Grafting rate prediction model for grafting reaction of mah-g-sbs modified asphalt gap filling adhesive

Abstract

The present application relates to a grafting rate estimation model of MAH-g-SBS modified asphalt gap filling adhesive grafting reaction, comprising: S1: injecting toluene solvent, adding SBS, adding grafting functional monomer and BPO initiator; S2: obtaining grafting modified SBS material with set purity; S3: using gravimetric method to determine grafting product; S4: using single factor test design; S5: establishing grafting rate multivariate nonlinear regression model of MAH-g-SBS grafting reaction; S6: obtaining grafting rate estimation model of MAH-g-SBS modified asphalt gap filling adhesive grafting reaction; S7: randomly selecting a group of single factor test design results, substituting them into the grafting rate multivariate nonlinear regression model to carry out error analysis; The present application has the advantages that: the influence of reaction time, initiator dosage, reaction monomer dosage and reaction temperature on MAH-g-SBS grafting rate is studied, and the grafting rate under specific conditions is realized.

Description

Technical Field

[0001] This invention relates to the field of constitutive models for grafting rate, and in particular to a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant. Background Technology

[0002] MAH-g-SBS, a modified polymer material, possesses structural characteristics intermediate between styrene-butadiene-styrene block copolymers (SBS) and functionalized polymers grafted with maleic anhydride (MAH). It consists of an SBS backbone and grafted MAH branches, and the introduction of special functional groups endows it with unique properties. Due to its relatively complex molecular chain structure, intermolecular forces undergo new changes, improving its compatibility with matrix materials. In applications requiring high overall material performance, such as the preparation of polymer composites, MAH-g-SBS can effectively enhance compatibilization and modification. However, when used alone, it still has limitations in certain properties, such as long-term weather resistance and high-temperature stability, which require further improvement.

[0003] In leading countries in materials science and technology, there has been considerable research on MAH-g-SBS. Regarding performance optimization, various modification methods are widely used, with a particular focus on enhancing performance through the addition of specific additives and composite modification. Taking nanomaterial composite modification as an example, the small size and surface effects of nanomaterials have significantly enhanced the mechanical properties and thermal stability of MAH-g-SBS, successfully expanding its application areas. In terms of performance research and model building, researchers utilize advanced testing techniques to comprehensively study the performance changes of MAH-g-SBS under different temperatures, humidity levels, and external forces. Grafting rate is considered a key parameter to reveal the performance regulation mechanism, and a correlation model is constructed between synthesis process parameters, grafting rate, material performance indicators, and application effects to evaluate the overall performance of the material and predict its applicability. Furthermore, by utilizing modern material characterization techniques and computer simulation methods, a comprehensive constitutive model was constructed to accurately describe the deformation and performance changes of MAH-g-SBS under complex working conditions. The model fully considers the multiphase structure and internal interactions, and introduces various parameters to characterize its mechanical and other behaviors, thus laying a solid theoretical foundation for its application in various fields.

[0004] In China, the environmental performance and industrial promotion of MAH-g-SBS are highly valued for their alignment with the trend of green materials development. In industries with stringent sustainability requirements, such as packaging and building materials, it is widely praised for its recyclability and low environmental impact. With the continuous maturation and industrialization of related modification technologies, MAH-g-SBS, together with other high-performance modified polymer materials, is driving the domestic polymer materials industry towards high performance, multifunctionality, and green development. In the areas of performance research and model application expansion, domestic researchers have conducted in-depth research on the performance of MAH-g-SBS, achieving remarkable results in performance change observation, grafting rate research, and correlation model construction, complementing international research. Furthermore, they are actively combining the needs of domestic characteristic industries, such as building energy-saving materials and green packaging, to explore the application expansion of constitutive models, further improve the models, and effectively enhance the application efficiency of MAH-g-SBS in actual production.

[0005] Looking to the future, research on MAH-g-SBS will continue to intensify both domestically and internationally. On the one hand, efforts will focus on developing more efficient modification technologies to overcome its shortcomings in long-term weather resistance and high-temperature stability. On the other hand, constitutive models will be further optimized to enhance their accurate predictive capabilities in different application scenarios, enabling MAH-g-SBS to achieve breakthroughs in more emerging fields such as new energy materials and biomedical materials, and powerfully promoting its industrialization and widespread application globally.

[0006] In existing technology 1, Cong, PL, et al., in "Preparation and properties of bitumen modified with the maleic anhydride grafted styrene-butadiene-styrene triblock copolymer," prepared MAH-g-SBS by grafting maleic anhydride (MAH) onto the backbone of styrene-butadiene block copolymer (SBS) to improve the poor compatibility and easy segregation of conventional SBS modified bitumen during storage, and used it as a modifier. They found that with the increase of MAH-g-SBS grafting rate, the high-temperature rutting resistance and storage stability of the modified bitumen were significantly improved, verifying that the grafting rate is a core indicator determining the final material properties. However, this study failed to systematically investigate the comprehensive influence of the four core synthesis process parameters—reaction time, initiator dosage, reactant dosage, and reaction temperature—and their interactions on the grafting rate, and also failed to provide a quantitative description of the grafting rate. This means that in actual engineering and industrial production, researchers can only explore the grafting rate through tedious trial-and-error experiments, making it difficult to achieve scientific prediction and precise control of this indicator.

[0007] Prior art 2, Chinese patent CN1528798A, discloses a solvothermal synthesis method for maleic anhydride-grafted styrene-butadiene-styrene. To address the problems of long reaction time and low grafting rate in traditional solution grafting methods, this patent proposes dissolving styrene-butadiene-styrene (SBS), maleic anhydride monomer (MAH), initiator, and comonomer together in a solvent and placing the solution in a high-pressure reactor. Under specific temperature and time conditions, the system undergoes a solvothermal synthesis reaction under closed and high-pressure conditions. After the reaction, the product, MAH-SBS graft copolymer, is obtained after washing and drying. This invention patent features relatively simple operation and high grafting efficiency, and the prepared MAH-g-SBS can be used as an excellent compatibilizer for various polymer blends. Although this invention patent successfully provides a solvothermal MAH-g-SBS preparation process, its synthesis parameters are based on empirical settings of a specific experimental system and do not consider the interaction of various influencing factors during the synthesis process, nor does it extract the quantitative relationship between these influencing factors and the final grafting rate. Therefore, the method provided by this patent lacks a universal means of predicting grafting rate. When faced with different performance design requirements, such as different aging index requirements of composite pavement crack sealant, technicians cannot use existing theoretical models to optimize the best combination of synthesis process parameters, resulting in low R&D efficiency and high trial and error costs. Summary of the Invention

[0008] In view of the above problems, the purpose of this invention is to provide a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant, which is used to study the effects of reaction time, initiator dosage, reactant dosage and reaction temperature on the grafting rate of MAH-g-SBS, so as to predict the grafting rate under specific conditions and overcome the shortcomings of the prior art.

[0009] This invention provides a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant, comprising the following steps: S1: Using a flask as the reaction vessel, inject toluene solvent, add SBS, and maintain the water bath temperature while stirring until dissolved; under constant temperature conditions, add the grafted functional monomer and BPO initiator in a preset ratio; after the reaction is terminated, cool to room temperature, add anhydrous ethanol dropwise until precipitate forms, and filter to separate the solid product; place the filter cake in a vacuum drying oven to remove residual solvent. S2: The dried sample was placed in a Soxhlet extraction apparatus and continuously refluxed for 24 hours with acetone as solvent; the final product was subjected to a second vacuum drying process to obtain grafted modified SBS material with the set purity. S3: The effects of reaction time, initiator dosage, reactant dosage and reaction temperature on the grafting rate of MAH-g-SBS were studied by single-factor experimental design, and the grafted products were determined by gravimetric analysis. S4: A single-factor experimental design was used to study the effects of changing the reaction time, initiator dosage, monomer dosage and reaction temperature on the grafting rate of MAH-g-SBS. S5: Conduct orthogonal experiments to investigate the combined effects of reaction time, initiator dosage, reactant dosage, and reaction temperature on the grafting rate, determine the grafting rate of MAH-g-SBS under different influencing factors, and establish a multivariate nonlinear regression model for the grafting rate of MAH-g-SBS grafting reaction based on the fitting equation of the single-factor experiment. S6: Based on orthogonal experimental data, nonlinear regression analysis was performed using SPSS software to obtain a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt sealant. S7: To verify the prediction accuracy and effectiveness of the grafting rate multiple nonlinear regression model, a set of single-factor experimental design results were randomly selected and substituted into the grafting rate multiple nonlinear regression model for error analysis to obtain the absolute and relative errors of the predicted and actual values.

[0010] As a preferred embodiment of the present invention, in step S3, the grafted product is determined by gravimetric analysis: ; In the formula: Grafting rate; Yield of purified graft; The quality of the added SBS; The initiator dosage is the mass ratio of BPO to SBS, and the reactant dosage is the mass ratio of MAH to SBS.

[0011] As a preferred embodiment of the present invention, in step S4, a corresponding fitting equation is obtained based on the relationship curves between the factors affecting reaction time, initiator dosage, reactant dosage, reaction temperature, and grafting rate: Fitting equation for reaction time and grafting rate : , ; Fitting equation between initiator dosage and grafting rate : , ; Fitting equation between reactant dosage and grafting rate : , ; Fitting equation between reaction temperature and grafting rate : , ; in, Reaction time; This refers to the amount of initiator used; This refers to the amount of reactant monomer used; The reaction temperature. The coefficient of determination.

[0012] As a preferred embodiment of the present invention, in step S5, the grafting rate of the MAH-g-SBS grafting reaction is determined using a multivariate nonlinear regression model: ; In the formula: Grafting rate; Influencing factors; The number of influencing factors; The fitting parameters are constants.

[0013] As a preferred embodiment of the present invention, in step S6, the grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant is as follows:

[0014] ; ; In the formula: Grafting rate; Reaction time; This refers to the dosage of the initiator; This refers to the amount of reactant monomer used; The reaction temperature, The coefficient of determination.

[0015] As a preferred embodiment of the present invention, in step S1, the reaction vessel is a 500 mL three-necked round-bottom flask, the toluene solvent is analytical grade and the amount used is accurate to 100 mL, and the SBS weighing accuracy is 10.0 g; the dissolution process is carried out by temperature control in a water bath and continuous stirring to ensure complete dissolution of the polymer; the grafted functional monomer and BPO initiator are added according to the mass ratio preset in the experiment; when precipitation occurs, anhydrous ethanol is added dropwise until the solid phase is completely precipitated, and vacuum filtration is performed using a Buchner funnel; the vacuum drying oven is preset to 60 °C, and the treatment time is controlled to 12 h.

[0016] As a preferred embodiment of the present invention, in step S1, after the reaction is terminated, the room temperature is 25°C. When adding anhydrous ethanol, it is necessary to stir slowly at 200 rpm. The amount of anhydrous ethanol used is 3 to 5 times the volume of the solution after cooling to room temperature to ensure complete precipitation of the polymer. During separation, a Buchner funnel is used with medium-speed quantitative filter paper until there is no obvious liquid residue on the surface of the filter cake. In the drying stage of the vacuum drying oven, the filter cake is evenly spread in a petri dish and placed in a vacuum drying oven preheated to 60°C for continuous treatment for 12 hours.

[0017] The beneficial effects of this invention are as follows: A grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant under the coupled effects of different influencing factors can predict the grafting rate under specific conditions, thus replacing the traditional "trial and error method." This shifts process design from experience-driven to data-driven, significantly reducing the number of experiments and accelerating the formulation development process, providing a theoretical basis for customizing material properties by controlling the grafting reaction. The increased grafting rate significantly improves the heat and oxygen resistance and UV aging resistance of the crack sealant, extending its service life after road repair. This model, along with subsequent performance studies, verifies the advantages of MAH-g-SBS modified asphalt crack sealant in overcoming the technical bottlenecks of insufficient high-temperature stability and poor low-temperature flexibility in traditional crack sealants, laying the foundation for its application in high-demand scenarios such as highways. This prediction model is not only a testing tool but also a bridge connecting microscopic chemical grafting reactions and macroscopic material properties; its beneficial effects permeate the entire process of research, optimization, and engineering application of high-performance road repair materials. Attached Figure Description

[0018] Figure 1 The curves showing the grafting rate as a function of reaction time and the fitted curves are shown. Figure 2 The curves showing the grafting rate as a function of initiator dosage and the fitted curves are shown. Figure 3 The curves showing the grafting rate as a function of the amount of reactant monomers and the fitted curves are shown. Figure 4 The curves showing the grafting rate as a function of reaction temperature and the fitted curves are shown. Detailed Implementation

[0019] Example 1

[0020] This embodiment provides a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant, characterized by the following steps: S1: Using a flask as the reaction vessel, inject toluene solvent, add SBS, and maintain the water bath temperature while stirring until dissolved; under constant temperature conditions, add the grafted functional monomer and BPO (benzoyl peroxide) initiator in a preset ratio; after the reaction is terminated, cool to room temperature, add anhydrous ethanol dropwise until precipitation occurs, and filter to separate the solid product; place the filter cake in a vacuum drying oven to remove residual solvent. S2: To further purify the product, the dried sample was placed in a Soxhlet extraction apparatus and continuously refluxed for 24 hours with acetone as the solvent; the final product was subjected to a second vacuum drying process to obtain (high purity) grafted modified SBS material with the set purity. S3: The effects of reaction time, initiator dosage, reactant dosage and reaction temperature on the grafting rate of MAH-g-SBS were studied by single-factor experimental design, and the grafted product was determined by gravimetric analysis as shown in Equation (1). (1) In the formula: For grafting rate, ; The yield of the purified graft is expressed in g. The mass of SBS added is in grams; The amount of initiator is the mass ratio of BPO to SBS, and the amount of reactant monomer is the mass ratio of MAH to SBS. S4: Repeat the relevant experiments, using a single-factor experimental design, and change the reaction time, initiator dosage, reactant dosage, and reaction temperature respectively to study their effects on the grafting rate of MAH-g-SBS. For the relationship curve between each influencing factor and the grafting rate, the corresponding fitting equations are obtained as shown in equations (2) to (5): Fitting equation for reaction time and grafting rate : , (2) Fitting equation between initiator dosage and grafting rate : , (3) Fitting equation between reactant dosage and grafting rate : , (4) Fitting equation between reaction temperature and grafting rate : , (5) S5: Conduct orthogonal experiments to comprehensively investigate the effects of reaction time, initiator dosage, monomer dosage, and reaction temperature on the grafting rate, determine the grafting rate of MAH-g-SBS under different influencing factors, and establish a multivariate nonlinear regression model of the grafting rate of MAH-g-SBS grafting reaction based on the fitting equation of the single-factor experiment (6): (6) In the formula: The grafting rate is % Influencing factors; The number of influencing factors; The fitting parameters are constants; S6: Based on orthogonal experimental data, nonlinear regression analysis was performed using SPSS software (statistical software for social sciences), and the grafting rate prediction model of MAH-g-SBS modified asphalt crack sealant (7) was obtained:

[0021]

[0022] (7) In the formula: The grafting rate is % The reaction time is in hours (h). The initiator dosage is %; The amount of reactant monomer used is % The reaction temperature is in °C. The coefficient of determination refers to the degree of linear correlation between the independent variables (reaction time, initiator dosage, reactant dosage, and reaction temperature) and the dependent variable (grafting rate). S7: To verify the prediction accuracy and effectiveness of the grafting rate multiple nonlinear regression model, a set of single-factor experimental design results were randomly selected and substituted into the grafting rate multiple nonlinear regression model for error analysis to obtain the absolute and relative errors of the predicted and actual values.

[0023] Furthermore, in this embodiment, in step S1, the reaction vessel is a 500 mL three-necked round-bottom flask, the toluene solvent is analytical grade (the purity level of the chemical reagent) and the amount is accurate to 100 mL (the volume is accurate to about 100.00 mL), and the SBS weighing accuracy is 10.0 g; the dissolution process is carried out by temperature control in a water bath and continuous stirring to ensure complete dissolution of the polymer; the grafted functional monomer and BPO initiator are added according to the mass ratio preset in the experiment, wherein BPO, as a free radical initiator, needs to be controlled in an appropriate amount; when precipitation occurs, anhydrous ethanol is added dropwise until the solid phase is completely precipitated, and vacuum filtration is performed using a Buchner funnel; the vacuum drying oven is preset at 60°C, and the treatment time is strictly controlled to 12 h to completely remove residual solvent.

[0024] Furthermore, in this embodiment, in step S1, after the reaction is terminated, the room temperature is 25°C. When adding anhydrous ethanol, it is necessary to stir slowly at 200 rpm. The amount of anhydrous ethanol used is 3 to 5 times the volume of the solution after cooling to room temperature to ensure complete precipitation of the polymer (until the supernatant is clear). During separation, a Buchner funnel with medium-speed quantitative filter paper is used until there is no obvious liquid residue on the surface of the filter cake. In the drying stage of the vacuum drying oven, the filter cake is evenly spread in a petri dish and placed in a vacuum drying oven preheated to 60°C for 12 hours to completely remove residual toluene and ethanol solvents.

[0025] Example 2 See Figure 1-4 As shown, this embodiment provides a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant, which is carried out according to the following steps: Using 90# base asphalt produced by Changchun Pengwei Road Construction Co., Ltd. as the base material, MAH produced by Shanghai Maclean Biochemical Technology Co., Ltd. as the modifier, BPO produced by Xilong Scientific Co., Ltd. as the initiator, cyclohexane produced by Xilong Scientific Co., Ltd. as the solvent, ethanol produced by Jiangsu Huating Biotechnology Co., Ltd. as the additive, and acetone produced by Shanghai Hengli Chemical Co., Ltd. as the detergent, MAH-g-SBS modified asphalt joint sealant was prepared using YH-792 type SBS produced by Sinopec. The basic performance indicators of YH-792 type SBS are shown in Table 1, and the technical performance indicators of 90# base asphalt are shown in Table 2.

[0026] Table 1 Basic Performance Indicators of YH-792 SBS structure Linear S / B ratio 40 / 60 Oil filling rate (%) 0 (≤%) 0.70 Ash content (≤%) 0.2 300% constant tensile stress (≥MPa) 2.8 Tensile strength (≥MPa) 20 Elongation at break (≥%) 700 Tear (≤%) 55 (A) 90±5 Tear strength (≥KN / m) 40 Melt flow rate (g / min) 0.10-5.00 Table 2 Technical Properties of 90# Base Asphalt 90# Asphalt unit Test value specification Needle penetration (25℃, 100g, 5s) 0.1mm 65 60-80 softening point ℃ 48.3 ≥43 Ductility (15℃) cm >100 ≥100 Mass change in a rotary film drying oven (163℃, 85min) % -0.11 ±0.8 Residual penetration ratio % 63 ≥58 Residual ductility cm 19 ≥15 S1: Using a three-necked round-bottom flask (500 mL) as the reaction vessel, 100 mL of analytical grade toluene solvent was first added to the system, followed by 10.0 g of SBS. The mixture was stirred continuously while maintaining the water bath temperature until the polymer was completely dissolved. Under constant temperature conditions, the grafted functional monomer and an appropriate amount of BPO free radical initiator were added sequentially according to the preset mass ratio. After terminating the reaction, the system was allowed to cool to room temperature. Sufficient anhydrous ethanol was added dropwise until the precipitate was completely formed. The solid product was separated by vacuum filtration through a Buchner funnel. The resulting filter cake was placed in a vacuum drying oven at 60 °C for 12 h to remove residual solvent. To further purify the product, the dried sample was placed in a Soxhlet extraction apparatus and continuously refluxed with acetone as the solvent for 24 h. The final product was subjected to a second vacuum drying treatment to obtain high-purity grafted modified SBS material.

[0027] S2: Grafted products were determined using gravimetric analysis. First, the grafted SBS polymer was dried in a vacuum oven at 60 °C. Then, it was extracted with acetone for 24 h to remove unreacted grafted monomers. After extraction, it was vacuum dried again, and the weight of the dried product was measured. Based on the measured weight, the grafting rate was calculated using equation (1).

[0028] (1) In the formula: The grafting rate is % The yield of the purified graft is expressed in g. The mass of SBS added is in grams.

[0029] S3: In order to study the effect of reaction time on the grafting rate of MAH-g-SBS, the amount of initiator was set to 1.1%, the amount of reactant monomer was set to 30%, the reaction temperature was set to 80 ℃, and the reaction time was set to 4 h, 6 h, 8 h and 10 h. The experimental scheme is shown in Table 3.

[0030] Table 3. Effect of reaction time on grafting rate: experimental scheme Sample Reaction time (h) Initiator dosage (%) Amount of reactant monomer used (%) Reaction temperature (°C) H1 4 1.1 30 80 H2 6 1.1 30 80 H3 8 1.1 30 80 H4 10 1.1 30 80 according to Figure 1 As shown, by fitting the curve of the relationship between reaction time and grafting rate, the fitting equation of reaction time and grafting rate is obtained, as shown in Equation 2: , (2) S4: In order to study the effect of initiator dosage on the grafting rate of MAH-g-SBS, the reaction time was set to 8 h, the amount of reactant monomer was set to 30%, the reaction temperature was set to 80 ℃, and the initiator dosage was set to 0.7%, 0.9%, 1.1% and 1.3%. The experimental scheme is shown in Table 4.

[0031] Table 4. Experimental scheme for the effect of initiator dosage on grafting rate Sample Reaction time (h) Initiator dosage (%) Amount of reactant monomer used (%) Reaction temperature (°C) B1 8 0.7 30 80 B2 8 0.9 30 80 B3 8 1.1 30 80 B4 8 1.3 30 80 according to Figure 2 As shown, by fitting the curve of the relationship between initiator dosage and grafting rate, the fitting equation of initiator dosage and grafting rate is obtained, as shown in Equation 3: , (3) S5: In order to study the effect of the amount of reactant monomer on the grafting rate of MAH-g-SBS, the reaction time was set to 8 h, the amount of initiator was set to 1.1%, the reaction temperature was set to 80 ℃, and the amount of reactant monomer was set to 10%, 20%, 30% and 40%. The experimental scheme is shown in Table 5.

[0032] Table 5. Experimental scheme for the effect of reactant dosage on grafting rate Sample Reaction time (h) Initiator dosage (%) Amount of reactant monomer used (%) Reaction temperature (°C) M1 8 1.1 10 80 M2 8 1.1 20 80 M3 8 1.1 30 80 M4 8 1.1 40 80 according to Figure 3 As shown, by fitting the curve of the relationship between the amount of reactant monomer and the grafting rate, the fitting equation of the relationship between the amount of reactant monomer and the grafting rate is obtained, as shown in Equation 4; , (4) S6: In order to study the effect of reaction temperature on the grafting rate of MAH-g-SBS, the reaction time was set to 8 h, the amount of initiator was set to 1.1%, the amount of reactant monomer was set to 30%, and the reaction temperature was set to 40 ℃, 60 ℃, 80 ℃ and 100 ℃. The experimental scheme is shown in Table 6.

[0033] Table 6. Effect of reaction temperature on grafting rate: Experimental scheme Sample Reaction time (h) Initiator dosage (%) Amount of reactant monomer used (%) Reaction temperature (°C) T1 8 1.1 30 40 T2 8 1.1 30 60 T3 8 1.1 30 80 T4 8 1.1 30 100 according to Figure 4 As shown, by fitting the curve of the relationship between reaction temperature and grafting rate, the fitting equation of reaction temperature and grafting rate is obtained, as shown in Equation 5: , (5) S7: In order to investigate the combined effects of reaction time, initiator dosage, reactant dosage and reaction temperature on grafting rate, an orthogonal experimental table as shown in Table 7 was established to determine the grafting rate of MAH-g-SBS under the combined effect of various influencing factors. Table 7 Orthogonal Experimental Design Parameters

[0034] To investigate the combined effects of reaction time, initiator dosage, reactant dosage, and reaction temperature on the grafting rate, a multivariate nonlinear regression model of the grafting rate of MAH-g-SBS modified asphalt sealant was established by combining the grafting rate fitting equation of a single factor with equation (6): (6) In the formula: The grafting rate is % Influencing factors; The number of influencing factors; The fitting parameters are constants.

[0035] Based on orthogonal experimental data, nonlinear regression analysis was performed using SPSS software to determine the regression coefficients of the equations, as shown in Table 8. Substituting these regression coefficients into the multivariate nonlinear regression model of the grafting rate, a model for predicting the grafting rate of MAH-g-SBS modified asphalt sealant was obtained. The regression equation... The value of 0.982 indicates that the goodness of fit of the equation is high.

[0036]

[0037]

[0038] (7) In the formula: The grafting rate is % The reaction time is in hours (h). The initiator dosage is %; The amount of reactant monomer used is % The reaction temperature is in °C. The coefficient of determination refers to the degree of linear correlation between the independent variables (reaction time, initiator dosage, reactant dosage, and reaction temperature) and the dependent variable (grafting rate). Table 8. Estimated values ​​of fitting function parameters

[0039] As can be seen from the estimation results of the regression coefficients in Table 8, a 3 (0.548, CI: 0.184–0.912) and a The confidence intervals for 4 (0.351, CI: 0.098-0.604) did not cross zero, indicating that these two parameters... a The significance level was statistically significant at 0.05. To further verify the overall explanatory power of the model, a systematic test of the regression equation was performed using analysis of variance, as shown in Table 9.

[0040] Table 9 ANOVA Analysis Table source sum of squares Degrees of freedom Mean Square return 1536.352 9 170.706 residual 8.228 7 1.175 Total before correction 1544.58 16 Total after correction 186.657 15 To verify the prediction accuracy and effectiveness of the grafting rate multiple nonlinear regression model, a set of single-factor experimental results were randomly selected and substituted into the grafting rate multiple nonlinear regression model for error analysis. The analysis results are shown in Table 10.

[0041] Table 10 Random parameter values ​​for error analysis Time (h) Initiator dosage (%) Amount of reactant monomer used (%) Reaction temperature (°C) Actual value (%) Forecast value (%) 8 1.1 30 40 10.5 10.588 The predicted grafting rate of MAH-g-SBS was calculated based on the established regression equation, and the error was quantified using equations (8) and (9) to obtain Table 11: (8) (9) In the formula: The absolute error is %; The actual value is % (based on the experimental results). These are the model's predicted values; The percentage represents the relative error.

[0042] Table 11 Error Analysis Table parameter Actual value (%) Forecast value (%) Absolute error (AE / %) Relative error (RE / %) Grafting rate 10.500 10.588 0.088 0.838 As shown in Table 11, the model predicts a grafting rate of 10.588% for the validation sample, which is in high agreement with the actual value of 10.500%. The absolute error is 0.088% and the relative error is 0.838%, indicating that the grafting rate prediction model for MAH-g-SBS modified asphalt crack sealant based on the combined effect of various factors is reliable.

[0043] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant, characterized in that, Includes the following steps: S1: Using a flask as the reaction vessel, inject toluene solvent, add SBS, and maintain the water bath temperature while stirring until dissolved; under constant temperature conditions, add the grafted functional monomer and BPO initiator in a preset ratio; after the reaction is terminated, cool to room temperature, add anhydrous ethanol dropwise until precipitate forms, and filter to separate the solid product; place the filter cake in a vacuum drying oven to remove residual solvent. S2: The dried sample was placed in a Soxhlet extraction apparatus and continuously refluxed for 24 hours with acetone as solvent; the final product was subjected to a second vacuum drying process to obtain grafted modified SBS material with the set purity. S3: The effects of reaction time, initiator dosage, reactant dosage and reaction temperature on the grafting rate of MAH-g-SBS were studied by single-factor experimental design, and the grafted products were determined by gravimetric analysis. S4: A single-factor experimental design was used to study the effects of changing the reaction time, initiator dosage, monomer dosage and reaction temperature on the grafting rate of MAH-g-SBS. S5: Conduct orthogonal experiments to investigate the combined effects of reaction time, initiator dosage, reactant dosage, and reaction temperature on the grafting rate, determine the grafting rate of MAH-g-SBS under different influencing factors, and establish a multivariate nonlinear regression model for the grafting rate of MAH-g-SBS grafting reaction based on the fitting equation of the single-factor experiment. S6: Based on orthogonal experimental data, nonlinear regression analysis was performed using SPSS software to obtain a grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt sealant. S7: To verify the prediction accuracy and effectiveness of the grafting rate multiple nonlinear regression model, a set of single-factor experimental design results were randomly selected and substituted into the grafting rate multiple nonlinear regression model for error analysis to obtain the absolute and relative errors of the predicted and actual values.

2. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S3, the grafted product is determined by gravimetric analysis: ； In the formula: Grafting rate; Yield of purified graft; The quality of the added SBS; The initiator dosage is the mass ratio of BPO to SBS, and the reactant dosage is the mass ratio of MAH to SBS.

3. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S4, the corresponding fitting equation is obtained by analyzing the relationship curves between the effects of changing reaction time, initiator dosage, reactant dosage, reaction temperature, and grafting rate: Fitting equation for reaction time and grafting rate : ， ； Fitting equation between initiator dosage and grafting rate : ， ； Fitting equation between reactant dosage and grafting rate : ， ； Fitting equation between reaction temperature and grafting rate : ， ； in, Reaction time; This refers to the dosage of the initiator; This refers to the amount of reactant monomer used; The reaction temperature, The coefficient of determination.

4. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S5, the grafting rate of the MAH-g-SBS grafting reaction is determined using a multiple nonlinear regression model: ； In the formula: Grafting rate; Influencing factors; The number of influencing factors; The fitting parameters are constants.

5. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S6, the grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant is as follows: ； ； In the formula: Grafting rate; Reaction time; This refers to the dosage of the initiator; This refers to the amount of reactant monomer used; The reaction temperature, The coefficient of determination.

6. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S1, the reaction vessel is a 500 mL three-necked round-bottom flask, the toluene solvent is analytical grade and the amount used is accurate to 100 mL, and the SBS weighing accuracy is 10.0 g; the dissolution process is carried out by temperature control in a water bath and continuous stirring to ensure complete dissolution of the polymer; the grafted functional monomer and BPO initiator are added according to the mass ratio preset in the experiment; when precipitation occurs, anhydrous ethanol is added dropwise until the solid phase is completely precipitated, and vacuum filtration is performed using a Buchner funnel; the vacuum drying oven is preset to 60 °C and the treatment time is controlled to 12 h.

7. The grafting rate prediction model for the grafting reaction of MAH-g-SBS modified asphalt crack sealant according to claim 1, characterized in that, In step S1, after the reaction is terminated, the room temperature is 25 °C. When adding anhydrous ethanol, the mixture should be slowly stirred at 200 rpm. The amount of anhydrous ethanol used should be 3 to 5 times the volume of the solution after cooling to room temperature to ensure complete precipitation of the polymer. During separation, a Buchner funnel with medium-speed quantitative filter paper is used until there is no obvious liquid residue on the surface of the filter cake. In the drying stage of the vacuum drying oven, the filter cake is evenly spread in a petri dish and placed in a vacuum drying oven preheated to 60 °C for 12 h.

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