Method for improving blackness of blue phase of TPV material

Abstract

The invention provides a method for improving the blackness of a blue phase of a TPV material, and belongs to the technical field of the blackness of the TPV material.The method comprises the steps that modified carbon nanotubes and a titanate coupling agent are mixed for ball-milling surface treatment, the specific surface area change rate is used as a key control parameter, the optimal grinding time is calculated in combination with a surface energy density mechanism equation, and the blackness of the blue phase of the TPV material is improved. A gradual dispersion process of premixing, double-rotor internal mixing and single-screw extrusion is adopted, real-time parameter adjustment and dispersion state prediction are performed by applying a dispersion optimization model, and an upper-layer model taking maximization of blue phase blackness as a target and a lower-layer model taking optimization of grinding time matching as a target are established for game optimization; the optimal process parameter combination is obtained through multi-round iteration until convergence, finally ideal dispersion and optical performance matching of the carbon nanotubes in the TPV material are achieved, and the technical problem that the blackness of the blue phase of the TPV material is not high enough is solved.

Description

Technical Field

[0001] This invention belongs to the field of TPV material blackness technology, specifically, it relates to a method for improving the blackness of the blue phase of TPV materials. Background Technology

[0002] Thermoplastic vulcanizates (TPVs), as an important elastomer material, are widely used in fields with extremely high requirements for blackness, such as automotive seals, wire and cable sheaths, building sealing materials, and electronic product housings. Traditional black filler modification techniques mainly use fillers such as carbon black, graphite, and iron oxide black to disperse in the polymer matrix through mechanical mixing to improve the material's blackness and light-blocking properties. This method has been widely used in industrial production, but the resulting blackness often appears grayish-black, lacking a deep blue-hue effect. However, traditional filler modification methods have significant drawbacks. Insufficient blue-hue blackness is mainly manifested in the material's insufficient black depth and lack of blue hue tendency, resulting in a visual effect that leans towards grayish-black rather than a deep blue-black. This problem of insufficient blackness stems from the limitations of the optical properties and poor dispersion uniformity of traditional fillers, which cannot form an ideal light absorption and scattering structure in the material. Especially in high-end applications such as luxury packaging and precision instrument housings, where extremely high blackness quality is required, traditional methods are unable to meet the demand for a deep blue-black effect. In current TPV material blackness modification technology, due to the lack of precise control over the surface properties of fillers and optimized control over the dispersion state, it is difficult to achieve ideal interfacial bonding and optical performance matching between fillers and polymer matrix. As a result, the blackness of the blue phase of the final product is not high enough, and it cannot meet the strict requirements of the high-end market for material appearance quality. Summary of the Invention

[0003] In view of this, the present invention provides a method for improving the blackness of the blue phase of TPV materials, which can solve the technical problem that the blackness of the blue phase of TPV materials is not high enough in the prior art.

[0004] This invention is implemented as follows: A method for improving the blackness of the blue phase in TPV materials includes mixing modified carbon nanotubes with a titanate coupling agent and grinding them in a ball mill to obtain surface-modified carbon nanotubes and an initial surface energy density adjustment factor; premixing the surface-modified carbon nanotubes with EVA wax, polypropylene, and an antioxidant to obtain a premix; feeding the premix into a twin-rotor internal mixer for a first mixing to obtain a first-mixed material; extruding the first-mixed material through a single-screw extruder to obtain a first-extruded material and real-time dispersion parameters; re-feeding the first-extruded material into the twin-rotor internal mixer for a second mixing to obtain a second-mixed material; performing blackness game optimization on the second-mixed material to obtain the game optimization result and an updated surface energy density adjustment factor; inputting the updated surface energy density adjustment factor into the surface energy density mechanism equation to calculate a new optimal grinding time and performing iterative optimization; and finally molding the material corresponding to the final game optimization result through a single-screw extruder to obtain the final TPV material product.

[0005] The grinding process involves mixing modified carbon nanotubes and titanate coupling agent at a mass ratio of 5:1 and then placing them in a ball mill for multiple grinding experiments. The grinding speed is set to 350 rpm. The change rate of the specific surface area of ​​carbon nanotubes at different grinding times is measured as indirect data. The optimal grinding time is calculated by combining the surface energy density mechanism equation. During the grinding process, the process is paused for 5 minutes every 15 minutes for heat dissipation and specific surface area data is collected.

[0006] This includes establishing the relationship between carbon nanotube grinding time and surface energy density changes through a surface energy density mechanism equation and linking it to the final blue phase blackness to achieve precise control.

[0007] The premixing process involves premixing 20-30 parts of surface-modified carbon nanotubes with 1-5 parts of EVA wax, 70-90 parts of polypropylene, and 1-3 parts of antioxidant according to the formula ratio. The premixing process is carried out in a high-speed mixer, with the mixing temperature controlled at 60-80℃ and the mixing time being 20 minutes.

[0008] The first mixing process involves feeding the premixed materials into a twin-rotor internal mixer for the first mixing. The temperature of the twin rotors is set to 90-180℃, the main machine speed is set to 45Hz, and the discharge gate opening is 50%. During the mixing process, the material temperature changes are monitored and the temperature distribution uniformity index is recorded.

[0009] The plasticizing extrusion process involves extruding the first batch of mixed materials through a single-screw extruder. The single screw temperature is set to 90-200℃ and the screw speed is 30-50 rpm. During the extrusion process, a carbon nanotube dispersion optimization model is used to adjust the extrusion parameters in real time to ensure the uniform dispersion of carbon nanotubes in the polymer matrix.

[0010] The blackness game optimization process involves establishing an upper-level model aimed at maximizing the blackness of the blue phase and a lower-level model aimed at optimizing the grinding time matching. The lower-level model optimizes the grinding parameters using specific surface area change rate data, while the upper-level model maximizes the final blackness effect based on the optimized grinding parameters.

[0011] The surface energy density mechanism equation is used to describe the relationship between carbon nanotube grinding time and surface energy density change and to establish a correlation with the final blue phase blackness. The inputs include grinding time, specific surface area change rate, ball milling speed, coupling agent concentration, grinding media hardness, and surface energy density adjustment factor. The output is the predicted blackness value and the updated surface energy density adjustment factor.

[0012] Among them, the surface energy density adjustment factor in the surface energy density mechanism equation is dynamically adjusted by the specific surface area change rate. When the specific surface area change rate is in the optimal range, the surface energy density adjustment factor reaches its maximum value. When it deviates from the optimal range, the surface energy density adjustment factor decreases according to the exponential decay law.

[0013] Among them, the carbon nanotube dispersion optimization model is based on the sequence prediction network of the Transformer-XL architecture, which includes an encoder layer for processing historical grinding parameters and specific surface area change sequences, a memory module for storing long-term grinding mode information, and a decoder layer for predicting the optimal grinding time and surface treatment parameters.

[0014] Among them, the specific surface area change rate refers to the degree of change of the specific surface area of ​​carbon nanotubes per unit time during ball milling. It is used to reflect the effect of grinding on the surface structure of carbon nanotubes. Excessive grinding will reduce the specific surface area change rate and affect the subsequent dispersion effect.

[0015] The carbon nanotube dispersion optimization model employs a multi-head attention mechanism to capture the nonlinear relationship between grinding time and the rate of change of specific surface area. The memory length parameter is dynamically adjusted based on the rate of change of specific surface area, grinding speed, and coupling agent concentration. When the rate of change of specific surface area fluctuates significantly, the number of memory segments is increased to capture more historical grinding pattern information. The training dataset for the carbon nanotube dispersion optimization model includes collecting surface treatment data of carbon nanotubes under different grinding times. Grinding time, rate of change of specific surface area, ball milling speed, and coupling agent concentration are recorded as input parameters, along with the corresponding surface energy density adjustment factor, final blackness value, and blue phase index as output results. The dataset contains 8000 sets of experimental data under different grinding conditions. Training the carbon nanotube dispersion optimization model involves updating model parameters using the AdamW optimizer, with a learning rate of 0.0008, a batch size of 64, and 300 training epochs. The loss function uses a dynamically weighted combination of Huber loss and Focal loss, with the weights dynamically adjusted based on the prediction accuracy of the rate of change of specific surface area.

[0016] The memory length adjustment function is used to adjust the number of memory segments in the carbon nanotube dispersion optimization model. The memory length adjustment function obtains the first and second segment points through the segment point calculation process based on the game model iterative convergence index and the surface area change rate stability index, and then calculates the memory adjustment value. The number of memory segments is adjusted according to the relationship between the memory adjustment value and the segment points.

[0017] The upper objective function is used to find the combination of process parameters that can obtain the best blue phase blackness. The inputs include blue phase index, carbon nanotube concentration, surface energy density adjustment factor, specific surface area change rate and optimal specific surface area change rate. The output is the upper model objective value used to guide the blackness optimization decision.

[0018] The lower-level objective function is used to determine the optimal grinding time and maximize the specific surface area utilization efficiency. The inputs include grinding time, theoretical maximum specific surface area change rate, specific surface area change rate, grinding frequency adjustment parameters, and grinding efficiency coefficient. The output is the target value of the lower-level model used to guide the optimization decision of grinding parameters.

[0019] This invention significantly improves the blackness of the blue phase in TPV materials by using surface-modified carbon nanotubes as a black filler, combined with precise surface treatment processes and game-theoretic optimization control methods, thus overcoming the technical defect of insufficient blackness in traditional fillers. This invention utilizes the excellent optical properties and high specific surface area of ​​carbon nanotubes, enhances their interfacial bonding with the polymer matrix through surface modification treatment with titanate coupling agents, and optimizes surface treatment parameters using precise grinding control based on the specific surface area change rate and the surface energy density mechanism equation. Combined with an upper and lower layer game model, global optimization of process parameters is achieved, ensuring that carbon nanotubes form an ideal dispersion structure and optical properties in the polymer matrix, thereby obtaining a deep blue phase blackness effect. This invention achieves intelligent prediction and dynamic control of the dispersion state through a Transformer-XL neural network model, and eliminates agglomeration through a multi-round compounding and extrusion process, ensuring the uniformity and stability of carbon nanotube dispersion, ultimately achieving a significant improvement in the blackness of the blue phase in TPV materials. In summary, this invention solves the technical problem of insufficient blue phase blackness in TPV materials mentioned in the background art. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 This is a graph showing the relationship between carbon nanotube dispersion and grinding time in Example 2.

[0022] Figure 3 This is a real-time monitoring graph of blackness value and blue phase index during the extrusion process in Example 2. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0024] like Figure 1 The diagram shown is a flowchart of a method for improving the blackness of the blue phase in TPV materials according to the present invention. This method includes the following steps:

[0025] S01. Modified carbon nanotubes and titanate coupling agent were mixed at a mass ratio of 5:1 and placed in a ball mill for multiple grinding experiments. The grinding speed was set to 350 rpm. The change rate of specific surface area of ​​carbon nanotubes under different grinding times was measured as indirect data. The optimal grinding time was calculated by combining the surface energy density mechanism equation. During the grinding process, the process was paused for 5 minutes every 15 minutes for heat dissipation and specific surface area data was collected to obtain the surface modified carbon nanotubes and the initial surface energy density adjustment factor.

[0026] S02. Premix 20-30 parts of surface-modified carbon nanotubes with 1-5 parts of EVA wax, 70-90 parts of polypropylene and 1-3 parts of antioxidant according to the formula ratio. The premixing process is carried out in a high-speed mixer, the mixing temperature is controlled at 60-80℃ and the mixing time is 20 minutes to obtain the premixed material.

[0027] S03. The premixed materials are fed into a twin-rotor internal mixer for the first mixing. The temperature of the twin rotors is set to 90-180℃, the main machine speed is set to 45Hz, and the discharge gate opening is 50%. During the mixing process, the material temperature change is monitored and the temperature distribution uniformity index is recorded to obtain the first mixed material.

[0028] S04. The first compounded material is plasticized and extruded through a single screw extruder. The single screw temperature is set to 90-200℃ and the screw speed is 30-50rpm. During the extrusion process, the carbon nanotube dispersion optimization model is used to adjust the extrusion parameters in real time to ensure the uniform dispersion of carbon nanotubes in the polymer matrix and obtain the first extruded material and real-time dispersion state parameters.

[0029] S05. The material extruded in the first time is put back into the twin-rotor internal mixer for a second mixing. The mixing process parameters are the same as the first time. The carbon nanotube agglomeration phenomenon is eliminated by the second mixing, and the dispersion uniformity and blackness stability are improved to obtain the second mixed material.

[0030] S06. Perform blackness game optimization on the second mixing material, establish an upper-level model with the goal of maximizing the blackness of the blue phase and a lower-level model with the goal of optimizing the grinding time matching. The lower-level model optimizes the grinding parameters through the specific surface area change rate data, and the upper-level model maximizes the final blackness effect based on the optimized grinding parameters, and obtains the game optimization results and the updated surface energy density adjustment factor.

[0031] S07. Input the updated surface energy density adjustment factor into the surface energy density mechanism equation, calculate the new optimal grinding time, and end the iteration when the relative error between the new optimal grinding time and the previous optimal grinding time is less than 3% or the number of iterations reaches 15. Otherwise, return to step S01 and use the new optimal grinding time for the next iteration.

[0032] S08. The material corresponding to the final game optimization result is finally shaped through a single screw extruder. The extrusion temperature is determined according to the game optimization result. The blackness value and blue phase index of the material are detected in real time during the extrusion process. When the blackness value is lower than the set threshold, the extrusion parameters are automatically adjusted to obtain the final TPV material product.

[0033] The specific surface area change rate refers to the degree of change in the specific surface area of ​​carbon nanotubes per unit time during ball milling. It is used to reflect the effect of grinding on the surface structure of carbon nanotubes. Excessive grinding will reduce the specific surface area change rate and affect the subsequent dispersion effect.

[0034] The surface-modified carbon nanotubes refer to carbon nanotubes that have better dispersibility after being treated with titanate coupling agents. The surface of the surface-modified carbon nanotubes contains organic groups, which can form a stronger interfacial bond with the polymer matrix.

[0035] The blue phase index is a quantitative indicator of the degree to which a material exhibits a blue hue under specific spectral conditions; the higher the value, the more pronounced the blue hue.

[0036] The temperature distribution uniformity index is a quantitative indicator of the uniformity of temperature distribution in different parts of the material during the mixing process, and is used to evaluate the mixing quality.

[0037] The real-time dispersion state parameters refer to the real-time monitoring data of the dispersion uniformity of carbon nanotubes in the polymer matrix during the extrusion process, including the degree of aggregation and distribution density.

[0038] The surface energy density mechanism equation describes the relationship between carbon nanotube grinding time and surface energy density change, and establishes a correlation with the final blue phase blackness. Inputs include grinding time, specific surface area change rate, ball milling speed, coupling agent concentration, grinding media hardness, and a surface energy density adjustment factor. Outputs are the predicted blackness value and the updated surface energy density adjustment factor. The surface energy density adjustment factor in the surface energy density mechanism equation is dynamically adjusted based on the specific surface area change rate. The adjustment factor reaches its maximum value when the specific surface area change rate is within the optimal range; when it deviates from the optimal range, the adjustment factor decreases according to an exponential decay law, thereby achieving precise control of the final blue phase blackness by grinding time.

[0039] The upper-level objective function is used to find the combination of process parameters that can obtain the optimal blue phase blackness. The inputs include the blue phase index, carbon nanotube concentration, surface energy density adjustment factor, specific surface area change rate and optimal specific surface area change rate. The output is the upper-level model objective value used to guide the blackness optimization decision.

[0040] The lower-level objective function is used to determine the optimal grinding time and maximize the specific surface area utilization efficiency. The inputs include grinding time, theoretical maximum specific surface area change rate, specific surface area change rate, grinding frequency adjustment parameters, and grinding efficiency coefficient. The output is the target value of the lower-level model used to guide the optimization decision of grinding parameters.

[0041] The carbon nanotube dispersion optimization model is based on a sequence prediction network with a Transformer-XL architecture. It includes an encoder layer for processing historical grinding parameters and specific surface area change sequences, a memory module for storing long-term grinding mode information, and a decoder layer for predicting optimal grinding time and surface treatment parameters. The carbon nanotube dispersion optimization model uses a multi-head attention mechanism to capture the nonlinear relationship between grinding time and specific surface area change rate. The memory length parameter is dynamically adjusted according to the specific surface area change rate, grinding speed, and coupling agent concentration. When the specific surface area change rate fluctuates greatly, the number of memory segments is increased to capture more historical grinding mode information.

[0042] The training dataset for the carbon nanotube dispersion optimization model includes collecting carbon nanotube surface treatment data under different grinding times, recording grinding time, specific surface area change rate, ball milling speed, and coupling agent concentration as input parameters, and corresponding surface energy density adjustment factors, final blackness value, and blue phase index as output results, constructing grinding time series data samples. Each sample contains a continuous grinding parameter change sequence and a corresponding surface performance change sequence. The dataset contains 8000 sets of experimental data under different grinding conditions and corresponding material surface performance test results.

[0043] The training of the carbon nanotube dispersion optimization model includes updating model parameters using the AdamW optimizer, setting the learning rate to 0.0008, the batch size to 64, and the number of training epochs to 300. The loss function is a dynamically weighted combination of Huber loss and Focal loss, with the weights dynamically adjusted based on the prediction accuracy of the surface area change rate. During training, cosine annealing learning rate scheduling and gradient clipping are used to prevent training instability. Training stops when the prediction error of the surface area change rate on the validation set is below 5% for 15 consecutive epochs. Finally, the model achieves a grinding time prediction accuracy of over 94% on the test set.

[0044] The memory length adjustment function is used to adjust the number of memory segments in the carbon nanotube dispersion optimization model. The memory length adjustment function obtains the first and second segment points through the segment point calculation process based on the game model iterative convergence index and the surface area change rate stability index, and then calculates the memory adjustment value. When the memory adjustment value is less than the first segment point, the number of memory segments is reduced to adapt to the grinding stage where the surface area change rate is relatively stable. When the memory adjustment value is between the first and second segment points, the current memory length is maintained to maintain sensitivity to changes in grinding parameters. When the memory adjustment value is greater than the second segment point, the number of memory segments is increased to capture complex grinding patterns when the surface area changes drastically. Finally, the game model and the neural network are coordinated and optimized based on indirect data of surface area change rate.

[0045] The game model iterative convergence index is a quantitative indicator of the convergence degree between the objective values ​​of the upper-level model and the objective values ​​of the lower-level model in continuous iterations, used to judge the stability of game optimization.

[0046] The surface area change rate stability index is a quantitative indicator of the fluctuation of the surface area change rate during the grinding process, used to evaluate the stability of the grinding process. The memory adjustment value is a parameter value calculated based on the game model iterative convergence index and the surface area change rate stability index, used to adjust the number of memory fragments. The number of memory fragments refers to the number of historical grinding pattern information fragments stored in the memory module of the carbon nanotube dispersion optimization model.

[0047] The optimal specific surface area change rate refers to the specific surface area change rate that corresponds to the maximum value of the surface energy density adjustment factor, calculated through the surface energy density mechanism equation. The theoretical maximum specific surface area change rate refers to the maximum specific surface area change rate that carbon nanotubes can achieve under ideal grinding conditions.

[0048] The grinding frequency adjustment parameter refers to the parameter used to adjust the operating frequency of the ball mill during the grinding process, which affects the grinding efficiency and the specific surface area change rate. The grinding efficiency coefficient is the ratio of the specific surface area change rate per unit time during the grinding process to the theoretical maximum specific surface area change rate.

[0049] The carbon nanotube concentration refers to the mass fraction of surface-modified carbon nanotubes in the final TPV material. The upper-level model objective value refers to the value calculated by the upper-level objective function to evaluate the optimization effect of the blue phase blackness.

[0050] The segmentation point calculation process refers to the process of determining the values ​​of the first and second segmentation points by calculating them using the quantile method based on historical data statistical analysis of the game model's iterative convergence index and the surface area change rate stability index. The first segmentation point is the boundary value obtained through the segmentation point calculation process used to distinguish between the low and middle ranges of the memory adjustment value. The second segmentation point is the boundary value obtained through the segmentation point calculation process used to distinguish between the middle and high ranges of the memory adjustment value.

[0051] The specific implementation methods of the above steps are described in detail below.

[0052] The specific implementation of step S01 involves precisely mixing modified carbon nanotubes and titanate coupling agent at a mass ratio of 5:1, with an electronic analytical balance used to ensure a mixing accuracy of ±0.1%. First, the prepared mixture is placed into the grinding jar of a planetary ball mill. Zirconia balls with a hardness of HRC62 are used as the grinding media, with a ball-to-material ratio controlled at 10:1. The ball mill speed is set to 350 rpm, and the rotation is alternating between forward and reverse rotation, rotating forward for 15 minutes followed by reverse rotation for 5 minutes, repeating this cycle to improve grinding uniformity. During the grinding process, a 5-minute pause is taken every 15 minutes for temperature control and data acquisition. During the pause, nitrogen is used to purge the inside of the grinding jar to prevent oxidation. Specific surface area is measured using the nitrogen adsorption method, calculated using the Bruner-Emmett-Teller equation. The rate of change of specific surface area is defined as the difference between the current and initial specific surface area divided by the grinding time. The surface energy density mechanism equation is based on Hertz contact theory and fracture mechanics principles. It comprehensively considers the effects of parameters such as grinding time, specific surface area change rate, ball milling speed, and coupling agent concentration on surface energy density, and obtains the initial value of the surface energy density adjustment factor through least squares fitting. The purpose of this step is to obtain carbon nanotubes with enhanced surface activity through controlled grinding, laying the foundation for subsequent dispersion optimization.

[0053] The specific implementation of step S02 involves premixing 20-30 parts of the surface-modified carbon nanotubes obtained in step S01 with 1-5 parts of EVA wax, 70-90 parts of polypropylene, and 1-3 parts of antioxidant according to the designed formula. A high-speed vertical mixer is used for premixing, with plow-type mixing blades to improve mixing efficiency. The mixing temperature is controlled within the range of 60-80℃ by an electric heating system, and a temperature sensor monitors the material temperature change in real time, with a temperature control accuracy of ±2℃. The mixing speed is set to 300-500 rpm, and the mixing time is strictly controlled to 20 minutes. The machine is stopped every 5 minutes during the mixing process to check the mixing status of the materials. The role of EVA wax is to improve the wettability and dispersibility of carbon nanotubes in the polymer matrix, and the antioxidant is used to prevent polymer degradation during high-temperature processing. The premixing process adopts a batch feeding method: first, polypropylene and antioxidant are added and mixed for 2 minutes, then EVA wax is added and mixed for 3 minutes, and finally, surface-modified carbon nanotubes are added and mixed for 15 minutes. The purpose of this step is to achieve a preliminary uniform distribution of each component, creating favorable conditions for subsequent melt processing.

[0054] The specific implementation of step S03 involves feeding the premixed materials into a twin-rotor internal mixer for the first mixing. The internal mixer uses a co-rotor structure to provide strong shearing action. The temperature of the twin rotors is set to 90–180°C via an independent temperature control system. Temperature zone control includes a feeding zone, a mixing zone, and a discharging zone, with the temperature gradient of each zone set to an increasing mode. The main motor speed is set to 45Hz, corresponding to an actual rotor speed of approximately 60–80 rpm, and the speed is precisely controlled by a frequency converter. The discharge gate opening is 50%, with the specific time determined based on the degree of plasticization of the material. During the mixing process, an infrared thermometer is used to monitor the material temperature in real time, record temperature distribution data, and calculate the temperature distribution uniformity index. The temperature distribution uniformity index is defined as the ratio of the standard deviation of the temperature at each point in the material to the average temperature; the smaller the value, the more uniform the temperature distribution. A force sensor is installed inside the mixing chamber to monitor changes in mixing torque. When the torque stabilizes within the set range, it indicates that mixing is complete. The purpose of this step is to achieve the initial dispersion of carbon nanotubes and the full plasticization of the polymer through strong shearing action.

[0055] The specific implementation of step S04 involves plasticizing and extruding the first-mixed material using a single-screw extruder with a length-to-diameter ratio of 24:1. The screw design employs a gradual pitch and variable depth screw channel, and the screw surface is nitrided to improve wear resistance. The extrusion temperature is zoned from 90 to 200°C, including the feeding section, compression section, metering section, and die head section, with a gradient temperature distribution in each section. The screw speed is controlled within the range of 30 to 50 rpm, precisely controlled by a servo motor. During extrusion, a carbon nanotube dispersion optimization model is used for real-time parameter adjustment. This model is based on a sequence prediction network constructed using the Transformer-XL architecture. The carbon nanotube dispersion optimization model receives parameters such as extrusion temperature, screw speed, and material pressure in real time and outputs optimal process parameter suggestions. Real-time dispersion state parameters are monitored using an online rheometer and optical microscope system, including shear viscosity change rate, carbon nanotube agglomeration degree, and distribution density. When the carbon nanotube agglomeration degree exceeds a set threshold of 15%, the system automatically adjusts the screw speed and extrusion temperature. The purpose of this step is to achieve uniform plasticization of the material while maintaining the dispersion of carbon nanotubes.

[0056] The specific implementation of step S05 involves re-feeding the material from the first extrusion into a twin-rotor internal mixer for a second mixing, maintaining the same mixing process parameters as the first mixing. The second mixing employs a more stringent temperature control strategy, with temperature fluctuations controlled within ±3℃. During the mixing process, the agglomeration state of the carbon nanotubes is closely monitored, and particle size distribution is measured using a laser particle size analyzer, with agglomerated particle size controlled below 100nm. The second mixing time is dynamically adjusted based on the dispersion state, ending when the carbon nanotube dispersion reaches 90% or higher. Dispersion is calculated through transmission electron microscopy image analysis, determining the proportion of monodisperse carbon nanotubes in the total. Ultrasonic-assisted technology is used during the mixing process, with an ultrasonic generator installed at the bottom of the mixing chamber, an ultrasonic frequency set to 40kHz, and a power density controlled between 2 and 5W / cm³. 2 The cavitation effect of ultrasound helps to break down carbon nanotube aggregates and improve dispersion uniformity. The purpose of this step is to completely eliminate carbon nanotube agglomeration through secondary mixing and ultrasound assistance, thereby obtaining a composite material with high dispersion.

[0057] The specific implementation of step S06 involves performing a blackness game-theoretic optimization on the second-stage mixed material, establishing a two-layer game-theoretic optimization model. The upper-layer model aims to maximize the blackness of the blue phase. The objective function input parameters include the blue phase index, carbon nanotube concentration, surface energy density adjustment factor, specific surface area change rate, and optimal specific surface area change rate. The blue phase index is measured using a spectrophotometer in the wavelength range of 420–480 nm, with a value range of 0–100. The lower-layer model aims to optimize the grinding time matching. The objective function input parameters include grinding time, theoretical maximum specific surface area change rate, specific surface area change rate, grinding frequency adjustment parameter, and grinding efficiency coefficient. The game-theoretic optimization algorithm employs Stackelberg game theory. The upper-layer model, acting as the leader, first determines the decision variables, while the lower-layer model, acting as the follower, responds based on the upper-layer decision. The optimization solution uses a hybrid strategy of particle swarm optimization (PSO) and genetic algorithm. PSO is used for global search, and genetic algorithm is used for local optimization. The algorithm parameters are set as follows: 50 particles, 100 iterations, and the inertia weight is linearly reduced from 0.9 to 0.4. The convergence criterion for the game theory model is that the change in the objective function values ​​of both the upper and lower layers is less than 1% in 10 consecutive iterations. The purpose of this step is to achieve multi-objective coordinated optimization through game theory to obtain the optimal combination of process parameters.

[0058] The specific implementation of step S07 involves inputting the updated surface energy density adjustment factor into the surface energy density mechanism equation for iterative calculation. The surface energy density mechanism equation is based on interfacial thermodynamics and fractal theory, considering the influence of the fractal dimension of the carbon nanotube surface on surface energy. The input parameters of the mechanism equation include grinding time, specific surface area change rate, ball milling speed, coupling agent concentration, grinding media hardness, and the surface energy density adjustment factor. The outputs are the predicted emissivity value and the updated surface energy density adjustment factor. The calculation process uses a numerical integration method to solve the differential equation system, with an integration step size set to 0.01 s and a calculation accuracy controlled within 10. -6 The new optimal grinding time is obtained by solving the nonlinear equation using the Newton-Raphson iterative method. The convergence condition is that the relative error is less than 3% or the number of iterations reaches 15. The iteration ends when the convergence condition is met; otherwise, it returns to step S01 to use the new optimal grinding time for the next iteration. During the iteration process, the objective function value and parameter change trajectory are recorded for each round to analyze the algorithm's convergence performance. The purpose of this step is to achieve a precise match between the grinding parameters and the final product performance through closed-loop iterative optimization.

[0059] The specific implementation of step S08 involves finalizing the material corresponding to the final game optimization result using a single-screw extruder. The extrusion process parameters are determined based on the game optimization results. The extrusion temperature adopts the optimized temperature distribution curve, with temperature deviations controlled within ±2℃ in each segment. The screw speed and extrusion rate are precisely adjusted using a proportional-integral-derivative (PID) controller, with a response time of less than 5 seconds. During extrusion, an online detection system monitors the material's blackness value and blue phase index in real time, with a detection frequency of 10 times per second. Blackness value measurement uses an integrating sphere spectrophotometer, covering the entire visible light spectrum. When the blackness value falls below the set threshold of 85, the system automatically triggers a parameter adjustment program to adjust the extrusion temperature and screw speed. Parameter adjustment uses a fuzzy control algorithm, determining the adjustment range based on the degree of blackness deviation, with an adjustment range of ±5%. The extruded product is cooled and shaped using a water-cooled stretching line, with the stretch ratio controlled within the range of 3 to 5 times. The final product undergoes quality inspection after pelletizing, with inspection items including blackness value, blue phase index, mechanical properties, and thermal stability. The purpose of this step is to achieve efficient and continuous production while ensuring product quality.

[0060] Further explanation is needed regarding the carbon nanotube dispersion optimization model, which uses the Transformer-XL architecture as its core framework. The overall model structure comprises three main components: an encoder layer, a memory module, and a decoder layer. The encoder layer consists of 12 identical Transformer layers, each containing a multi-head self-attention mechanism and a feedforward neural network. The multi-head attention mechanism uses eight attention heads, each with a 64-dimensional dimension, resulting in a total hidden layer dimension of 512. The encoder layer processes the input historical grinding parameter sequence and surface area change sequence, learning the temporal dependencies and interactions between parameters through positional encoding and the self-attention mechanism. The memory module employs a piecewise linear memory mechanism, with the memory length dynamically adjusted based on the stability of the surface area change rate. The minimum memory length is 50 time steps, and the maximum is 200 time steps. The memory module stores the hidden state information from the previous time window, providing long-term historical information for the current prediction and effectively solving the gradient vanishing problem in long sequence modeling. The decoder layer contains six Transformer layers, with a structure similar to the encoder but adding a masked self-attention mechanism to ensure that only historical information is used during prediction. The output of the decoder layer predicts the optimal grinding time and surface treatment parameters through two fully connected layers. The output layer uses ReLU activation function and Dropout regularization to prevent overfitting.

[0061] The model's training dataset setup process comprises four key steps: data acquisition, preprocessing, feature engineering, and data augmentation. In the data acquisition phase, an orthogonal experimental scheme was designed to systematically collect experimental data under different grinding conditions. Experimental factors included grinding time (0.5–8 hours), milling speed (200–500 rpm), coupling agent concentration (1%–10%), and grinding media hardness (HRC50–HRC65). Three parallel experiments were conducted under each experimental condition, resulting in a total of 8000 sets of valid experimental data. The experimental data records included input parameters such as grinding time, specific surface area change rate, milling speed, and coupling agent concentration, as well as output results including surface energy density adjustment factor, final blackness value, and blue phase index. In the data preprocessing phase, outlier detection and processing were first performed. The interquartile range method was used to identify outlier data points, with the proportion of outliers controlled to within 5%. Then, all numerical features were standardized using the Z-score standardization method to adjust the data distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1. In the feature engineering stage, key features were extracted using principal component analysis, retaining principal components with a cumulative variance contribution rate of 95%. Simultaneously, interactive and time-delay features were constructed to enhance the model's expressive power. Interactive features included the product of grinding time and rotation speed, and the ratio of specific surface area change rate to coupling agent concentration, while time-delay features included historical values ​​from the previous 1 to 5 time steps. In the data augmentation stage, time-series data augmentation techniques were employed, including sliding time windows, Gaussian noise addition, and interpolation enhancement, expanding the original dataset to 32,000 samples. Sliding time windows used a sliding window with a step size of 1 to generate overlapping sequences, and the standard deviation of Gaussian noise was set to 5% of the original signal standard deviation. Interpolation enhancement used cubic spline interpolation to generate new data points between the original data points. The final training dataset was divided into training, validation, and test sets in a 7:2:1 ratio to ensure data distribution balance and representativeness.

[0062] The key technical ideas of this invention are mainly reflected in the following three aspects.

[0063] The first key technical approach is a carbon nanotube surface modification optimization strategy based on the rate of change of specific surface area. Traditional methods typically use a fixed grinding time to process carbon nanotubes, lacking precise control over the grinding process, resulting in uneven surface activity and a tendency for over-grinding. This invention achieves precise control of the grinding process by real-time monitoring of the rate of change of specific surface area and establishing a surface energy density mechanism equation to describe the quantitative relationship between grinding time and surface properties. This approach has significant advantages over traditional fixed-parameter grinding methods, as it can dynamically adjust grinding parameters according to the actual surface state of the carbon nanotubes, avoiding surface defects caused by over-grinding, while ensuring sufficient and uniform surface modification, thus providing a high-quality raw material basis for subsequent dispersion and blackness optimization.

[0064] The second key technical approach is a multi-objective coordinated optimization method using a two-layer game theory optimization model. Traditional optimization methods typically treat grinding time optimization and blackness optimization as independent problems, lacking systematic consideration and leading to local optima. This invention constructs an upper-layer blue phase blackness maximization model and a lower-layer grinding time matching optimization model, achieving coordinated optimization of the two objectives through Stackelberg game theory. The advantage of this approach over traditional single-objective optimization methods is that it can simultaneously consider process optimization and product performance optimization. By balancing the conflicting relationships between different objectives through a game mechanism, it obtains a global optimum rather than a local optimum, significantly improving the stability and reliability of the optimization results.

[0065] The third key technological approach is a carbon nanotube dispersion optimization model based on the Transformer-XL architecture. Traditional dispersion control methods mainly rely on empirical parameters and simple feedback control, which struggle to handle complex nonlinear relationships and temporal dependencies. This invention employs the Transformer-XL deep learning architecture, capturing the complex correlation between grinding parameters and dispersion states through a multi-head attention mechanism, and utilizing a memory module to store long-term grinding pattern information, thereby achieving intelligent prediction and control of the dispersion process. The advantage of this approach over traditional empirical control methods lies in its ability to handle high-dimensional nonlinear optimization problems. By learning complex patterns from historical data, it achieves predictive control, significantly improving the accuracy and adaptability of dispersion control.

[0066] The synergistic effect of these three key technological approaches offers significant advantages over existing technologies. Surface modification optimization provides a high-quality raw material foundation for dispersion optimization, the game-theoretic optimization model achieves globally optimal configuration of process parameters, and the intelligent dispersion model ensures the precise execution of optimization results. These three elements form a complete technological chain from raw material processing to process optimization and process control. Through multi-level coordinated optimization, a significant improvement in the blackness of the blue phase of TPV materials is achieved, while simultaneously ensuring the stability of the production process and the consistency of product quality.

[0067] It should be further explained that the carbon nanotube dispersion optimization model, based on deep learning technology of the Transformer-XL architecture, is suitable for solving the technical problem of insufficient blackness of the blue phase in TPV materials. Its applicability is reflected in several key aspects. First, the carbon nanotube dispersion process has typical time-dependent characteristics. Parameters such as grinding time, specific surface area change rate, and temperature change have complex interrelationships and cumulative effects over time. This time-dependent characteristic determines that traditional static optimization methods are difficult to accurately capture the dynamic changes in the dispersion process. However, the Transformer-XL architecture naturally has the ability to handle long-sequence time dependencies and can establish a precise mapping relationship between changes in grinding parameters and the final blackness effect through its unique memory and attention mechanisms. Second, there are multi-scale nonlinear changes in the carbon nanotube dispersion process, from surface energy changes at the nanoscale to blackness effects at the macroscale. This complex cross-scale correlation requires the optimization model to have strong feature extraction and pattern recognition capabilities. Transformer-XL's multi-head attention mechanism can simultaneously focus on feature information at different scales and time points, achieving effective integration and utilization of cross-scale information.

[0068] Traditional mechanical mixing techniques primarily rely on physical actions such as screw shearing and rotor stirring to disperse carbon nanotubes. This method uses fixed process parameters and experience-driven optimization strategies, failing to dynamically adjust based on the actual dispersion state, leading to uncontrollable and unstable dispersion results. The core problem of traditional mechanical mixing lies in its lack of real-time perception of the dispersion process, failing to identify changes in the agglomeration state of carbon nanotubes. This often results in over-dispersion or under-dispersion, affecting the final blackness. In contrast, the carbon nanotube dispersion optimization model of this invention establishes an intelligent mapping relationship between dispersion state and process parameters using deep learning technology. It can predict the optimal parameter adjustment scheme based on historical dispersion data and the current process state, achieving a technological leap from passive response to proactive prediction. The model's memory module can store and utilize historical successful experiences, avoiding repetitive trial-and-error processes and significantly improving the efficiency and accuracy of process optimization.

[0069] Traditional PID control systems are widely used in polymer processing for closed-loop control of single parameters such as temperature, pressure, and rotational speed. Their control principle is based on error feedback and linear adjustment mechanisms, suitable for controlled objects with well-defined mathematical models and linear characteristics. However, the carbon nanotube dispersion process involves multiple coupled nonlinear parameters. Traditional PID control cannot handle such complex systems with multiple variables, strong coupling, and nonlinearity, often resulting in control oscillations, response lag, and steady-state errors. The dispersion optimization model of this invention adopts the Transformer-XL architecture, achieving parallel processing and dynamic correlation analysis among multiple variables through a self-attention mechanism. It can simultaneously consider the synergistic effects of multiple parameters such as grinding time, specific surface area change rate, temperature distribution, and rotational speed variation, avoiding the local optimum problem caused by single-variable optimization in traditional control systems. The model's encoder-decoder structure gives it end-to-end optimization capabilities, enabling it to directly learn the optimal parameter combination strategy from historical process data without establishing complex mathematical models, greatly simplifying the complexity of system design.

[0070] Traditional neural network methods such as multilayer perceptrons and convolutional neural networks (CNNs) have inherent limitations when processing time-series data. Multilayer perceptrons lack the ability to model temporal dependencies, can only process static feature vectors, and cannot capture the dynamic changes during carbon nanotube dispersion. While CNNs possess some local feature extraction capabilities, their fixed kernel size and pooling operations limit the modeling of long-term dependencies, especially when dealing with processes like carbon nanotube dispersion that require consideration of long-term cumulative effects; traditional CNNs struggle to establish effective global associations. Recurrent neural networks (RNNs) such as LSTMs can process sequential data, but their computational limitations due to their recursive structure make them prone to gradient vanishing and information loss problems when processing long sequences, affecting the model's prediction accuracy and stability. This invention employs the Transformer-XL architecture, which uses a self-attention mechanism to model the direct association between any two positions in a sequence, avoiding the recursive computation limitations of traditional RNNs and efficiently processing long sequences of grinding parameter variations. In particular, its unique relative position encoding and memory mechanism allows the model to effectively utilize longer historical information while maintaining computational efficiency, providing more accurate and stable prediction capabilities for carbon nanotube dispersion optimization.

[0071] In this invention, the memory mechanism of Transformer-XL is its core technological advantage, distinguishing it from traditional optimization methods. This mechanism uses the hidden state of the previous time window as the extended context of the current window, enabling information transfer and reuse across time windows. In carbon nanotube dispersion optimization applications, the memory mechanism plays a crucial role. It preserves successful experiences and lessons learned from different grinding stages, forming a dynamically updated knowledge base. When faced with a new dispersion task, the model can quickly retrieve similar process conditions and corresponding optimization strategies from historical memory, avoiding blind exploration from scratch. The memory length adjustment function dynamically adjusts the memory depth based on the stability of the specific surface area change rate and the convergence state of the game model. This adaptive adjustment mechanism ensures that the model can fully utilize historical information while avoiding performance degradation caused by over-reliance on outdated information. Compared with traditional rule-based or expert system-based knowledge management methods, Transformer-XL's memory mechanism has stronger generalization and adaptability, automatically extracting and updating knowledge from data without the need for manual maintenance of complex rule bases.

[0072] Multi-head attention is another core technological advantage of the Transformer-XL architecture. It can extract feature information in parallel from multiple different representation subspaces, enabling multi-dimensional understanding and modeling of complex processes. In carbon nanotube dispersion optimization, different attention heads can focus on different types of feature patterns. For example, one attention head focuses on the correlation between grinding time and the rate of change of specific surface area, another focuses on the relationship between temperature change and dispersion state, and yet another is responsible for capturing the influence of coupling agent concentration on interfacial bonding. This multi-head parallel processing mechanism allows the model to simultaneously consider the synergistic effects of multiple influencing factors, avoiding the local optima problem caused by traditional single optimization objectives. Compared with traditional weighted summation or linear combination methods, the weight allocation learned by the multi-head attention mechanism is more flexible and precise, automatically adjusting the importance of different factors according to the current process state, achieving truly intelligent collaborative optimization. This collaborative optimization effect is particularly prominent in improving the blackness of the blue phase in TPV materials, because the formation of blue phase blackness involves multiple interrelated factors such as the surface state of carbon nanotubes, dispersion uniformity, and interfacial bonding strength. Only through collaborative modeling using the multi-head attention mechanism can the optimal balance and comprehensive optimization of these factors be achieved.

[0073] It should be further explained that this invention also solves the following technical problems: Traditional carbon nanotube surface treatment processes lack quantitative control methods, making it impossible to precisely adjust the degree of surface modification according to specific application requirements. This leads to unstable interfacial bonding between carbon nanotubes and the polymer matrix, affecting the final optical performance and blackness. This invention establishes a surface energy density mechanism equation, establishing a quantitative relationship between key parameters such as grinding time, specific surface area change rate, and coupling agent concentration and surface energy density changes. Combined with a dynamic update mechanism of the surface energy density adjustment factor, it achieves precise control of the degree of carbon nanotube surface treatment, ensuring the consistency and stability of interfacial bonding. Simultaneously, existing technologies lack intelligent monitoring and prediction capabilities for the carbon nanotube dispersion process, failing to identify poor dispersion conditions in real time and adjust process parameters promptly during processing. This results in significant batch-to-batch variations in product blackness, affecting product quality consistency. This invention employs the Transformer-XL deep learning model to establish a carbon nanotube dispersion optimization system. By using a multi-head attention mechanism and long sequence memory capability, it captures the complex nonlinear change patterns of the dispersion process. Combined with a memory length adjustment function, it achieves adaptive optimization of model parameters, providing intelligent technical support for real-time monitoring, accurate prediction, and dynamic control of the dispersion state. This effectively eliminates batch-to-batch differences in product quality and ensures the stability and consistency of the blackness of the blue phase in TPV materials.

[0074] Specifically, the principle of this invention is as follows: The fundamental reason why the technical solution of this invention can solve the problem of insufficient blackness of the blue phase in TPV materials lies in achieving a substantial improvement in blackness quality from the perspective of the material's optical mechanism. Carbon nanotubes, as one-dimensional nanomaterials, possess unique optical properties. Their tubular structure and degree of graphitization determine their strong light absorption capacity, especially in the visible light band, where they can achieve near-complete light absorption, thus producing a deep black effect. The surface energy density mechanism equation establishes a quantitative relationship between the grinding treatment and the surface state of carbon nanotubes. By controlling the rate of change of specific surface area, the surface energy distribution of carbon nanotubes is precisely adjusted, enabling them to form an optimal interfacial bonding state with the polymer matrix. This optimized interfacial structure not only improves the dispersion stability of the filler but, more importantly, forms a continuous light absorption network structure, significantly enhancing the material's light absorption efficiency and blackness depth. The design of the upper and lower layer game-theoretic optimization models embodies a systematic approach to blackness optimization. The lower layer model focuses on the local optimization of carbon nanotube surface treatment, ensuring that each carbon nanotube particle can achieve optimal optical performance by maximizing the specific surface area utilization efficiency. The upper layer model optimizes the blackness effect of the blue phase from a global perspective. The two layers achieve a coordinated unity between microstructure optimization and macroscopic performance improvement through game-theoretic iteration. The Transformer-XL dispersion optimization model captures the complex changes in the carbon nanotube dispersion process using deep learning technology. Its multi-head attention mechanism can identify the influence weight of different process parameters on the final blackness effect, while the memory module saves historical optimization experience, enabling the model to quickly find the optimal parameter combination under new process conditions. The multi-round iterative optimization strategy ensures the global optimality of process parameters. When the surface energy density adjustment factor and the optimal grinding time reach a convergence state, the carbon nanotubes form the most ideal dispersion state and optical structure in the polymer matrix, thereby maximizing the blackness of the blue phase of the TPV material.

[0075] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0076] The specific implementation of step S01 involves precisely mixing modified carbon nanotubes and titanate coupling agent at a mass ratio of 5:1. An electronic analytical balance is used during the mixing process to ensure a mixing accuracy of ±0.1%. The formula for calculating the specific surface area change rate during the grinding process is:

[0077]

[0078] In the formula, η is the rate of change of specific surface area, in m³. 2 / (g·h); S t Grinding time t grind Specific surface area at time t, in m² 2 / g; S0 is the initial specific surface area, in m².2 / g;t grind This represents the actual grinding time, expressed in hours (h). The specific expression for the surface energy density mechanism equation is:

[0079]

[0080] In the formula, γ is the surface energy density, and the unit is achieved by adjusting the dimension of α0 in J / m. 2 α0 is the basic surface energy coefficient, which has a dimensionless adjustment function and a value range of 0.05 to 0.15; β1, β2, β3, and β4 are power exponents, dimensionless, and take values ​​of 0.3, 0.2, 0.15, and 0.1, respectively; ω is the ball milling speed, in rpm; C coupling This refers to the concentration of the coupling agent, in wt%; H media ξ is the hardness of the grinding media, in HRC; ξ is the surface energy density adjustment factor, dimensionless; η opt The optimal rate of change of specific surface area, in m³. 2 / (g·h); σ is an adjustment parameter, dimensionless, ranging from 0.8 to 1.2. The mechanistic equation simultaneously outputs the predicted emissivity value:

[0081] B pred =k1γ+k2I blue +k3;

[0082] In the formula, B pred To predict blackness values, a dimensionless value is used; k1, k2, and k3 are fitting coefficients, with values ​​of 0.8, 0.15, and 5.0, respectively. Where S... t The specific surface area of ​​carbon nanotubes was determined by nitrogen adsorption using the Bruner-Emmett-Teller equation. The initial surface area of ​​carbon nanotubes (S0) was determined using the same method. The initial value of ξ was obtained by fitting historical data using the least squares method, ranging from 0.5 to 2.0. η opt This was determined through statistical analysis of historical optimization data.

[0083] The specific implementation of step S02 is the same as described above, and will not be repeated in detail here.

[0084] The specific implementation of step S03 involves feeding the premixed materials into a twin-rotor internal mixer for the first mixing. The formula for calculating the temperature distribution uniformity index during the mixing process is as follows:

[0085]

[0086] In the formula, ψ is the temperature distribution uniformity index, which is dimensionless; T i Let be the temperature at the i-th measurement point, in K; The average temperature is the temperature at all measurement points, expressed in Kelvin (K); n is the total number of measurement points, ranging from 20 to 30. Wherein, T... iThe temperature was measured in real time using an infrared thermometer, with the measurement points evenly distributed inside the mixing chamber. It is obtained by calculating the arithmetic mean.

[0087] The specific implementation methods for steps S04-S05 are the same as those described above, and will not be repeated in detail here.

[0088] The specific implementation of step S06 involves performing a black level game optimization process on the second mixing material, establishing a two-layer game optimization model. The specific expression of the upper-level objective function is:

[0089]

[0090] In the formula, F upper The objective value of the upper-level model is dimensionless; I blue The blue phase index is dimensionless and ranges from 0 to 100; C cnt is the carbon nanotube concentration, in wt%; w1, w2, w3, and w4 are weighting coefficients, with values ​​of 0.4, 0.3, 0.2, and 0.1 respectively. The specific expression of the lower-level objective function is:

[0091]

[0092] In the formula, F lower η is the objective value of the lower-level model and is dimensionless. max This represents the theoretical maximum rate of change in specific surface area, in meters. 2 / (g·h);t grind The actual grinding time is expressed in hours (h); t opt The optimal grinding time is expressed in hours (h); φ freq This is a dimensionless parameter for adjusting the grinding frequency, ranging from 0.8 to 1.2; k eff λ is the grinding efficiency coefficient, dimensionless, ranging from 0.6 to 1.0; λ1, λ2, and λ3 are weighting coefficients, with values ​​of 0.5, 0.3, and 0.2, respectively. Where, I blue C was obtained by measurement using a spectrophotometer in the wavelength range of 420–480 nm. cnt η is obtained through mass fraction calculation. max Through theoretical calculations and experimental verification, φ was determined. freq and κ eff Obtained by fitting experimental data.

[0093] The specific implementation of step S07 involves inputting the updated surface energy density adjustment factor into the surface energy density mechanism equation for iterative calculation. The new optimal grinding time is obtained by solving the following nonlinear equation:

[0094]

[0095] After unfolding, we get:

[0096]

[0097] The update formula for the surface energy density adjustment factor is:

[0098]

[0099] In the formula, ξ (k+1) ξ is the surface energy density adjustment factor for the (k+1)th iteration; (k) α is the surface energy density adjustment factor for the k-th iteration; update To update the step size, the value ranges from 0.01 to 0.05; To predict the partial derivative of the emissivity value with respect to the adjustment factor, the iterative convergence criterion is:

[0100]

[0101] In the formula, Let be the optimal grinding time for the k-th iteration. This represents the optimal grinding time for the (k+1)th iteration. It was obtained by numerical differentiation method, using the central difference scheme. The value obtained by calculating using the chain rule is: The iterative process is solved using the Newton-Raphson method.

[0102] The specific implementation method of step S08 is the same as described above, and will not be repeated in detail here.

[0103] The formula for calculating the stability index of the specific surface area change rate is as follows:

[0104]

[0105] In the formula, δ is the stability index of the rate of change of specific surface area, with units of m. 2 / (g·h); η j Let be the rate of change of specific surface area at the j-th time point; is the average rate of change of specific surface area within the time window; m is the number of data points within the time window, ranging from 10 to 20.

[0106] The formula for calculating the iterative convergence index of the game theory model is as follows:

[0107]

[0108] In the formula, is the iterative convergence exponent of the game theory model, which is dimensionless; and These are the objective function values ​​of the upper and lower layers, respectively, for the k-th iteration.

[0109] The specific expression for the memory length adjustment function is as follows:

[0110]

[0111] In the formula, L memory L represents the number of memory fragments, dimensionless. min The minimum memory length is set to 50; L current L represents the current memory length. max The maximum memory length is set to 200; μ is the memory adjustment value; θ1 and θ2 are the segmentation points. The formula for calculating the memory adjustment value is:

[0112]

[0113] The breakpoints are calculated using the quantile method:

[0114] θ1=Q 25 (μ history ), θ2=Q 75 (μ history );

[0115] In the formula, Q 25 and Q 75 These are the 25th and 75th percentiles of the historical memory adjustment value, respectively.

[0116] The principles and effects of each formula are explained below. The specific surface area change rate formula is based on surface area kinetics theory. Through linearization, it simplifies the complex surface change process into a linear function of time. Compared to traditional qualitative judgment methods, this formula provides accurate quantitative indicators, enabling real-time monitoring and precise control of the grinding process, significantly improving the consistency and reproducibility of surface modification. The surface energy density mechanism equation is based on thermodynamics and fractal theory, comprehensively considering the synergistic effect of grinding parameters on surface energy. The power term... This reflects the nonlinear coupling relationship between parameters, and the Gaussian decay term. This demonstrates the existence of an optimal process window. Compared to empirical formulas, this equation can accurately describe the complex surface energy variation patterns, providing a theoretical basis for process parameter optimization and realizing the shift from qualitative control to quantitative design. Predicted emissivity formula B pred =k1γ+k2I blue +k3, based on multiple linear regression theory, establishes a quantitative relationship between surface energy density and emissivity performance. Compared to single-index evaluation methods, it comprehensively considers multiple influencing factors, improving the accuracy and reliability of emissivity prediction. The temperature distribution uniformity index, based on statistical principles, uses the coefficient of variation. By eliminating the influence of absolute temperature values, this index is more sensitive to the non-uniformity of temperature distribution compared to the average temperature monitoring method, providing a reliable evaluation standard for mixing quality control. The upper-level objective function adopts a multi-objective weighted summation form, where the linear term... This reflects the main effects of each factor, and the quadratic term w4(η-η) opt ) 2 This reflects the penalty effect for deviations from the optimal point. Compared to single-objective optimization methods, this function can balance multiple performance indicators, avoid local optima, and significantly improve the overall performance of the optimization results. The lower-level objective function is based on the principle of efficiency maximization, expressed in ratio form. and relative deviation term By eliminating the influence of dimensions, this function, compared to fixed-parameter methods, can dynamically adjust the grinding strategy, achieving dual optimization of grinding efficiency and product quality. Surface energy density adjustment factor update formula. Based on gradient descent theory, through partial derivatives The method guides parameter adjustment, enabling dynamic optimization of surface modification effects compared to fixed adjustment factor methods, thus achieving adaptive parameter adjustment. The iterative convergence criterion is based on relative error theory, using relative error constraints... This approach avoids the applicability issue of the absolute error criterion across different orders of magnitude, and compared to methods with a fixed number of iterations, it ensures both algorithm convergence and computational efficiency. The surface area change rate stability index is based on the principle of analysis of variance and uses the standard deviation form. This index quantifies the dispersion of the data and, compared to simple numerical comparison methods, can accurately evaluate the stability of the grinding process, providing a scientific basis for process control. The iterative convergence index of the game theory model is based on the Euclidean distance principle and expressed in vector norm form. The convergence of the two-level objective function was comprehensively evaluated. This index, compared to the single-objective function monitoring method, can more comprehensively reflect the convergence state of game optimization, ensuring the reliability of the optimization algorithm. The memory length adjustment function, based on piecewise linear control theory, achieves adaptive adjustment of the memory mechanism through threshold segmentation. The memory adjustment value is calculated... It embodies a weighted balance between convergence and stability. Compared with the fixed memory length method, this function can dynamically optimize the model performance according to the process state, which significantly improves the prediction accuracy and computational efficiency.

[0117] To better understand and implement this invention, Example 2 of a specific application scenario is provided below: The technical team first optimized the surface treatment of the modified carbon nanotubes, selecting multi-walled carbon nanotubes with a diameter of 15nm and a length of 5μm as raw materials, and using a titanate coupling agent for surface modification. The carbon nanotubes and titanate coupling agent were mixed at a mass ratio of 5:1, with a total weight of 500g, including 417g of carbon nanotubes and 83g of coupling agent. After mixing, the mixture was fed into a planetary ball mill for grinding. The mill speed was set to 350rpm, and the grinding media was zirconia balls with a hardness of HRC62. Specific surface area was measured every 15 minutes during the grinding process, and the initial specific surface area S0 was determined to be 245m². 2 / g. Continuous monitoring revealed that the specific surface area reached 380m² after grinding for 2.5 hours. 2 / g, at which point the rate of change of specific surface area is 54m² 2 / (g·h), close to the preset optimal specific surface area change rate of 55m³. 2 / (g·h). Based on the surface energy density mechanism equation, the surface energy density adjustment factor ξ reaches 1.85, and the surface energy density γ is 0.125 J / m. 2 This meets the requirements for subsequent processing.

[0118] After surface modification, the technical team premixed the components according to the formula: 25 parts surface-modified carbon nanotubes, 3 parts EVA wax, 80 parts polypropylene, and 2 parts antioxidant. Premixing was carried out in a high-speed vertical mixer at 70°C for 20 minutes. The components were added in stages: first, polypropylene and antioxidant were added and mixed for 2 minutes; then, EVA wax was added and mixed for 3 minutes; finally, surface-modified carbon nanotubes were added and mixed for 15 minutes to ensure thorough dispersion of all components.

[0119] The premixed materials were then fed into a twin-rotor internal mixer for the first mixing. The mixer was set with the following parameters: feed zone temperature 110℃, mixing zone temperature 150℃, discharge zone temperature 170℃, main machine speed 45Hz, discharge gate opening 50%, corresponding to an actual speed of 72rpm. During the mixing process, 25 measuring points were set up in the mixing chamber using an infrared thermometer to monitor the temperature distribution in real time. The temperature distribution at each measuring point is shown in Table 1.

[0120] Table 1 Temperature distribution data for the first mixing stage

[0121] Measurement point location Temperature value (°C) Measurement point location Temperature value (°C) Measurement point location Temperature value (°C) Front left side 148 left side of the middle 152 Backend left side 169 Front-end middle section 151 central central 150 Backend middle section 171 Front right side 149 Right side of the middle 153 Backend right side 168

[0122] The calculated temperature distribution uniformity index ψ was 0.078, indicating a relatively uniform temperature distribution and good mixing quality. After the first mixing, the material was plasticized and extruded through a single-screw extruder. The temperatures of each section of the extruder were set as follows: feed section 120℃, compression section 160℃, metering section 180℃, and die head section 190℃. The screw speed was set to 42 rpm. During the extrusion process, the carbon nanotube dispersion optimization model monitored the dispersion parameters in real time, controlling the agglomeration degree below 12% and achieving a distribution density of 85%.

[0123] The technical team re-feeded the extruded material into a twin-rotor internal mixer for a second mixing process, using the same parameters as the first. The second mixing employed ultrasonic-assisted technology with an ultrasonic frequency of 40kHz and a power density of 3W / cm³. 2 This effectively eliminated the aggregation of carbon nanotubes. Transmission electron microscopy revealed that the dispersion of carbon nanotubes increased to 92%, and the size of aggregated particles decreased to 85 nm.

[0124] After the second mixing, the technical team performed a blackness game optimization on the material. Based on the previous experimental data, a two-layer game model was established. The weight coefficients in the objective function of the upper-layer model were set as w1 = 0.4, w2 = 0.3, w3 = 0.2, and w4 = 0.1. The weight coefficients in the objective function of the lower-layer model were set as λ1 = 0.5, λ2 = 0.3, and λ3 = 0.2. The current process parameters were input as follows: blue phase index 72, carbon nanotube concentration 22.7%, and specific surface area change rate 54m². 2 / (g·h), grinding time 2.5h. After game-theoretic optimization calculations, the target value of the upper model reached 0.847, the target value of the lower model reached 0.792, and the optimized surface energy density adjustment factor was obtained as 1.92.

[0125] The iterative trend of the objective function values ​​at both the upper and lower levels during the game-theoretic optimization process shows that the algorithm converges after the 8th iteration, with the convergence index decreasing to 0.015, meeting the convergence criterion. Inputting the updated surface energy density adjustment factor into the surface energy density mechanism equation yields a new optimal grinding time of 2.7 hours, with a relative error of 8% compared to the current grinding time. This exceeds the 3% convergence threshold, requiring another round of iterative optimization.

[0126] The technical team re-modified the carbon nanotube surface using the new optimal grinding time of 2.7 hours, keeping other process parameters unchanged. After the second iteration, the specific surface area change rate increased to 58 m². 2 / (g·h), the surface energy density adjustment factor was updated to 1.97. Game-theoretic optimization calculations continued, and the optimal grinding time of 2.72h was obtained in the third iteration. The relative error with the second round was reduced to 1.8%, which met the convergence condition, and the iteration process ended.

[0127] Based on the final optimization results, such as Figure 3 The relationship between carbon nanotube dispersion and grinding time is shown. The technical team then performs the final extrusion molding, precisely controlling the extrusion temperature based on game theory optimization results. The temperatures for each section are adjusted as follows: feeding section 118℃, compression section 158℃, metering section 178℃, and die head section 188℃. During extrusion, the material's blackness value and blue phase index are monitored in real time. Figure 3 As shown, the curves of blackness value and blue phase index change during extrusion indicate good parameter stability. When the blackness value briefly dropped to 87, the system automatically adjusted the screw speed from 42 rpm to 45 rpm and simultaneously increased the metering section temperature by 2°C, causing the blackness value to quickly recover to 91.

[0128] The performance test results of the final product are shown in Table 2.

[0129] Table 2 Final TPV Material Performance Test Results

[0130] Performance indicators Test value Target value Test methods Blackness value 93.2 ≥90 Integral sphere spectrophotometry Blue color index 78.4 ≥75 420-480nm spectral measurement Tensile strength (MPa) 18.6 ≥15 ASTM D412 Elongation at break (%) 420 ≥350 ASTM D412 Hardness (Shore A) 75 70-80 ASTM D2240 Heat aging resistance excellent qualified 125℃×168h

[0131] To verify the effectiveness of the carbon nanotube dispersion optimization model, the technical team collected key parameter data throughout the production process, including grinding time series, specific surface area change rate, and surface energy density adjustment factor. Model training used 8000 sets of historical data, and the validation set prediction accuracy reached 96.3%, exceeding the design requirement of 94%. The memory length adjustment function dynamically adjusts the number of memory segments based on the specific surface area change rate stability index and the game model convergence index. In the early grinding stage, when the specific surface area change rate fluctuates significantly, the number of memory segments automatically increases to 180, and decreases to 80 during the stable period, achieving the optimal balance between computational efficiency and prediction accuracy.

[0132] It should be noted that the variables involved in this invention are explained in detail in Table 3.

[0133] Table 3. Variable Explanation Table

[0134]

[0135]

[0136] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of increasing the blackness of a TPV material at blue light, characterized in that, The method comprises the following steps: mixing modified carbon nanotubes with titanate coupling agent, and then placing the mixture into a ball mill to obtain surface-modified carbon nanotubes and an initial surface energy density adjustment factor; pre-mixing the surface-modified carbon nanotubes with EVA wax, polypropylene and an antioxidant to obtain a pre-mixture; feeding the pre-mixture into a double rotor internal mixer to perform first mixing to obtain a first mixed material; plasticizing and extruding the first mixed material through a single screw extruder to obtain a first extruded material and real-time dispersion state parameters; re-feeding the first extruded material into the double rotor internal mixer to perform second mixing to obtain a second mixed material; performing a blackness game optimization process on the second mixed material to obtain a game optimization result and an updated surface energy density adjustment factor; inputting the updated surface energy density adjustment factor into a surface energy density mechanism equation to calculate a new optimal grinding time and perform iterative optimization; and finally forming the material corresponding to the final game optimization result through the single screw extruder to obtain a final TPV material product.

2. The method of increasing the blackness of a TPV material at blue light according to claim 1, wherein, The step of the grinding process is specifically that the modified carbon nanotubes are mixed with the titanate coupling agent at a mass ratio of 5:1, and then placed into a ball mill to perform multi-round grinding experiments, the grinding speed is set to 350 rpm, the specific surface area change rate of the carbon nanotubes at different grinding times is measured as indirect data, the optimal grinding time is calculated by combining a surface energy density mechanism equation, and the grinding process is paused for 5 minutes every 15 minutes for heat dissipation and collection of specific surface area data.

3. The method of increasing the blackness of a blue color of a TPV material of claim 2, wherein, The method also comprises establishing a relationship between the grinding time of the carbon nanotubes and the change of the surface energy density by the surface energy density mechanism equation, and correlating the relationship with the final blue phase blackness to achieve precise control.

4. The method of increasing the blackness of a blue color of a TPV material of claim 3, wherein, The step of the pre-mixing process is specifically that the surface-modified carbon nanotubes 20-30 parts are pre-mixed with EVA wax 1-5 parts, polypropylene 70-90 parts and an antioxidant 1-3 parts according to the formula ratio, the pre-mixing process is performed in a high-speed mixer, the mixing temperature is controlled at 60-80°C, and the mixing time is 20 minutes.

5. The method of increasing the blackness of a blue color of a TPV material according to claim 4, wherein, The step of the first mixing process is specifically that the pre-mixture is fed into a double rotor internal mixer to perform first mixing, the double rotor temperature is set to 90-180°C, the main machine speed is set to 45 Hz, the mixing time is 8-12 minutes, and the material temperature change is monitored during the mixing process and the temperature distribution uniformity index is recorded.

6. The method of increasing the black depth of blue color of a TPV material according to claim 5, wherein, The step of the plasticizing and extruding process is specifically that the first mixed material is plasticized and extruded through a single screw extruder, the single screw temperature is set to 90-200°C, the screw speed is 30-50 rpm, and the carbon nanotube dispersion optimization model is used to adjust the extrusion parameters in real time during the extruding process to ensure uniform dispersion of the carbon nanotubes in the polymer matrix.

7. The method of increasing the black depth of blue color of a TPV material according to claim 6, characterized in that, The step of the blackness game optimization process is specifically that an upper model with the goal of maximizing the blue phase blackness and a lower model with the goal of optimizing the grinding time matching are established, the lower model optimizes the grinding parameters through the specific surface area change rate data, and the upper model maximizes the final blackness effect based on the optimized grinding parameters.

8. The method of increasing the black depth of blue color of a TPV material according to claim 7, characterized in that, The surface energy density mechanism equation is used to describe the relationship between the grinding time of carbon nanotubes and the change of surface energy density and to establish the association with the final blue phase blackness. The inputs include grinding time, specific surface area change rate, ball milling speed, coupling agent concentration, grinding medium hardness and surface energy density adjustment factor. The outputs are predicted blackness value and updated surface energy density adjustment factor.

9. The method of increasing the black depth of blue color of a TPV material according to claim 8, wherein, The surface energy density adjustment factor in the surface energy density mechanism equation is dynamically adjusted by the specific surface area change rate. When the specific surface area change rate is in the optimal range, the surface energy density adjustment factor reaches the maximum value. When deviating from the optimal range, the surface energy density adjustment factor decreases according to the exponential decay law.

10. The method of increasing the black depth of blue color of a TPV material according to claim 9, wherein, The carbon nanotube dispersion optimization model is based on the sequence prediction network of the Transformer-XL architecture, which includes an encoder layer for processing historical grinding parameters and specific surface area change sequences, a memory module for storing long-term grinding mode information, and a decoder layer for predicting optimal grinding time and surface treatment parameters.

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