Method for simulating diffusion of molecules in amorphous polymers by non-equilibrium molecular dynamics

Abstract

The application discloses a method for simulating diffusion of molecules in amorphous polymer by non-equilibrium molecular dynamics, which comprises the following steps: constructing an amorphous polymer region box model, a high-pressure region box model and a low-pressure region box model; fixing atoms and splicing the models in the order of high-pressure region box-polymer region box-low-pressure region box-polymer region box-high-pressure region box to establish a non-equilibrium molecular dynamics model; placing gas molecules in the high-pressure region box model and adjusting the number of gas molecules to start the non-equilibrium molecular dynamics simulation; performing GCMC+NVT operation for multiple times in a loop until the gas molecules in the high-pressure region and the low-pressure region box model tend to be balanced; and calculating the diffusion coefficient based on the simulation data recorded in each loop operation. The application simulates diffusion of gas molecules in amorphous polymer by non-equilibrium molecular dynamics and calculates the diffusion coefficient, and the accuracy and efficiency of the simulation and calculation result of the diffusion coefficient are optimized.

Description

Technical Field

[0001] This invention relates to the field of microscale numerical simulation technology, and in particular to a method for simulating the diffusion of molecules in amorphous polymers using nonequilibrium molecular dynamics. Background Technology

[0002] Nonequilibrium molecular dynamics is often used to study the diffusion properties of gas molecules across materials under pressure differentials. It aligns with the "pressure differential method" experiments used to study gas diffusion, as both consider the influence of pressure differentials on gas diffusion performance. Compared to equilibrium molecular dynamics, nonequilibrium molecular dynamics takes into account the effect of pressure differentials, making it more consistent with the diffusion of gas molecules under actual pressure differential conditions in engineering applications such as gas pipelines, gas cylinders, and food packaging. Therefore, the simulation results of nonequilibrium molecular dynamics are closer to reality.

[0003] Currently, nonequilibrium molecular dynamics is mostly used to study the separation, transport, and diffusion of gas molecules in materials such as carbon films and nanopores. These materials remain stationary during the simulation, preventing them from exceeding the simulation range. However, when the research material is an amorphous polymer, it is impossible to fix the polymer molecular chains. During the simulation, the polymer molecular chains will move beyond the simulation range, leading to errors in the calculation results and reducing their accuracy.

[0004] Furthermore, nonequilibrium molecular dynamics often employs multiple cyclic operations of Grand Canonical Monte Carlo (GCMC) + Canonical ensemble NVT (keeping the number of particles N, volume V, and temperature T constant during the calculation). The simulation results can only be calculated after numerous GCMC operations have filled the high-pressure region with gas molecules from zero to equilibrium. Since GCMC involves stochastic processes, it typically requires a single core in a computer. Therefore, the simulation results obtained from the numerous GCMC+NVT operations before the gas molecules in the high-pressure region reach equilibrium cannot be used to calculate the final diffusion performance. Moreover, using numerous GCMC+NVT operations increases simulation time and reduces computational efficiency. Summary of the Invention

[0005] To address the shortcomings of the existing technology, this invention provides a method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics. This method employs non-equilibrium molecular dynamics to simulate the diffusion of gas molecules in amorphous polymers and calculates their diffusion coefficients. This significantly reduces the probability of amorphous polymer molecular chains exceeding the simulation range during the non-equilibrium molecular dynamics simulation process, greatly improves simulation efficiency, and optimizes the accuracy and efficiency of the diffusion coefficient simulation results.

[0006] In a first aspect, this disclosure provides a method for simulating the diffusion of molecules in amorphous polymers using nonequilibrium molecular dynamics.

[0007] A method for simulating molecular diffusion in amorphous polymers using nonequilibrium molecular dynamics includes:

[0008] An initial amorphous polymer region box model was constructed, the density of the amorphous polymer was determined according to the simulation conditions, and the amorphous polymer region box model was reconstructed based on the density of the amorphous polymer.

[0009] Construct box models for the high-voltage zone and the low-voltage zone;

[0010] The main atoms of the polymer molecular chain on the edge side of the amorphous polymer region box model are fixed, and the model is spliced ​​in the order of high pressure region box - polymer region box - low pressure region box - polymer region box - high pressure region box to establish a non-equilibrium molecular dynamics model.

[0011] Based on the non-equilibrium molecular dynamics model, gas molecules are placed in the high-pressure box model and the number of gas molecules is adjusted to start the non-equilibrium molecular dynamics simulation.

[0012] The GCMC+NVT operation is executed multiple times until the gas molecules in the high-pressure and low-pressure box models tend to reach equilibrium. Simulation data for each cycle is recorded, and gas molecules in the low-pressure box model are deleted before the next cycle.

[0013] The diffusion coefficient was calculated based on the recorded simulation data.

[0014] A further technical solution involves calculating the gas molecule diffusion coefficient D using the following formula:

[0015]

[0016] In the above formula, D is the diffusion coefficient of gas molecules; N is the number of gas molecules that diffuse into the low-pressure region at diffusion equilibrium; L mz denoted as , where is the length of the polymer region box along the z-direction, i.e., the distance between the high-pressure region box and the low-pressure region box; 2 indicates that gas molecules from two high-pressure regions diffuse into the low-pressure region; A is the diffusion area, which is... t is the simulation duration of each NVT; n is the number of NVT simulations at diffusion equilibrium; N h V represents the number of gas molecules in the high-pressure region at diffusion equilibrium. h This represents the volume of the high-pressure zone.

[0017] In a second aspect, this disclosure also provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method described in the first aspect.

[0018] Thirdly, this disclosure also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps of the method described in the first aspect.

[0019] The above one or more technical solutions have the following beneficial effects:

[0020] 1. This invention provides a method for simulating the diffusion of molecules in amorphous polymers using non-equilibrium molecular dynamics. The method employs non-equilibrium molecular dynamics to simulate the diffusion of gas molecules in amorphous polymers and calculate their diffusion coefficients. In the non-equilibrium molecular dynamics simulation, the polymer density in the polymer region is controlled to prevent polymer molecular chains from crossing the polymer region and reaching the low-pressure region during their movement. This significantly reduces the probability of amorphous polymer molecular chains exceeding the simulation range during the non-equilibrium molecular dynamics simulation and improves the accuracy of the calculation results.

[0021] 2. This invention first rapidly fills a large number of gas molecules in the high-pressure region using GCMC, and then fine-tunes the number of gas molecules in the high-pressure region. This can save a lot of GCMC+NVT operations, greatly improve simulation efficiency, and thus improve the calculation efficiency of gas molecule diffusion coefficient. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1 This is a schematic diagram of the structure of the non-equilibrium molecular dynamics model in an embodiment of the present invention;

[0024] Figure 2 This is a physical schematic diagram of the non-equilibrium molecular dynamics model in an embodiment of the present invention. Detailed Implementation

[0025] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0026] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0027] Example 1

[0028] To address the problems encountered in existing technologies using non-equilibrium molecular dynamics to simulate the diffusion of gas molecules in amorphous polymers—namely, the amorphous polymer molecular chains moving beyond the simulation range during the simulation, leading to poor calculation accuracy; and the extensive use of GCMC+NVT operations resulting in low simulation efficiency—this embodiment provides a method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics, improving both the accuracy and efficiency of the simulation. This method specifically includes the following steps:

[0029] An initial amorphous polymer region box model was constructed, the density of the amorphous polymer was determined according to the simulation conditions, and the amorphous polymer region box model was reconstructed based on the density of the amorphous polymer.

[0030] Construct box models for the high-voltage zone and the low-voltage zone;

[0031] The main atoms of the polymer molecular chain on the edge side of the amorphous polymer region box model are fixed, and the model is spliced ​​in the order of high pressure region box - polymer region box - low pressure region box - polymer region box - high pressure region box to establish a non-equilibrium molecular dynamics model.

[0032] Based on the non-equilibrium molecular dynamics model, gas molecules are placed in the high-pressure box model and the number of gas molecules is adjusted to start the non-equilibrium molecular dynamics simulation.

[0033] The GCMC+NVT operation is executed multiple times until the gas molecules in the high-pressure and low-pressure box models tend to reach equilibrium. Simulation data for each cycle is recorded, and gas molecules in the low-pressure box model are deleted before the next cycle.

[0034] The diffusion coefficient was calculated based on the recorded simulation data.

[0035] The following content provides a more detailed description of the method proposed in this embodiment for calculating the diffusion coefficient of molecules in amorphous polymers using nonequilibrium molecular dynamics simulation.

[0036] Step S1: Determination of amorphous polymer density. First, a three-dimensional periodic amorphous polymer box model is established as the initial amorphous polymer box model. In this model, amorphous polymer molecular chains are allowed to extend beyond the box in the x, y, and z directions. Simulation conditions are set, namely the temperature T and the high-pressure side pressure P. Under the conditions of temperature T, pressure of 0.1 MPa in the x and y directions, and pressure P / 2 in the z direction, the amorphous polymer box is subjected to NPT relaxation to obtain the density ρ of the amorphous polymer under the above simulation conditions.

[0037] Step S2: Remodel the amorphous polymer region box. Step S1 yields the density ρ of the amorphous polymer under the conditions of temperature T, pressure 0.1 MPa in the x and y directions, and pressure P / 2 in the z direction. Based on the density ρ of the amorphous polymer, the z-direction length L is remodeled. mz A three-dimensional periodic amorphous polymer region box model was constructed, requiring that the polymer molecular chains cannot exceed the box in the z-direction, but are allowed to exceed it in the x and y directions. Finally, based on the reconstructed box model and combined with preset conditions, a length L in both the x and y directions can be obtained. xy The volume of the box is V. m The amorphous polymer box model is then remodeled. Additionally, an identical amorphous polymer box model is replicated. It is important to note that the shortest side length of the amorphous polymer box model must be greater than twice the cutoff radius. The shortest side refers to the shortest side in the x, y, and z directions, and is the shortest side of the entire amorphous polymer box; the lengths in the x, y, and z directions are all possible. The cutoff radius is a specific concept in molecular simulation, referring specifically to the computational range of each atom.

[0038] Step S3: Modeling the high-pressure zone box and the low-pressure zone box. The high-pressure zone box is used to hold gas molecules, and the low-pressure zone box is used to receive gas molecules diffused from the high-pressure zone box through the amorphous polymer. Based on step S2, models with a z-direction length of L are created respectively. hz and L lz The lengths in both the x and y directions are L. xy The high-pressure region box model and the low-pressure region empty box model are required, where the z-direction length L of the high-pressure region box model is required. hz And the length L in the z-direction of the low-pressure zone box model lz Both must be greater than twice the cutoff radius, and the final volumes are V. h and V l Create a high-voltage box model and a low-voltage box model. Also, duplicate the same high-voltage box model and low-voltage box model.

[0039] Step S4: Fix atoms. On both sides of the amorphous polymer box model along the z-direction, fix atoms at a distance of no more than 5% L from the edge. hz The main atoms of the amorphous polymer molecular chains are fixed; for example, carbon atoms are chosen for polyethylene polymers. This step fixes some atoms at the edge of the polymer zone box, preventing the amorphous polymer molecular chains from crossing the polymer zone box and entering the low-pressure zone box during subsequent NVT operations, thus ensuring the integrity and density of the polymer within the polymer zone box. Simultaneously, only atoms within 5% L of the edge are fixed. hz The main atoms of the polymer molecular chain are fixed. Compared with the entire amorphous polymer, there are fewer fixed atoms, and the impact on the overall movement of the polymer during NVT simulation is also smaller.

[0040] Step S5: Model assembly. (e.g.) Figure 1 As shown, in the z-direction, the model is assembled in the order of "high-pressure region box - polymer region box - low-pressure region box - polymer region box - high-pressure region box" to establish a non-equilibrium molecular dynamics model (which is actually also a box model). The length of the constructed non-equilibrium molecular dynamics model in the z-direction is L, calculated according to equation (1), and the lengths in the x and y directions are both L. xy .

[0041] L = 2L hz +2L mz +L lz (1)

[0042] In the above equation, L is the total length in the z-direction of the nonequilibrium molecular dynamics model; L hz L represents the length of the high-voltage box model in the z-direction. mz L represents the length of the amorphous polymer region box model in the z-direction. lz Let be the length of the low-pressure zone box model in the z-direction.

[0043] Step S6: Place gas molecules. (e.g.) Figure 2 As shown, by performing GCMC operations, a certain number of gas molecules are placed in two high-pressure box models to coarsely adjust the number of gas molecules in the high-pressure box models. This number of gas molecules is related to temperature, pressure, box size, and the molecular force field being simulated. This step saves the computation time of multiple GCMC operations for placing gas molecules in the high-pressure box models and multiple NVT operations, greatly improving computational efficiency.

[0044] Step S7: GCMC Adjustment of Gas Molecule Count. Step S6 allows for the rapid placement of gas molecules in the two high-pressure box models; however, the number of gas molecules still differs from the equilibrium count in the high-pressure box models. Therefore, fine-tuning via GCMC is necessary. Multiple GCMC operations are performed under controlled temperature (T) and pressure (P) conditions to fine-tune the gas molecule count, bringing the gas molecules in the two high-pressure zones towards equilibrium. This step saves computation time from multiple NVT operations, further improving computational efficiency.

[0045] Step S8: Begin nonequilibrium molecular dynamics simulation. Following step S7, once the gas molecules in the high-pressure region box model have reached equilibrium, the GCMC+NVT operation is executed multiple times. From this step onwards, the nonequilibrium molecular dynamics simulation process begins. This embodiment, by first using GCMC to coarsely and then finely adjust the number of gas molecules, reduces the number of subsequent GCMC+NVT operations. For example, simulation calculations can only begin when the high-pressure region has K molecules. Existing technology repeatedly executes GCMC+NVT starting from 0 molecules in the high-pressure region until it has K molecules. However, the method in this embodiment, through the coarse and fine adjustments in S6 and S7, ensures that the high-pressure region starts with K / 2 molecules, significantly reducing the number of subsequent GCMC+NVT operations.

[0046] Step S9: Acquire and record data. During the simulation process of repeatedly performing GCMC+NVT operations, the corresponding simulation data is recorded after each cycle, including the number of gas molecules N in the low-pressure box model after each NVT operation. N represents the number of gas molecules from the high-pressure side in the high-pressure region that diffuse through the polymer region to reach the low-pressure region. Before the next GCMC operation cycle, all gas molecules in the low-pressure box model are deleted to ensure that the low-pressure box model is in a vacuum state.

[0047] After performing multiple GCMC+NVT simulations on the non-equilibrium molecular dynamics model, the number N of gas molecules in the high-pressure box model is determined. h When the number N of gas molecules diffused to the low-pressure region of the box model both tend to be in equilibrium, the gas molecule diffusion coefficient D is calculated.

[0048] In addition, the recorded simulation data also includes the simulation duration of each NVT operation during the cyclic simulation, the number of simulations in which the NVT operation is executed when diffusion equilibrium is reached, and the number of gas molecules in the high-pressure box model when diffusion equilibrium is reached.

[0049] Step S10: Calculate the gas molecule diffusion coefficient D. The formula for calculating the gas molecule diffusion coefficient D is shown in equation (2).

[0050]

[0051] In the above formula, D is the diffusion coefficient of gas molecules; N is the number of gas molecules that diffuse into the low-pressure region at diffusion equilibrium; L mz denoted as , where is the length of the polymer region box along the z-direction, i.e., the distance between the high-pressure region box and the low-pressure region box; 2 indicates that gas molecules from two high-pressure regions diffuse into the low-pressure region; A is the diffusion area, which is... t is the simulation duration of each NVT; n is the number of NVT simulations at diffusion equilibrium; N h V represents the number of gas molecules in the high-pressure region at diffusion equilibrium. h This represents the volume of the high-pressure zone.

[0052] Through the above simulation steps, the method described in this embodiment controls the polymer density in the polymer region during non-equilibrium molecular dynamics simulation, preventing polymer molecular chains from passing through the polymer region and reaching the low-pressure region during movement, thereby improving the accuracy of the calculation results. By rapidly filling a large number of gas molecules in the high-pressure region first by GCMC, and then fine-tuning the number of gas molecules in the high-pressure region, a large number of GCMC+NVT operations can be saved, greatly improving the simulation efficiency and thus improving the calculation efficiency of the gas molecule diffusion coefficient.

[0053] Example 2

[0054] This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it performs the steps in the method described above for simulating the diffusion of molecules in an amorphous polymer using non-equilibrium molecular dynamics.

[0055] Example 3

[0056] This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps in the method described above for simulating the diffusion of molecules in amorphous polymers using non-equilibrium molecular dynamics.

[0057] The steps and methods involved in Embodiments 2 and 3 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0058] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0059] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for simulating molecular diffusion in amorphous polymers using nonequilibrium molecular dynamics, characterized in that, include: An initial amorphous polymer region box model was constructed, the density of the amorphous polymer was determined according to the simulation conditions, and the amorphous polymer region box model was reconstructed based on the density of the amorphous polymer. Construct box models for the high-voltage zone and the low-voltage zone; The main atoms of the polymer molecular chain on the edge side of the amorphous polymer region box model are fixed, and the model is spliced ​​in the order of high pressure region box - polymer region box - low pressure region box - polymer region box - high pressure region box to establish a non-equilibrium molecular dynamics model. Based on a nonequilibrium molecular dynamics model, gas molecules are placed in a high-pressure box model and the number of gas molecules is adjusted to begin the nonequilibrium molecular dynamics simulation. This process of placing gas molecules in the high-pressure box model and adjusting the number of gas molecules includes: Based on GCMC operation, a certain number of gas molecules are placed in two high-pressure box models to coarsely adjust the number of gas molecules in the high-pressure box model. Fine-tuning is performed based on GCMC operation. Multiple GCMC operations are performed in an environment with temperature T and pressure P until the number of gas molecules in the two high-pressure zones tends to be in equilibrium. The GCMC+NVT operation is executed multiple times until the gas molecules in the high-pressure and low-pressure box models tend to reach equilibrium. Simulation data for each cycle is recorded, and gas molecules in the low-pressure box model are deleted before the next cycle. The diffusion coefficient was calculated based on the recorded simulation data.

2. The method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics as described in claim 1, characterized in that, The determination of the density of the amorphous polymer based on simulation conditions includes: According to the preset temperature T and high-pressure side pressure P， At temperature T , x and y Directional pressure of 0.1 MPa and z Direction under pressure P In the case of / 2, NPT relaxation is performed on the initial amorphous polymer region box model to obtain the density of the amorphous polymer. ρ .

3. The method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics as described in claim 1, characterized in that, The process of reconstructing the amorphous polymer region box model based on the density of the amorphous polymer includes: Based on the density of amorphous polymers ρ Rebuild z directional length is L mz , xy Both directional lengths L xy The box has a volume of V m A box model of amorphous polymer regions, in which the molecular chains of the amorphous polymer are in... z The direction cannot exceed the box model, in x and y It can exceed the allowed direction; The shortest side length of the amorphous polymer region box model is more than twice the truncation radius.

4. The method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics as described in claim 1, characterized in that, The construction of the high-pressure area box model and the low-pressure area box model includes: Establish z The directional lengths are respectively L hz and L lz ,and xy Both directional lengths L xy The high-pressure area box model and the low-pressure area empty box model, wherein the high-pressure area box model z Directional length L hz and low-pressure area box model z Directional length L lz All are greater than twice the cutoff radius.

5. The method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics as described in claim 1, characterized in that, The main atoms of the polymer molecular chains on the edge side of the fixed amorphous polymer region box model are: Box model in amorphous polymer region z A high-voltage zone box model with a fixed distance of no more than 5% from the edge on both sides of the direction. z Directional length L hz The main atoms of the amorphous polymer molecular chain.

6. A method for simulating molecular diffusion in amorphous polymers using nonequilibrium molecular dynamics as described in claim 1, characterized in that, The recorded simulation data includes: the number of gas molecules in the low-pressure zone box model after each cycle of NVT operation. N、 The simulation duration of each NVT operation during the cyclic simulation, the number of simulations in which the NVT operation is executed when diffusion equilibrium is reached, and the number of gas molecules in the high-pressure box model when diffusion equilibrium is reached.

7. The method for simulating molecular diffusion in amorphous polymers using non-equilibrium molecular dynamics as described in claim 1, characterized in that, gas molecule diffusion coefficient D The calculation formula is: In the above formula, D is the diffusion coefficient of gas molecules; N This represents the number of gas molecules that diffuse into the low-pressure region at diffusion equilibrium. L mz For polymer zone box z The length of the direction, i.e., the distance between the high-pressure zone box and the low-pressure zone box; 2 indicates that gas molecules from two high-pressure zones diffuse into the low-pressure zone; A Where is the diffusion area, and is ; t This refers to the simulation duration of each NVT. n The number of NVT simulations at diffusion equilibrium; N h This represents the number of gas molecules in the high-pressure region at diffusion equilibrium. V h This represents the volume of the high-pressure zone.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of a method for simulating the diffusion of molecules in an amorphous polymer using non-equilibrium molecular dynamics as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of a method for simulating the diffusion of molecules in an amorphous polymer using non-equilibrium molecular dynamics as described in any one of claims 1-7.

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