In current research, atoms inside a Pbbased buckyballs and uraniumbased compounds interact with each other during t = 0.1 fs time steps for 10 ns. Technically, all atomic models were simulated via 2021 version of LAMMPS software [21–23]. By using this package, uraniumbased structures simulated as U, O, Na, and F atoms as depicted in Fig. 1 which visualized by ... version of OVITO graphical package[24]. Our MD simulation box has 150 Å lengths in x, y, and z directions. Periodic boundary conditions were used in all directions. Considering the importance of interatomic potential in MD simulation results, the Universal Force Field (UFF) and Embedded Atom Model (EAM) has been applied in the representation of atombase compounds to perform interaction between particles inside computational box [25–27]. In UFF forcefield, possible energy for atomistic samples is represented by a superposition of the bonded and nonbonded forces. Theoretically, nonbonded forces calculated by LennardJones (LJ) potential as Eq. (1) [28],
\({\phi _{}}({r_{ij}})=4{\varepsilon _{}}\left[ {{{\left( {\frac{\sigma }{{{r_{ij}}}}} \right)}^{12}}  {{\left( {\frac{{{\sigma _{}}}}{{{r_{ij}}}}} \right)}^6}} \right]\) \({r_{ij}} \leqslant {r_c}\) (1)
here, ε parameter describes the depth of the potential function well, σ parameter describes the distance at which the potential ratio converged to zero, and distance between various particles in modeled samples is resented by rij. In LJ formalism, cutoff parameter is shown with rc,. This computational parameter set to 12 Å [25]. These described parameters in this section listed in Table 1 [25]. Furthermore, bonded term of UFF function don’t implemented in current work. This simplification in our simulations due to the lack of bonding force in modeled structures.
Table 1
The length and energy constants for LJ potential in simulated models [25].
Element

ε(kcal/mol)

σ(Å)

Pb

0.663

4.297

O

0.060

3.500

U

0.022

3.395

Na

0.030

2.983

F

0.050

3.364

He

0.056

2.362

Also, buckball’s particles interaction defined with EAM forcefield which formulated as Eq. (2) [26–27]:
$${E}_{i}={F}_{\alpha }\left(\sum _{i\ne j}{\rho }_{\beta }\left({r}_{ij}\right)\right)+\frac{1}{2}\sum _{j\ne i}{\phi }_{\alpha \beta }\left({r}_{ij}\right)$$
2
where, F constant is the embedding energy which is a function of the atomic electron density ρ, φ is a pair potential interaction, and α and β are the element types of atoms i and j. To describe the atomic displacement, Newton’s formalism at the nanoscale systems is applied as the gradient of the forcefield function [29–30],
$${F_i}=\sum\limits_{{i \ne j}} {{F_{ij}}={m_i}\frac{{{d^2}{r_i}}}{{d{t^2}}}={m_i}\frac{{d{v_i}}}{{dt}}}$$
3
$${F_{ij}}={\text{ }}  grad{\text{ }}{V_{ij}}$$
4
After forcefield defining, computational ensemble used to initial conditions in current simulations. The NPT algorithm is implemented in our atomistic simulations to equilibrate the pressure and temperature of modeled samples [31–32]. This computational algorithm equilibrates the defined structures at T0 = 300 K and P0 = 0 bar with 0.01/0.1 damping ratio for temperature/pressure parameter.
After simulation settings defining in MD box, simulations in this computational study carried out as fellow:
Step 1: The uranium compound with/without Pbbased buckyball was simulated with UFF/EAM forcefield and equilibrated by NPT algorithm for 5 ns. For this purpose, atomic structures temperature and pressures set at 300 K, and 1 bar, respectively. After, atomic equilibrium phase, the physical stability of simulated structures reported by the temperature and total energy calculating.
Step 2: Next, atomic interaction between uraniumbased compound and free He atom (detector) calculated for 50000000 time steps (5ns). Computationally, in our simulation NVE ensemble used with/without Pbbased buckyball [33–34]. After atomic interaction occur, physical parameters such as: kinetic energy, interaction energy, interaction force, and structure volume are reported to describe the atomic behavior of buckyball compound for radiation protection process. Our computational study details listed in Table 2.
Table 2
MD simulation settings inside computational box.
Computational Parameter

Value/Setting

Computational Box Length

150×150×150 Å3

Boundary Condition

Periodic

Initial Temperature

300 K

Initial Pressure

1 bar

Time Step

1 fs

Temperature Damping Ratio

0.01

Pressure Damping Ratio

0.1

Equilibrium Time

5 ns

Total Simulation Time

10 ns
