A method for determining the collision recovery coefficient of nanosphere particles based on molecular dynamics

Abstract

The present invention relates to a method for measuring the coefficient of restitution of nano-sphere particle collision based on molecular dynamics, comprising: establishing two nano-sphere Al2O3 particle models using OVITO software; placing a nitrogen molecule model, an oxygen molecule model, and the two particle models in a simulation box to form a simulation object system, and importing the LAMMPS software; using comb3 and lj / cut mixed potential; setting simulation parameters, performing molecular dynamics simulation, obtaining parameter data during the movement of the particle model, and observing the deformation of the particle model during the collision process; post-processing the parameter data to obtain a force-displacement curve of the particle model, judging the collision occurrence and end time of the particle model, and determining the collision velocity of the particle model and the separation velocity during rebound, and calculating the collision coefficient of restitution of the particle model based on the velocity changes before and after the collision. The present invention overcomes the limitations of traditional methods and improves measurement accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of collision recovery coefficient determination of nano spherical particles, in particular to a method for determining the collision recovery coefficient of nano spherical particles based on molecular dynamics. Background Art

[0002] In nanoparticle research, particularly in characterizing their collision behavior, the coefficient of restitution is a key parameter. It describes the degree of energy loss during a collision and directly impacts the performance and application of a material. Furthermore, a material's performance under extreme conditions determines its range of applications.

[0003] Traditional methods for measuring the collision restitution coefficient of nanoparticles often rely on optical or mechanical testing equipment in the laboratory. These methods are not only complex to operate, but are often limited by the size and surface properties of the nanoparticles and difficult to operate under extreme conditions. Furthermore, most particle simulations are based on continuum models using methods such as DEM and FEM from a macroscopic perspective, lacking technical solutions for reasonably accurate simulation of nanoparticles from a microscopic perspective. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention provides a method for measuring the collision restitution coefficient of nanosphere particles based on molecular dynamics, which overcomes the limitations of traditional methods and improves the measurement accuracy and reliability.

[0005] The technical solution adopted in the present invention is as follows:

[0006] The present invention provides a method for measuring the collision restitution coefficient of nanosphere particles based on molecular dynamics, comprising the following steps:

[0007] Establishing a particle model includes: selecting a standard α-Al2O3 crystal structure from a material database, importing it into OVITO software, expanding the α-Al2O3 crystal structure to obtain a three-dimensional crystal model, selecting the three-dimensional crystal model, deleting unselected parts to obtain a nano-spherical Al2O3 particle model, and duplicating it to obtain two particle models;

[0008] Define the interatomic bond lengths, randomly generate atoms in the simulation box of the OVITO software, and obtain nitrogen and oxygen molecular models;

[0009] Placing the nitrogen molecule model, the oxygen molecule model, and the two particle models in a simulation box to form a simulation object system;

[0010] Convert the simulation object system into the required format and import it into LAMMPS software to set the initial simulation parameters;

[0011] Setting potential functions: the potential function between aluminum atoms and oxygen atoms uses the third-generation charge-optimized multi-body potential function, and the potential function between nitrogen molecules and oxygen molecules uses the lj / cut potential function;

[0012] Use the min_style command to minimize energy, select the NPT ensemble to simulate the equilibrium constraint of the object system, use the Nose-Hoover heat bath method to adjust the system temperature, and set the number of relaxation steps;

[0013] The initial velocities of the two particle models were set, and molecular dynamics simulations were performed to obtain parameter data of the particle models during motion. The obtained parameter data were imported into OVITO software to observe the deformation of the particle models during the collision. The parameter data included the displacement, velocity, and force of the particle model's center of mass.

[0014] The parameter data is post-processed to obtain the force-displacement curve of the particle model, determine the collision and end time of the particle model, and determine the collision speed and separation speed of the particle model during rebound. According to the speed changes before and after the collision, the collision recovery coefficient of the particle model is calculated.

[0015] Further technical solutions are:

[0016] By adjusting the diameter of the nano-spherical Al2O3 particle model, the initial velocity of the particle model and the system temperature, the collision process simulation results of the particle model under different working conditions were obtained.

[0017] The setting of the initial simulation parameters includes: setting the spatial dimension to three dimensions; setting the model atoms to metal units; setting the boundary conditions to periodic boundary conditions; and setting the time step and iteration step.

[0018] The diameter of the nano-spherical Al2O3 particle model is less than 100 nm.

[0019] The system temperature is 2000K to 3000K, and the pressure is 8.2MPa.

[0020] The initial velocity of the nano-spherical Al2O3 particle model is not less than 70m / s.

[0021] The beneficial effects of the present invention are as follows:

[0022] The present invention starts from the nanoscale and applies the molecular dynamics (MD) method to realize the dynamic simulation of the whole process of nanoparticle collision under high temperature and high pressure environment. By analyzing the collision recovery coefficient, it can obtain the influence of different initial speeds, temperatures, and particle diameters on the particle collision results, and accurately obtain the motion data of nanoparticle collision under extreme working conditions. At the same time, the collision deformation of nano-molten particles in a high-pressure gas environment can be observed intuitively and clearly, avoiding the limitations of nano-size, real-time observation and extreme working conditions in traditional experiments. It is of great significance to explore the dynamics of nanoparticles and the material properties of nanoparticles such as viscoelasticity.

[0023] The method of the present invention has high precision: based on molecular dynamics simulation, it can accurately capture the microscopic information during the collision of nanoparticles, thereby accurately measuring the collision recovery coefficient of nano-spherical particles.

[0024] The method of the present invention has wide applicability: it is not limited by nanoparticle materials and working conditions, and is applicable to nanoparticle materials of various types and conditions.

[0025] The method of the present invention is easy to operate: compared with traditional experiments, the simulation calculation is simple to operate and has strong repeatability.

[0026] Other features and advantages of the present invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the structure of the simulation object system according to an embodiment of the present invention.

[0028] Figure 2 This is the simulation result under the first set of time step intervals of the embodiment of the present invention.

[0029] Figure 3 This is the simulation result under the second set of time step intervals of the embodiment of the present invention.

[0030] Figure 4 Comparison results of the collision recovery coefficient and the viscoelastic-plastic curve calculated under different initial conditions in the embodiment of the present invention. DETAILED DESCRIPTION

[0031] The specific embodiments of the present invention are described below with reference to the accompanying drawings.

[0032] A method for measuring the collision restitution coefficient of nanosphere particles based on molecular dynamics in this embodiment includes the following steps:

[0033] (1) Establishing a particle model, including: selecting a standard α-Al2O3 crystal structure from the material project open source material database such as Figure 1As shown in (b), import the OVITO software and use the replicate command to expand the α-Al2O3 crystal structure to obtain a three-dimensional crystal model; use the expression selection command to enter the sphere formula x 2 +y 2 +z 2 <r 2 , x, y, z are coordinates, r represents the radius of the sphere, the three-dimensional crystal model is selected, the atoms within the sphere are selected, the unselected parts are deleted, and a nano-spherical Al2O3 particle model with a diameter of 20nm is obtained. After duplication, two particle models are obtained; the sphere diameter can be adjusted as needed;

[0034] (2) Compile nitrogen and oxygen molecule txt files, which define the interatomic bond lengths; Based on the txt files, use the create_atom random command to randomly generate atoms in the simulation box of the OVITO software to establish 78,000 nitrogen molecule models and 21,000 oxygen molecule models; the number of molecular models can be adjusted as needed;

[0035] (3) The nitrogen molecule model, oxygen molecule model, and two particle models are placed in a simulation box to form a simulation object system as shown in FIG. Figure 1 As shown in (a);

[0036] (4) Convert the simulation object system into the data format file required by the LAMMPS software, import it into the LAMMPS software, and set the initial simulation parameters, including: setting the spatial dimension to three dimensions; setting the model atoms to metal units; setting the boundary conditions to periodic boundary conditions; setting the time step to 1 femtosecond and the iteration step to 10 steps.

[0037] (5) Setting potential functions, including: the potential function between aluminum atoms and oxygen atoms uses the third-generation charge-optimized multi-body (comb3) potential function, and the potential function between nitrogen molecules and oxygen molecules uses the lj / cut potential function;

[0038] The simulation system of this embodiment uses a hybrid potential of lj / cut and comb3. Compared with the traditional single EAM potential function or LJ potential function, this potential function can more realistically reflect the interactions between metal oxides and gas molecules and complex atoms, and is more suitable for the application scenario of this embodiment. The total interatomic force Utot is as follows:

[0039] U tot [{q},{r}]

[0040] =U es [{q},{r}]

[0041] +U short [{q},{r}]

[0042] +U vdW [{q},{r}]

[0043] +U corr [{q},{r}]

[0044] In the above formula, U tot represents the total interatomic force, q represents the atomic charge, r represents the atomic coordinates, and U es represents the non-bonding potential between atoms, U short represents the short-range force between atoms, U vdW represents the interatomic van der Waals force, U corr represents the interatomic correlation potential;

[0045]

[0046] In the above formula, i and j represent two atoms of Al, N, and O, respectively. ij represents the interaction force between atoms i and j, r ij Represents the distance between atoms i and j, when r ij <r c ,σ ij and ε ij are the distance at which the interatomic potential decreases to zero and the depth of the potential well, respectively;

[0047] (6) Use the min_style command to minimize energy, select the NPT ensemble to simulate the equilibrium constraint of the object system, use the Nose-Hoover heat bath method to adjust the system temperature, and set the number of relaxation steps;

[0048] Specifically, the scale that is difficult to achieve and observe in experiments is generally less than 100 nm, and the temperature is usually higher than 2000 K, so this embodiment uses the NPT ensemble at 3000 K and 8.2 MPa, and relaxes for 20,000 steps;

[0049] (7) Set the initial velocity of the two particle models to 70 m / s, perform molecular dynamics simulation, and obtain parameter data during the movement of the particle models: displacement, velocity, and force of the particle model's center of mass. Import the obtained parameter data into OVITO software to observe the deformation of the particle model during the collision process;

[0050] (8) Post-processing the parameter data to obtain the force-displacement curve of the particle model, determine the time when the particle model collides and ends the collision, and determine the collision speed and separation speed of the particle model during rebound. According to the speed changes before and after the collision, the collision recovery coefficient of the particle model is calculated.

[0051] The simulation results are as follows Figure 2 and Figure 3 shown. Figure 2 (a) to (e) are snapshots of the particle model collision and rebound at t = 0, 1000, 2000, 5000, and 10000 fs, respectively; Figure 2 (f) is the change of potential energy and kinetic energy of the particle model during the motion process; Figure 2 (g) is the force-displacement curve of the particle model during collision.

[0052] Figure 3 (a) to (e) are snapshots of the particle model collision and adhesion at t = 0, 2000, 5000, 10000, and 15000 fs, respectively; Figure 3 (f) is the change of potential energy and kinetic energy of the particle model during the motion process; Figure 3 (g) is the force-displacement curve of the particle model during collision.

[0053] A simulation revealed that two spherical Al2O3 particle models, each with a diameter of 20 nanometers, collided at step 2000, traveling toward each other at the same initial velocity of 70 m / s in an environment with a pressure of 8.2 MPa. Based on the force-displacement curves of the particle models and the velocities before and after the collision, the coefficient of restitution for the nano-spherical Al2O3 particle model under these conditions was calculated to be 0.75.

[0054] In order to further verify the accuracy of the molecular dynamics simulation results of this embodiment, the simulation results are compared with the viscoelastic-plastic model curve. The viscoelastic-plastic model curve equation is shown in the following equations (1)-(5):

[0055] V i ≤V s When: e=0(1);

[0056] V s ≤V i ≤V y hour:

[0057]

[0058] V i ≥V y hour:

[0059]

[0060] In the above formula, V S is the threshold impact velocity, below which particles adhere. V S It is mainly determined by the surface energy Γ, as shown in Equation (3). pis the particle diameter, ρ is the material density, E is the Young's modulus, V y is the characteristic velocity of the material related to yield strength, Young's modulus and density. V i is the relative velocity of the two particle models in the initial stage. The key variables in Equations (3) and (5) are all strongly correlated with temperature, so the semi-analytical model equation is constructed as follows:

[0061]

[0062] Equations (6) and (7) effectively reduce the number of fitting parameters by introducing temperature dependence and using lumped parameters, enriching the viscoelastic-plastic collision model given in equations (3) and (5), and can better and more accurately describe the restitution coefficient of nanoparticle collisions under different speeds, temperatures, and nanosize conditions.

[0063] By comparison, Figure 4 As shown in the figure, the collision recovery coefficient of the particle model with different diameters and initial velocities based on molecular dynamics simulation is very consistent with the viscoelastic-plastic model.

[0064] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the present invention and are 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 will be able to modify the technical solutions described in the foregoing embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for determining the collision recovery coefficient of nanosphere particles based on molecular dynamics, characterized in that: The following steps are involved: Establishing a particle model includes: selecting a standard α-Al2O3 crystal structure from a material database, importing it into OVITO software, expanding the α-Al2O3 crystal structure to obtain a three-dimensional crystal model, selecting the three-dimensional crystal model, deleting unselected parts to obtain a nano-spherical Al2O3 particle model, and duplicating it to obtain two particle models; Define the interatomic bond lengths, randomly generate atoms in the simulation box of the OVITO software, and obtain nitrogen and oxygen molecular models; Placing the nitrogen molecule model, the oxygen molecule model, and the two particle models in a simulation box to form a simulation object system; Convert the simulation object system into the required format and import it into LAMMPS software to set the initial simulation parameters; Setting potential functions: the potential function between aluminum atoms and oxygen atoms uses the third-generation charge-optimized multi-body potential function, and the potential function between nitrogen molecules and oxygen molecules uses the lj / cut potential function; Use the min_style command to minimize energy, select the NPT ensemble to simulate the equilibrium constraint of the object system, use the Nose-Hoover heat bath method to adjust the system temperature, and set the number of relaxation steps; The initial velocities of the two particle models were set, and molecular dynamics simulations were performed to obtain parameter data of the particle models during motion. The obtained parameter data were imported into OVITO software to observe the deformation of the particle models during the collision. The parameter data included the displacement, velocity, and force of the particle model's center of mass. The parameter data is post-processed to obtain the force-displacement curve of the particle model, determine the collision and end time of the particle model, and determine the collision speed and separation speed of the particle model during rebound. According to the speed changes before and after the collision, the collision recovery coefficient of the particle model is calculated.

2. The method according to claim 1, characterized in that By adjusting the diameter of the nano-spherical Al2O3 particle model, the initial velocity of the particle model and the system temperature, the collision process simulation results of the particle model under different working conditions were obtained.

3. The method according to claim 1, characterized in that The setting of the initial simulation parameters includes: setting the spatial dimension to three dimensions; setting the model atoms to metal units; setting the boundary conditions to periodic boundary conditions; and setting the time step and iteration step.

4. The method according to claim 1, wherein The diameter of the nano-spherical Al2O3 particle model is less than 100 nm.

5. The method according to claim 1, wherein The system temperature is 2000K to 3000K, and the pressure is 8.2MPa.

6. The method according to claim 1, characterized in that The initial velocity of the nano-spherical Al2O3 particle model is not less than 70m / s.

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