[M-GI30] Computational sciences on the universe, galaxies, stars, planets, and their environments

[MGI30-P05] Dust monomoer interaction explored by Molecular Dynamics Simulation: an extension of JKR theory

*Yuki Yoshida¹, Eiichiro Kokubo², Hidekazu Tanaka³ (1.University of Tokyo, 2.National Astronomical Observatory of Japan, 3.Tohoku University)

Keywords:planetesimal formation, dust growth, molecular dynamics simulation

Dust in protoplanetary disks is the material of planets. Initial dust is called a monomer whose size is smaller than μm, and monomers coalesce to form aggregates. Intermolecular forces dominate the growth of dust below cm-size, and the gravity is important for the growth of planetesimals to form planets. However, neither force is dominant in intermediate-size dust growth, and the growth process is not yet understood. To understand the growth by direct coalescence, it is important to know the physics of dust collisions. Numerical simulation studies have been performed to investigate the probability of coalescence in collisions, the critical velocity of dust compression and disruption, and the dust size evolution (e.g., Wada et al. 2008,2013; Suyama et al. 2008,2012). The numerical simulations used a contact theory called JKR theory to calculate the interactions between monomers in contact. However, differences between simulation results and experimental results have been reported. In monomer or aggregate collision experiments, the bouncing velocity is larger than the theoretical value and the temperature dependence was reported (e.g., Poppe et al. 2000, Blum & Wurm 2000, Wada et al. 2008). It has been pointed out that the difference between the numerical calculations and laboratory experiments is due to the energy conversion to molecular motion that occurs during the dust collision process (Krijt et al. 2013; Tanaka et al. 2015). The JKR theory does not take into account microscopic physics such as energy conversion due to molecular motion, and an extension of the JKR theory including microscopic physics is needed. Molecular dynamics (MD) simulation is an effective method to investigate the microscopic physics, which solves the N-body problem of molecules by constructing an bulk with many molecules. Previous studies that investigated particle collision using MD simulations used the model parameters outside the range of the protoplanetary disk, such as excessive collision velocities and underestimated sizes (e.g., Takato & Sen, 2014; Takato et al. 2015; Nietiadi et al. 2017). In addition, they simulated the head-on collisions with fixed temperatures, and the temperature dependence of the collision process has not yet been investigated.
In this study, we use MD simulations to reproduce monomer collisions. We simulated the head-on collisions of monomers and investigated the dependence of the coefficient of restitution on the monomer size, the impact velocity, and temperature. The results show that the coefficient of restitution increases with the monomer size and that it has a peak at ~50 m/s. It can be confirmed that the monomer is deformed in the high-velocity collisions, and this plasticity weakens the repulsive force at the contact area and decreases the coefficient of restitution. In terms of energy, we confirmed that the bulk kinetic energy changed to molecular kinetic energy and potential energy. We also found that monomers are inclined to coalece at higher temperatures.
Next, we attempted to extend the JKR theory. We tested that the extended model adding dissipative forces to the JKR theory could reproduce the results of MD simulations. The dissipative force is considered to be a viscous resistance proportional to the contact radius and relative velocity between monomers (Brilliantov et al. 1996, 2007, Krijt et al. 2013), but its validity has not been confirmed. We considered the dissipative force model varying the dependence on contact radius and relative velocity. We found that a dissipative force model proportional to the cube of the relative velocity and the 3/2 power of the contact radius reproduced the MD calculation well. However, for high-velocity collisions, other energy dissipation is required to reproduce the MD simulations.