Molecular dynamics simulations of dust monomer collisions

Collisional sticking of dust is the initial stage of planet formation. Dust is considered to form aggregates, which are composed of many sub-micrometer-sized particles, called dust monomers. The collisions between dust aggregates have been investigated using numerical simulations based on DEM (discrete element method). The DEM simulations calculate the contacting interaction between monomers based on the JKR model, which is an elastic contact model. However, the JKR model does not include the viscosity due to molecular motions. Then, we investigate the contact interaction between monomers, including molecular motions.

We perform molecular dynamics (MD) simulations, which calculate the molecular motions using the intermolecular potential. We use the Lennard-Jones potential as an intermolecular potential and prepare five kinds of monomers with radius of R/σ = 29, 58, 88, 147, and 294, where σ is the intermolecular distance (~0.3 nm); the number of molecules is from 10⁵ to 10⁸. We simulate the head-on collisions between equal-mass monomers with changes in the impact velocity as v_imp/C_s = 6.5×10^-3 - 4.8×10^-2, where C_s is the sound velocity, and analyze the inter-monomer force and the coefficient of restitution (COR). The COR is the ratio of relative velocities between before and after collisions and is a key parameter of the dissipation of monomers’ kinetic energy.

Figure 1 shows the enlarged views of the contact area before and after a collision. After the collision, some molecules move, and the surface becomes rough. The phase when two monomers approach is called “loading”, and the phase when they move away is called “unloading”. Figure 2 shows the inter-monomer force as a function of the distance between the centers of mass of two monomers. At the loading phase, the force obtained in the MD simulations agrees with that of the JKR model. However, the force at the unloading becomes smaller than that at the loading phase. This difference shows the hysteresis of the collisional process, which indicates the energy dissipation. Figure 3 shows the COR as a function of the impact velocity for the collisions between monomers with R/σ = 147. First, we find that the COR of MD simulations is smaller than that of the JKR model. This suggests that collisional kinetic energy is more dissipated in the MD simulations than in the JKR model. The decrease in collisional kinetic energy is converted to the molecular random kinetic energy and potential energy. The change in potential energy means the deformation. Second, we find that the COR has a peak. The decrease in COR appears in only the MD simulations because the feature comes from the significant monomer deformation, which is out of scope of the JKR model. The strong plastic deformation causes large energy dissipation and makes the COR small.

The small COR of the MD simulations suggests dissipative effects caused by molecular motions, which promote the sticking of monomers. The viscosity is not included in DEM simulations. Then, we suggest a new dissipation model, which has a resistance force proportional to the relative velocity between monomers and the contact radius. The dissipation force also depends on the pressure at the center of the contact surface exponentially. We fit the COR of the MD simulations and obtain the appropriate formula. The blue line in Fig. 3 shows the new model, and we can see that the model reproduces the MD simulations well for the low impact velocity. For the high impact velocity, the modeled COR is higher than that of the MD simulations since the model cannot reproduce the energy dissipation due to the strong plastic deformation. The model is a formulation of viscous resistance and cannot represent the physics of deformation.

In this presentation, we show and discuss the above results.