A method and device for representing orientation of a polymer based on a pca algorithm

Abstract

The application discloses a method and device for representing polymer chain orientation based on a PCA algorithm, and relates to the field of polymer material structure and performance representation. The method solves the problem that the prior art is easily affected by local conformation bending, chain end fluctuation or chain segment selection mode by relying on chain end vector, local bond vector or preset chain segment direction. The method comprises the following steps: constructing a polymer chain and a substrate or interface model, and obtaining a molecular dynamics simulation trajectory file; extracting three-dimensional atomic coordinates of a polymer chain to be analyzed at different simulation time frames; performing centroid translation and principal component analysis on the atomic coordinates of the polymer chain, and selecting a first principal component direction as a main orientation direction of the polymer chain; calculating an included angle theta between the main orientation direction and a substrate normal vector, and further obtaining parameters such as an average included angle, a standard deviation, a perpendicular orientation probability, a parallel orientation probability and an orientation index. The method is also suitable for application fields such as analysis and evaluation of polymer chain orientation states in biomedical materials.

Description

Technical Field

[0001] This invention relates to the field of polymer material structure and property characterization technology, specifically to a method and apparatus for characterizing polymer orientation based on the PCA algorithm. Background Technology

[0002] The molecular chain orientation of polymers is a crucial manifestation of their structural ordering, profoundly influencing the macroscopic physical and chemical properties of materials, such as mechanical strength, optical properties, thermal properties, permeability, and interfacial interactions. In materials science and engineering applications, accurately determining the degree of orientation of polymers in a specific direction and its dynamic evolution is a fundamental basis for understanding the structure-property relationship of materials, optimizing material design, and improving product performance.

[0003] In thin film coatings, composite material interfaces, and biomaterial-cell interaction interfaces, the alignment of polymer chain segments relative to the material surface or interface affects the material's surface energy, wettability, tribological behavior, and biocompatibility. During processing such as film stretching, extrusion molding, and fiber spinning, the degree of molecular chain orientation directly impacts the anisotropic properties of the product. For molecular dynamics simulations, the ability to accurately characterize the orientation state of polymer chains during the simulation process also affects the assessment of material interface behavior, confined spatial conformation, and changes in service performance.

[0004] Existing methods for characterizing polymer orientation typically include orientation tensor calculations based on chain segment vectors, Hermann orientation factor calculations, and orientation angle distribution function analysis. For example, in molecular dynamics simulations, an orientation tensor can be constructed by statistically analyzing the chain segment orientations within the simulation system.

[0005] Among them, u k Let be the unit direction vector of the k-th segment (e.g., the vectors of the two endpoints or the local bond vector of the main chain), where i and j are the coordinate components, and N is the number of segments. For Kronecker symbols.

[0006] However, existing methods still have certain limitations when applied to complex polymer systems, especially flexible chain systems near surfaces or interfaces. First, traditional methods often rely on chain end vectors, local bond vectors, or predefined chain segment directions, making them susceptible to local conformational bending, chain end fluctuations, or chain segment selection. Second, for dynamic conformational evolution in molecular dynamics trajectories, single-time averaging results are insufficient to reflect the stability and fluctuation range of orientation states over time. Third, when polymer chains are in an intermediate tilted state, simply classifying them as "parallel" or "perpendicular" can easily lead to misjudgments, lacking a quantitative description of continuous orientation angles.

[0007] Therefore, it is necessary to provide a method that can automatically extract the main orientation direction of polymer chains based on atomic coordinates and quantitatively calculate their orientation state relative to the substrate or interface. Summary of the Invention

[0008] This invention addresses the shortcomings of existing technologies that often rely on chain end vectors, local bond vectors, or preset chain segment directions, which are susceptible to influences from local conformational bending, chain end fluctuations, or chain segment selection. Furthermore, for dynamic conformational evolution in molecular dynamics trajectories, single-time averaging results are insufficient to reflect the stability and fluctuation range of the orientation state over time. Additionally, when polymer chains are in a tilted state, simply classifying them as "parallel" or "perpendicular" can easily lead to misjudgments and lacks quantitative description of continuous orientation angles. Therefore, this invention proposes a method and apparatus for characterizing polymer orientation based on the PCA algorithm. To solve the above technical problems, this invention achieves this through the following technical solution: Option 1: This invention proposes a method for characterizing the orientation of polymers based on the PCA algorithm, the method comprising the following steps: Step 1: Construct a model of the polymer and its substrate or interface to obtain a structure file containing atomic three-dimensional coordinate information and a molecular dynamics simulation trajectory file; Step 2: Extract the three-dimensional atomic coordinates of the polymer chain to be analyzed at different simulation time frames from the structure file and molecular dynamics simulation trajectory file mentioned in Step 1; Step 3: Perform principal component analysis on the atomic three-dimensional coordinates of the polymer chain to be analyzed in Step 2 under different simulation time frames, and extract the first principal component direction as the main orientation direction of the polymer chain. Step 4: Determine the normal vector of the substrate or interface as the reference direction, and calculate the angle θ between the main orientation direction of the polymer chain described in Step 3 and the normal vector of the substrate or interface; Step 5: Utilize the vertical orientation threshold and parallel orientation threshold The change in the angle θ between the substrate or interface normal vectors described in step 4 is statistically analyzed to obtain the average orientation angle, standard deviation of orientation angle, vertical orientation probability, parallel orientation probability, vertical orientation index, and parallel orientation index of the polymer chain, thereby characterizing the orientation state of the polymer relative to the substrate or interface.

[0009] Furthermore, the polymer mentioned in step 1 includes one or more of thermoplastic polymers, liquid crystal polymers, biopolymers, block polymers, hydrogel networks, and polymer electrolytes.

[0010] Furthermore, the method for constructing the polymer and its substrate or interface model in step 1 to obtain the structure file containing atomic three-dimensional coordinate information and the molecular dynamics simulation trajectory file is as follows: Step 1.1: Use molecular structure visualization software to draw polymer models, substrates, or interface models with dimensions and shapes; Step 1.2: Convert the polymer model, substrate, or interface model described in Step 1.1 into a three-dimensional atomic coordinate file; Step 1.3: Optimize the geometric configuration of the polymer model, substrate, or interface model constructed in Step 1.2 to obtain a stable initial structure; Step 1.4: Perform molecular dynamics simulation based on the optimized initial structure in Step 1.3, and output a trajectory file containing information on the changes of atomic coordinates over time.

[0011] Furthermore, in step 3, principal component analysis is performed on the atomic three-dimensional coordinates of the polymer chain to be analyzed in step 2 at different simulation time frames, and the first principal component direction is extracted as the main orientation direction of the polymer chain. Step 3.1: Extract the three-dimensional coordinates of all or selected atoms in the polymer chain at a certain simulation time frame to form a coordinate matrix; Step 3.2: Perform a centroid translation on the coordinate matrix described in Step 3.1 to obtain a centered coordinate matrix; Step 3.3: Construct the covariance matrix of the centered coordinate matrix; Step 3.4: Perform eigenvalue decomposition on the covariance matrix, select the eigenvector corresponding to the largest eigenvalue as the first principal component direction, and define it as the main orientation direction of the polymer chain.

[0012] Furthermore, the method for calculating the angle θ between the main orientation direction of the polymer chain mentioned in step 3 and the normal vector of the substrate or interface in step 4 is as follows:

[0013] Where u is the unit vector of the main orientation direction of the polymer chain, and n is the unit vector of the substrate or interface normal vector.

[0014] Furthermore, the vertical orientation probability mentioned in step 5 will As a criterion, the parallel orientation probability will As a criterion, among which and This is a preset threshold.

[0015] Furthermore, the method also includes the step of calculating spindle reliability parameters, that is, ,in , , These are the three eigenvalues ​​of the covariance matrix arranged in descending order.

[0016] Option 2: A device for characterizing polymer orientation based on PCA algorithm, the device comprising: The model building module is used to build models of polymers and their substrates or interfaces, and obtain structural files and molecular dynamics simulation trajectory files containing atomic three-dimensional coordinate information. The 3D coordinate extraction module is used to extract the atomic 3D coordinates of the polymer chain to be analyzed at different simulation time frames from the structural files and molecular dynamics simulation trajectory files described in the model building module. The main orientation direction extraction module is used to perform principal component analysis on the atomic three-dimensional coordinates of the polymer chain to be analyzed in the three-dimensional coordinate extraction module under different simulation time frames, and extract the first principal component direction as the main orientation direction of the polymer chain. Angle calculation module is used to determine the normal vector of the substrate or interface as a reference direction and calculate the angle θ between the main orientation direction of the polymer chain and the normal vector of the substrate or interface as described in the main orientation direction extraction module. The state characterization module is used to statistically analyze the change in the angle θ between the substrate or interface normal vectors in the angle calculation module, and obtain the average orientation angle, standard deviation of orientation angle, vertical orientation probability and parallel orientation probability of the polymer chain, thereby characterizing the orientation state of the polymer relative to the substrate or interface.

[0017] Option 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in Option 1.

[0018] Option 4: A computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in Option 1.

[0019] The advantages of this invention are: The method for characterizing polymer orientation based on PCA algorithm described in this invention uses PCA algorithm to directly extract the main orientation direction from the atomic coordinates of polymer chain, without the need to manually specify chain end atoms or local bond vectors, which can reduce the influence of chain end fluctuations, local conformational bending and manual selection of chain segment orientation on the results.

[0020] The method for characterizing polymer orientation based on PCA algorithm described in this invention can output the continuous angle θ between the main orientation direction of the polymer chain and the substrate normal vector. It can not only determine whether the polymer chain is close to perpendicular or parallel to the substrate surface, but also quantitatively describe the intermediate tilt orientation, avoiding misjudging the tilt orientation as completely parallel or completely perpendicular.

[0021] The method for characterizing polymer orientation based on PCA algorithm described in this invention can capture the dynamic changes in polymer chain orientation over simulation time. By analyzing different time frames in the molecular dynamics trajectory frame by frame, the orientation angle as a function of time can be obtained, and the stability of the polymer chain orientation state, whether abrupt flipping or randomization has occurred can be determined accordingly.

[0022] The PCA-based method for characterizing polymer orientation described in this invention can quantitatively distinguish the differences in chain orientation among different polymer composite systems. Taking PEG-PMMA, PEG-PLA, and PEG-PAA composite systems as examples, the method of this invention is used to calculate the angle between the main orientation direction of the single chain and the substrate normal vector. The results show that the average angle is 55.48°±2.42° for the PEG-PMMA system, 63.47°±3.07° for the PEG-PLA system, and 62.65°±2.74° for the PEG-PAA system. None of the three systems exhibited strictly perpendicular orientation (i.e., the probability of θ<10° was 0.00%); nor did they achieve strictly parallel orientation (i.e., the probability of |θ-90°|<10° was 0.00%). This result indicates that the PEG single chains in all three systems exhibit an inclined orientation relative to the substrate normal vector.

[0023] The method for characterizing polymer orientation based on the PCA algorithm described in this invention can further calculate the vertical orientation index and the parallel orientation index through the orientation angle, thereby achieving a quantitative comparison of the orientation strength of different systems. According to... and The orientations of three systems—PEG-PMMA, PEG-PLA, and PEG-PAA—can be obtained. Among these three systems, P... ∥ All are greater than P ⊥ This indicates that PEG single chains generally tend to align along the substrate plane; however, since the average included angle is not close to 90°, their orientation should be characterized as a "partially parallel tilted orientation". Specifically, the average included angle of PEG-PLA and PEG-PAA is greater than that of PEG-PMMA, and P... ∥ The values ​​are 0.800 and 0.789, respectively, indicating that PEG exhibits a more pronounced planar orientation trend near PLA and PAA substrates.

[0024] This invention is also applicable to the dynamic monitoring and analysis of polymer chain orientation behavior near material surfaces or interfaces, and can be applied to research and quality control in fields such as polymer films, fibers, composite materials and biomedical materials. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of the method for characterizing polymer orientation based on PCA algorithm as described in Embodiment 1.

[0026] Figure 2 This is a schematic diagram comparing the PEG single-chain conformation snapshots of the three composite systems PEG-PMMA, PEG-PLA and PEG-PAA described in Implementation Method 1, wherein (a) is the PEG-PMMA system, (b) is the PEG-PLA system and (c) is the PEG-PAA system.

[0027] Figure 3 This is a schematic diagram illustrating the definition of the angle θ between the main orientation direction of the polymer chain and the normal vector of the substrate or interface as described in Embodiment 1.

[0028] Figure 4 The diagram shows the single-chain orientation analysis results of the PEG-PMMA system described in Implementation Method 1, where (a) is the orientation angle distribution diagram and (b) is the orientation angle change curve over time.

[0029] Figure 5 The diagram shows the single-chain orientation analysis results of the PEG-PLA system described in Embodiment 1, where (a) is an orientation angle distribution diagram and (b) is a curve showing the change of orientation angle over time.

[0030] Figure 6 The diagram shows the single-chain orientation analysis results of the PEG-PAA system described in Embodiment 1, where (a) is an orientation angle distribution diagram and (b) is a curve showing the change of orientation angle over time. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0032] Implementation Method 1, see [link] Figures 1 to 6 This embodiment describes a method for characterizing polymer orientation based on the PCA algorithm. The method performs principal component analysis on the atomic coordinates of the polymer chain, extracts the first principal component direction as the principal orientation direction of the polymer chain, and calculates the angle between this principal orientation direction and the substrate normal vector, thereby achieving quantitative characterization of the polymer chain orientation state. The method specifically includes the following steps: S1. Construct a model of the polymer and its substrate or interface to obtain the three-dimensional atomic coordinate file and molecular dynamics simulation trajectory file of the polymer system; S2. Extract the three-dimensional atomic coordinates of the polymer chain to be analyzed in each simulation time frame; S3. Perform PCA analysis on the three-dimensional coordinates of the polymer chain atoms and extract the first principal component direction as the main orientation direction of the polymer chain. S4. Determine the substrate or interface normal vector and calculate the angle θ between the main orientation direction of the polymer chain and the substrate or interface normal vector. S5. Statistically analyze the change of the included angle θ with simulation time, and calculate the mean included angle, standard deviation, vertical orientation probability, parallel orientation probability, vertical orientation index, and parallel orientation index to determine the orientation state of the polymer chain relative to the substrate or interface.

[0033] Furthermore, a preferred embodiment is provided, wherein the polymer comprises thermoplastic polymers, liquid crystal polymers, biopolymers, block polymers, hydrogel networks, and polymer electrolytes.

[0034] Furthermore, a preferred embodiment is provided, wherein step S1 specifically comprises: S11. Use molecular structure visualization software to draw polymer models with certain sizes and shapes, as well as substrate or interface models; S12. Use the molecular structure visualization software to convert the polymer model and the substrate or interface model into a three-dimensional atomic coordinate file; S13. Optimize the geometric configuration of the constructed polymer model and the substrate or interface model to obtain a stable initial configuration; S14. Perform molecular dynamics simulation on the optimized system and output a trajectory file containing information on the changes of atomic coordinates over time.

[0035] Furthermore, a preferred embodiment is provided, wherein the molecular structure visualization software includes MaterialsStudio, Chem3D, VMD, and CYLview.

[0036] Furthermore, a preferred embodiment is provided, wherein the geometry optimization method includes one or more of density functional theory calculations, molecular force field optimization, or molecular dynamics energy minimization.

[0037] Furthermore, a preferred embodiment is provided, wherein the density functional theory calculation is performed using ORCA software; the functionals used include BLYP-D3, B3LYP-D3, M06-2X, and wB97XD; and the basis sets used include 6-31G(d), 6-31G(d,p), 6-311G(d), 6-311G(d,p), def2-SVP, def2-TZVP, and def2-TZVPP.

[0038] Furthermore, a preferred embodiment is provided, wherein step S2 specifically comprises: S21. Read the structure file and molecular dynamics trajectory file of the polymer system; S22. Select the polymer chain to be analyzed based on the molecule or residue name; S23. Extract the three-dimensional atomic coordinates of the polymer chain at different simulation time frames.

[0039] Furthermore, a preferred embodiment is provided, wherein step S3 specifically comprises: S31. Construct a coordinate matrix X from the atomic coordinates of the polymer chain at a certain time frame; S32. Calculate the centroids of the polymer chain atoms and center the coordinate matrix X to obtain the centered coordinate matrix X. c ; S33. Calculate the covariance matrix C based on the centered coordinate matrix; S34. Perform eigenvalue decomposition on the covariance matrix C, select the eigenvector corresponding to the largest eigenvalue as the first principal component direction, and define it as chain_vector, that is, the main orientation direction of the polymer chain.

[0040] Furthermore, a preferred embodiment is provided, wherein the theoretical basis of step S3 is as follows: for the centered atomic coordinate point cloud, the direction of the first principal component of PCA is the direction that maximizes the variance of the atomic coordinate projection; simultaneously, from a geometric perspective, this direction is also equivalent to the best fitting direction obtained by minimizing the sum of squares of the perpendicular distances from the atomic coordinate points to the fitted line. Therefore, the first principal component of PCA can effectively reflect the main extension direction of the polymer chain atomic point cloud and can be used as the main orientation direction of the polymer chain.

[0041] Furthermore, a preferred embodiment is provided in which the methods described in steps S31 to S34 can be implemented by a Python program.

[0042] Furthermore, a preferred embodiment is provided, in step S4, if the substrate or interface plane is known, its normal vector can be directly used as the reference direction; if the substrate or interface has certain structural fluctuations, its normal vector can be extracted as the reference direction by performing PCA analysis on the atomic coordinates of the substrate or interface.

[0043] Furthermore, in a preferred embodiment, in step S5, the angle θ between the main orientation direction of the polymer chain and the substrate normal vector is calculated using the following formula: (1) Where u is the unit vector of the main orientation direction of the polymer chain, and n is the unit vector of the basis normal vector. Since the principal axis directions obtained by PCA are equivalent in both positive and negative, the absolute value form is used to eliminate the influence of the orientation sign on the angle calculation.

[0044] When θ is close to 0°, it indicates that the main orientation direction of the polymer chain is close to the substrate normal vector, that is, it tends to be perpendicular to the substrate surface; when θ is close to 90°, it indicates that the main orientation direction of the polymer chain is close to the substrate plane direction, that is, it tends to be parallel to the substrate surface; when θ is in the middle angle range, it indicates that the polymer chain is tilted relative to the substrate surface.

[0045] Furthermore, a preferred embodiment is provided, further defining the vertical orientation index and the parallel orientation index: (3) (4) Among them, P ⊥ P is used to characterize the degree of orientation of polymer chains along the normal vector direction of the substrate. ∥ Used to characterize the degree of orientation of polymer chains along the substrate plane.

[0046] S35. The mathematical principle for determining the principal orientation direction of PCA is as follows: Calculate the covariance matrix based on the centered coordinate matrix: (5) Perform eigenvalue decomposition on the covariance matrix: (6) The eigenvector corresponding to the largest eigenvalue is selected as the main orientation direction of the polymer chain: (7) Xc is the centered coordinate matrix, and v1 is the eigenvector corresponding to the largest eigenvalue. If the basis or interface plane is known, its unit normal vector can be used directly. As a reference direction; if there are thermal fluctuations or morphological undulations in the substrate or interface, PCA analysis can be performed on the atomic coordinates of the substrate or interface, and the eigenvector corresponding to the smallest eigenvalue can be taken as the normal vector of the interface plane.

[0047] The angle between the main orientation direction of the polymer chain and the normal vector of the substrate Calculate using the following formula: (8) Since the principal axis directions obtained by PCA are equivalent in both positive and negative forms, the absolute value form is used to eliminate the influence of the direction's sign on the angle calculation. near When the polymer chain's main orientation direction is close to the substrate normal vector, it tends to be perpendicular to the substrate surface; when near When the main orientation direction of the polymer chain is close to the substrate plane, that is, it tends to be parallel to the substrate surface; when When the angle is in the middle range, it indicates that the polymer chain is tilted relative to the substrate surface.

[0048] right Statistical analysis was performed on each simulated time frame, and the mean orientation angle and standard deviation were as follows: (9) (10) The vertical orientation probability and the parallel orientation probability are defined as follows: (11) (12) in, For indicator functions, and The preset angle threshold is preferred. Further define the vertical orientation index and the horizontal orientation index: (13) (14) in, Used to characterize the degree of orientation of polymer chains along the normal vector direction of the substrate. This is used to characterize the degree of orientation of polymer chains along the substrate plane. To avoid misjudging noisy principal axes in approximately spherical or strongly coiled conformations as stable orientations, this invention can also output principal axis reliability parameters: (15) when The closer the value is to 1, the more pronounced the single principal axis extension characteristic of the point cloud; when near When the point cloud is nearly isotropic, the physical interpretation of the main orientation direction should be judged in conjunction with the conformational snapshot and time stability.

[0049] The geometric meaning of the direction of the first principal component in PCA can be explained by the following equivalence relation. For centered coordinates... and unit vector Its projection variance is: (16) Point to The sum of squares of the perpendicular distances from the fitted line passing through the centroid is: (17) Therefore, in Minimize the sum of squared vertical distances under the constraints. Equivalent to maximizing the projection variance The direction of maximum projective variance is the eigenvector corresponding to the largest eigenvalue of the covariance matrix. Therefore, the first principal component of PCA can be used as a representation of the main extension direction of the three-dimensional coordinate set of polymer chain atoms.

[0050] This embodiment also provides the following examples to further explain and illustrate Embodiment 1: Example 1: Taking the PEG-PMMA composite system as an example, the molecular dynamics simulation trajectory file was read, and the three-dimensional atomic coordinates of the PEG single chain at different simulation time frames were extracted. The centroid of the PEG single chain atomic coordinates in each frame were translated to construct a covariance matrix. The PCA method was used to obtain the first principal component direction corresponding to the largest eigenvalue, which was taken as the main orientation direction of the PEG single chain. The angle between the main orientation direction of the PEG single chain and the substrate normal vector was calculated, and the average angle between the PEG single chain and the substrate normal vector in the PEG-PMMA system was found to be 55.48°±2.42°. Further statistical analysis of the orientation angle distribution showed that the orientation angle of the PEG single chain in this system was mainly concentrated in the range of approximately 50°–60°, with a peak value around 55°. The orientation angle variation curve over time showed that within the simulation time of 0–2000 ps, ​​the orientation angle of the PEG single chain mainly fluctuated within the range of approximately 52°–60°, without significant orientation reversal. Using θ < 10° as the strict perpendicular orientation criterion, the perpendicular orientation probability in the EG-PMMA system is 0.00%; using |θ - 90°| < 10° as the strict parallel orientation criterion, the parallel orientation probability in the PEG-PMMA system is 0.00%. These results further demonstrate that the method of this invention can avoid misclassifying intermediate tilted orientations as completely perpendicular or completely parallel orientations.

[0051] Example 2: Taking the PEG-PLA composite system as an example, PCA analysis was performed on the atomic coordinates of the PEG single chains in the molecular dynamics trajectory using the same method as in Example 1. The direction of the first principal component was extracted as the main orientation direction of the PEG single chain, and the angle between this direction and the substrate normal vector was calculated. The calculation results show that the average angle between the PEG single chain and the substrate normal vector in the PEG-PLA system is 63.47° ± 3.07°. The orientation angle distribution plot shows that the orientation angle of the PEG single chain in this system is mainly concentrated in the range of approximately 58°–68°, with the peak value located near approximately 63°–65°. The orientation angle variation curve over time shows that the orientation angle of the PEG single chain mainly fluctuates around 60°–66° within the simulation time of 0–2000 ps, ​​indicating that the orientation state of the PEG single chain in this system has a certain degree of stability during the simulation. Using θ < 10° as the strict vertical orientation criterion, the vertical orientation probability in the PEG-PLA system is 0.00%; using |θ - 90°| < 10° as the strict parallel orientation criterion, the parallel orientation probability in the PEG-PLA system is 0.00%. The orientation angle distribution indicates that neither a vertical alignment of the PEG single-link near-substrate normal vectors nor a strictly parallel alignment to the substrate surface was observed in this system.

[0052] Example 3: Taking the PEG-PAA composite system as an example, the molecular dynamics trajectory file was read using the method of this invention, the three-dimensional atomic coordinates of the PEG single chain at different time frames were extracted, and the main orientation direction of the PEG single chain was calculated using the PCA method. The calculated average angle between the PEG single chain and the substrate normal vector in the PEG-PAA system was 62.65°±2.74°. The orientation angle distribution map shows that the orientation angle of the PEG single chain in this system is mainly concentrated in the range of approximately 58°–67°, with the peak value located near approximately 62°–64°. The orientation angle variation curve over time shows that within the simulation time of 0–2000 ps, ​​the orientation angle generally remained within the range of approximately 58°–66°, without showing a trend of continuous evolution towards 0° or 90°. Using θ<10° as a strict perpendicular orientation criterion, the probability of perpendicular orientation in the PEG-PAA system is 0.00%; using |θ-90°|<10° as a strict parallel orientation criterion, the probability of parallel orientation in the PEG-PAA system is 0.00%. This result indicates that although the PEG single chains in the PEG-PAA system are more inclined to planar orientation, they do not achieve a state of being strictly parallel to the substrate surface.

[0053] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0054] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for characterizing the orientation of polymer molecules based on the PCA algorithm, characterized in that, The method includes the following steps: Step 1: Construct a model of the polymer and its substrate or interface to obtain a structure file containing atomic three-dimensional coordinate information and a molecular dynamics simulation trajectory file; Step 2: Extract the three-dimensional atomic coordinates of the polymer chain to be analyzed at different simulation time frames from the structure file and molecular dynamics simulation trajectory file mentioned in Step 1; Step 3: Perform principal component analysis on the atomic three-dimensional coordinates of the polymer chain to be analyzed in Step 2 under different simulation time frames, and extract the first principal component direction as the main orientation direction of the polymer chain. Step 4: Determine the normal vector of the substrate or interface as the reference direction, and calculate the angle θ between the main orientation direction of the polymer chain described in Step 3 and the normal vector of the substrate or interface; Step 5: Utilize the vertical orientation threshold and parallel orientation threshold The change in the angle θ between the substrate or interface normal vectors described in step 4 is statistically analyzed to obtain the average orientation angle, standard deviation of orientation angle, vertical orientation probability, parallel orientation probability, vertical orientation index, and parallel orientation index of the polymer chain, thereby characterizing the orientation state of the polymer relative to the substrate or interface.

2. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, The polymer mentioned in step 1 includes one or more of thermoplastic polymers, liquid crystal polymers, biopolymers, block polymers, hydrogel networks, and polymer electrolytes.

3. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, The method for constructing the polymer and its substrate or interface model in step 1 to obtain the structure file containing atomic three-dimensional coordinate information and the molecular dynamics simulation trajectory file is as follows: Step 1.1: Use molecular structure visualization software to draw polymer models, substrates, or interface models with dimensions and shapes; Step 1.2: Convert the polymer model, substrate, or interface model described in Step 1.1 into a three-dimensional atomic coordinate file; Step 1.3: Optimize the geometric configuration of the polymer model, substrate, or interface model constructed in Step 1.2 to obtain a stable initial structure; Step 1.4: Perform molecular dynamics simulation based on the optimized initial structure in Step 1.3, and output a trajectory file containing information on the changes of atomic coordinates over time.

4. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, In step 3, principal component analysis is performed on the atomic three-dimensional coordinates of the polymer chain to be analyzed in step 2 at different simulation time frames. The method for extracting the first principal component direction as the main orientation direction of the polymer chain is as follows: Step 3.1: Extract the three-dimensional coordinates of all or selected atoms in the polymer chain at a certain simulation time frame to form a coordinate matrix; Step 3.2: Perform a centroid translation on the coordinate matrix described in Step 3.1 to obtain a centered coordinate matrix; Step 3.3: Construct the covariance matrix of the centered coordinate matrix; Step 3.4: Perform eigenvalue decomposition on the covariance matrix, select the eigenvector corresponding to the largest eigenvalue as the first principal component direction, and define it as the main orientation direction of the polymer chain.

5. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, The method for calculating the angle θ between the main orientation direction of the polymer chain mentioned in step 3 and the normal vector of the substrate or interface in step 4 is as follows: Where u is the unit vector of the main orientation direction of the polymer chain, and n is the unit vector of the substrate or interface normal vector.

6. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, The vertical orientation probability mentioned in step 5 will As a criterion, the parallel orientation probability will As a criterion, among which and This is a preset threshold.

7. The method for characterizing polymer orientation based on PCA algorithm according to claim 1, characterized in that, The method also includes the step of calculating spindle reliability parameters, namely, ,in , , These are the three eigenvalues ​​of the covariance matrix arranged in descending order.

8. A device for characterizing polymer orientation based on PCA algorithm, characterized in that, The device includes: The model building module is used to build models of polymers and their substrates or interfaces, and obtain structural files and molecular dynamics simulation trajectory files containing atomic three-dimensional coordinate information. The 3D coordinate extraction module is used to extract the atomic 3D coordinates of the polymer chain to be analyzed at different simulation time frames from the structural files and molecular dynamics simulation trajectory files described in the model building module. The main orientation direction extraction module is used to perform principal component analysis on the atomic three-dimensional coordinates of the polymer chain to be analyzed in the three-dimensional coordinate extraction module under different simulation time frames, and extract the first principal component direction as the main orientation direction of the polymer chain. Angle calculation module is used to determine the normal vector of the substrate or interface as a reference direction and calculate the angle θ between the main orientation direction of the polymer chain and the normal vector of the substrate or interface as described in the main orientation direction extraction module. The state characterization module is used to statistically analyze the change in the angle θ between the substrate or interface normal vectors in the angle calculation module, and obtain the average orientation angle, standard deviation of orientation angle, vertical orientation probability and parallel orientation probability of the polymer chain, thereby characterizing the orientation state of the polymer relative to the substrate or interface.

9. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1-7.

10. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the method of any one of claims 1-7.

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