Polymer main path extraction method based on molecular dynamics simulation

Abstract

The invention discloses a polymer main path extraction method based on molecular dynamics simulation, and relates to the technical field of material mechanics, and the method comprises the following steps: S1, mapping a polymer molecular chain into a coarse-grained bead model, and constructing a boundary model; s2, introducing a cross-linking agent into the model, and forming a cross-linked network through a thermostat; s3, performing multi-stage relaxation on the model by using an LAMMPS toolkit; s4, simulating and recording a three-dimensional motion track of a molecular chain in a system balance state; s5, calculating a fluctuation center line of the three-dimensional motion trail by adopting a fluctuation average method, and defining the center line as a main path of the molecular chain. According to the method, the dynamic trail center line can be extracted as the main path, the thermal motion characteristics of the molecular chain are integrated, the dynamic detail deficiency of a static method is overcome, and meanwhile, local stress analysis of a cross-linked network is combined, so that the reliability of the cross-linked network is improved. And the pipe diameter calculation based on the trajectory envelope volume breaks through the traditional theoretical hypothesis and is directly associated with the three-dimensional constraint effect.

Description

Technical Field

[0001] The present invention relates to the technical field of material mechanics, and in particular to a method for extracting a polymer main path based on molecular dynamics simulation. Background Art

[0002] In polymer physics, the tube model is a key theory for studying the confined motion of polymer chains in entangled or cross-linked networks. Traditional methods for extracting principal paths, such as the Z1+ method, are based on static geometry optimization and generate principal paths using minimum free energy paths. However, these methods have significant drawbacks.

[0003] First, they do not consider the dynamic fluctuation characteristics of molecular chains (such as thermal motion and local stress changes), resulting in insufficient analysis accuracy in non-uniform cross-linking or dynamic stretching systems; second, traditional methods assume that the two ends of the molecular chain are fixed, which makes it difficult to accurately reflect the limiting effect of cross-linking density on the fluctuation range of the molecular chain; in addition, the calculation of tube diameter relies on empirical formulas and cannot truly represent the constraint effect in three-dimensional space; although the development of molecular dynamics simulation technology has made dynamic behavior analysis possible, existing methods still lack in-depth integration of trajectory data, especially in the characterization of anisotropic deformation mechanisms of cross-linked networks; therefore, there is an urgent need for a main path extraction method that can integrate dynamic fluctuations and local stress states to improve the analysis capabilities in complex systems. To this end, a polymer main path extraction method based on molecular dynamics simulation is proposed. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art and to propose a method for extracting the main path of a polymer based on molecular dynamics simulation.

[0005] A method for extracting a polymer main path based on molecular dynamics simulation comprises the following steps:

[0006] S1. Map the polymer molecular chain into a coarse-grained bead model and construct a boundary model;

[0007] S2, introducing a cross-linking agent into the model to form a cross-linked network through a thermostat;

[0008] S3, use the LAMMPS toolkit to perform multi-stage relaxation of the model;

[0009] S4. Simulate and record the three-dimensional motion trajectory of the molecular chain in the equilibrium state of the system;

[0010] S5. Calculate the fluctuation centerline of the three-dimensional motion trajectory using the fluctuation average method, and define the centerline as the main path of the molecular chain;

[0011] S6. Analyze the effect of stretching ratio on main path length and tube diameter based on the local stress distribution and crosslinking density of the molecular chain;

[0012] S7. Calculate the pipe diameter based on the relationship between the envelope volume of the three-dimensional motion trajectory and the main path length.

[0013] Preferably, in step S3, performing multi-stage relaxation on the model using the LAMMPS toolkit comprises: running for 10 ns under the NVT ensemble, and then relaxing to a stable state at 298 K under the NPT ensemble.

[0014] Preferably, in step S5, calculating the fluctuation center line of the three-dimensional motion trajectory using the fluctuation average method includes:

[0015] The trajectory of each molecular chain is decomposed into a sequence of discrete points, and the three-dimensional spatial distribution of the trajectory is fitted by cubic spline interpolation;

[0016] Based on the time-weighted average algorithm, the center position of each discrete point is calculated to generate a smooth main path;

[0017] The main paths of the molecular chains in the stretching direction and the perpendicular direction were extracted respectively, and their average lengths were calculated.

[0018] Preferably, in step S7, the tube diameter is calculated based on the relationship between the envelope volume of the three-dimensional motion trajectory and the main path length as follows: d·l= <r 2 >, where d is the pipe diameter, l is the main path length, and r is the end distance.

[0019] Compared with the existing technology, the advantages of the present invention are:

[0020] The fluctuation averaging method disclosed in the present invention can extract the center line of the dynamic trajectory as the main path, integrate the thermal motion characteristics of the molecular chain, overcome the lack of dynamic details in the static method, and at the same time combine the local force analysis of the cross-linked network to improve the adaptability of complex systems. The tube diameter calculation based on the trajectory envelope volume breaks through the traditional theoretical assumptions and directly links to the three-dimensional constraint effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a schematic diagram of the process of the present invention.

[0022] Figure 2 Schematic diagram of the coarse-grained mapping of isoprene rubber according to the present invention.

[0023] Figure 3 Schematic diagram of the chemical cross-linking process of the present invention.

[0024] Figure 4 Schematic diagram of the change of total energy and total potential energy of the present invention.

[0025] Figure 5 It is a motion trajectory diagram of the molecular chain of the present invention and a schematic diagram of the center line of the trajectory.

[0026] Figure 6 The main path lengths in the stretching direction and the vertical direction are obtained by the oscillation average method of the present invention.

[0027] Figure 7 It is the main path length obtained in the stretching direction and the vertical direction using the Z1+ method of the present invention.

[0028] Figure 8 The end distances in the stretching direction and the vertical direction are obtained by the oscillation average method of the present invention.

[0029] Figure 9 The end distances obtained by the Z1+ method in the stretching direction and the vertical direction are shown in FIG.

[0030] Figure 10 It is the motion trajectory diagram of the molecular chain of the present invention and the envelope surface of the molecular chain trajectory.

[0031] Figure 11 The pipe diameters obtained in the stretching direction and the vertical direction by the oscillation average method are shown in FIG.

[0032] Figure 12 The pipe diameters obtained by the Z1+ method in the present invention in the stretching direction and the vertical direction are shown in FIG. DETAILED DESCRIPTION

[0033] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below in conjunction with specific implementation methods.

[0034] Reference Figure 1 As shown, a polymer main path extraction method based on molecular dynamics simulation (hereinafter referred to as "fluctuation average method") includes the following steps:

[0035] S1. Map the polymer molecular chain into a coarse-grained bead model and construct a boundary model;

[0036] S2, introducing a cross-linking agent into the model to form a cross-linked network through a thermostat;

[0037] S3, use the LAMMPS toolkit to perform multi-stage relaxation of the model;

[0038] S4. Simulate and record the three-dimensional motion trajectory of the molecular chain in the equilibrium state of the system;

[0039] S5. Calculate the fluctuation center line of the three-dimensional motion trajectory and define the center line as the main path of the molecular chain;

[0040] S6. Analyze the effect of stretching ratio on main path length and tube diameter based on the local stress distribution and crosslinking density of the molecular chain;

[0041] S7. Calculate the pipe diameter based on the relationship between the envelope volume of the three-dimensional motion trajectory and the main path length.

[0042] In step S3, the model is subjected to multi-stage relaxation using the LAMMPS toolkit, including running for 10 ns in the NVT ensemble and then relaxing to a stable state at 298 K in the NPT ensemble.

[0043] In step S5, calculating the fluctuation center line of the three-dimensional motion trajectory includes:

[0044] The trajectory of each molecular chain is decomposed into a sequence of discrete points, and the three-dimensional spatial distribution of the trajectory is fitted by cubic spline interpolation;

[0045] Based on the time-weighted average algorithm, the center position of each discrete point is calculated to generate a smooth main path;

[0046] The main paths of the molecular chains in the stretching direction and the perpendicular direction were extracted respectively, and their average lengths were calculated.

[0047] In step S7, the tube diameter is calculated based on the relationship between the volume of the three-dimensional motion trajectory envelope and the length of the main path: d·l= <r 2 >, where d is the pipe diameter, l is the main path length, and r is the end distance.

[0048] Example

[0049] The isoprene rubber (IR) molecular chain is mapped into a coarse-grained bead model, where each bead represents a molecular unit and the midpoint of the carbon double bond in the molecular chain is the center of the bead. Figure 2 As shown, a molecular chain with a degree of polymerization of 331 was constructed, with a total of 100 chains, forming a periodic boundary model (periodic boundary conditions were set in all three directions), and the total number of beads was 33,100.

[0050] exist Figure 6-9 、 Figure 11-12 The figure corresponding to "(a)" in the figure represents the stretching direction, and the figure corresponding to "(b)" represents the vertical direction.

[0051] Sulfur atoms (S) were introduced as crosslinkers in the model, and 1500, 2100, and 2500 S atoms were added, respectively. Dynamic crosslinking was performed at a high temperature of 500 K using a Langevin thermostat, and the bonding range in the crosslinking parameters was set to The bonding probability is 0.9, and a permanent chemical bond is generated, such as Figure 3 The final number of cross-linked bonds formed is 1380, 1978, and 2758, respectively, corresponding to cross-link densities of 4%, 6%, and 8%. The cross-link density calculation formula is: Where v is the number of cross-linked units and N0 is the total number of polymer units.

[0052] The bonding potential energy is described by the harmonic potential energy, and the non-bonding potential energy is described by the Lennard-Jones-12-6 potential energy; the bond energy constant Bond angle energy constant K Bend =1.53kcal / mol / rad 2 , potential well depth ε=0.388kcal / mol, equilibrium distance The actual distance between beads

[0053] Multi-stage relaxation was performed using the LAMMPS toolkit, specifically:

[0054] In the NVT ensemble (canonical ensemble), the initial conformational stress was eliminated by running for 10 ns with a time step of 1.0 fs at an initial temperature of 500 K and a pressure of 0 Pa;

[0055] There are two stages of relaxation in the NPT ensemble (isothermal and isobaric ensemble), specifically,

[0056] The first stage: 100ns relaxation at 500K to stabilize the system volume;

[0057] The second stage: Cool down to 298K and continue to relax for 100ns to allow the system to reach thermodynamic equilibrium.

[0058] Monitor the changes in total energy and potential energy of the system, such as Figure 4 As shown, it is confirmed that the energy fluctuation tends to be stable (the change in the last 1ns is less than 5%);

[0059] The cross-linked model after equilibrium was subjected to an engineering strain rate of 1×10 -8 fs -1 , simulating the uniaxial stretching process;

[0060] During the stretching process, the three-dimensional motion trajectory of the molecular chain in the 100ns dynamic relaxation stage was recorded, such as Figure 5 As shown in a, the sampling frequency is 1 ps / frame, ensuring that the data covers the complete fluctuation behavior of the molecular chain.

[0061] The recorded molecular chain trajectories are spatially averaged and the fluctuation center line of the trajectory is calculated, such as Figure 5 As shown in b, the specific method is:

[0062] The trajectory of each molecular chain is decomposed into a sequence of discrete points, and the three-dimensional spatial distribution of the trajectory is fitted by cubic spline interpolation;

[0063] Based on the time-weighted average algorithm, the center position of each discrete point is calculated to generate a smooth main path;

[0064] In the main path length analysis, the main paths of the molecular chains in the stretching direction (x axis) and the vertical direction (y, z axis) are extracted respectively, and their average lengths are calculated, such as Figure 6 As shown in Figure 3, the results indicate that the main path length increases with the increase of stretching ratio, and the main path of the sample with high cross-linking density (8%) is longer, verifying the restrictive effect of the cross-linking network on the movement of molecular chains.

[0065] In the calculation of tube diameter, the molecular chain trajectory is three-dimensionally enveloping, such as Figure 10 As shown in b, the envelope volume v is calculated, combined with the main path length l, by the formula Determine the pipe diameter, such as Figure 11 As shown, the results show that when the cross-linking density is 8%, the tube diameter is reduced by 30%-40% compared with the 4% sample.

[0066] Comparison of Z1+ method based on Doi-Edwards theoretical formula d·l= <r 2 >Calculate pipe diameter, such as Figure 12 As shown, the trend consistency of the two methods is verified, but the fluctuation average method of the present invention better reflects the three-dimensional constraint effect.

[0067] Analyze and calculate the end distance between the stretching direction and the vertical direction, such as Figure 8 、 9 As shown in the figure, the end-to-end distance growth rate of the high cross-linking density sample in the stretching direction is significantly higher than that of the low cross-linking density sample (for example, the growth rate of the 8% sample is 15% higher than that of the 4% sample), revealing the regulatory effect of the cross-linking network on the linear extension of the molecular chain.

[0068] By comparing the main path length, tube diameter and end distance of samples with different cross-linking densities, it was found that high cross-linking density significantly inhibited the lateral fluctuation of the molecular chain (the tube diameter in the vertical direction was reduced by 20%) and enhanced the axial stretching ability (the main path length in the stretching direction increased by 25%).

[0069] Establishing an empirical formula for elastic modulus based on main path parameters Combining the changing patterns of cross-linking density and stretch ratio, the macroscopic mechanical response of the material can be predicted (for example, the elastic modulus of a sample with an 8% cross-linking density is 50% higher than that of a sample with a 4% cross-linking density).

[0070] The fluctuation average method of the present invention is applied to the design of rubber materials or polymer composite materials. By adjusting the cross-linking density (4% to 8%) and the stretching ratio (0% to 200%), the elastic modulus (15 GPa) and the fracture toughness (210 MPa·m 1 / 2 ).

[0071] Comparing the main path differences between the Z1+ method and the oscillating average method, such as Figure 6 、 7 , 8, and 9, demonstrating the adaptability advantage of the fluctuation average method in heterogeneous cross-linking systems (error reduced by 20%).

[0072] In summary, the fluctuation averaging method disclosed in the present invention can extract the center line of the dynamic trajectory as the main path, integrate the thermal motion characteristics of the molecular chain, and overcome the lack of dynamic details in the static method; combine the local force analysis of the cross-linked network to improve the adaptability of complex systems; and calculate the tube diameter based on the trajectory envelope volume, breaking through traditional theoretical assumptions and directly linking the three-dimensional constraint effect.

[0073] It is understood from common technical knowledge that the present invention may be implemented by other embodiments that do not depart from its spirit or essential features. Therefore, the embodiments disclosed above are, in all respects, merely illustrative and not exclusive. All modifications within the scope of the present invention or equivalent to the scope of the present invention are intended to be encompassed by the present invention.

Claims

1. A method for extracting the main path of a polymer based on molecular dynamics simulation, characterized by: The following steps are involved: S1. Map the polymer molecular chain into a coarse-grained bead model and construct a boundary model; S2, introducing a cross-linking agent into the model to form a cross-linked network through a thermostat; S3, use the LAMMPS toolkit to perform multi-stage relaxation of the model; S4. Simulate and record the three-dimensional motion trajectory of the molecular chain in the equilibrium state of the system; S5. Calculate the fluctuation center line of the three-dimensional motion trajectory and define the center line as the main path of the molecular chain; S6. Analyze the effect of stretching ratio on main path length and tube diameter based on the local stress distribution and crosslinking density of the molecular chain; S7. Calculate the pipe diameter based on the relationship between the envelope volume of the three-dimensional motion trajectory and the main path length.

2. The method for extracting a polymer main path based on molecular dynamics simulation according to claim 1, characterized in that: In step S3, the model is subjected to multi-stage relaxation using the LAMMPS toolkit, including running for 10 ns in the NVT ensemble and then relaxing to a stable state at 298 K in the NPT ensemble.

3. The method for extracting a polymer main path based on molecular dynamics simulation according to claim 1, characterized in that: In step S5, calculating the fluctuation center line of the three-dimensional motion trajectory includes: The trajectory of each molecular chain is decomposed into a sequence of discrete points, and the three-dimensional spatial distribution of the trajectory is fitted by cubic spline interpolation; Based on the time-weighted average algorithm, the center position of each discrete point is calculated to generate a smooth main path; The main paths of the molecular chains in the stretching direction and the perpendicular direction were extracted respectively, and their average lengths were calculated.

4. The method for extracting a polymer main path based on molecular dynamics simulation according to claim 1, wherein: In step S7, the tube diameter is calculated based on the relationship between the volume of the three-dimensional motion trajectory envelope and the length of the main path: d·l= <r 2 >, where d is the pipe diameter, l is the main path length, and r is the end distance.

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