLVO system showed several-fold differences (6.70, 17.4, 35.7 × 10⁻²⁰ J). This was addressed by introducing the effective ionic charge coefficient γ into the DLVO theory. i Correcting for electrostatic interactions yields a consistent Hamaker constant (approximately 6.2 × 10⁻²⁰ J), confirming that Li + It can serve as a benchmark system. However, this method still relies on manual, iterative approximation calculations, and requires users to manually consult the γ values ​​of different ions. i The coefficient is not yet automated and lacks universality. Furthermore, a recently published patent (CN118961549A, 2024) proposes using DLS technology to simultaneously determine Na. + and K + The CCC of two ion systems can be solved simultaneously using the image intersection method to determine the Hamaker constant and surface charge density. While this method avoids dependence on prior values ​​of the Hamaker constant, it still requires simultaneous dynamic light scattering experiments on both ion systems, making the operation complex and doubling the workload. Furthermore, the intersection method is mathematically sensitive to experimental errors (i.e., the intersection point is easily shifted when the angle between the two curves is small), and the determination of the intersection point still relies on manual image interpretation, limiting its automation. The existing related technologies and their limitations are summarized below:

[0009] Table 1 Analysis of Existing Relevant Technologies

[0010]

[0011] In summary, existing technologies generally suffer from the following technical defects:

[0012] (1) The CCC interpretation and Hamaker constant inversion process rely on manual intervention, which is cumbersome, subjectively errory and inefficient;

[0013] (2) There is a lack of systematic and automated processing of the Hofmeister effect. Users need to manually look up and substitute the γ of different ions. i Coefficients are prone to errors and are not easy to promote;

[0014] (3) The double ion crossover method requires two ion systems (Na+, Na ... + K + The experiment is complex and lacks mathematical stability.

[0015] Therefore, there is an urgent need to develop a method and system for determining the Hamaker constant that is applicable to any ion system, fully automated, easy to operate, and provides reliable results.

[0016] Based on the above analysis, the urgent technical problems that need to be solved in the existing technology are:

[0017] Existing technologies suffer from problems such as high reliance on manual labor, cumbersome operation, inapplicability to any ion system, and lack of standardized procedures. Summary of the Invention

[0018] To address the problems existing in the prior art, this invention provides an automated method and system for determining the Hamaker constant of nanoparticles based on dynamic light scattering data, which is applicable to the determination of the Hamaker constant.

[0019] This invention is achieved by providing an automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data. The method includes:

[0020] S1: Perform dynamic light scattering experiments on the test particles in any electrolyte solution to obtain time-series data at multiple electrolyte concentrations. At the same time, determine the types of ions in the electrolyte solution through user input or automatic identification.

[0021] S2: Based on the ion type determined in step S1, automatically retrieve the effective charge coefficient γ of that ion from a pre-set ion-specific parameter database. i ;

[0022] S3: For each concentration C i Automatically calculates the total average coagulation rate (TAA);

[0023] S4: Construct a scatter set and use a piecewise linear fitting algorithm to automatically identify inflection points, thereby achieving automatic interpretation of critical coagulation concentration (CCC);

[0024] S5: Using the Hamaker constant A as an unknown parameter, establish a calculation model for the energy barrier ΔW(A) and automatically invert the Hamaker constant;

[0025] S6: Output results, outputting the critical flocculation concentration CCC and Hamaker constant A, and optionally outputting the TAA–C fitting line graph, energy barrier convergence curve, etc.

[0026] Furthermore, in step S1, a dynamic light scattering experiment is performed on the test particle in any electrolyte solution to obtain multiple electrolyte concentrations C. i Time series data (i = 1, 2, …, n), with different condensation times t recorded at each concentration. j The corresponding average hydrodynamic diameter D(t) j ).

[0027] Furthermore, in S2, the database includes at least Li + Na + K + Cs +Mg 2+ Ca 2+ It has an effective charge coefficient and supports users to add new ions.

[0028] Furthermore, in S3, for each concentration C i Perform the following sub-steps:

[0029] S3.1: Calculate the true condensation rate V1(t) at each time point. j ):

[0030] (1)

[0031] In the formula, D0(nm) and D(t) j (nm) represent the initial time and t = t, respectively. j The average hydraulic diameter of the condensate can be directly obtained by DLS measurement.

[0032] S3.2: Calculate the overall average coagulation rate from t = 0 to the preset endpoint t0 using a numerical integration method (preferably the trapezoidal rule):

[0033] (2)

[0034] In the formula, TAA(C i ) represents the overall average coagulation rate during the time period from t = 0 to t = t0.

[0035] Furthermore, S4 includes the following steps:

[0036] S4.1: Using electrolyte concentration C i Construct a scatter set {(C) = x-axis and TAA = y-axis. i ,TAA i )};

[0037] S4.2: Automatically identify turning points using a piecewise linear fitting algorithm: Traverse all possible breakpoints k (k=2, …,n−1) and divide the data into left segment (1…k) and right segment (k+1…n);

[0038] Linear fitting was performed on the left segment data (reaction-limited aggregation stage, RLCA) to obtain the straight line L1(C) = a1C. i +b1;

[0039] Linear fitting of the right segment data (diffusion-limited condensation stage, DLCA) yields the straight line L2(C) = a2C. i +b2;

[0040] Calculate the total sum of squared residuals:

[0041] (3)

[0042] S4.3: Select the breakpoint k that minimizes RSS(k). ∗ As the dividing point between RLCA and DLCA;

[0043] S4.4: Calculate the x-coordinate of the intersection point of the fitted line on the left and right sides:

[0044] (4)

[0045] Furthermore, S5 includes the following steps:

[0046] S5.1: Based on the modified double-layer theory, utilizing γ i Correction of interfacial potential values ​​of nanoparticles under different ionic systems:

[0047] (5)

[0048] (6)

[0049] In the above formula, It is the surface potential of charged particles; Z i It is the ionic valence, F(Cmol) –1 R is the Faraday constant, where R(J mol) –1 K –1 ) and T (K) represent the gas constant and thermodynamic temperature, respectively, and κ (m –1 ) represents the Debye parameter. γ i σ(C m) is a quantitative characterization parameter for ion-specific effects. –2 ) is the surface charge density of the nanoparticles, a = tanh(Z) i F / RT);

[0050] S5.2: Based on DLVO theory, using the Hamaker constant A as an unknown parameter, a calculation model for the energy barrier ΔW(A) is established:

[0051] (7)

[0052] (8)

[0053] (9)

[0054] (10)

[0055] In the above formula, λ (m) is the distance between two adjacent particles; PEDL (λ) is the electrostatic repulsion pressure between particles, P vdW (λ) represents the pressure of the van der Waals attraction between particles;

[0056] S5.3: Construct a nonlinear equation for A: f(A) = ΔW(A) - 0.2 kT = 0, where 0.2 kT is the actual average kinetic energy during the Brownian particle collision;

[0057] S5.4: Solve the equation f(A) = 0 using Newton's iteration method. The iteration formula is:

[0058] (11)

[0059] Where the derivative f′(A) n Numerical difference calculation is used, with a step size of A. n ×10 –6 Or preset a minimum value;

[0060] S5.5: Set the convergence tolerance ε (preferably 1×10⁻⁶). -25 J), when |A n+1 -A n Stop iterating when | < ε and output the value of A.

[0061] Another object of the present invention is to provide an automated system for determining the Hamaker constant of nanoparticles based on dynamic light scattering data, the system comprising:

[0062] The data acquisition and ion recognition module is used to acquire time-series data at multiple electrolyte concentrations and the types of ions in the electrolyte solution.

[0063] The ion-specific parameter automatic retrieval module is used to automatically retrieve the effective charge coefficient of the ion from a preset ion-specific parameter database.

[0064] The Total Average Coagulation Rate (TAA) automatic calculation module is used for each concentration C i Automatically calculates the total average coagulation rate (TAA);

[0065] The Critical Coagulation Concentration (CCC) Automatic Interpretation Module is used to construct a scatter plot and automatically identify inflection points using a piecewise linear fitting algorithm to achieve automatic interpretation of the Critical Coagulation Concentration (CCC).

[0066] The Hamaker constant automatic inversion module is used to build a computational model and iteratively solve for the Hamaker constant.

[0067] The results output module is used to output the critical coagulation concentration (CCC) and Hamaker constant (A), and optionally outputs TAA-C. iFitting straight line graphs, energy barrier convergence curves, etc.

[0068] Furthermore, the automatic calculation module for the overall average coagulation rate takes the initial average hydrodynamic diameter obtained from the dynamic light scattering experiment at each electrolyte concentration, the average hydrodynamic diameter corresponding to each coagulation time point, and the preset endpoint time as inputs. It determines the actual coagulation rate at each time point according to the relationship between the average hydrodynamic diameter and the initial average hydrodynamic diameter over time, and performs numerical integration and time averaging on the actual coagulation rate within the preset endpoint time range to output the overall average coagulation rate corresponding to each electrolyte concentration. The overall average coagulation rate serves as the input data for the automatic determination module of critical sedimentation concentration.

[0069] Furthermore, the automatic critical flocculation concentration determination module uses the electrolyte concentration and its corresponding total average flocculation rate as input to construct a concentration-total average flocculation rate scatter set. Based on the relationship that the reaction-limited flocculation stage exhibits linear changes and the diffusion-limited flocculation stage tends to a stable plateau, the module performs left-segment linear fitting and right-segment linear fitting on both sides of the candidate breakpoints, respectively. By comparing the sum of squared total residuals corresponding to each candidate breakpoint, the boundary breakpoint is determined, and the critical flocculation concentration determined by the intersection of the left-segment linear relationship and the right-segment linear relationship is output. The critical flocculation concentration is then entered into the Hamaker constant automatic inversion module as the concentration condition for inversion calculation.

[0070] Furthermore, the automatic Hamaker constant inversion module takes the critical agglomeration concentration, the effective charge coefficient corresponding to the ion type, the surface charge density of nanoparticles, temperature, ion valence, and interparticle spacing parameters as inputs. It determines the particle interface potential under different ion systems according to the relationship between the effective charge coefficient and the interface potential. Based on the relationship between electrostatic repulsion and van der Waals attraction, which jointly determine the energy barrier of interparticle interaction, the Hamaker constant is used as the unknown parameter to establish an energy barrier calculation model. The automatic Hamaker constant inversion module further takes the difference between the energy barrier and the average kinetic energy of Brownian particle collisions as the iteration target. It uses numerical difference to obtain the iteration derivative and corrects the Hamaker constant according to the Newton iteration update relationship. The iteration stops when the results of two adjacent iterations meet the preset convergence tolerance, and the Hamaker constant is output to the result output module.

[0071] Another object of the present invention is to provide a computer device including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the automated determination method for the Hamaker constant of nanoparticles based on dynamic light scattering data.

[0072] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the automated determination method for the Hamaker constant of nanoparticles based on dynamic light scattering data.

[0073] Another objective of this invention is to provide an information data processing terminal, which includes the aforementioned automated determination system for the Hamaker constant of nanoparticles based on dynamic light scattering data.

[0074] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] Fully automated process: Traditional manual calculations require first calculating the TAA using Excel, then fitting and interpreting the CCC, and finally calculating 12-16 assumed Hamaker constants to approximate the true value, typically taking 2-3 hours. In this invention, however, CCC interpretation and Hamaker constant inversion are both automatically completed by the algorithm, eliminating the need for manual calculations or step-by-step approximation calculations, thus eliminating subjective errors. Data import and automatic algorithm calculations are completed in approximately 5 minutes. Therefore, this invention significantly improves measurement efficiency and repeatability.

[0077] Applicable to any ion system: Through its built-in ion-specific parameter database, the method of this invention is applicable to common ion systems; and the user only needs to select the ion type, and the system automatically calls the corresponding γ-ion. i This value solves the problems of errors and incompatibility when manually checking parameters, and truly achieves unified processing for different ion systems.

[0078] Simple to operate and cost-effective: Only a single-ion system is needed for dynamic light scattering experiments, which reduces the workload by more than 50% compared to a dual-ion system (such as CN118961549A), thus reducing time and reagent costs.

[0079] High mathematical stability: This method uses piecewise linear fitting to automatically identify CCC and Newton's iteration method to solve for the Hamaker constant. It has a fast convergence speed and ensures the accuracy of the results by setting reasonable tolerance.

[0080] Highly standardizable and scalable: This invention provides a complete automated measurement process that is easy to promote as an industry standard method; the database supports user-defined addition of new ions, facilitating subsequent expansion.

[0081] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0082] This invention provides a software module or stand-alone data analysis system that can be directly embedded into existing dynamic light scattering instruments. The global market for dynamic light scattering particle size analyzers was valued at approximately US$127 million in 2025 and is projected to grow to approximately US$189 million by 2032, representing a CAGR of approximately 5.9%. This invention can serve as a complementary data analysis module for the aforementioned instruments, allowing direct entry into the supply chain through software licensing or system integration.

[0083] Compared to existing manual processing methods, this invention reduces the data analysis time for a single measurement from several hours to minutes, eliminating manual interpretation and trial calculations, allowing operators without a background in colloid chemistry to complete the measurements. This software module is compatible with the data formats of different brands of DLS instruments and is sold as standalone software or an embedded module, or as a paid upgrade feature for existing instruments.

[0084] Furthermore, the methodological results of this invention can be further transformed into group standards or industry standards, providing standardized operating guidelines for relevant testing institutions and generating continuous intellectual property benefits through standard reference.

[0085] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0086] Currently, there is no standard method for determining the Hamaker constant, either domestically or internationally. Existing methods either rely on expensive equipment such as atomic force microscopes and have stringent sample requirements, or are based on theoretical calculations and require prior knowledge of the material's dielectric or spectral properties across the entire frequency range. While measurement pathways based on dynamic light scattering have been explored, existing schemes all rely on manual interpretation of the CCC inflection point (from TAA to C). i The Hamaker constant was calculated by visual estimation in the scatter plot and by manual approximation, but no standardized and repeatable operating procedure was formed.

[0087] This invention is the first to incorporate the correction parameters for ion-specific effects into an automatically accessible database. Users only need to select the ion type, and the system automatically completes the γ-ray correction. i The complete process of value retrieval, automatic CCC interpretation, and automatic Hamaker constant inversion achieves fully automated output from raw DLS data to Hamaker constants. This technical approach has not been disclosed in any domestic or international literature or patents.

[0088] (3) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully:

[0089] The field of colloid and interface science has long faced a paradox: the Hamaker constant is a fundamental parameter describing van der Waals interactions between particles, yet a simple and reliable method for its measurement is lacking. Theoretical calculations require knowledge of the dielectric properties of materials across the entire frequency range, experimental methods (such as AFM) have extremely high requirements for equipment and samples, and the CCC rule based on DLVO theory relies on manual operation and yields results that vary from person to person. This paradox has led to the Hamaker constant being either ignored or subjected to rough estimates in practical research and engineering applications.

[0090] This invention replaces manual interpretation and trial calculation with an algorithm, making the determination of the Hamaker constant a standardized process that can be completed by ordinary experimental personnel, thus solving the long-standing technical problem in this field that the parameter is important but cannot be measured accurately or quickly. Attached Figure Description

[0091] Figure 1 This is a flowchart of an automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data, provided in an embodiment of the present invention.

[0092] Figure 2 This is a block diagram of an automated determination system for the Hamaker constant of nanoparticles based on dynamic light scattering data, provided in an embodiment of the present invention.

[0093] Figure 3 The data show the change in Li system particle size over time (Figure a) and the TAA segmented fitting CCC interpretation output (Figure b);

[0094] Figure 4 The data show the change in particle size of the K system over time (Figure a) and the TAA segmented fitting CCC interpretation results (Figure b). Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0096] like Figure 1 As shown in the figure, this invention provides an automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data. The method includes:

[0097] S1: Perform dynamic light scattering experiments on the test particles in any electrolyte solution to obtain time-series data at multiple electrolyte concentrations. At the same time, determine the types of ions in the electrolyte solution through user input or automatic identification.

[0098] S2: Based on the ion type determined in step S1, automatically retrieve the effective charge coefficient γ of that ion from a pre-set ion-specific parameter database.i ;

[0099] S3: For each concentration C i Automatically calculates the overall average coagulation rate (TAA);

[0100] S4: Construct a scatter set and use a piecewise linear fitting algorithm to automatically identify inflection points to achieve automatic interpretation of critical sedimentation concentration;

[0101] S5: Using the Hamaker constant A as an unknown parameter, establish a calculation model for the energy barrier ΔW(A) and automatically invert the Hamaker constant;

[0102] S6: Output results, outputting the critical flocculation concentration CCC and Hamaker constant A, and optionally outputting the TAA–C fitting curve, energy barrier convergence curve, etc.

[0103] In step S1, a dynamic light scattering experiment is performed on the test particles in any electrolyte solution to obtain multiple electrolyte concentrations C. i Time series data (i = 1, 2, …, n), with different condensation times t recorded at each concentration. j The corresponding average hydrodynamic diameter D(t) j ).

[0104] In S2, the database includes at least Li + Na + K + Cs + Mg 2+ Ca 2+ The effective charge coefficient, data source: Luo et al., 2018, and supports user-defined addition of new ions.

[0105] S3, for each concentration C i Perform the following sub-steps:

[0106] S3.1: Calculate the true condensation rate V1(t) at each time point. j ):

[0107] (1)

[0108] In the formula, D0(nm) and D(t) j (nm) represent the initial time and t = t, respectively. j The average hydraulic diameter of the condensate can be directly obtained by DLS measurement.

[0109] S3.2: Calculate the overall average coagulation rate from t = 0 to the preset endpoint t0 using numerical integration:

[0110] (2)

[0111] In the formula, TAA(C i ) represents the overall average coagulation rate during the time period from t = 0 to t = t0.

[0112] S4 includes the following steps:

[0113] S4.1: Using electrolyte concentration C i Construct a scatter set {(C) = x-axis and TAA = y-axis. i ,TAA i )};

[0114] S4.2: Automatically identify turning points using a piecewise linear fitting algorithm: Traverse all possible breakpoints k (k=2, …,n−1) and divide the data into left segment (1…k) and right segment (k+1…n);

[0115] Linear fitting was performed on the left segment of the data (RLCA region) to obtain the straight line L1(C) = a1C. i + b1;

[0116] Linear fitting was performed on the right segment of the data (DLCA region), resulting in the straight line L2(C) = a2C. i + b2, where the absolute value of a2 is much smaller than a1, characterizing the slow change in TAA with concentration in the DLCA region; calculate the total residual sum of squares:

[0117] (3)

[0119] S4.3: Select the breakpoint k that minimizes RSS(k). ∗ As the dividing point between RLCA and DLCA;

[0120] S4.4: Calculate the x-coordinate of the intersection point of the fitted line L1(C) on the left and the fitted line L2(C) on the right:

[0121] (4)

[0122] S5 includes the following steps:

[0123] S5.1: Based on the modified double-layer theory, utilizing γ i Correction of interfacial potential values ​​of nanoparticles under different ionic systems:

[0124] (5)

[0125] (6)

[0126] In the above formula, It is the surface potential of charged particles; Z i It is the ionic valence, F(Cmol) –1 R is the Faraday constant; ) represents R(J mol –1 K –1 ) and T (K) represent the gas constant and thermodynamic temperature, respectively; κ (m –1 ) represents the Debye parameter. γ i σ(C m) is a quantitative characterization parameter for ion-specific effects, used to quantitatively characterize the differences in the strength of interfacial interaction energies between different isovalent ions; –2 ) is the surface charge density of the nanoparticles; a = tanh(Z) i F / RT).

[0127] S5.2: Based on DLVO theory, using the Hamaker constant A as an unknown parameter, a calculation model for the energy barrier ΔW(A) is established:

[0128] (7)

[0129] (8)

[0130] (9)

[0131] (10)

[0132] In the above formula, λ (m) is the distance between two adjacent particles; P EDL (λ) represents the electrostatic repulsion pressure between particles, the magnitude of which depends on the potential at the point of overlap of the double electric layers, i.e., the midpoint potential φ(λ / 2); P vdW (λ) is the van der Waals attraction pressure between particles, and its value depends on the Hamaker constant of the nanoparticles, A.

[0133] S5.3: Construct a nonlinear equation for A: f(A) = ΔW(A) - 0.2 kT = 0, where 0.2 kT is the actual average kinetic energy during the Brownian particle collision (Li et al., 2015).

[0134] S5.4: Solve the equation f(A) = 0 using Newton's iteration method. The iteration formula is:

[0135] (11)

[0136] Where the derivative f′(A) nNumerical difference calculation is used, with a step size of A. n ×10 –6 Or preset a minimum value;

[0137] S5.5: Set the convergence tolerance ε, when |A n+1 -A n Stop iterating when | < ε and output the value of A.

[0138] like Figure 2 As shown, this embodiment of the invention provides an automated system for determining the Hamaker constant of nanoparticles based on dynamic light scattering data. The system includes:

[0139] The data acquisition and ion recognition module is used to acquire time-series data at multiple electrolyte concentrations and the types of ions in the electrolyte solution.

[0140] The ion-specific parameter automatic retrieval module is used to automatically retrieve the effective charge coefficient of the ion from a preset ion-specific parameter database.

[0141] The Total Average Coagulation Rate (TAA) automatic calculation module is used for each concentration C i Automatically calculates the total average coagulation rate (TAA);

[0142] The Critical Coagulation Concentration (CCC) Automatic Interpretation Module is used to construct a scatter plot and automatically identify inflection points using a piecewise linear fitting algorithm to achieve automatic interpretation of the Critical Coagulation Concentration (CCC).

[0143] The Hamaker constant automatic inversion module is used to build a computational model and iteratively solve for the Hamaker constant.

[0144] The results output module is used to output the critical coagulation concentration (CCC) and the Hamaker constant (A), and optionally outputs TAA–C. i Fitting curves, energy barrier convergence curves, etc.

[0145] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0146] 1. Example 1: Montmorillonite colloid in Li + Determination of Hamaker constant in the system

[0147] Experimental materials: montmorillonite colloid, LiNO3 electrolyte solution (analytical grade).

[0148] Experimental conditions: temperature 25℃, montmorillonite colloid particle concentration 0.07 g / L. -1 The LiNO3 concentration gradient was set to 10, 30, 50, 70, 100, 150, 200, 300, and 500 mmol / L.-1 The average hydrodynamic diameter was continuously measured for 30 minutes at a scattering angle of 90° using a dynamic light scattering instrument (BI-200SM, Brookhaven), and recorded every 30 seconds.

[0149] Experimental steps:

[0150] (1) Prepare LiNO3 solution according to concentration gradient, add an equal amount of montmorillonite colloidal suspension, shake well and immediately put it into DLS sample cell;

[0151] (2) Start the DLS measurement and record the change data of particle size over time at each concentration;

[0152] (3) Import the data into the automated determination system described in this embodiment of the invention, and select "Li" as the ion species. + ”;

[0153] (4) The system automatically calls γ Li =1.063, proceed with steps S3–S5.

[0154] Result: System outputs CCC Li = 277.3 mmol L -1 Hamaker constant A = 6.20 × 10 -20 J. This result is consistent with the literature-reported range of Hamaker constant for montmorillonite (6.0~6.6×10). -20 The high degree of agreement between the two methods verifies the reliability of this approach.

[0155] Figure 3 Data on the change of Li system particle size over time (Figure a) and the TAA segmented fitting CCC interpretation output (Figure b).

[0156] 2. Example 2: Montmorillonite colloid in K + Determination of the Hamaker constant in the system (verification of generality)

[0157] Experimental conditions: Similar to Example 1, but the electrolyte was changed to KNO3, and the concentration gradient was set to 10, 20, 30, 40, 50, 70, 100, 150, 200 mmol / L. -1 .

[0158] Operation: Select "K" as the ion type in the system. + ", automatically call γ K = 1.942, execute steps S3–S5.

[0159] Result: The system output CCC = 80.3 mmol / L -1 Hamaker constant A = 6.09 × 10 -20J. and Li + System results (6.20×10) -20 The relative deviation of J) is less than 2%, which proves the universality and consistency of the results under different ion systems.

[0160] Figure 4 Data on the change of particle size of the K system over time (Figure a) and the CCC interpretation results of TAA segmented fitting (Figure b).

[0161] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0162] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. An automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data, characterized in that, The method specifically includes: S1: Perform dynamic light scattering experiments on the test particles in any electrolyte solution to obtain time-series data at multiple electrolyte concentrations. At the same time, determine the types of ions in the electrolyte solution through user input or automatic identification. S2: Based on the ion type determined in step S1, automatically retrieve the effective charge coefficient γ of that ion from a pre-set ion-specific parameter database. i ; S3: For each concentration C i Automatically calculates the overall average coagulation rate (TAA); S4: Construct a scatter set and use a piecewise linear fitting algorithm to automatically identify inflection points to achieve automatic interpretation of critical sedimentation concentration; S5: Using the Hamaker constant A as an unknown parameter, establish a calculation model for the energy barrier ΔW(A) and automatically invert the Hamaker constant; S6: Output results, showing the critical coagulation concentration (CCC) and Hamaker constant (A), with optional output of TAA-C. i Fitting curve and energy barrier convergence curve.

2. The automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 1, characterized in that, In step S1, a dynamic light scattering experiment is performed on the test particles in any electrolyte solution to obtain multiple electrolyte concentrations C. i Time series data for i = 1, 2, …, n, with different coagulation times t recorded at each concentration. j The corresponding average hydrodynamic diameter D(t) j ).

3. The automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 1, characterized in that, In S2, the database includes at least Li + Na + K + Cs + Mg 2+ Ca 2+ It has an effective charge coefficient and supports users to add new ions.

4. The automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 1, characterized in that, S3, for each concentration C i Perform the following sub-steps: S3.1: Calculate the true condensation rate V1(t) at each time point. j ): (1) In the formula, D0(nm) and D(t) j (nm) represent the initial time and t = t, respectively. j The average hydraulic diameter of the condensate can be directly obtained by DLS measurement. S3.2: Calculate the overall average coagulation rate from t = 0 to the preset endpoint t0 using numerical integration: (2) In the formula, TAA(C i ) represents the overall average coagulation rate during the time period from t = 0 to t = t0.

5. The automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 1, characterized in that, S4 includes the following steps: S4.1: Using electrolyte concentration C i Construct a scatter set {(C) = x-axis and TAA = y-axis. i ,TAA i )}; S4.2: Automatically identify turning points using a piecewise linear fitting algorithm: Traverse all possible breakpoints k (k=2, …, n−1) and divide the data into left segment (1…k) and right segment (k+1…n); Linear fitting was performed on the left segment of the data (RLCA region) to obtain the straight line L1(C) = a1C. i + b1; Linear fitting was performed on the right segment of the data (DLCA region), resulting in the straight line L2(C) = a2C. i + b2, where the absolute value of a2 is much smaller than a1, characterizing the slow change in TAA with concentration in the DLCA region; calculate the total residual sum of squares: (3) S4.3: Select the breakpoint k that minimizes RSS(k). ∗ As the dividing point between RLCA and DLCA; S4.4: Calculate the x-coordinate of the intersection point of the fitted line L1(C) on the left and the fitted line L2(C) on the right: (4)。 6. The automated method for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 1, characterized in that, S5 includes the following steps: S5.1: Based on the modified double-layer theory, utilizing γ i Correction of interfacial potential values ​​of nanoparticles under different ionic systems: (5) (6) In the above formula, It is the surface potential of charged particles; Z i It is the ionic valence, F(Cmol) -1 R is the Faraday constant, where R (J / mol) is the constant. -1 K -1 ) and T (K) represent the gas constant and thermodynamic temperature, respectively, and κ (m -1 ) represents the Debye parameter. γ i σ(C m) is a quantitative characterization parameter for ion-specific effects. −2 ) is the surface charge density of the nanoparticles, a = tanh(Z) i F / RT); S5.2: Based on DLVO theory, using the Hamaker constant A as an unknown parameter, a calculation model for the energy barrier ΔW(A) is established: (7) (8) (9) (10) In the above formula, λ (m) is the distance between two adjacent particles; P EDL (λ) is the electrostatic repulsion pressure between particles, P vdW (λ) represents the pressure of the van der Waals attraction between particles; S5.3: Construct a nonlinear equation for A: f(A) = ΔW(A) - 0.2 kT = 0, where 0.2 kT is the actual average kinetic energy during the Brownian particle collision; S5.4: Solve the equation f(A) = 0 using Newton's iteration method. The iteration formula is: (11) Where the derivative f′(A) n Numerical difference calculation is used, with a step size of A. n ×10 −6 Or preset a minimum value; S5.5: Set the convergence tolerance ε, when |A n+1- A n Stop iterating when | < ε and output the value of A.

7. An automated system for determining the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claims 1-6, characterized in that, The system specifically includes: The data acquisition and ion recognition module is used to acquire time-series data at multiple electrolyte concentrations and the types of ions in the electrolyte solution. The ion-specific parameter automatic retrieval module is used to automatically retrieve the effective charge coefficient of the ion from a preset ion-specific parameter database. The overall average coagulation rate automatic calculation module is used for each concentration C i Automatically calculates the overall average coagulation rate; The critical sedimentation concentration automatic interpretation module is used to construct a scatter set and automatically identify the turning point using a piecewise linear fitting algorithm to achieve automatic interpretation of the critical sedimentation concentration. The Hamaker constant automatic inversion module is used to build a computational model and iteratively solve for the Hamaker constant. The results output module is used to output the critical flocculation concentration CCC and the Hamaker constant A, and can optionally output the TAA-C fitting line graph and the energy barrier convergence curve.

8. The automated determination system for the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 7, characterized in that, The automatic calculation module for the overall average coagulation rate takes the initial average hydrodynamic diameter obtained from dynamic light scattering experiments at each electrolyte concentration, the average hydrodynamic diameter corresponding to each coagulation time point, and the preset endpoint time as inputs. It determines the actual coagulation rate at each time point according to the relationship between the average hydrodynamic diameter and the initial average hydrodynamic diameter over time, and performs numerical integration and time averaging on the actual coagulation rate within the preset endpoint time range. It outputs the overall average coagulation rate corresponding to each electrolyte concentration. The overall average coagulation rate is used as input data for the automatic determination module of critical sedimentation concentration.

9. The automated determination system for the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 7, characterized in that, The automatic critical flocculation concentration determination module takes the electrolyte concentration and its corresponding total average flocculation rate as input, constructs a concentration-total average flocculation rate scatter set, and performs left-segment linear fitting and right-segment constant characterization on both sides of the candidate breakpoint according to the relationship that the reaction-limited flocculation stage shows linear changes and the diffusion-limited flocculation stage tends to a stable plateau. By comparing the total residual sum of squares corresponding to each candidate breakpoint, the boundary breakpoint is determined, and the critical flocculation concentration determined by the intersection of the left-segment linear relationship and the right-segment plateau relationship is output. The critical flocculation concentration is entered into the Hamaker constant automatic inversion module as the concentration condition for inversion calculation.

10. The automated determination system for the Hamaker constant of nanoparticles based on dynamic light scattering data as described in claim 7, characterized in that, The automatic Hamaker constant inversion module takes the critical agglomeration concentration, the effective charge coefficient corresponding to the ion type, the surface charge density of nanoparticles, temperature, ion valence, and interparticle spacing parameters as inputs. It determines the particle interface potential under different ion systems according to the relationship between the effective charge coefficient and the interface potential. Based on the relationship between electrostatic repulsion and van der Waals attraction, which jointly determine the energy barrier of interparticle interaction, the Hamaker constant is used as the unknown parameter to establish an energy barrier calculation model. The automatic Hamaker constant inversion module further uses the difference between the energy barrier and the average kinetic energy of Brownian particle collisions as the iteration target. It uses numerical difference to obtain the iteration derivative and corrects the Hamaker constant according to the Newton iteration update relationship. The iteration stops when the results of two adjacent iterations meet the preset convergence tolerance, and the Hamaker constant is output to the result output module.

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