Adsorbing material surface functional group analysis method and system based on Gaussian function model

Abstract

The invention relates to the technical field of functional group analysis, and discloses an adsorption material surface functional group analysis method and system based on a Gaussian function model.According to the method, proton binding isotherm data of an adsorption material under different pH conditions are obtained through an incremental titration method, and the proton binding isotherm data are input into a Gaussian function model; the method comprises the following steps: carrying out characterization analysis on different types of functional groups, fitting experimental data by using a nonlinear least square method to obtain optimized parameters, verifying the accuracy of the optimized parameters by using a preparatory test means, analyzing the proportions of various functional groups in the adsorption material based on the verified optimized parameters, and generating a surface functional group distribution map. According to the method, distribution of different functional groups is accurately analyzed through the Gaussian function model, the defect that quantitative analysis of a traditional method is not accurate is overcome, high accuracy of a result is ensured, detailed data support is provided for design and optimization of an adsorption material, and the problem that in the prior art, when multiple functional groups coexist, the detection effect is not accurate is solved.

Description

Technical Field

[0001] This invention relates to the technical field of functional group analysis, and in particular to a method and system for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model. Background Art

[0002] Adsorbent materials are widely used in environmental protection, catalysis, and energy storage. Their adsorption performance is closely related to the type, concentration, and distribution of functional groups on the material surface. By studying the surface functional groups of adsorbent materials, their performance in pollutant removal, catalytic reactions, and electrochemical applications can be effectively improved. Common surface functional groups of adsorbent materials include carboxyl groups (–COOH), phenolic hydroxyl groups (–OH), and lactones (–COO–). Different functional groups have different chemical properties and adsorption characteristics. For example, carboxyl groups have strong acidity, phenolic hydroxyl groups can form complexes with metal ions, while lactones may interact with other functional groups or molecules. Therefore, accurate and quantitative analysis of the surface functional group distribution of adsorbent materials is crucial for optimizing adsorption performance. Traditional titration methods (such as Boehm titration and pH titration) can only provide qualitative or semi-quantitative data and cannot accurately reflect the specific concentration of functional groups, especially when multiple functional groups coexist, which can easily lead to inaccurate data. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, aiming to solve the problem of inaccurate detection results when multiple functional groups coexist in the prior art.

[0004] This invention is implemented as follows: Firstly, this invention provides a method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, comprising: Proton binding isotherm data of the adsorbent material under different pH conditions were obtained by incremental titration. The proton binding isotherm data are input into a Gaussian function model, which then performs characterization analysis on the proton binding isotherm data for carboxyl, lactone, and phenolic hydroxyl functional groups to obtain experimental parameters. The Gaussian function model has the following functional form: N i denoted as , where μi is the molar concentration of the i-th functional group, μi is the average pK value of the corresponding functional group, and σi is the standard deviation of the distribution, for carboxyl groups (pK≈2.0-6.0), lactones (pK≈6.0-9.0), and phenolic hydroxyl groups (pK≈9.0-13.0). The experimental parameters were fitted using a nonlinear least squares method to generate optimized parameters; The accuracy of the optimization parameters is verified by using pre-prepared testing methods to confirm their accuracy. When the accuracy of the optimized parameters meets expectations, the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups in the adsorbent material is analyzed based on the optimized parameters to generate a surface functional group distribution map of the adsorbent material.

[0005] Secondly, the present invention provides a functional group analysis system for the surface of adsorbent materials based on a Gaussian function model, used to implement the functional group analysis method for the surface of adsorbent materials based on a Gaussian function model as described in any one of the first aspects.

[0006] This invention provides a method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, which has the following advantages: This invention employs incremental titration to obtain proton binding isotherm data of adsorbent materials under different pH conditions. The proton binding isotherm data are input into a Gaussian function model for characterization analysis of different types of functional groups. The experimental data are fitted using nonlinear least squares to obtain optimized parameters. The accuracy of the optimized parameters is verified through preliminary testing. Based on the verified optimized parameters, the proportion of various functional groups in the adsorbent material is analyzed, and a surface functional group distribution map is generated. This method accurately analyzes the distribution of different functional groups through a Gaussian function model, overcoming the inaccuracy of quantitative analysis in traditional methods, ensuring high accuracy of the results, providing detailed data support for the design and optimization of adsorbent materials, and solving the problem of inaccurate detection results when multiple functional groups coexist in existing technologies. Attached Figure Description

[0007] Figure 1 This is a schematic diagram illustrating the steps of a method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, as provided in an embodiment of the present invention. Detailed Implementation

[0008] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0009] The implementation of the present invention will be described in detail below with reference to specific embodiments.

[0010] Reference Figure 1 The diagram shows a preferred embodiment of the present invention.

[0011] In a first aspect, the present invention provides a method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, comprising: S1: Proton binding isotherm data of the adsorbent material under different pH conditions were obtained by incremental titration. S2: Input the proton binding isotherm data into the Gaussian function model, and let the Gaussian function model perform characterization analysis on the proton binding isotherm data for carboxyl, lactone and phenolic hydroxyl functional groups to obtain experimental parameters; The Gaussian function model has the following functional form: N i Let be the molar concentration of the i-th type of functional group, μi be the average pK value of the corresponding functional group, and σi be the standard deviation of the distribution. S3: Fit the experimental parameters using the nonlinear least squares method to generate optimized parameters; S4: Verify the accuracy of the optimization parameters using pre-prepared testing methods to confirm the accuracy of the optimization parameters; S5: When the accuracy of the optimized parameters meets expectations, the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups of the adsorbent material is analyzed according to the optimized parameters to generate a surface functional group distribution map of the adsorbent material.

[0012] Specifically, in step S1 of the embodiment provided by the present invention, the adsorbent material needs to be dried and ground to ensure its uniform particle size. This is to ensure the accuracy of the test results, because adsorbent material with uniform particle size can provide more consistent adsorption data. The pretreated adsorbent material needs to be accurately weighed to ensure that its quality specifications meet the experimental requirements and is used as the test object.

[0013] More specifically, this is achieved by preparing acidic and alkaline electrolyte solutions of specific concentrations. The selection and concentration of the titration solutions should cover the required pH range to ensure the comprehensiveness of the experiment. During the experiment, known volumes and concentrations of acidic or alkaline electrolyte solutions are gradually added to the adsorbent material solution. After each addition of a certain amount of solution, the pH value of the solution is monitored in real time. A titration curve is generated by continuously recording pH changes during the titration process.

[0014] More specifically, a blank control experiment without adsorbent material was conducted simultaneously to correct the titration curve. The data from the blank experiment can be used to correct for the proton consumption and release of the solution itself during the titration process, thereby avoiding interference and ensuring the accuracy of the experimental data. During the titration process, the proton balance equation was used to transform the titration curve to obtain the proton binding isotherm. The proton binding isotherm reflects the ability of the adsorbent material surface to bind protons under different pH conditions, and can be used to analyze the properties and concentration of its surface functional groups.

[0015] Understandably, precise titration and real-time monitoring of pH changes can yield highly accurate proton binding isotherm data, providing a reliable experimental basis for subsequent functional group analysis. Incremental titration allows for testing under a wide range of pH conditions, comprehensively reflecting the proton binding characteristics of adsorbent materials under different acidic and alkaline environments. This comprehensiveness helps to gain a deeper understanding of the surface properties of adsorbent materials, especially their behavior under different environments. By meticulously monitoring the pH changes after each addition of acid or alkaline solution during titration, the interaction between functional groups and protons on the surface of the adsorbent material can be sensitively captured, and even minute changes can be detected, thus obtaining more detailed proton binding information.

[0016] More specifically, the blank control experiment provides crucial support for the correction of titration data, ensuring the accuracy of the titration results. By correcting for the data on proton consumption and release in the solution itself, experimental errors can be effectively eliminated, ensuring the acquisition of authentic adsorption material data. Through the calculation of proton binding isotherms, the surface functional groups of the adsorption material (such as carboxyl groups, lactones, and phenolic hydroxyl groups) can be further analyzed using methods such as Gaussian function models. This helps to accurately identify the types and quantities of surface functional groups in the material, thereby providing a theoretical basis for optimizing the performance of the adsorption material.

[0017] Specifically, in step S2 of the embodiment provided by the present invention, the proton binding amount (i.e., proton binding isotherm data) obtained by incremental titration under different pH conditions is input into the mathematical model. Typically, pH is used as the abscissa and the molar amount of bound protons is used as the ordinate to form a continuous fitting curve.

[0018] More specifically, through extensive experimental data collection and analysis, it was confirmed that the dissociation behavior of each type of surface functional group can be approximated by a normal distribution (Gaussian distribution function), the expression of which is: N i Let be the molar concentration of the i-th type of functional group, μi be the average pK value of the corresponding functional group, and σi be the standard deviation of the distribution.

[0019] More specifically, a numerical optimization algorithm is used to perform nonlinear least squares fitting to minimize the error between the model's predicted proton binding amount and the experimental data.

[0020] Understandably, by utilizing the differences in pKa values ​​of different functional groups, it is possible to effectively distinguish surface groups such as carboxyl groups (generally pKa ~4–5), lactones (pKa ~6–7), and phenolic hydroxyl groups (pKa ~9–10). The molar concentration of each type of functional group can be accurately determined, providing a quantitative analysis of the number of functional groups on the material surface. Unlike traditional single-point pKa analysis, the introduction of distribution parameters can simulate the heterogeneity of real material surfaces, improving the physical realism of the fit and the explanatory power of the model.

[0021] More specifically, Gaussian function models typically outperform traditional Langmuir models or monobasic acid-base models in fitting actual proton binding isotherm data. They are particularly suitable for complex multifunctional materials (such as biochar, porous carbon materials, and graphene oxide). The parameters obtained (such as which functional group has a high proportion and which has a wide pKa range) can be used to guide the direction of material synthesis or modification, such as increasing the number of carboxyl groups to enhance the adsorption capacity of metal ions. Gaussian function models can process data from multiple material samples in batches, and have good scalability and automation potential.

[0022] Specifically, in step S3 of the embodiment provided by the present invention, proton binding isotherm data (i.e., experimental data) obtained by incremental titration are acquired. These data are typically curves comparing pH with proton binding amount (e.g., adsorption amount). These data (pH value and proton binding amount) are prepared for subsequent fitting processes.

[0023] More specifically, determine the form of the model to be fitted, define an error function to represent the deviation between the model's predicted values ​​and the experimental data, usually using the squared error and minimizing the objective function, and select a suitable optimization algorithm for parameter fitting. Common algorithms include the Levenberg-Marquardt algorithm (LM) and gradient descent. The Levenberg-Marquardt algorithm is particularly effective in handling nonlinear least squares fitting and is suitable for multi-parameter optimization.

[0024] More specifically, the basic steps of the Levenberg-Marquardt algorithm are: to calculate the gradient and Hessian matrix (i.e., the second derivative) of the objective function, to update the parameters to minimize the error function, and to update the step size based on the error function value in order to find the minimum error point.

[0025] More specifically, the selected optimization algorithm is used to fit the experimental data. Through iterative processing, the values ​​of the model parameters are continuously adjusted to minimize the objective function, i.e., to minimize the difference between the model's predicted values ​​and the experimental data.

[0026] More specifically, after the fitting is complete, the optimization algorithm outputs the optimal fitting parameter values, namely the molar concentration of functional groups, pKa value, and standard deviation of the distribution. The fitting results are then analyzed to check the degree of matching between the fitted curve and the experimental data. The fitting effect can be verified by plotting a comparison graph of the fitted curve and the experimental data.

[0027] More specifically, to verify the validity of the fitting results, methods such as cross-validation and residual analysis can be used. Residual analysis mainly ensures the validity of the fitting results by observing the deviation between the fitted data and the experimental data. If necessary, other technical means (such as Boehm titration, FTIR analysis, etc.) can be used to verify the accuracy of the model parameters.

[0028] Understandably, the nonlinear least squares method can accurately fit experimental data through optimization algorithms, obtaining optimized parameters that closely approximate the experimental results. It has high accuracy and is particularly suitable for fitting data of complex systems and nonlinear relationships. It can better reproduce the distribution and properties of functional groups. This method is suitable for the optimization of multivariate models. In this case, the distribution of multiple functional groups is involved, and these functional groups have different dissociation characteristics. Using a Gaussian function model for fitting can accurately analyze the concentration, pKa value, and distribution width of different functional groups.

[0029] More specifically, the introduction of optimization algorithms such as Levenberg-Marquardt can effectively avoid the local optimum problem that traditional methods may encounter, ensure the global optimum of parameter fitting, and thus improve the robustness of the fitting process. Through detailed characterization of the functional groups on the surface of the adsorbent material, the optimized parameters (such as functional group concentration and pKa value) can provide theoretical guidance for the performance optimization of the material. For example, by increasing the concentration of a certain functional group, the adsorption capacity of the material under a specific environment can be improved.

[0030] More specifically, by using fitting methods to transform complex experimental data into quantitative parameters, the properties of functional groups on the surface of materials can be theoretically evaluated and optimized without the need for complex manual analysis and experimental operations. This method can not only be applied to parameter fitting of single materials, but also efficiently process experimental data of multiple different materials. It has good high-throughput analysis capabilities and is suitable for batch experiments and multi-sample material characterization.

[0031] Specifically, in step S4 of the embodiment provided by the present invention, a predicted value is generated by fitting a model based on the optimized parameters, and compared with the experimental data to calculate the residual. The residual analysis can reveal the deviation between the fitted model and the experimental data. If the residual distribution is random and there is no systematic error, it indicates that the model fits the experimental data relatively accurately and the optimized parameters are reliable. If the residual shows regularity or has obvious deviation, it indicates that the model may be improperly fitted or the optimized parameters may be insufficient, and the optimization results need to be re-evaluated.

[0032] More specifically, a dataset different from the original experimental dataset (such as different materials or different experimental conditions) is selected for validation. The optimized parameters fitted by nonlinear least squares method are used to predict the external dataset, and the prediction results are compared with the actual results. External validation can verify the applicability of the optimized parameters on new data and ensure that the obtained optimized parameters still have good predictive ability under different conditions. If the prediction results of the optimized parameters on the external dataset match the actual data well, it indicates that the optimized parameters have broad adaptability, further verifying their accuracy.

[0033] More specifically, the experiment is repeated multiple times under the same experimental conditions to obtain different datasets. The optimized parameters are then fitted, and the consistency between the fitting results of each experiment and the experimental data is compared to ensure that the optimized parameters have good repeatability and stability. Experimental replication can ensure that the optimized parameters remain consistent in different experimental repetitions, thereby enhancing their reliability. If the fitting results of each experiment are similar, it indicates that the optimized parameters have good accuracy and repeatability.

[0034] More specifically, other physicochemical methods are used to verify the rationality of the optimized parameters. For example: Boehm titration: used to verify whether the concentration of surface functional groups is consistent with the optimization results; FTIR analysis: through FTIR analysis, to confirm whether the fitted pKa value and functional group type are consistent with the actual values; acid-base titration: to detect the acid-base properties of the material and verify the accuracy of the pKa value. Physicochemical verification can directly measure the characteristics related to the optimized parameters, ensuring that the fitted optimized parameters have corresponding physicochemical properties in the actual material. If the experimental results are consistent with the optimized parameters, it further proves the accuracy of the optimized parameters.

[0035] Understandably, methods such as residual analysis, cross-validation, and external validation can ensure the accuracy of the optimized parameter fitting, avoid overfitting, and guarantee that the model has good generalization ability. Sensitivity analysis can help identify parameters that have a significant impact on the results, optimize these parameters, and improve the robustness and stability of the model, thereby ensuring that the parameters can effectively predict experimental results under different experimental conditions. Physicochemical validation and experimental replication validation can enhance the credibility of the optimized parameters in practical applications, ensuring that the optimized parameters are not only the fitting results of the mathematical model, but also consistent with the properties of actual materials. Combining mathematical fitting, experimental data, physicochemical analysis, and model prediction can verify the accuracy of the optimized parameters from multiple perspectives, ensuring that the results have higher reliability and practical application value.

[0036] Specifically, in step S5 of the embodiment provided by the present invention, a suitable experimental method is selected based on the optimized parameters to quantitatively analyze the content of functional groups such as carboxyl groups, lactones, and phenolic hydroxyl groups in the adsorbent material. Commonly used quantitative analysis methods include: Fourier transform infrared spectroscopy (FTIR): identifying the characteristic absorption peaks of different functional groups through infrared spectra, and quantitatively analyzing the content of each functional group by combining known spectral data and optimized parameters; titration analysis: measuring the concentration of functional groups in the adsorbent material using acid-base titration or other chemical titration methods, for example, titrating carboxyl functional groups with NaOH solution or titrating phenolic hydroxyl functional groups with phenolic reagents; and X-ray photoelectron spectroscopy (XPS): analyzing the elemental composition and chemical state of the adsorbent material surface through XPS to further infer the type and proportion of functional groups. By selecting a suitable quantitative analysis method, the concentration and distribution of functional groups on the surface of the adsorbent material can be accurately determined, ensuring the reliability and accuracy of the data and providing a basis for the analysis of the proportion of surface functional groups.

[0037] More specifically, based on the selected analytical method (such as FTIR, titration, or XPS), the adsorbent material sample is analyzed to obtain the concentration data of each functional group. Combined with optimized parameters (such as the concentration of functional groups and related physicochemical properties), data processing and calculations are performed to obtain the proportion of each type of functional group in the adsorbent material. The proportion of each functional group is calculated based on stoichiometry. The proportion of surface functional groups obtained through quantitative calculation provides detailed data support for the functional group distribution spectrum of the material surface, which helps to comprehensively understand the surface properties of the adsorbent material, ensures that the proportion of each type of functional group can accurately reflect the chemical characteristics of the adsorbent material, and helps to predict the adsorption performance of the material.

[0038] More specifically, by using the calculated proportions of various functional groups, a surface functional group distribution map of the adsorbent material can be plotted. This map can be displayed in the form of a pie chart, bar chart, or other visual charts. The proportions of various functional groups should be clearly marked in the map, ensuring that the content information of each functional group is clear and intuitive. The surface functional group distribution map provides an intuitive graphical representation of the material's structural characteristics, which helps to understand the surface properties and structural features of the material. Through the map display, the influence of the proportions of different functional groups on the adsorption performance can be quickly assessed, further guiding the optimization of the material.

[0039] More specifically, the analysis of the surface functional group ratio results explores the role and influence of various functional groups in adsorbent materials. For example, carboxyl functional groups typically have strong hydrophilicity and are suitable for adsorbing positively charged ions; while phenolic hydroxyl functional groups may have a strong adsorption capacity for certain organic molecules. Based on adsorption performance requirements, suggestions are made to further optimize the surface functional group ratio of the material, such as increasing the proportion of a certain type of functional group through chemical modification to improve the performance of the adsorbent material. By analyzing the functional group ratio data, a comprehensive understanding of the surface properties of the adsorbent material can be obtained, providing a basis for optimizing the adsorption performance of the material, providing a clear direction for further modification and functional optimization of the material, guiding experimental design and operation, and improving adsorption efficiency.

[0040] Understandably, quantitative analysis and proportion calculations can accurately determine the concentration and ratio of different functional groups on the surface of adsorbent materials, thus providing a scientific basis for optimizing adsorption performance. Distribution maps of surface functional groups allow us to understand the current state of functional groups on the material surface, helping to identify key functional groups. Furthermore, surface modification methods can be used to adjust the proportion of functional groups, thereby improving the material's adsorption performance. Surface functional group distribution maps visually demonstrate the distribution of functional groups on the material surface, helping researchers quickly understand the surface properties of the material and perform more precise performance adjustments. Analysis of the proportions of various functional groups can effectively guide the design and optimization of adsorbent materials, enabling them to achieve better performance in terms of adsorption efficiency and selectivity, meeting practical application needs.

[0041] This invention provides a method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, which has the following advantages: This invention employs incremental titration to obtain proton binding isotherm data of adsorbent materials under different pH conditions. The proton binding isotherm data are input into a Gaussian function model for characterization analysis of different types of functional groups. The experimental data are fitted using nonlinear least squares to obtain optimized parameters. The accuracy of the optimized parameters is verified through preliminary testing. Based on the verified optimized parameters, the proportion of various functional groups in the adsorbent material is analyzed, and a surface functional group distribution map is generated. This method accurately analyzes the distribution of different functional groups through a Gaussian function model, overcoming the inaccuracy of quantitative analysis in traditional methods, ensuring high accuracy of the results, providing detailed data support for the design and optimization of adsorbent materials, and solving the problem of inaccurate detection results when multiple functional groups coexist in existing technologies.

[0042] Preferably, the step of obtaining proton binding isotherm data of the adsorbent material under different pH conditions by incremental titration includes: S11: The adsorbent material is dried and ground to obtain an adsorbent material with a uniform particle size. S12: The adsorbent material with uniform particle size is dried at a specified temperature and for a specified time under an inert atmosphere, and then accurately weighed according to a specified mass specification to obtain the adsorbent material as the test object. S13: The adsorbent material used as the test object is titrated step by step with acidic electrolyte solution and alkaline electrolyte solution of specified volume specifications, and the change of pH value is monitored in real time. The titration curve is generated by combining the titration operation data of electrolyte solution and the change of pH value. S14: Simultaneously, a blank control experiment is performed on the solution without adsorbent material, so as to correct the data of proton consumption and release of the solution itself on the titration curve based on the results of the blank control experiment. S15: The titration curve is transformed using the proton balance equation to obtain the proton binding isotherm.

[0043] Specifically, the adsorbent material is dried to remove moisture, typically within the range of 50°C to 100°C, until the quality of the adsorbent material is stable. The adsorbent material is then ground to ensure uniform particle size, facilitating subsequent titration analysis. Through drying and grinding, the uniformity of the adsorbent material in subsequent experiments is ensured, improving the accuracy and reliability of measurements.

[0044] More specifically, the ground adsorbent material is dried under an inert atmosphere (such as nitrogen or argon) at a specified temperature (e.g., 80°C to 120°C) and for a specified time (e.g., 4 hours). The dried adsorbent material is accurately weighed according to the specified mass specifications and used as the test object for subsequent experiments. Drying under an inert atmosphere can effectively remove moisture and other volatile substances from the adsorbent material, ensuring the stability and consistency of the material. Accurate weighing can ensure the correct mass of the adsorbent material used in the titration experiment and avoid experimental errors.

[0045] More specifically, select appropriate acidic electrolyte solutions (such as HCl solution) and alkaline electrolyte solutions (such as NaOH solution) to ensure their concentrations are suitable for the titration experiment requirements. Gradually add the acidic or alkaline electrolyte solution to the adsorbent material, monitor the pH value changes in real time, and record the solution volume and corresponding pH value for each titration. Based on the data recorded during the titration, plot the relationship curve between pH value and solution volume (i.e., the titration curve). Gradual titration can effectively simulate the proton binding process under different pH conditions. By monitoring the pH value changes in real time, experimental data can be provided for the generation of proton binding isotherms.

[0046] More specifically, a blank experiment without adsorbent material is conducted using acidic and alkaline solutions of the same concentration and volume under the same conditions. The titration curve is then corrected based on the results of the blank control experiment to remove the proton consumption and release of the solution itself, ensuring that the experimental data accurately reflects the proton binding behavior of the adsorbent material. The blank control experiment can remove the proton reaction effect of the solution itself, ensuring that the titration curve reflects only the proton binding and release behavior of the adsorbent material, thus improving the accuracy of the experimental data.

[0047] More specifically, based on the titration curve and experimental data, the proton balance equation is applied to convert the titration curve into a proton binding isotherm. The calculation of the proton binding isotherm needs to consider factors such as the acid-base balance in the solution and the interaction between the adsorbent material and the protons. Through the conversion of the proton balance equation, an accurate proton binding isotherm is obtained, which provides a quantitative analysis of the proton binding characteristics of the adsorbent material. The proton binding isotherm can be further used to evaluate the adsorption capacity of the adsorbent material under different pH conditions, providing in-depth material performance analysis.

[0048] Understandably, precise titration operations can accurately record the proton binding process. Combined with blank control experiments and proton balance equations, this yields truly valid proton binding isotherm data. This helps to deeply understand the proton adsorption and release characteristics of adsorbent materials under different pH conditions. Pretreatment steps (such as drying, grinding, and baking) ensure the uniformity and stability of the adsorbent material. The data in the titration experiment have also been corrected by the blank control experiment, greatly improving the reliability of the experimental results. By generating titration curves, the relationship between the solution pH value and the volume of the titrated solution can be intuitively displayed, helping researchers identify the proton binding points and adsorption capacity of the adsorbent material. The proton binding isotherm reflects the proton adsorption performance of the material and can provide important data support for subsequent material optimization. By understanding the behavior of the material at different pH values, the design of the adsorbent material can be further optimized, improving its application performance under different environmental conditions.

[0049] Preferably, the steps of inputting the proton binding isotherm data into a Gaussian function model, and having the Gaussian function model characterize the proton binding isotherm data for carboxyl, lactone, and phenolic hydroxyl functional groups to obtain experimental parameters include: S21: Input the proton binding isotherm data into the Gaussian function model, and let the Gaussian function model calculate the actual proton binding amount under different pH ranges for the proton binding isotherm data; S22: Based on the calculation results, reasonable estimated parameter values ​​are made for the functional groups of carboxyl, lactone, and phenolic hydroxyl groups to obtain experimental parameters composed of reasonable estimated parameter values ​​of the functional groups of carboxyl, lactone, and phenolic hydroxyl groups.

[0050] Specifically, proton binding isotherm data obtained through incremental titration are input into a Gaussian function model. This data includes the amount of proton binding recorded during the titration process at different pH ranges (i.e., the amount of proton adsorption at each pH value). After inputting the proton binding isotherm data into the Gaussian function model, proton binding curves related to different pH values ​​can be obtained by fitting, thereby analyzing the proton adsorption behavior of the material under different pH conditions.

[0051] More specifically, the actual proton binding capacity of the adsorbent material under different pH ranges is calculated using a Gaussian function model. This includes fitting the proton binding isotherm with a Gaussian function to solve for the proton binding capacity corresponding to different pH values. In this process, the model calculates the proton binding capacity at each pH point and provides a fitting result, which can show the proton binding characteristics of the adsorbent material under different pH values. The Gaussian function model can effectively fit the proton binding isotherm, helping to quantify and predict the actual proton binding capacity under different pH conditions, laying the foundation for subsequent functional group analysis.

[0052] More specifically, by analyzing the fitting results of the Gaussian function model, the contributions of various functional groups in the adsorbent material are estimated based on proton binding characteristics. These include: carboxyl groups (–COOH): the proton binding amount associated with carboxyl functional groups can be estimated using the Gaussian model curves. Carboxyl groups typically have a strong proton binding capacity under acidic conditions, therefore their related parameters affect the binding amount in the low pH region; lactone groups (–C=O): lactone functional groups exhibit different proton binding behaviors at higher pH levels, and the model can help identify the behavioral characteristics of lactone functional groups; phenolic hydroxyl groups (–OH): the proton binding characteristics of phenolic hydroxyl functional groups also typically differ at different pH values, and their corresponding binding amounts can be calculated by fitting the Gaussian function model.

[0053] More specifically, by analyzing the fitting results of the Gaussian function model (such as the peak position and width of the curve) and combining them with the known proton binding rules of functional groups, the predicted parameters of these functional groups can be estimated. This estimation is based on the characteristics of the Gaussian fitting curve, including the amplitude (A), position ($\mu$), and width ($\sigma$) of the peak. By reasonably predicting the parameters of each functional group, a basis can be provided for further quantitative analysis of functional groups. This step can help researchers more clearly understand the proton binding characteristics of different functional groups in adsorbent materials and their behavior under different pH conditions.

[0054] More specifically, by combining the fitting results of the Gaussian function model and the predicted parameters of each functional group, experimental parameters of carboxyl, lactone, and phenolic hydroxyl functional groups in the adsorbent material are obtained. These parameters include: the proton binding capacity (amplitude A) of each functional group, the pH range of binding of each functional group (peak position), and the binding width of each functional group (standard deviation). Through reasonable prediction and calculation, the obtained experimental parameters can be used to analyze the composition of functional groups in the material and their performance at different pH values, providing important quantitative basis for the design and optimization of the material.

[0055] Understandably, Gaussian function models, by fitting proton binding isotherm data, can accurately quantify the proton binding amount of materials under different pH conditions, revealing the proton adsorption characteristics of adsorbent materials. Through analysis of the fitting results of Gaussian function models, the proton binding capacity of different types of functional groups (such as carboxyl groups, lactones, and phenolic hydroxyl groups) in adsorbent materials can be accurately predicted, providing theoretical support for the performance evaluation of adsorbent materials. By obtaining reasonably predicted experimental parameters, researchers can gain a deeper understanding of the functional group interactions of adsorbent materials under different pH conditions, thereby designing and optimizing the structure of adsorbent materials in a targeted manner to improve their adsorption performance in different environments. Through the application of Gaussian function models, the quantitative analysis of proton binding isotherm data makes the performance evaluation of adsorbent materials more scientific and accurate, providing a reliable mathematical model for material design.

[0056] Preferably, the step of fitting the experimental parameters using a nonlinear least squares method to generate optimized parameters includes: S31: Initial configuration of key parameters Ni, μi, and σi for carboxyl, lactone, and phenolic hydroxyl functional groups using historical databases; S32: Calculate the sum of squared residuals for the key parameters of the initial configuration and the reasonable predicted parameter values ​​for various functional groups of the experimental parameters to generate residual vectors for various functional groups. S33: Solve the partial derivatives of the reasonable predicted parameter values ​​of various functional groups of the experimental parameters to generate a sensitivity matrix corresponding to the reasonable predicted parameter values ​​of various functional groups. S34: Using the residual vector and the sensitivity matrix as supervision conditions, the reasonable estimated parameter values ​​are continuously iterated and updated using the damped least squares method until the optimized parameters corresponding to the maximum number of iterations or the residual vector satisfying the preset threshold are obtained.

[0057] Specifically, initial parameters are obtained from the historical database. Through the historical database, key parameters for the initial configuration of various functional groups (carboxyl, lactone, and phenolic hydroxyl functional groups) are obtained, including: Ni (the amplitude of the proton binding capacity of each functional group), μi (the pH position of the proton binding of the functional group, i.e., the peak position), and σi (the width of the proton binding of the functional group, i.e., the standard deviation). The initial parameter configuration is based on relevant information known in the historical database to ensure that the optimization process starts from a reasonable starting point. With a reasonable initial configuration, the optimization process can converge to the optimal solution more quickly, avoiding possible excessive iteration and computational complexity when starting from random initial values.

[0058] More specifically, based on the initial configuration, the sum of squared residuals between the estimated parameter values ​​and the experimental parameters is calculated. For each functional group, a residual vector is generated by comparing the experimental data with the model predictions. The calculation of the sum of squared residuals provides an error metric for subsequent optimization, helps to evaluate the fitting quality, and provides a clear objective for minimizing the error.

[0059] More specifically, by calculating the partial derivatives of the objective function of the residual sum of squares, the sensitivity matrix of each functional group is obtained. The sensitivity matrix describes the influence of changes in each predicted parameter value (such as Ni, μi, σi) on the residual sum of squares. The sensitivity matrix can reveal the degree of influence of each parameter on the fitting process, providing accurate gradient information for the optimization process, thereby improving the efficiency and accuracy of optimization.

[0060] More specifically, based on the residual vector and the sensitivity matrix, iterative optimization is performed using the damped least squares method. The damped least squares method prevents oscillations or over-optimization caused by large step sizes by adjusting the update step size in each iteration. The damped least squares method can avoid overfitting or oscillation problems during the optimization process, ensuring that the optimization process converges to the optimal parameters stably, effectively and reliably.

[0061] More specifically, through continuous iterative updates, the optimized parameters of each functional group (such as carboxyl, lactone, and phenolic hydroxyl functional groups) under different pH conditions are finally obtained. These optimized parameters include: Ni (the amplitude of proton binding capacity), μi (the pH position of proton binding), and σi (the width of proton binding). By calculating the optimized parameters, more accurate functional group characteristics that conform to experimental data can be obtained, providing an important basis for subsequent material performance analysis and design.

[0062] Understandably, the initial configuration obtained from the historical database ensures the effectiveness of the optimization process, avoids starting from unreasonable initial values, saves computation time and improves convergence speed. By calculating the sum of squared residuals, the fitting accuracy of the model can be measured, ensuring that the optimization objective is clear and the optimization effect can be quantified. The sensitivity matrix provides detailed information on the impact of each parameter on the optimization process, making the optimization process more accurate and reducing unnecessary calculation steps. The application of damped least squares effectively avoids oscillations or overfitting problems in the iteration process, making parameter optimization more stable and converging to the global optimum. The final optimized parameters can accurately reflect the proton binding characteristics of various functional groups in the material, which is crucial for the design, optimization and performance prediction of materials.

[0063] Preferably, the step of verifying the accuracy of the optimization parameters through pre-prepared testing methods to confirm the accuracy of the optimization parameters includes: S41: The adsorbent material is quantitatively analyzed for basic and extended functional groups using preliminary testing methods such as Boehm titration, infrared spectroscopy, or X-ray photoelectron spectroscopy to obtain basic and extended quantitative analysis parameters; wherein, the basic functional groups include carboxyl, lactone, and phenolic hydroxyl functional groups, and the extended functional groups include sulfonic acid and amino functional groups; S42: Perform principal component analysis on the basic quantitative analysis parameters to extract the main eigenvectors, and construct the principal component space based on each of the main eigenvectors; S43: Project parameters onto the principal component space according to the optimization parameters to establish a mapping relationship between the optimization parameters and the principal component space. Analyze the parameter consistency of the optimization parameters based on the mapping relationship to obtain the deviation characteristics between the optimization parameters and the basic quantitative analysis parameters. S44: Based on the extended quantitative analysis parameters, perform a forward probability analysis of the possibility of functional group coexistence and a reverse probability analysis of the possibility of functional group conflict on the optimized parameters, so as to perform an error fluctuation range and weight analysis on the optimized parameters, and generate several error levels and corresponding confidence weights for the optimized parameters. S45: Perform a joint analysis of the accuracy of the optimization parameters based on the various error levels of the optimization parameters, the corresponding confidence weights, and the deviation characteristics, in order to confirm the accuracy of the optimization parameters.

[0064] Specifically, preliminary testing methods, such as Boehm titration, Fourier transform infrared spectroscopy (FTIR), or X-ray photoelectron spectroscopy (XPS), are used to quantitatively analyze the basic and extended functional groups in the adsorbent material. The basic functional groups include carboxyl, lactone, and phenolic hydroxyl groups, while the extended functional groups include sulfonic acid and amino groups.

[0065] More specifically, the basic quantitative analysis parameters are obtained by quantitative analysis using the methods described above to obtain the content and distribution of basic functional groups in the material. The extended quantitative analysis parameters are obtained by performing similar quantitative analysis on extended functional groups (such as sulfonic acid groups and amino functional groups) to obtain information such as their concentration. Through these quantitative analyses, the presence and concentration of different functional groups in the material can be accurately identified, thereby providing experimental basis for the verification of optimized parameters.

[0066] More specifically, principal component analysis (PCA) is performed on basic quantitative analysis parameters (such as the content of carboxyl, lactone, and phenolic hydroxyl functional groups) to extract the main eigenvectors. These eigenvectors represent the main variation trends and important properties of basic functional groups in the material. Through PCA, a principal component space is constructed, which can represent the comprehensive properties of functional groups in the material. PCA can effectively reduce data dimensionality and extract the most significant variation features in the material, providing a simplified and effective data representation for subsequent optimization parameter verification.

[0067] More specifically, the optimization parameters (such as Ni, μi, σi, etc.) obtained by the nonlinear least squares method are mapped to the principal component space. Through this mapping, a relationship is established between the optimization parameters and the eigenvectors in the principal component space. By analyzing the mapping relationship, we can analyze how the optimization parameters affect each eigencomponent in the principal component space and determine their influence on the distribution of functional groups in the material. The mapping relationship helps to directly link the changes in the optimization parameters with the characteristics in the material (such as the concentration and distribution of functional groups), which helps to verify the rationality and accuracy of the optimization results.

[0068] More specifically, based on the established mapping relationship, parameter consistency analysis is performed on the optimized parameters to analyze the deviation characteristics between the optimized parameters and the basic quantitative analysis parameters. If the deviation between the optimized parameters and the basic quantitative analysis parameters is too large, it indicates that there may be a problem with the optimization result. This step can reveal the difference between the optimization result and the experimental data, and provide a basis for verification and further adjustment of the reliability of the optimization process.

[0069] More specifically, based on extended quantitative analysis parameters (such as sulfonic acid groups and amino functional groups), a forward probability analysis of functional group coexistence is conducted, which analyzes the synergistic effect or coexistence probability between different types of functional groups. A reverse probability analysis of functional group conflict is also conducted, which analyzes the probability of possible conflict or inhibition between different functional groups. Based on the optimized parameters, the range and weight analysis of error fluctuations are performed to assess the possible error range of the optimized parameters under different conditions. According to the analysis results, an error level is generated for each optimized parameter, and a corresponding confidence weight is assigned to each error level. This forward and reverse probability analysis can further reveal the interaction between different functional groups, assess the stability and reliability of the optimized parameters under different conditions, and thus enhance the credibility of the optimized parameters.

[0070] More specifically, based on the various error levels, confidence weights, and deviation characteristics of the optimization parameters, a joint analysis of the accuracy of the optimization parameters is conducted. Combining all the analysis results, the accuracy of the optimization parameters is finally confirmed. This step ensures the accuracy of the optimization parameters through multi-angle analysis, taking into account the error range of the optimization parameters in the experiment, the interaction between functional groups, and the rationality of the optimization results, ultimately yielding a highly reliable optimization result.

[0071] Understandably, Boehm titration, infrared spectroscopy, and X-ray photoelectron spectroscopy can accurately obtain quantitative data on basic and extended functional groups in adsorbent materials, providing accurate experimental basis for the verification of optimization parameters. Principal component analysis (PCA) effectively reduces dimensionality and extracts the most important features of the material, simplifying the complexity of optimization parameter verification while retaining key change information in the data. Mapping the optimization parameters to the principal component space reveals the influence of the optimization parameters on the functional group properties of the material, providing an intuitive verification basis for the accuracy of the optimization results. Through error fluctuation range, weight analysis, and probability analysis, the stability and reliability of the optimization parameters are evaluated, providing comprehensive support for the final confirmation of the accuracy of the optimization parameters. Finally, through multi-level joint accuracy analysis, the accuracy and practicality of the optimization parameters are ensured, avoiding errors or deviations caused by a single factor.

[0072] Preferably, the step of performing a joint analysis of the accuracy of the optimization parameters based on the various error levels of the optimization parameters, their corresponding confidence weights, and the deviation characteristics to confirm the accuracy of the optimization parameters includes: S451: Construct a three-dimensional tensor matrix based on the error levels of the optimization parameters, the corresponding confidence weights, and the deviation features; S452: Perform tensor dimensionality reduction on the three-dimensional tensor matrix to extract potential correlation features; S453: Using the latent association features as prior conditions, construct a Bayesian model, and perform uncertainty sampling quantification and result transformation on the Bayesian model to determine the accuracy of the optimization parameters. Specifically, each optimization parameter corresponds to a different error level, and each error level has a corresponding confidence weight. The confidence weight reflects the reliability of the optimization parameter, while the error level shows the possible error range of the parameter. Deviation features are used to represent the differences between the optimization parameters and the basic quantitative analysis parameters. These features can be the deviations between the optimization results and the experimental data.

[0073] More specifically, a three-dimensional tensor matrix is ​​constructed based on error levels, confidence weights, and deviation features. The first dimension represents different error levels of the optimization parameters, the second dimension represents different confidence weights, and the third dimension represents different quantization values ​​of the deviation features. This three-dimensional structure can comprehensively capture the changes of optimization parameters under different conditions and provide a detailed data structure for subsequent analysis. Constructing a three-dimensional tensor matrix helps to systematically manage the complex relationship between optimization parameters and their errors, confidence weights, and deviation features, providing high-dimensional data support for subsequent dimensionality reduction and modeling.

[0074] More specifically, three-dimensional tensor matrices are typically high-dimensional, making direct analysis complex and computationally intensive. Dimensionality reduction techniques (such as tensor decomposition and principal component analysis) can extract the most critical latent correlation features from the data, simplifying the data structure. Tensor decomposition algorithms (such as Higher-Order Singular Value Decomposition (HOSVD) or Tucker decomposition) can effectively identify the intrinsic relationships between different error levels, confidence weights, and deviation features. The latent features extracted through dimensionality reduction will help to further construct Bayesian models, enabling accurate analysis and inference in a lower-dimensional space. Tensor dimensionality reduction can significantly reduce the complexity and dimensionality of data, making subsequent model construction and computation more efficient, while preserving the most important patterns and features in the data and avoiding information loss.

[0075] More specifically, a Bayesian model is constructed using the dimensionality-reduced latent correlation features as prior conditions. This model provides a probabilistic assessment of the accuracy of the optimization parameters through the calculation of prior probabilities, likelihood functions, and posterior probabilities. It considers uncertainty—the variation of optimization parameters under different error levels and confidence weights—and thus performs probabilistic inference. Latent correlation features, error levels, confidence weights, and deviation features serve as inputs to the model. The Bayesian model provides an intuitive framework for quantifying the accuracy of optimization parameters and allows for uncertainty analysis under different conditions. This model can adapt to different sources of uncertainty, ensuring more flexible and in-depth accuracy assessment.

[0076] More specifically, a key step in Bayesian models is to sample the potential uncertainty of the optimization parameters. Commonly used sampling methods include Markov Chain Monte Carlo (MCMC) methods. These methods can extract the uncertainty of the parameters from the posterior distribution and generate a series of samples. The results obtained through sampling are transformed into specific accuracy indicators of the optimization parameters, usually expressed as confidence intervals or expected values ​​of certain optimization indicators. This uncertainty quantification and sampling process ensures that the optimization parameters not only have a point estimate (i.e., the optimal value) but also have an overall distribution of accuracy, reflecting the possible range of variation in practical applications.

[0077] More specifically, through uncertainty analysis using Bayesian models, the accuracy results of the optimization parameters are ultimately generated. These results typically include: the posterior distribution of each optimization parameter (i.e., the probability distribution of its accuracy), expressing the accuracy based on confidence intervals, sample mean, or other statistics, helping decision-makers judge the stability and reliability of the parameters. The final accuracy assessment results can intuitively reflect the reliability of the optimization parameters in the experiment, providing a scientific basis to support or adjust the optimization results.

[0078] Understandably, constructing a three-dimensional tensor matrix systematically stores and organizes information such as errors, confidence weights, and deviation features of optimization parameters, providing a high-dimensional data structure for subsequent analysis. Tensor dimensionality reduction extracts the most potentially correlated features from the data, simplifying the data structure, improving computational efficiency, and preserving key information. The Bayesian model provides a flexible framework for the accuracy of optimization parameters, not only quantifying parameter accuracy but also considering various uncertainties that may exist during the optimization process. By sampling and quantifying uncertainty, it can provide a more detailed accuracy analysis of the optimization parameters, including confidence intervals and probability distributions, ensuring more reliable results. The final result provides a comprehensive accuracy assessment of the optimization parameters, ensuring that the optimization process provides reliable parameters and avoiding erroneous judgments due to errors or uncertainties.

[0079] Preferably, the step of analyzing the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups in the adsorbent material according to the optimized parameters to generate a surface functional group distribution map of the adsorbent material includes: S51: Analyze the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups in the optimized parameters, and generate a data proportion map of each type based on the analysis results; S52: Based on the proportion data of carboxyl, lactone, and phenolic hydroxyl functional groups fed back by the optimization parameters, generate digital simulation units of carboxyl, lactone, and phenolic hydroxyl functional groups. S53: Perform digital simulation and form evaluation of the adsorption form on the surface of the adsorbent material for the digital simulation units corresponding to the functional groups of carboxyl, lactone, and phenolic hydroxyl groups, and iteratively optimize the digital simulation based on the form evaluation results to obtain the digital simulation model of the adsorption form on the surface of the adsorbent material with the best evaluation results. S54: Extract information from multiple observation perspectives of the digital simulation model to generate several functional group proportion display information. S55: Map key features of the information displayed for the proportion of various functional groups to obtain the display information feature matrix corresponding to the proportion of various functional groups. S56: Perform clustering pattern analysis on the matrix feature vectors of each of the displayed information feature matrices to divide the displayed information feature matrices into sets of similar clustering patterns, so as to obtain several matrix sets. S57: By analyzing the information entropy and visual saliency of each of the display information feature matrices, the most representative display information feature matrix is ​​selected from each of the matrix sets, and the functional group proportion display information corresponding to each selected display information feature matrix and the data proportion map are used together as the surface functional group distribution map.

[0080] Specifically, the proportion data of carboxyl, lactone, and phenolic hydroxyl functional groups from the optimization parameter feedback are analyzed. By analyzing this data, the distribution and relative proportion of each type of functional group on the surface of the adsorbent material are understood. Based on the analysis results, a graph containing the proportion of different types of functional groups is generated. This can be a bar chart, pie chart, etc., reflecting the proportion of each type of functional group on the surface. The data proportion graph provides an intuitive illustration, which can quickly show the proportional relationship of different types of functional groups, laying the foundation for subsequent optimization and evaluation.

[0081] More specifically, the proportion data of carboxyl, lactone, and phenolic hydroxyl functional groups are converted into digital simulation units to form digital model units. The proportion data of each functional group is mapped to a simulation unit for further simulation analysis. Through digitization, the data can be directly applied to the simulation system, which facilitates subsequent simulation calculations and optimizations and improves the efficiency of the analysis.

[0082] More specifically, digital simulations of the adsorption forms on the surface of adsorbent materials are performed on these digital simulation units. The interactions between functional groups on the surface of the adsorbent material and adsorbent molecules are simulated, and the contribution of different functional groups to the adsorption performance is evaluated. Based on the simulation results, the adsorption forms are evaluated to determine the influence of each functional group on the adsorption performance during the adsorption process. According to the evaluation results, the digital simulation model is optimized to ensure that the best adsorption form simulation results are obtained. This digital simulation and form evaluation can provide accurate adsorption process simulation, help determine the optimal adsorption form, and help optimize the design and performance of adsorbent materials.

[0083] More specifically, by extracting information from different observation perspectives, the distribution of functional groups on the surface of adsorbent materials and the adsorption forms can be observed from multiple angles. Each perspective may reveal different details or patterns. By extracting information from multiple perspectives, we can gain a comprehensive understanding of the distribution of functional groups on the surface of adsorbent materials, providing a rich source of information for subsequent feature mapping and optimization.

[0084] More specifically, the information on the proportion of various functional groups is mapped into a unified information feature matrix. This matrix combines various information (such as proportion, location, adsorption form, etc.) to facilitate subsequent analysis. Each information feature matrix reflects the distribution and interrelationship of different functional groups on the surface of the adsorbent material. The information mapping integrates different data sources and analysis results into one matrix, which facilitates further analysis and comparison, and ensures the comprehensiveness and efficient use of information.

[0085] More specifically, clustering pattern analysis of matrix eigenvectors is performed on the feature matrix of the displayed information to identify similar patterns and divide them into several matrix sets. Clustering analysis can reveal the intrinsic relationship between the proportion of different functional groups and the adsorption form. Clustering analysis helps to identify the similarity of functional group distribution patterns, thereby grouping similar materials together. This helps to find material groups with similar adsorption properties and simplifies the complexity of subsequent analysis and optimization.

[0086] More specifically, information entropy analysis is used to evaluate the amount of information contained in each matrix set, helping to identify which display information feature matrices are the most representative. Combined with visual saliency, it is analyzed which display information feature matrices are most prominent and useful when observed by the human eye, helping to select the most representative display information. Information entropy and visual saliency analysis make the selection of the most representative matrix set more accurate and ensure that the final displayed feature matrix has high information density and visual effect.

[0087] More specifically, by combining the most representative display information feature matrix with the data proportion map, a surface functional group distribution map of the adsorbent material is generated. This surface functional group distribution map clearly shows the distribution of different types of functional groups on the surface of the adsorbent material, providing an intuitive and data-driven view for the performance analysis and optimization of the material.

[0088] Understandably, by analyzing the proportion of optimized parameters, we can systematically understand the distribution of various functional groups, providing accurate data support for subsequent simulation and optimization. The generation of digital simulation units and the simulation of the adsorption process can provide efficient prediction and evaluation, ensuring that the surface adsorption form of the optimized adsorption material can achieve the best effect. Multi-angle observation and information interception can comprehensively understand the surface condition of the adsorption material, ensuring that the analysis results are more accurate and comprehensive. Mapping the functional group proportion information to the display feature matrix and using cluster analysis can discover potential patterns and correlations, further optimizing the design of the adsorption material. Information entropy and visual saliency analysis ensure that the final display information has both high information content and can be presented in the most intuitive and effective way. The final generated surface functional group distribution map provides a clear visualization of the surface characteristics of the adsorption material, which is helpful for further design optimization and performance evaluation.

[0089] Secondly, the present invention provides a functional group analysis system for the surface of adsorbent materials based on a Gaussian function model, used to implement the functional group analysis method for the surface of adsorbent materials based on a Gaussian function model as described in any one of the first aspects.

[0090] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, characterized in that, include: Proton binding isotherm data of the adsorbent material under different pH conditions were obtained by incremental titration. The proton binding isotherm data are input into a Gaussian function model, which then performs characterization analysis on the proton binding isotherm data for carboxyl, lactone, and phenolic hydroxyl functional groups to obtain experimental parameters. The Gaussian function model has the following functional form: N i denoted as , where μi is the molar concentration of the i-th functional group, μi is the average pK value of the corresponding functional group, and σi is the standard deviation of the distribution, for carboxyl groups (pK≈2.0-6.0), lactones (pK≈6.0-9.0), and phenolic hydroxyl groups (pK≈9.0-13.0). The experimental parameters were fitted using a nonlinear least squares method to generate optimized parameters; The accuracy of the optimization parameters is verified by using pre-prepared testing methods to confirm their accuracy. When the accuracy of the optimized parameters meets expectations, the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups in the adsorbent material is analyzed based on the optimized parameters to generate a surface functional group distribution map of the adsorbent material.

2. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 1, characterized in that, The steps for obtaining proton binding isotherm data of adsorbent materials under different pH conditions by incremental titration include: The adsorbent material is dried and ground to obtain an adsorbent material with a uniform particle size. The adsorbent material with uniform particle size was dried at a specified temperature and for a specified time under an inert atmosphere, and then accurately weighed according to a specified mass specification to obtain the adsorbent material as the test object. The adsorbent material used as the test object was titrated step by step with acidic and alkaline electrolyte solutions of specified volumes, and the pH value was monitored in real time. The titration curve was generated by combining the titration data of the electrolyte solution with the pH value changes. Simultaneously, a blank control experiment was conducted on the solution without adsorbent material, so as to correct the titration curve for the consumption and release of protons in the solution itself based on the results of the blank control experiment. The titration curve was transformed using the proton balance equation to obtain the proton binding isotherm.

3. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 1, characterized in that, The steps of inputting the proton binding isotherm data into a Gaussian function model, and having the Gaussian function model characterize the proton binding isotherm data for carboxyl, lactone, and phenolic hydroxyl functional groups to obtain experimental parameters include: The proton binding isotherm data is input into a Gaussian function model, which then calculates the actual proton binding amount under different pH ranges based on the proton binding isotherm data. Based on the calculation results, reasonable predicted parameter values ​​are estimated for carboxyl, lactone, and phenolic hydroxyl functional groups to obtain experimental parameters composed of reasonable predicted parameter values ​​for carboxyl, lactone, and phenolic hydroxyl functional groups.

4. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 1, characterized in that, The steps of fitting the experimental parameters using a nonlinear least squares method to generate optimized parameters include: Initial configuration of key parameters Ni, μi, and σi for carboxyl, lactone, and phenolic hydroxyl functional groups was performed using historical databases. The residual sum of squares is calculated for the key parameters of the initial configuration and the reasonable predicted parameter values ​​of various functional groups of the experimental parameters to generate residual vectors for various functional groups. The partial derivatives of the reasonable predicted parameter values ​​for various functional groups of the experimental parameters are solved to generate the sensitivity matrix corresponding to the reasonable predicted parameter values ​​for various functional groups. Using the residual vector and the sensitivity matrix as supervision conditions, the reasonable estimated parameter values ​​are continuously iterated and updated using the damped least squares method until the optimized parameters corresponding to the maximum number of iterations or the residual vector satisfying the preset threshold are obtained.

5. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 1, characterized in that, The steps for verifying the accuracy of the optimization parameters through pre-prepared testing methods to confirm their accuracy include: The adsorbent material was subjected to quantitative analysis of basic and extended functional groups using preliminary testing methods such as Boehm titration, infrared spectroscopy, or X-ray photoelectron spectroscopy to obtain basic and extended quantitative analysis parameters. The basic functional groups included carboxyl, lactone, and phenolic hydroxyl groups, and the extended functional groups included sulfonic acid and amino groups. Principal component analysis is performed on the basic quantitative analysis parameters to extract the main eigenvectors, and a principal component space is constructed based on each of the main eigenvectors. The principal component space is parametrically projected according to the optimization parameters to establish a mapping relationship between the optimization parameters and the principal component space. Based on the mapping relationship, the parameter consistency of the optimization parameters is analyzed to obtain the deviation characteristics between the optimization parameters and the basic quantitative analysis parameters. Based on the extended quantitative analysis parameters, a forward probability analysis of the possibility of functional group coexistence and a reverse probability analysis of the possibility of functional group conflict are performed on the optimization parameters to analyze the range and weight of error fluctuations of the optimization parameters, so as to generate several error levels of the optimization parameters and corresponding confidence weights. The accuracy of the optimization parameters is confirmed by a joint analysis of the error levels of the optimization parameters, their corresponding confidence weights, and the deviation characteristics.

6. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 5, characterized in that, The steps for confirming the accuracy of the optimization parameters by jointly analyzing the accuracy of the optimization parameters based on the various error levels of the optimization parameters, their corresponding confidence weights, and the deviation characteristics include: A three-dimensional tensor matrix is ​​constructed based on the error levels of the optimization parameters, the corresponding confidence weights, and the deviation features. Tensor dimensionality reduction is performed on the three-dimensional tensor matrix to extract potential correlation features; Using the potential correlation features as prior conditions, a Bayesian model is constructed, and the uncertainty of the Bayesian model is sampled, quantified, and the results are transformed to determine the accuracy of the optimization parameters.

7. The method for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model as described in claim 1, characterized in that, The steps of analyzing the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups in the adsorbent material according to the optimized parameters to generate a surface functional group distribution map of the adsorbent material include: The optimized parameters were analyzed for the proportion of carboxyl, lactone, and phenolic hydroxyl functional groups, and data proportion maps of each type were generated based on the analysis results. The proportions of carboxyl, lactone, and phenolic hydroxyl functional groups fed back by the optimization parameters are converted into digital simulation units for carboxyl, lactone, and phenolic hydroxyl functional groups. The adsorption forms on the surface of the adsorbent material are digitally simulated and evaluated for the digital simulation units corresponding to carboxyl, lactone, and phenolic hydroxyl functional groups. Based on the results of the form evaluation, the digital simulation is iteratively optimized to obtain the digital simulation model of the adsorption form on the surface of the adsorbent material with the best evaluation results. Information is extracted from multiple observation perspectives of the digital simulation model to generate several types of functional group proportion display information; Key features are mapped to the display information of various functional group proportions to obtain the display information feature matrix corresponding to the display information of various functional group proportions. Clustering pattern analysis of matrix eigenvectors is performed on each of the displayed information feature matrices to divide each of the displayed information feature matrices into sets of similar clustering patterns, so as to obtain several matrix sets. By analyzing the information entropy and visual saliency of each of the aforementioned display information feature matrices, the most representative display information feature matrix is ​​selected from each set of matrices. The functional group proportion display information corresponding to each selected display information feature matrix and the data proportion map are used together as the surface functional group distribution map.

8. A system for analyzing functional groups on the surface of adsorbent materials based on a Gaussian function model, characterized in that, This method is used to implement the Gaussian function model-based method for analyzing functional groups on the surface of adsorbent materials as described in any one of claims 1-7.

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