A method for designing a waterborne, abrasion-resistant, plasticized, flat oil coating formulation

Abstract

The present application relates to a kind of wear-resistant water-based plastic replacement matte oil coating formula design method in the field of information technology, comprising: obtaining the wear resistance threshold and the flexibility threshold of coating in target application scenario;According to the wear resistance threshold and the flexibility threshold, at least one candidate soft resin and at least one candidate hard resin are selected from pre-established resin material library;For the candidate resin combination screened out, the dispersion uniformity index of hard resin in soft resin matrix under different soft-hard resin ratio is calculated using molecular dynamics simulation method;According to the optimized ratio, the microstructure morphology characteristics of the coating after curing are predicted by combining the phase separation kinetics model of coating curing process;The microstructure morphology characteristics are input into the pre-trained performance prediction neural network, and the predicted wear resistance value and the predicted flexibility value of the coating under the optimized ratio are output.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method for designing a wear-resistant water-based plasticizer matte coating formulation. Background Technology

[0002] Water-based plastic substitute matte oils, as environmentally friendly printing coating materials, play a significant role in reducing plastic pollution. However, this field has long faced a key challenge: simultaneously improving the coating's abrasion resistance and flexibility. Enhancing abrasion resistance often sacrifices the coating's bending and folding capabilities, making it prone to cracking on products requiring frequent bending, such as book covers and packaging boxes. This directly limits its widespread application in the high-end printing market.

[0003] Existing technologies attempt to improve wear resistance by adding hard fillers or enhancing chemical crosslinking, but these methods have inherent limitations. Adding inorganic fillers disrupts the uniformity of the coating, leading to weak bonding between the filler and the resin matrix, making it prone to detachment during friction and accelerating wear. Increasing the crosslinking density, on the other hand, hinders molecular chain movement, making the coating brittle and unable to withstand bending. These methods address only one aspect of the material's performance, failing to coordinate the interaction between the soft and hard components within the coating, thus failing to fundamentally resolve the contradiction. The core technical challenge lies in the fact that the macroscopic properties of the coating depend on its internal microstructure. If there is too much soft component, the coating, while flexible, lacks hard support points to resist friction; if there is too much hard component, although there are many support points, they lack tough connections and are prone to breakage.

[0004] Therefore, precisely controlling the ratio of soft to hard resins to form a specific microstructure after curing—that is, allowing hard particles to be properly dispersed within a soft, continuous matrix, rather than agglomerating or forming a rigid, monolithic network—is key to achieving performance breakthroughs. If this ratio is imbalanced, the hard particles cannot effectively withstand and disperse external frictional forces, and the soft matrix will be quickly worn through due to a lack of protection.

[0005] Therefore, designing a water-based plastic substitute matte oil formulation, and precisely controlling the ratio of soft and hard resins to construct a stable coating structure at the microscopic level that can effectively withstand friction while ensuring overall flexibility, has become a key issue in promoting the replacement of traditional plastic films with this environmentally friendly material and meeting the durability requirements of high-end printed materials. Summary of the Invention

[0006] This invention provides a method for designing a wear-resistant water-based plasticizer matte oil coating formulation, mainly including:

[0007] The process involves obtaining the wear resistance and flexibility thresholds of the coating for the target application scenario; selecting at least one candidate soft resin and at least one candidate hard resin from a pre-established resin material library based on these thresholds; calculating the dispersion uniformity index of the hard resin in the soft resin matrix under different soft-hard resin ratios using molecular dynamics simulation for the selected candidate resin combinations; adjusting the type of candidate hard resin or surface modification parameters and recalculating the dispersion uniformity index until a resin combination and initial ratio range that meet the dispersion threshold requirements are obtained; and simulating the stress distribution of the coating under a preset friction load using finite element analysis within the initial ratio range that meets the dispersion threshold requirements to obtain the hard resin particle size distribution. The stress-sharing ratio borne by the particles is determined; it is then determined whether the stress-sharing ratio reaches a preset load-bearing threshold. If not, the ratio of rigid resin is increased within the initial ratio range, and the stress distribution simulation is repeated until the stress-sharing ratio meets the load-bearing threshold, thus obtaining an optimized ratio. Based on the optimized ratio and combined with the phase separation kinetic model of the coating curing process, the microstructure morphology of the cured coating is predicted. The microstructure morphology is input into a pre-trained performance prediction neural network, which outputs the predicted wear resistance and predicted flexibility values ​​of the coating under the optimized ratio. The predicted wear resistance value is compared with the wear resistance threshold, and the predicted flexibility value is compared with the flexibility threshold. If both meet the threshold requirements, the optimized ratio is determined as the final coating formulation design parameter. Furthermore, obtaining the wear resistance and flexibility thresholds of the coating for the target application scenario includes: obtaining the wear resistance and flexibility thresholds of the coating corresponding to the target application scenario through a preset database of printed material durability standards, thus obtaining a threshold set; for the threshold set, using coating matching verification, extracting additional durability indicators from the database to determine the applicability of the thresholds in the target scenario; based on the applicability, extracting the wear resistance and flexibility thresholds from the threshold set as input parameters for subsequent screening of candidate soft resins and candidate hard resins; comparing the thresholds with a pre-established resin material library using the input parameters, screening for soft resins with high compatibility, thus obtaining candidate soft resins; based on the candidate soft resins, extracting hard resins from the resin material library, using a matching degree calculation method to determine the compatibility matching degree, thus determining candidate hard resins; and forming a candidate resin combination for the candidate hard resins and the candidate soft resins, which is used in the subsequent calculation process of the molecular dynamics simulation method.Furthermore, for the selected candidate resin combinations, molecular dynamics simulation is used to calculate the dispersion uniformity index of the hard resin in the soft resin matrix under different hard and soft resin ratios. This includes: obtaining different hard and soft resin ratios from the candidate resin combinations; constructing a simulation system using molecular dynamics simulation; calculating molecular trajectories by setting the force field parameters of interatomic interactions to obtain molecular interaction data under the specified ratios; and setting simulation parameters, including temperature and time step, for the molecular interaction data, running the simulation under periodic boundary conditions to obtain the positional distribution of the hard resin in the soft resin matrix. The distribution map is used to calculate the radial distribution function between rigid resin particles. By statistically analyzing the probability density of finding another rigid resin particle within different distance intervals, the aggregation degree between rigid resin particles is determined. If the aggregation degree exceeds a preset threshold, the non-bonded interaction parameters in the force field parameters are adjusted, and the simulation is rerun to obtain the calibrated dispersion pattern. Based on the calibrated dispersion pattern, the Euclidean distances between all pairs of rigid resin particles are statistically analyzed, and the variance of the Euclidean distances is calculated. The reciprocal of the variance is used as the dispersion uniformity index to obtain the final index value under different ratios. Furthermore, if the dispersion uniformity index is lower than a preset dispersion threshold, the type of candidate rigid resin or surface modification parameters are adjusted, and the dispersion uniformity index is recalculated until a resin combination and initial ratio range that meet the dispersion threshold requirement are obtained. This includes: obtaining an initial ratio range from the candidate resin combination; calculating the dispersion uniformity index of the rigid resin in the soft resin matrix using molecular dynamics simulation; running molecular trajectories by setting force field parameters to obtain the index value; comparing the index value with the preset dispersion threshold; if the index value is lower than the threshold, adjusting the type of candidate rigid resin or surface modification parameters to obtain an adjusted resin combination; reconstructing the simulation system using the adjusted resin combination; running molecular dynamics simulation to obtain updated molecular interaction data; determining the degree of aggregation by statistically analyzing the interparticle distance probability density, thereby determining the updated dispersion uniformity index; repeating the threshold comparison process based on the updated dispersion uniformity index until the index value meets the threshold requirement to obtain an optimized resin combination and initial ratio range; and extracting the ratio parameters that meet the dispersion threshold requirement for the optimized resin combination as input data for subsequent finite element analysis methods.Furthermore, within the initial proportion range that meets the dispersion threshold requirement, the finite element analysis method is used to simulate the stress distribution of the coating under a preset friction load to obtain the stress sharing ratio borne by the hard resin particles. This includes: obtaining spatial coordinate data of the hard resin particles from the initial proportion range; constructing a coating geometric model containing the spatial coordinate data using the finite element analysis method; applying a preset friction load to the coating geometric model to perform mechanical simulation and obtain stress field distribution data inside the coating; extracting the stress value of the interface region between the hard resin particles and the soft resin matrix through the stress field distribution data; calculating the average value of the interface stress around each hard resin particle, where the average value is defined as the particle interface stress characterization value; based on the particle interface stress characterization values ​​of all hard resin particles, counting the number of particles higher than the overall stress field average value, calculating the ratio of the number to the total number of particles, where the ratio is determined as the stress sharing ratio borne by the hard resin particles; determining whether the stress sharing ratio reaches a preset bearing threshold, which serves as the basis for subsequent adjustment of the proportion parameters; and generating an optimized initial proportion range based on the above criteria for subsequent prediction of the phase separation kinetic model.Furthermore, the step of determining whether the stress sharing ratio reaches a preset bearing threshold, and if not, increasing the proportion parameter of the rigid resin within the initial ratio range and re-simulating the stress distribution until the stress sharing ratio meets the bearing threshold to obtain an optimized ratio, includes: obtaining the proportion parameter of the rigid resin particles from the initial ratio range; constructing a coating geometric model using the finite element analysis method; applying a preset friction load and particle size distribution data to the coating geometric model to perform mechanical simulation and obtain stress field distribution data inside the coating; extracting the stress value of the interface region between the rigid resin particles and the soft resin matrix through the stress field distribution data; calculating the average value of the interface stress around each rigid resin particle, and determining the average value as the particle interface stress characterization value; counting the number of particles higher than the overall stress field average value based on the particle interface stress characterization value of all rigid resin particles, and calculating the ratio of the number to the total number of particles. The ratio is determined as the stress sharing proportion borne by the rigid resin particles. It is then determined whether the stress sharing proportion reaches a preset bearing threshold. If not, the ratio parameter of the rigid resin is increased within the initial mixing ratio range, and the particle size distribution data is adjusted. The finite element analysis method is used to reconstruct the coating geometric model, and a preset friction load is applied for mechanical simulation to obtain updated stress field distribution data. The stress values ​​at the interface between the rigid resin particles and the soft resin matrix are extracted using the updated stress field distribution data, and the particle interface stress characterization value and stress sharing proportion are recalculated. It is then determined whether the stress sharing proportion reaches the preset bearing threshold. If not, the ratio parameter is increased and the particle size distribution data is adjusted, and the simulation and calculation are iteratively performed until the stress sharing proportion meets the bearing threshold. Finally, the ratio parameter and particle size distribution data that meet the bearing threshold are obtained, and the optimized mixing ratio is determined based on the initial mixing ratio range.Furthermore, the step of predicting the microstructure morphology of the cured coating based on the optimized ratio and the phase separation kinetic model of the coating curing process includes: obtaining phase separation model input data from the optimized ratio parameters, the input data including component concentration and curing temperature; simulating the curing process using the phase separation kinetic model; numerically solving the spatiotemporal evolution of the component concentration field using the finite difference method to obtain phase separation distribution data inside the cured coating; extracting the hard region contour from the phase separation distribution data; calculating the equivalent circle diameter of each hard region to determine the hard region size characterization value; extracting the center coordinates of the hard region from the phase separation distribution data; and calculating the coordinates of all adjacent hard regions. The Euclidean distance between the center points of the regions is used to calculate the distribution histogram of the distance, thus obtaining the hard region spacing distribution characteristics. A distribution uniformity index is calculated based on these spacing distribution characteristics. It is then determined whether the distribution uniformity index reaches a preset threshold. If it does not, the curing temperature parameters in the phase separation model input data are adjusted, and the simulation process of the phase separation kinetic model is re-executed to obtain updated phase separation distribution data. If the distribution uniformity index reaches the preset threshold, the hard region size characterization value and the hard region spacing distribution characteristics are integrated based on the phase separation distribution data to determine the final microstructure morphology characteristics, which serve as the input for the subsequent performance prediction neural network. Furthermore, the step of inputting the microstructure morphology features into a pre-trained performance prediction neural network and outputting the predicted wear resistance and predicted flexibility values ​​of the coating under the optimized formulation includes: obtaining an input vector from the microstructure morphology features; processing the input vector using the pre-trained performance prediction neural network to obtain the predicted wear resistance and predicted flexibility values ​​of the coating; obtaining a preset performance threshold for the predicted wear resistance and predicted flexibility values; determining a performance deviation index by comparing the predicted values ​​with the preset performance threshold; if the performance deviation index exceeds a preset deviation range, adjusting the component concentration in the optimized formulation parameters and re-extracting the adjusted microstructure morphology features; inputting the re-extracted microstructure morphology features into the performance prediction neural network to output updated predicted wear resistance and predicted flexibility values ​​of the coating; repeating the process of determining the performance deviation index based on the updated predicted values ​​until the performance deviation index meets the preset deviation range; comparing the predicted values ​​that meet the preset deviation range with the wear resistance threshold and the flexibility threshold as the basis for determining the final coating formulation design parameters.

[0008] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0009] Addressing the unique business challenge of simultaneously meeting abrasion resistance and flexibility thresholds in target applications for printed coatings, this method integrates the logically related challenges of obtaining thresholds from a pre-set database, screening soft and hard resins, and optimizing the ratio to balance abrasion resistance and flexibility. The solution employs a multi-step approach: molecular dynamics simulation to calculate the dispersion uniformity index and adjust resin type or parameters; finite element analysis to simulate stress distribution and iteratively increase the proportion of hard resin; phase separation kinetics model to predict microstructural characteristics; and neural network output of predicted performance values ​​compared to thresholds. Ultimately, the optimized ratio is determined as the design parameter for waterborne coating formulations. This method highlights its most significant innovation: iterative optimization through multi-scale simulation and AI prediction. This ensures that the hard resin effectively shares stress under frictional loads while maintaining a flexible matrix, achieving precise design for highly durable coatings and thus improving the overall durability and application reliability of printed materials. Attached Figure Description

[0010] Figure 1 A flowchart illustrating the design method of a wear-resistant water-based plasticizer matte oil coating formulation according to the present invention;

[0011] Figure 2 This is a schematic diagram of the module framework of step S104 in the design method of a wear-resistant water-based plastic substitute matte oil coating of the present invention.

[0012] Figure 3 This is a schematic diagram of the module framework of step S105 in the design method of a wear-resistant water-based plastic substitute matte oil coating formulation of the present invention.

[0013] Figure 4 This is a schematic diagram of the module framework of step S106 in the design method of a wear-resistant water-based plastic substitute matte oil coating of the present invention.

[0014] Figure 5 This is a schematic diagram of the module framework of step S107 in the design method of a wear-resistant water-based plastic substitute matte oil coating of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] like Figures 1-5 The design method for a wear-resistant water-based plasticizer matte coating formulation in this embodiment may specifically include:

[0017] Step S101: Obtain the wear resistance threshold and flexibility threshold of the coating for the target application scenario. The thresholds are derived from a preset database of printed material durability standards.

[0018] By using a pre-defined database of printed material durability standards, the abrasion resistance and flexibility thresholds of the coating corresponding to the target application scenario are obtained, resulting in the threshold set. For this threshold set, coating matching verification is performed, and additional durability indicators are extracted from the database to determine the applicability of the thresholds in the target scenario.

[0019] In one implementation, the process of obtaining the abrasion resistance and flexibility thresholds of the coating for a target application scenario first requires determining the specific application scenario of the printed material, such as a book cover or packaging material. These scenarios affect the performance requirements of the coating, and the thresholds are derived from a pre-defined database of printed material durability standards, which contains industry standard data, such as abrasion resistance test indicators under ISO specifications. Through a query interface, the user inputs scenario parameters, and the system automatically matches the corresponding thresholds to ensure that the coating meets durability requirements in actual use.

[0020] Specifically, the pre-set database of printed matter durability standards is a structured collection of data that stores performance standards corresponding to various types of printed matter.

[0021] For example, in the context of book covers, the abrasion resistance threshold might be set based on a specific number of cycles in a friction test, while the flexibility threshold is defined as the minimum bending radius through a bending test. These thresholds are derived from a compilation of experimental data and industry standards, and the database is regularly updated to reflect the latest standards. Furthermore, when obtaining thresholds, the system first parses the description of the target application scenario, such as "outdoor advertising prints," and then extracts matching items from the database.

[0022] For example, if the scenario involves packaging materials, the abrasion resistance threshold can be set to withstand 1000 cycles of friction without detachment, while the flexibility threshold is set to be able to bend at an angle greater than 90 degrees without cracking. This approach ensures that the thresholds are highly relevant to the scenario, supporting the optimization of coating design.

[0023] Preferably, the database uses a categorized index structure to store threshold data hierarchically according to application scenarios. For example...

[0024] In one possible implementation, a user searches for "magazine cover" using keywords, and the system returns a wear resistance threshold of less than 0.5 and a flexibility threshold of greater than 20%.

[0025] It should be noted that this acquisition process does not involve real-time calculations, but directly calls pre-stored data to improve efficiency.

[0026] In one embodiment, for high-durability printed materials such as label materials, threshold acquisition includes a verification step: the system compares the input scenario with database entries; if the match is high, it outputs the threshold; otherwise, it prompts the user to adjust the scenario description. This method enhances the accuracy of threshold acquisition and can be used in the printing industry for quality control to ensure coating performance meets standards.

[0027] Understandably, in practice, the database connects to external interfaces, allowing for batch retrieval of thresholds, such as simultaneously querying abrasion resistance and flexibility indicators for multiple scenarios. This flexibility supports large-scale printing production planning, avoiding product problems caused by coating failure. Through the above steps, the obtained thresholds are directly applied to coating formulation adjustments, such as optimizing polymer components based on flexibility thresholds to achieve long-term durability of printed materials.

[0028] Step S102: Based on the wear resistance threshold and flexibility threshold, at least one candidate soft resin and at least one candidate hard resin are selected from the pre-established resin material library.

[0029] Using a pre-established resin material library, soft resins with high compatibility are screened based on the wear resistance threshold and the flexibility threshold using a threshold comparison method. Candidate soft resins are obtained. Based on the candidate soft resins, hard resins are extracted from the resin material library, and the compatibility is determined using a matching degree calculation method. Candidate hard resins are then determined.

[0030] In one implementation, the process of screening candidate soft and hard resins from a pre-established resin material library first involves parameter matching based on acquired abrasion resistance and flexibility thresholds. This resin material library is a pre-built database containing performance data for various resin materials, such as hardness, elastic modulus, and coefficient of friction. This data is collected through experimental testing and from material suppliers, ensuring that each resin in the library has corresponding abrasion resistance and flexibility property values.

[0031] Specifically, soft resins generally refer to materials with high flexibility, such as polyurethane-based resins, which provide good flexural strength, while hard resins refer to materials with strong abrasion resistance, such as epoxy-based resins, used to enhance surface resistance. Through this classification, the system can screen materials based on threshold values. Furthermore, the screening process involves comparing the performance values ​​of the resin materials with these threshold values.

[0032] For example, in scenarios where the wear resistance threshold is set to a friction cycle count greater than 500, the system extracts data for all hard resins from the database and checks which materials have a friction coefficient that meets or exceeds this threshold. Simultaneously, for flexibility performance thresholds such as a bending angle greater than 60 degrees, the system screens soft resins to ensure their elongation meets the requirements. This matching method uses a step-by-step comparison to output at least one candidate soft resin and one candidate hard resin.

[0033] Preferably, in the case of printed materials such as label materials, the resin material library is stored in layers according to performance ranges, for example, the abrasion resistance value is divided into three levels: low, medium and high, which facilitates quick retrieval.

[0034] For example, if the target application is a packaging box coating, and the system inputs an abrasion resistance threshold of withstanding 800 cycles of friction and a flexibility threshold of a minimum bending radius of less than 5 cm, then a polyethylene-based soft resin is selected as a candidate because its flexibility value matches the threshold requirements. Simultaneously, an acrylic-based hard resin is chosen because its abrasion resistance exceeds the threshold. This approach supports initial optimization of the coating formulation.

[0035] It should be noted that the pre-established resin material library is updated regularly to include new material data to cover more printing scenarios.

[0036] In one possible implementation, the screening process involves multiple iterations: first, hard resins that do not meet the abrasion resistance threshold are filtered out; then, from the remaining soft resins, those with the best flexibility are selected, but not limited to a single match; instead, multiple candidates are output for subsequent selection. This iteration ensures the comprehensiveness of the screening process, particularly in book page coating applications.

[0037] For example, when the threshold requirement for wear resistance is a coefficient of friction of less than 0.4, the system may output two types of hard resin, such as silicone-based and phenolic-based, for the user to compare.

[0038] Specifically, the screening of candidate resins also considers compatibility factors, such as the potential for mixing soft and hard resins.

[0039] For example, in outdoor poster printing scenarios, rigid resins are preferred when abrasion resistance thresholds are high, while soft resins are emphasized when flexibility thresholds dominate. Automated filtering is achieved through a database query interface, avoiding manual intervention and improving efficiency.

[0040] In one embodiment, for highly durable printed materials such as brochures, the screening process integrates threshold weights: abrasion resistance accounts for 60% of the weight, and flexibility accounts for 40%. The system calculates a comprehensive score for each resin and selects the candidate with the highest score. This weighting mechanism is adjusted based on the application scenario to ensure that the output resin is suitable for actual coating preparation.

[0041] Understandably, this filtering method is applicable across different printing sub-scenarios, such as from magazine covers to product labels, all of which operate using the same library.

[0042] For example, in labeling scenarios, selected candidate soft resins, such as vinyl ester resins, provide flexibility and support, while hard resins, such as polyester-based resins, ensure abrasion resistance, together forming the coating base. Furthermore, the establishment of the resin material library involves the interpretation of classification criteria: soft resins are defined as materials with an elastic modulus less than 100 MPa, while hard resins are defined as those greater than 500 MPa. Pre-classification using these criteria facilitates threshold matching.

[0043] For example, in a mass production scenario, the system simultaneously filters multiple threshold combinations and outputs a candidate resin list, such as filtering three soft resins and two hard resins for flexible packaging, supporting large-scale applications.

[0044] Step S103: For the selected candidate resin combinations, the molecular dynamics simulation method is used to calculate the dispersion uniformity index of the hard resin in the soft resin matrix under different hard resin ratios.

[0045] Different ratios of hard and soft resins were obtained from the candidate resin combinations. A simulation system was constructed using molecular dynamics simulation. The molecular dynamics simulation calculated molecular trajectories by setting force field parameters for interatomic interactions, obtaining molecular interaction data for the specified ratios. For this molecular interaction data, simulation parameters, including temperature and time step, were set, and the simulation was run with periodic boundary conditions to obtain a positional distribution map of the hard resin in the soft resin matrix. Based on the positional distribution map, the radial distribution function among the hard resin particles was calculated. The calculation process for the radial distribution function involves statistically analyzing the probability density of finding another hard resin particle within different distance intervals to determine the aggregation degree between the hard resin particles. If the aggregation degree exceeds a preset threshold, the non-bonded interaction parameters in the force field parameters were adjusted, and the simulation was rerun to obtain a calibrated dispersion pattern. Based on the calibrated dispersion pattern, the Euclidean distances between all pairs of hard resin particles were statistically analyzed, and the variance of these Euclidean distances was calculated. The reciprocal of the variance was used as the dispersion uniformity index to obtain the final index value for different ratios.

[0046] In one implementation, molecular dynamics simulations are used to evaluate the microstructural uniformity of the selected candidate soft and hard resin combinations. Molecular dynamics simulation is a computational method based on Newtonian mechanics, which simulates the dynamic behavior of materials under specific conditions by constructing models of atomic or molecular motion in a computer, thereby obtaining their structural, thermodynamic, and kinetic properties. Specifically, in this application, the goal is to quantify the dispersion state of the hard resin component in the soft resin matrix.

[0047] Specifically, the implementation process begins with building an initial atomic model. It should be noted that full-atom simulations involve enormous computational costs. In one possible implementation, a coarse-grained force field can be used to simplify the model.

[0048] For example, repeating units of soft resins are mapped to one or more coarse-grained beads, and hard resin molecules are treated similarly. Based on the chemical structures of the screened candidate resins, corresponding bonding and non-bonding parameters are retrieved from a pre-established library of force field parameters. These parameters define the interaction potential energy between beads, such as bond stretching, bond angle bending, and van der Waals interactions. Furthermore, a simulation box is constructed.

[0049] In one embodiment, based on a target ratio, such as a 70:30 mass ratio of soft resin to hard resin, the required number of coarse-grained beads of both resins is calculated. The calculated number of soft resin beads are randomly placed in a cubic simulation box to form an initial soft resin melt. Subsequently, a corresponding number of hard resin beads are randomly inserted into this melt. This process simulates the initial incorporation of hard resin particles into a soft resin matrix.

[0050] Preferably, to more closely resemble the actual process, the rigid resin beads can be initially aggregated to a certain extent during insertion to observe whether they can spontaneously disperse during the simulation. After the model is built, the energy minimization and equilibrium stage begins.

[0051] For example, the system is first minimized in terms of energy to eliminate any excessive overlap or unreasonable high-energy states that may exist between atoms in the initial configuration. Then, an equilibrium simulation is performed for a period of time under isothermal and isochoric conditions.

[0052] For example, the simulation temperature is set to a common curing or service temperature for printed coatings, such as 350 Kelvin, and a Langevin thermostat is used for temperature control. The purpose of the equilibrium simulation is to bring the system to thermodynamic equilibrium, at which point the conformation and distribution of resin molecules tend to stabilize. The equilibrium process typically requires hundreds of thousands to millions of simulation steps, each representing a very short time step, such as 1 femtosecond. Based on the stable system after equilibrium, a formal production simulation is performed to collect data for analyzing dispersion uniformity. In one implementation, the simulation continues to run for a sufficiently long time under the same thermodynamic conditions, for example, a total simulation duration of 100 nanoseconds, and a snapshot of the atomic coordinates of the system is saved at regular intervals. These snapshots record the trajectory of the spatial distribution of the rigid resin component in the flexible resin matrix over time.

[0053] It should be noted that calculating the dispersion uniformity index is the core of this step. The dispersion uniformity index is a scalar value used to quantitatively characterize the uniformity of the distribution of the second-phase component in the matrix. In one specific implementation, a statistical method based on spatial grid division is used for calculation. First, the entire simulation box is uniformly divided into several small cubic grids in three-dimensional space, for example, into 10×10×10 grids, totaling 1000 grids. Then, for a specific frame of simulation snapshot, the number of rigid resin beads contained in each small grid is counted.

[0054] Understandably, if the rigid resin is completely and uniformly dispersed, then the number of rigid resin beads in each grid should be approximately equal; conversely, if the distribution is uneven, the number of beads in some grids will be significantly more or less than the average.

[0055] Specifically, the dispersion uniformity index can be defined by calculating the coefficient of variation of the number of rigid resin beads in all grids. The coefficient of variation is the ratio of the standard deviation to the mean; the smaller the value, the smaller the difference in quantity between grids, indicating a more uniform dispersion.

[0056] For example, let the number of rigid resin beads in the i-th grid be n_i, the average value of all grids be μ, and the standard deviation be σ. Then, the dispersion uniformity index D can be defined as D = σ / μ. The closer the D value is to 0, the higher the uniformity. In another possible implementation, a more complex function, such as a function that considers the concentration gradient between adjacent grids, can be used to comprehensively evaluate local aggregation.

[0057] Preferably, to obtain more reliable results, instead of analyzing only a single snapshot, the dispersion uniformity index is calculated for multiple consecutive snapshots saved during the production simulation phase. The average of these indices is then taken as the final uniformity evaluation index for that specific resin ratio. This method can eliminate the influence of instantaneous fluctuations and reflect the statistical average properties of the system.

[0058] In one embodiment, polyurethane-based flexible resin A and epoxy-based rigid resin B, selected from screening, are used as examples. The goal is to find the optimal ratio for a book cover coating. Three ratios were simulated and compared: ratio one was 85:15 (flexible:rigid resin mass ratio), ratio two was 70:30, and ratio three was 55:45. For each ratio, a coarse-grained model was constructed according to the above procedure. The model box had a side length of approximately 20 nanometers and contained approximately 5000 coarse-grained beads. After energy minimization and balancing at 350 Kelvin for 50 nanoseconds, a production simulation of 50 nanoseconds was performed, saving one frame every 10 picoseconds, resulting in 5000 frames. For each frame, the simulation box was divided into an 8×8×8 grid, and the coefficient of variation D of the number of rigid resin beads was calculated. Finally, the average of the 5000 D values ​​was calculated to obtain the average dispersion uniformity indices for the three formulations: D1=0.18 for formulation 1, D2=0.22 for formulation 2, and D3=0.35 for formulation 3. The results show that under these simulation conditions, formulation 1 (85:15) exhibits the best dispersion uniformity, with the hard resin B being most evenly distributed within the soft resin A matrix; while formulation 3 (55:45) shows relatively poor uniformity, possibly indicating some degree of aggregation of the hard component. This provides a microstructural reference for subsequent determination of the coating formulation.

[0059] Understandably, the above simulation process can be automated.

[0060] One possible implementation integrates molecular dynamics simulation software with a scripting program. After inputting parameters such as the molecular identifier of the candidate resin, the target ratio, and the simulation temperature, the program automatically calls the corresponding force field parameters, completing the entire process from modeling and simulation to uniformity index calculation and output. This approach can efficiently compare the dispersion performance of multiple candidate combinations at different ratios, accelerating the research and optimization process of coating materials.

[0061] Step S104: If the dispersion uniformity index is lower than the preset dispersion threshold, adjust the type of candidate rigid resin or the surface modification parameters, recalculate the dispersion uniformity index, until a resin combination and initial ratio range that meet the dispersion threshold requirement are obtained.

[0062] An initial mixing ratio range is obtained from the candidate resin combinations. A molecular dynamics simulation is used to calculate the dispersion uniformity index of the rigid resin in the soft resin matrix. The molecular dynamics simulation obtains the index value by running molecular trajectories with set force field parameters. The index value is compared with a preset dispersion threshold. If the index value is lower than the threshold, the type of candidate rigid resin or surface modification parameters are adjusted to obtain an adjusted resin combination. The simulation system is reconstructed using the adjusted resin combination, and molecular dynamics simulations are run to obtain updated molecular interaction data. This molecular interaction data is used to calculate the radial distribution function between rigid resin particles. The radial distribution function determines the degree of aggregation by statistically analyzing the inter-particle distance probability density, thereby determining the updated dispersion uniformity index. The threshold comparison process is repeated based on the updated dispersion uniformity index until the index value meets the threshold requirement, resulting in an optimized resin combination and the initial mixing ratio range.

[0063] In one embodiment, when the calculated dispersion uniformity index is lower than a preset dispersion threshold, the candidate rigid resin needs to be adjusted to improve its dispersion state in the soft resin matrix.

[0064] Specifically, the dispersion threshold can be set as an empirical value, such as 0.2, representing the minimum requirement for uniformity. If the index is higher than this value, it indicates uneven distribution, which may lead to unstable performance of the coating material in book cover printing, such as easy cracking or peeling.

[0065] For example, adjusting the types of candidate rigid resins involves selecting alternatives from a pre-defined resin library.

[0066] It should be noted that the resin library includes a variety of rigid resin options, such as epoxy or acrylic resins of different molecular weights, which are pre-screened based on chemical compatibility. In book cover coating applications, if the initial rigid resin is an epoxy-based type with a dispersion index of 0.25, exceeding the threshold of 0.2, it is replaced with an acrylic-based rigid resin, which has better hydrophilicity and contributes to uniform distribution in the flexible polyurethane matrix. Subsequently, based on the new type, the coarse-graining model is reconstructed and molecular dynamics simulations are performed to calculate the updated dispersion uniformity index. Furthermore, if the threshold is still not met after type adjustment, surface modification parameters can be modified. Surface modification parameters refer to altering the surface properties of rigid resin particles through chemical or physical methods to enhance their interfacial compatibility with flexible resins. For example...

[0067] In one possible implementation, surface modification involves adding silane coupling agents or surfactants, with parameters quantified such as coupling agent concentration or modification temperature. For example, in coating formulation optimization, if the initial index is 0.23, increasing the coupling agent concentration from 1% to 2% reduces interfacial tension and promotes uniform dispersion of the rigid resin. After adjustment, the simulation is recalculated to assess whether the new index is below a threshold.

[0068] In one embodiment, taking a combination of polyurethane flexible resin and initial epoxy rigid resin as an example, for a scratch-resistant coating on a book cover, the preset threshold is 0.15. The initial simulated index is 0.28, higher than the threshold. First, the type is adjusted to modified epoxy resin, and the recalculated index is 0.19, still higher than the threshold. Then, the surface modification parameters are modified, introducing polyethylene glycol as a modifier, with a concentration set at 1.5%. After simulation, the index drops to 0.12, meeting the requirements. This iterative process ensures the optimization of the resin combination, obtaining an initial ratio range such as 60:40 to 80:20.

[0069] Preferably, the adjustment and recalculation can be performed cyclically until the index meets the threshold.

[0070] Understandably, this method provides a systematic optimization path in coating material development, such as testing and adjusting effects under different temperature conditions, such as simulating at room temperature or under heating conditions, to cover a variety of printing scenarios.

[0071] Specifically, the adjustment of surface modification parameters is based on the compatibility principle. The compatibility principle refers to the degree of matching of intermolecular forces between two materials; modification enhances this matching by introducing functional groups. In practice, the difference between the current index and the threshold is first assessed. If the difference is greater than 0.1, the type is adjusted first; otherwise, parameters are finely adjusted, such as changing the modifier type from silane to titanate. This helps achieve a uniform microstructure in the book cover coating, avoiding performance defects caused by local aggregation. Further, in another embodiment, for a flexible book cover coating, the initial combination index is 0.24, higher than the threshold of 0.18. When adjusting the surface modification parameters, a nanoparticle coating method is used to coat the hard resin surface with a silica nanolayer, with parameters including a coating thickness of approximately 5 nanometers. After resimulation, the index is 0.16, meeting the requirements. This approach expands the flexibility of adjustment, supporting iterative optimization of various coating ratios.

[0072] For example, the entire iterative process can be integrated into an automated workflow. After inputting thresholds and initial combinations, the system automatically determines and adjusts parameters, outputting resin combinations and proportion ranges that meet the conditions. This improves efficiency in coating development and ensures that the final material has stable dispersion characteristics.

[0073] Step S105: Within the initial ratio range that meets the dispersion threshold requirement, the finite element analysis method is used to simulate the stress distribution of the coating under a preset friction load to obtain the stress sharing ratio borne by the hard resin particles.

[0074] Spatial coordinate data of the rigid resin particles are obtained from the initial proportion range. A coating geometric model incorporating the spatial coordinate data is constructed using the finite element method. A preset friction load is applied to the coating geometric model to perform a mechanical simulation, obtaining stress field distribution data within the coating. The stress values ​​at the interface between the rigid resin particles and the soft resin matrix are extracted from the stress field distribution data. The average value of the interface stress around each rigid resin particle is calculated, and this average value is defined as the particle interface stress characterization value. Based on the particle interface stress characterization values ​​of all rigid resin particles, the number of particles with stress values ​​higher than the overall stress field average is counted, and the ratio of this number to the total number of particles is calculated. This ratio is determined as the stress sharing proportion borne by the rigid resin particles.

[0075] In one embodiment, after the initial mixing ratio range that meets the dispersion threshold requirement is determined, the coating is simulated using the finite element analysis method to evaluate its performance under a preset friction load.

[0076] Specifically, finite element analysis (FEM) is a numerical simulation technique that solves for the mechanical response of complex structures by discretizing a coating model into a finite number of elements. In book cover coating applications, a three-dimensional geometric model of the coating is first constructed, comprising a soft resin matrix and uniformly distributed hard resin particles. The model sets material properties, such as elastic modulus and Poisson's ratio, based on an initial mixing ratio such as 70:30. These properties are obtained from experimental data or databases to ensure the accuracy of the simulation. Subsequently, a mesh is generated, dividing the model into tetrahedral elements. The mesh density is adjusted according to the coating thickness to capture subtle stress variations.

[0077] For example, the simulation process involves applying a preset friction load that simulates the scratching or friction of a book cover during use.

[0078] Specifically, the friction load can be set to a constant value, such as a 5N tangential force, applied to the coating surface. The solution is executed using finite element software to calculate the stress distribution of each element, including von Mises stress, to assess overall deformation and potential failure points. In this step, the rigid resin particles, due to their higher stiffness, will bear more stress, thus affecting the coating's scratch resistance. Furthermore, the stress distribution ratio borne by the rigid resin particles is obtained through post-processing analysis.

[0079] It should be noted that the stress sharing ratio is defined as the ratio of the total stress in the rigid resin particle region to the total stress of the coating as a whole. This ratio is calculated by extracting the stress integral of the particle region from the output data after simulation and comparing it with the substrate stress.

[0080] For example, in a simulation of a wear-resistant coating for a book cover, with an initial mix ratio of 75:25, after applying a frictional load, the particle stress sharing ratio was calculated to be 45%, indicating that the rigid resin effectively shared the load, reducing the risk of damage to the substrate. Obtaining this ratio helps optimize the mix ratio and ensure the stability of the coating during the printing process. In another embodiment, for flexible book cover coatings, the preset frictional load can be adjusted to a dynamic load, such as periodic friction, to simulate repeated page turning. The finite element analysis method is here extended to consider nonlinear material behavior, such as the viscoelasticity of the soft resin. Through iterative solving, the stress distribution is simulated, and the particle stress sharing ratio is calculated, such as 50% obtained at a mix ratio of 80:20. This approach demonstrates the applicability of the method under different friction conditions, supporting flexible adjustments to the coating design.

[0081] Preferably, the entire simulation process can be integrated into the workflow, first verifying the initial mix ratio range, and then performing finite element analysis. For example, if the simulation shows uneven stress distribution and the particle share is lower than expected, such as 30%, the mix ratio can be fine-tuned to 65:35, and the simulation can be repeated to obtain a more balanced stress distribution. This iteration ensures the reliable performance of the coating in book cover applications.

[0082] Understandably, the principle of finite element analysis is based on continuum mechanics, treating the coating as a composite material and solving for displacement and stress through equilibrium equations. In practice, the selection of preset friction loads is based on the actual printing environment, such as the contact force between the cover and the equipment, to make the simulation results more closely match application requirements. For example...

[0083] In one embodiment, for a hard book cover coating, the load is set to 10N, and the particle distribution ratio reaches 55% after simulation. This helps to evaluate the long-term durability of the coating and avoid premature peeling.

[0084] Specifically, the challenge in simulating stress distribution lies in setting boundary conditions, such as fixing the bottom of the coating to simulate its adhesion to paper. Accurate stress maps are obtained through fine meshing and multi-step solutions, allowing for the calculation of the stress distribution ratio. In book cover coating optimization, this method provides quantitative indicators, supporting the transition from initial proportions to the final formulation. Furthermore...

[0085] In one possible implementation, the frictional load simulation considering the effects of temperature is performed, for example, by conducting the analysis at room temperature, and the resulting load-sharing ratio is used to compare the results under heated conditions. This extension enhances the versatility of the method, ensuring consistent coating performance across various printing scenarios.

[0086] Step S106: Determine whether the stress sharing ratio reaches the preset bearing threshold. If not, increase the ratio parameter of rigid resin within the initial ratio range and re-simulate the stress distribution until the stress sharing ratio meets the bearing threshold to obtain the optimized ratio.

[0087] The proportion parameters of hard resin particles are obtained from the initial mixing ratio range. A coating geometric model is constructed using the finite element method (FEM). A preset friction load and particle size distribution data are applied to the coating geometric model for mechanical simulation to obtain the internal stress field distribution data of the coating. The stress values ​​of the interface region between the hard resin particles and the soft resin matrix are extracted from the stress field distribution data. The average value of the interface stress around each hard resin particle is calculated, and this average value is determined as the particle interface stress characterization value. Based on the particle interface stress characterization values ​​of all hard resin particles, the number of particles higher than the overall stress field average value is counted, and the ratio of this number to the total number of particles is calculated. This ratio is determined as the stress sharing ratio borne by the hard resin particles. It is determined whether the stress sharing ratio reaches a preset bearing threshold. If it does not reach the threshold, the proportion parameters of hard resin are increased within the initial mixing ratio range, and the particle size distribution data is adjusted. The coating geometric model is reconstructed using the finite element method, and a preset friction load is applied for mechanical simulation to obtain updated stress field distribution data. The stress values ​​at the interface between the rigid resin particles and the soft resin matrix are extracted using the updated stress field distribution data. The stress characterization values ​​and stress sharing ratio at the particle interface are recalculated. It is determined whether the stress sharing ratio reaches a preset bearing threshold. If it does not, the proportional parameters are increased and the particle size distribution data are adjusted. The simulation and calculation are iteratively performed until the stress sharing ratio meets the bearing threshold. The proportional parameters and particle size distribution data that meet the bearing threshold are obtained, and the optimized ratio is determined in conjunction with the initial ratio range.

[0088] In one implementation, determining whether the stress sharing ratio has reached a preset bearing threshold is done by comparing the simulated value with the threshold.

[0089] Specifically, the stress sharing ratio is a ratio extracted from the post-processing of the finite element analysis, such as the ratio of the total stress in the particle region to the total stress of the overall coating. A preset load-bearing threshold can be set to 40% based on the requirements of book cover printing to ensure the coating's durability under friction. If the simulation results show a ratio of 35%, it is determined that the threshold has not been reached. This judgment process is based on numerical comparison logic to ensure an objective evaluation of coating performance. Furthermore, if the threshold is not reached, the proportion of hard resin is increased within the initial mixing ratio range.

[0090] It should be noted that the initial mixing ratio range is such as 70:30 to 60:40 for soft resin and hard resin. Increasing the ratio parameter means gradually increasing the proportion of hard resin, for example, from 30% to 32%. This adjustment aims to improve the stress-bearing capacity of the particles, supporting the stability of the coating during the printing process without exceeding the range to maintain material balance. Subsequently, stress distribution simulation is performed again until the stress sharing ratio meets the load-bearing threshold.

[0091] For example, in optimizing book cover coatings, the model is rebuilt using the finite element method after adjustments, and the same frictional load, such as a 3N tangential force, is applied to calculate the new stress distribution. If the ratio still does not meet the target, the ratio is iteratively increased until the threshold is met. This cyclical process demonstrates the iterative nature of the method, ensuring final ratio optimization. In another implementation, for flexible book cover coatings, the load-bearing threshold is set to 45%. If the ratio is 42% after assessment, the rigid resin parameter is increased to the upper limit of the initial range. Resimulation involves updating material properties and mesh generation to obtain a new ratio. This approach demonstrates applicability across different cover types.

[0092] Preferably, the entire optimization process is integrated into the printing coating design flow. An initial simulation and assessment are performed first; if the threshold is not reached, the simulation is repeated in a loop, increasing the scaling factor.

[0093] For example, in a hard coating scenario, the initial ratio of 70:30 resulted in a proportion of 38%. After two iterations, this was increased to 65:35, reaching a proportion of 41%, which met the threshold and yielded an optimized ratio. This iteration reduced experimental trial and error and supported efficient design.

[0094] Understandably, the stress distribution simulation is re-performed based on an update of the previous model, with only the proportioning parameters adjusted to speed up the calculation. In practice, this approach helps assess the reliability of coatings under repeated use and avoids premature failure.

[0095] In one possible implementation, the load-bearing threshold is set considering printing environment factors, such as the effect of cover thickness on friction. The judgment process is automated through software comparison; if the threshold is not met, the percentage is increased in increments of 2% until it is satisfied.

[0096] For example, simulations showed that the adjusted proportion increased to 46%, with an optimized ratio of 68:32, which was used in actual coating formulations. This process provides a quantitative optimization path. Furthermore, achieving this optimized ratio marks the end of the iteration, ensuring a uniform distribution of hard particles in the coating for book cover applications, thus improving overall scratch resistance.

[0097] For example, in an embodiment targeting glossy book covers, the threshold was set to 50%, the initial simulation ratio was 47%, and after increasing the ratio and resimulating once, the target was achieved, resulting in an optimized ratio of 72:28. This example highlights the rapid convergence of the method.

[0098] Step S107: Based on the optimized ratio and combined with the phase separation kinetics model of the coating curing process, predict the microstructure morphology characteristics of the cured coating, including the size and spacing distribution of the hard regions.

[0099] Input data for the phase separation model is obtained from the optimized mixing parameters. This input data includes component concentration and curing temperature. A phase separation kinetic model is used to simulate the curing process. The model is based on the Cahn-Hilliard equation and uses the finite difference method to numerically solve for the spatiotemporal evolution of the component concentration field, obtaining phase separation distribution data within the cured coating. The contour of the hard region is extracted from the phase separation distribution data, and the equivalent circle diameter of each hard region is calculated and determined as the size characterization value of the hard region. The center coordinates of the hard regions are extracted from the phase separation distribution data, and the Euclidean distance between the center points of all adjacent hard regions is calculated. A histogram of the distance distribution is plotted to obtain the spacing distribution characteristics of the hard regions. A distribution uniformity index is calculated based on the spacing distribution characteristics. It is determined whether the distribution uniformity index reaches a preset threshold. If it does not, the curing temperature parameter in the phase separation model input data is adjusted, and the simulation process of the phase separation kinetic model is re-executed to obtain updated phase separation distribution data. If the distribution uniformity index reaches a preset threshold, then based on the phase separation distribution data, the hard region size characterization value and the hard region spacing distribution characteristics are integrated to determine the final microstructure morphology characteristics.

[0100] In one embodiment, the microstructure morphology of the cured coating is predicted based on the optimized ratio and a phase separation kinetic model of the coating curing process. This process first uses the optimized ratio as the model input parameter, for example, 35% rigid resin and 65% flexible resin, and then simulates component separation during the curing process using a phase separation kinetic model. The phase separation kinetic model is based on thermodynamic principles and describes the phase separation phenomenon formed by differences in solubility of the resin mixture during curing.

[0101] Specifically, the model considers free energy changes and diffusion equations to simulate the process of rigid resin agglomerating into hard regions, thereby predicting the size and spacing distribution of these regions. This prediction helps assess the structural stability of book cover coatings under printing friction. Furthermore, the implementation of the phase separation kinetics model involves numerical simulation methods, such as using the Cahn-Hilliard equations to describe the evolution of phase separation. In this model, optimized proportions affect the initial concentration field; a higher proportion of rigid resin results in a faster separation rate, leading to an increase in the size of the hard regions.

[0102] It should be noted that this model is solved using the finite difference method. The inputs include the proportioning parameters, curing temperature (e.g., 80°C), and time (e.g., 30 minutes), and the output is the microstructure characteristic value.

[0103] For example, in optimizing the coating of book covers, the model predicts that the average size of the hard areas is 5 micrometers, with a uniform spacing of 10 micrometers. This simulation process ensures the accuracy of the prediction and supports subsequent coating design.

[0104] For example, in an implementation targeting flexible book covers, the optimized ratio is 68:32, and the microstructure is predicted using a phase separation kinetic model. The model first establishes the initial mixture state and then simulates the curing heating process, where phase separation leads to the formation of isolated domains of rigid resin. The size of the rigid regions is obtained by calculating the domain growth rate, for example, from an initial 0.5 micrometers to 3 micrometers; the spacing distribution is based on concentration gradient analysis, showing an average spacing of 8 micrometers. This prediction reveals the microscopic uniformity of the coating in flexographic printing, providing a structural reference.

[0105] Preferably, the entire prediction process is integrated into the coating design software. Based on the optimized ratio, the model iteratively calculates the phase separation path, taking into account the influence of viscosity parameters.

[0106] Specifically, if the proportion of rigid resin increases by 2%, the model is re-simulated, and the predicted size distribution is adjusted from 4 micrometers to 6 micrometers, while the spacing decreases from 12 micrometers to 9 micrometers. In the scenario of rigid book covers, this method is used to evaluate scratch resistance. The model output shows that the size of the rigid region is 7 micrometers, and the spacing distribution is arranged in a chain-like pattern, supporting the durability of the coating in high-friction environments. In another implementation, for glossy book cover coatings, the optimized ratio is 72:28, and predictions are made using a phase separation kinetics model. The model simulates the diffusion kinetics during the curing process. The size of the rigid region is calculated by integrating the phase field variables, for example, with an average of 4.5 micrometers; the spacing distribution is quantified using statistical methods, showing a standard deviation of 2 micrometers. This approach demonstrates the applicability of the model under different cover types, ensuring reliable prediction of microscopic features.

[0107] Understandably, the principle of phase separation kinetics models lies in simulating the evolution of non-uniform systems, driving separation through energy minimization. Furthermore, in practical applications, this prediction step seamlessly integrates with the aforementioned optimized formulation; for example, the proportions obtained from previous iterations can be directly input into the model, avoiding redundant calculations. In book cover printing, this combination improves the accuracy of coating micro-design; for instance, the prediction results are used to adjust the formulation to achieve a uniform distribution of hard regions.

[0108] Specifically.

[0109] In one possible implementation, the model also considers the effect of curing rate on the features. After optimizing the input mix proportions, simulations show that the size of the hard regions increases to 6 micrometers under slow curing, with a more sparse spacing. This analysis is obtained by comparing simulation results at different rates, supporting the selection of suitable curing conditions.

[0110] For example, in an embodiment targeting matte book covers, the optimized ratio is 65:35, and the model predicts a hard area size of 5.5 micrometers with a random spacing of 11 micrometers. This prediction is based on a phase-separated random diffusion mechanism, demonstrating the model's adaptability to business variations.

[0111] Step S108: Input the microstructure morphology features into a pre-trained performance prediction neural network, and output the predicted wear resistance and predicted flexibility values ​​of the coating with the optimized ratio.

[0112] An input vector is obtained from the microstructure morphology features. This input vector is processed by a pre-trained performance prediction neural network to obtain predicted wear resistance and flexibility values ​​for the coating. For each predicted wear resistance and flexibility value, a preset performance threshold is obtained. By comparing the predicted values ​​with the preset performance threshold, a performance deviation index is determined. If the performance deviation index exceeds a preset deviation range, the component concentrations in the optimized formulation parameters are adjusted, and the adjusted microstructure morphology features are re-extracted. These re-extracted microstructure morphology features are input into the performance prediction neural network, which outputs updated predicted wear resistance and flexibility values ​​for the coating.

[0113] In one embodiment, the pre-trained performance prediction neural network is used to establish a quantitative mapping relationship between the microstructure morphology features of the coating and its macroscopic physical properties.

[0114] Specifically, this neural network is a multilayer perceptron model, where the input layer nodes correspond to a set of standardized microstructural feature values. These feature values ​​include not only the average size and average spacing of the hard regions, but also the standard deviation of the size distribution, the roundness factor of the region shape, and the gradient information of the resin concentration within the region. The output layer is designed with two nodes, corresponding to the predicted abrasion resistance value and the predicted flexibility value of the coating, respectively.

[0115] It should be noted that wear resistance is typically quantified as the mass loss or thickness reduction per unit area under specific friction conditions, while flexibility is characterized by the minimum bending radius or maximum tensile strain that the coating can withstand before cracking. The training process of the performance prediction neural network relies on a pre-built sample database.

[0116] For example, the database contains data on hundreds of coating samples with different ratios. Each set of data was obtained through experimental measurements, including actual values ​​of microstructural morphology features obtained from electron microscopy image analysis, and actual wear resistance and flexibility values ​​measured using standard abrasion and bending testing machines. During training, the actual values ​​of microstructure features are used as input, and the measured performance values ​​are used as the target output. The backpropagation algorithm is used to continuously adjust the connection weights and bias parameters within the network. The goal of training is to minimize the mean square error between the predicted values ​​and measured values ​​output by the neural network.

[0117] Understandably, this training process ensures that the network can learn nonlinear laws ranging from complex microscopic morphology to macroscopic performance.

[0118] Preferably, in applications targeting book cover coatings, the performance prediction neural network employs a structure containing a single hidden layer. The hidden layer contains ten neurons and uses the ReLU activation function to introduce non-linearity. The input feature vector specifically includes four key parameters: average size of the hardened region, average spacing between regions, coefficient of variation of size distribution, and region area percentage. The output layer uses a linear activation function to directly output the predicted wear amount (in milligrams) and minimum bending radius (in millimeters). After training, the network model is permanently stored for subsequent rapid performance prediction.

[0119] Specifically, after obtaining the microstructural features predicted by the phase separation kinetics model, these feature values ​​are first processed using the same standardization method as the training data, and then input into the saved neural network model. The model's forward propagation calculation is completed instantaneously, outputting two specific numerical values.

[0120] For example, in one embodiment for glossy book covers, the input predicted average size of the hard areas is 4.5 micrometers, average spacing is 9 micrometers, size distribution standard deviation is 1.8 micrometers, and area ratio is 32%. After neural network calculation, the output predicted abrasion resistance value is 2.3 milligrams, and the predicted flexibility value is 5.1 millimeters. This prediction result directly quantifies the coating's ability to resist printing friction and adapt to cover bending at this ratio. In another embodiment, for matte book cover coatings, different optimized ratios lead to differences in microstructure characteristics. The predicted feature values, such as the average size of the hard areas being 5.5 micrometers and the spacing distribution exhibiting relatively wide randomness (standard deviation of 2.5 micrometers), are input into the same neural network model. Based on the patterns it has learned, the model may output a predicted abrasion resistance value of 1.9 milligrams and a predicted flexibility value of 6.5 millimeters. This indicates that the coating's flexibility is improved while sacrificing a small amount of abrasion resistance. This process demonstrates the universal applicability of this performance prediction neural network to different microstructure patterns within the same field, providing key performance prediction criteria for cover coatings with different surface effect requirements. Furthermore, the prediction accuracy of the neural network can be continuously optimized by expanding the sample database and retraining.

[0121] For example, by introducing sample data prepared with new resin materials or new curing processes, incremental training or retraining of the network can broaden its prediction range and make the results more reliable. The entire prediction process enables rapid and quantitative evaluation from microstructural design parameters to macroscopic performance, avoiding the limitations of traditional methods that require cumbersome experimental testing to determine performance.

[0122] Step S109: Compare the predicted wear resistance value with the wear resistance threshold and the predicted flexibility value with the flexibility threshold. If both meet the threshold requirements, then determine the optimized ratio as the final water-based coating formulation design parameter.

[0123] Obtain the predicted abrasion resistance value, the predicted flexibility value, the abrasion resistance threshold, and the flexibility threshold. Based on a comparison of the predicted abrasion resistance value and the abrasion resistance threshold, and a comparison of the predicted flexibility value and the flexibility threshold, determine whether both abrasion resistance and flexibility meet the threshold requirements. If both abrasion resistance and flexibility meet the threshold requirements, record the optimized formulation parameters that generated the predicted performance value as qualified formulation parameters. From these qualified formulation parameters, determine the final waterborne coating formulation design parameters.

[0124] In one embodiment, the abrasion resistance threshold and flexibility threshold are quantitative standards pre-set based on the specific application requirements of the book cover coating.

[0125] Specifically, the abrasion resistance threshold is usually determined based on the number of frictions and pressures that the cover needs to withstand during printing, transportation, and daily handling.

[0126] For example, the abrasion resistance threshold for the cover of textbooks or reference books that need to be frequently flipped through might be set at a mass loss per unit area of ​​no more than 2.5 milligrams under standard friction testing. The flexibility threshold is set according to the bookbinding method and the degree of bending during flipping.

[0127] For example, for book covers that use perfect binding and need to be completely flat, the flexibility performance threshold may be set so that the minimum bending radius that the coating can withstand before cracking is no more than six millimeters.

[0128] It should be noted that these thresholds are design targets, specified by the product specification or industry standards. After obtaining the predicted abrasion resistance and flexibility values ​​output by the performance prediction neural network, the system automatically compares these two predicted values ​​with the corresponding preset thresholds.

[0129] Specifically, the system executes a logical judgment process.

[0130] For example, in one embodiment targeting a hardcover book cover, the preset abrasion resistance threshold is 2.2 mg, and the flexibility threshold is 5.5 mm. If the neural network outputs a predicted abrasion resistance value of 2.0 mg and a predicted flexibility value of 5.2 mm for a given optimized formulation, the system determines that the predicted abrasion resistance value of 2.0 mg is less than or equal to the threshold of 2.2 mg, and the predicted flexibility value of 5.2 mm is less than or equal to the threshold of 5.5 mm; both meet the threshold requirements. Based on the above determination, the system then determines the optimized formulation currently used for prediction, i.e., the specific proportions of each component such as resin, curing agent, and additives, which can be used as the final waterborne coating formulation design parameters. This parameter will be output to guide actual coating production.

[0131] Understandably, if any one or more of the predicted values ​​fail to meet the corresponding threshold requirements—for example, if the predicted abrasion resistance value exceeds the threshold or the predicted flexibility value exceeds the threshold—the system will determine that the optimized formulation is substandard and will not adopt it as the final formulation. In this case, the design process may need to return to previous steps, readjust the formulation parameters, or optimize the phase separation conditions to find a formulation that meets all performance requirements.

[0132] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for designing a wear-resistant water-based plasticizer matte oil coating formulation, characterized in that, include: The process involves: obtaining the wear resistance and flexibility thresholds for the coating in the target application scenario; selecting at least one candidate soft resin and at least one candidate hard resin from a pre-established resin material library based on these thresholds; calculating the dispersion uniformity index of the hard resin in the soft resin matrix under different soft-hard resin ratios using molecular dynamics simulation for the selected candidate resin combinations; adjusting the type or surface modification parameters of the candidate hard resins and recalculating the dispersion uniformity index until a resin combination and initial ratio range that meet the dispersion threshold requirements are obtained; simulating the stress distribution of the coating under a preset friction load using finite element analysis to obtain the stress sharing ratio borne by the hard resin particles within the initial ratio range that meets the dispersion threshold requirements; determining whether the stress sharing ratio reaches a preset load-bearing threshold; if not, increasing the proportion of the hard resin within the initial ratio range and re-simulating the stress distribution until the stress sharing ratio meets the load-bearing threshold to obtain an optimized ratio. Based on the optimized ratio and combined with the phase separation kinetics model of the coating curing process, the microstructure morphology of the cured coating is predicted. The microstructure morphology features are input into a pre-trained performance prediction neural network, which outputs the predicted wear resistance value and the predicted flexibility value of the coating under the optimized ratio. The predicted wear resistance value is compared with the wear resistance threshold, and the predicted flexibility value is compared with the flexibility threshold. If both meet the threshold requirements, the optimized ratio is determined as the final coating formulation design parameter.

2. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, The process of obtaining the wear resistance and flexibility thresholds of the coating for the target application scenario includes: obtaining the wear resistance and flexibility thresholds of the coating corresponding to the target application scenario through a preset database of printed material durability standards, thus obtaining a threshold set; for the threshold set, using coating matching verification, extracting additional durability indicators from the database to determine the applicability of the thresholds in the target scenario; based on the applicability, extracting the wear resistance and flexibility thresholds from the threshold set as input parameters for subsequent screening of candidate soft resins and candidate hard resins; comparing the thresholds with a pre-established resin material library using the input parameters, screening for soft resins with high compatibility, thus obtaining candidate soft resins; based on the candidate soft resins, extracting hard resins from the resin material library, using a matching degree calculation method to determine the compatibility matching degree, thus determining candidate hard resins; and forming a candidate resin combination for the candidate hard resins and the candidate soft resins, which is used in the subsequent calculation process of the molecular dynamics simulation method.

3. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, For the selected candidate resin combinations, molecular dynamics simulation is used to calculate the dispersion uniformity index of the hard resin in the soft resin matrix under different hard and soft resin ratios. This includes: obtaining different hard and soft resin ratios from the candidate resin combinations; constructing a simulation system using molecular dynamics simulation; calculating molecular trajectories by setting the force field parameters of interatomic forces to obtain molecular interaction data under the specified ratios; and setting simulation parameters, including temperature and time step, for the molecular interaction data, running the simulation under periodic boundary conditions to obtain a positional distribution map of the hard resin in the soft resin matrix. Based on the location distribution map, the radial distribution function among the rigid resin particles is calculated. By statistically analyzing the probability density of finding another rigid resin particle within different distance intervals, the aggregation degree among the rigid resin particles is determined. If the aggregation degree exceeds a preset threshold, the non-bonded interaction parameters in the force field parameters are adjusted, and the simulation is rerun to obtain the calibrated dispersion pattern. Based on the calibrated dispersion pattern, the Euclidean distances between all pairs of rigid resin particles are statistically analyzed, and the variance of the Euclidean distances is calculated. The reciprocal of the variance is used as the dispersion uniformity index to obtain the final index value under different proportions.

4. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, If the dispersion uniformity index is lower than a preset dispersion threshold, the type of candidate rigid resin or surface modification parameters are adjusted, and the dispersion uniformity index is recalculated until a resin combination and initial ratio range that meet the dispersion threshold requirement are obtained. This includes: obtaining an initial ratio range from the candidate resin combination; calculating the dispersion uniformity index of the rigid resin in the soft resin matrix using molecular dynamics simulation; running molecular trajectories by setting force field parameters to obtain the index value; comparing the index value with the preset dispersion threshold; if the index value is lower than the threshold, adjusting the type of candidate rigid resin or surface modification parameters to obtain an adjusted resin combination; reconstructing the simulation system using the adjusted resin combination; running molecular dynamics simulation to obtain updated molecular interaction data; determining the degree of aggregation by statistically analyzing the interparticle distance probability density, and thus determining the updated dispersion uniformity index; repeating the threshold comparison process based on the updated dispersion uniformity index until the index value meets the threshold requirement to obtain an optimized resin combination and initial ratio range; and extracting the ratio parameters that meet the dispersion threshold requirement for the optimized resin combination as input data for subsequent finite element analysis methods.

5. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, Within the initial mixing ratio range that meets the dispersion threshold requirement, the finite element method is used to simulate the stress distribution of the coating under a preset friction load to obtain the stress sharing ratio borne by the hard resin particles. This includes: obtaining spatial coordinate data of the hard resin particles from the initial mixing ratio range; constructing a coating geometric model containing the spatial coordinate data using the finite element method; applying a preset friction load to the coating geometric model to perform mechanical simulation and obtain stress field distribution data inside the coating; extracting the stress value of the interface region between the hard resin particles and the soft resin matrix from the stress field distribution data; calculating the average value of the interface stress around each hard resin particle, which is defined as the particle interface stress characterization value; based on the particle interface stress characterization values ​​of all hard resin particles, counting the number of particles higher than the overall stress field average value, calculating the ratio of the number to the total number of particles, which is determined as the stress sharing ratio borne by the hard resin particles; determining whether the stress sharing ratio reaches a preset bearing threshold, which serves as the basis for subsequent adjustment of the ratio parameters; and generating an optimized initial mixing ratio range based on the above criteria for subsequent prediction of the phase separation kinetic model.

6. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, The determination of whether the stress sharing ratio reaches the preset bearing threshold, if not, involves increasing the proportion of rigid resin within the initial ratio range and re-simulating the stress distribution until the stress sharing ratio meets the bearing threshold, thus obtaining an optimized ratio. This includes: obtaining the proportion of rigid resin particles from the initial ratio range; constructing a coating geometric model using finite element analysis; applying a preset friction load and particle size distribution data to the coating geometric model for mechanical simulation to obtain internal stress field distribution data; extracting the stress value at the interface between the rigid resin particles and the soft resin matrix using the stress field distribution data; calculating the average value of the interface stress around each rigid resin particle, which is determined as the particle interface stress characterization value; and counting the number of particles higher than the overall stress field average value based on the particle interface stress characterization value of all rigid resin particles, and calculating the ratio of this number to the total number of particles. The ratio is determined as the stress-sharing proportion borne by the rigid resin particles. It is then determined whether the stress-sharing proportion reaches a preset bearing threshold. If not, the ratio parameter of the rigid resin is increased within the initial mixing ratio range, and the particle size distribution data is adjusted. The finite element analysis method is used to reconstruct the coating geometric model, and a preset friction load is applied for mechanical simulation to obtain updated stress field distribution data. The stress values ​​at the interface between the rigid resin particles and the soft resin matrix are extracted using the updated stress field distribution data, and the particle interface stress characterization value and stress-sharing proportion are recalculated. It is then determined whether the stress-sharing proportion reaches the preset bearing threshold. If not, the ratio parameter is increased and the particle size distribution data is adjusted, and the simulation and calculation are iteratively performed until the stress-sharing proportion meets the bearing threshold. Finally, the ratio parameter and particle size distribution data that meet the bearing threshold are obtained, and the optimized mixing ratio is determined based on the initial mixing ratio range.

7. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, The step of predicting the microstructure morphology of the cured coating based on the optimized ratio and the phase separation kinetic model of the coating curing process includes: obtaining phase separation model input data from the optimized ratio parameters, the input data including component concentration and curing temperature; simulating the curing process using the phase separation kinetic model; numerically solving the spatiotemporal evolution of the component concentration field using the finite difference method to obtain phase separation distribution data inside the cured coating; extracting the contour of the hard region from the phase separation distribution data; calculating the equivalent circle diameter of each hard region to determine the size characterization value of the hard region; extracting the center coordinates of the hard region from the phase separation distribution data; and calculating the coordinates of all adjacent hard regions. The Euclidean distance between the center points is used to calculate the distribution histogram of the distance to obtain the hard region spacing distribution characteristics. A distribution uniformity index is calculated based on these spacing distribution characteristics. It is then determined whether the distribution uniformity index reaches a preset threshold. If it does not, the curing temperature parameters in the phase separation model input data are adjusted, and the simulation process of the phase separation kinetic model is re-executed to obtain updated phase separation distribution data. If the distribution uniformity index reaches the preset threshold, the hard region size characterization value and the hard region spacing distribution characteristics are integrated based on the phase separation distribution data to determine the final microstructure morphology characteristics, which serve as the input for the subsequent performance prediction neural network.

8. The design method for a wear-resistant water-based plasticizer matte oil coating as described in claim 1, characterized in that, The step of inputting the microstructure morphology features into a pre-trained performance prediction neural network and outputting the predicted wear resistance and predicted flexibility values ​​of the coating under the optimized formulation includes: obtaining an input vector from the microstructure morphology features; processing the input vector using the pre-trained performance prediction neural network to obtain the predicted wear resistance and predicted flexibility values ​​of the coating; obtaining a preset performance threshold for the predicted wear resistance and predicted flexibility values; determining a performance deviation index by comparing the predicted values ​​with the preset performance threshold; if the performance deviation index exceeds a preset deviation range, adjusting the component concentration in the optimized formulation parameters and re-extracting the adjusted microstructure morphology features; inputting the re-extracted microstructure morphology features into the performance prediction neural network to output updated predicted wear resistance and predicted flexibility values ​​of the coating; repeating the process of determining the performance deviation index based on the updated predicted values ​​until the performance deviation index meets the preset deviation range; comparing the predicted values ​​that meet the preset deviation range with the wear resistance threshold and the flexibility threshold as the basis for determining the final coating formulation design parameters.

Images