3.1.1. Polystyrene

For polystyrene simulation, 322 atoms in 1 cell (total 10 cells) were drawn using Avogadro and are shown in Figure 2. We optimized the atoms in Avogadro, and converted the modeling file to the LAMMPS data file.

#### 3.1.2. Fluorinated Polystyrene

For the fluorinated polystyrene simulation, we substituted the benzene ring of polystyrene with fluorine to evaluate the radiation enhancement. We optimized the atoms in Avogadro with the UFF force field and converted the modeling to the LAMMPS data file.

#### *3.2. Reactive Molecular Dynamics Simulation*

The scission rate was calculated using molecular dynamics simulations to evaluate the radiation resistance of polystyrene and fluorinated polystyrene. These materials were simulated using the LAMMPS code. We applied the reactive hydrocarbon potential AIREBO developed by Brenner for polystyrene and reactive force field potential (ReaxFF) developed by Van Duin et al. for fluorinated polystyrene [18,19].

High-energy particle irradiation has often been simulated using molecular dynamics codes such as LAMMPS and PARCAS, for instance, in the study of Beardmore et al. [20,21]. The high-energy particle irradiation to material is simulated by applying the interaction between the particles, the colliding electron, and the lattice atom. This method was studied by giving initial kinetic energy, the recoil energy, to some randomly chosen atom in the lattice [22–24].

However, this study simulated the interaction between γ-rays and atoms by providing γ-ray energy in a specific area of the chain of polymers. We converted the γ-ray energy to the velocity of the primary knock-on atom (PKA) that existed in a randomly chosen area (included recoil atom) and calculated the scission rate of each bond. This approach is suitable for investigating the scission rate of each bond during initial energy conversion.

The energy of the γ-ray was 1332 keV, and we converted it to a momentum term to calculate the velocity of the initial primary knock-on atom. The momentum of the initial primary knock on the atom was calculated using the following equation:

$$P = \frac{E}{c} \tag{1}$$

where *c* denotes the velocity of light. The initial velocity was calculated by the equation:

$$P = mv, \quad v = \frac{E}{mc} \tag{2}$$

where *m* is the mass of the initial primary knock-on atom. We assumed that all of the γ-ray energy converted to the kinetic energy of the primary knock-on atom. The calculated velocity was 274 Å/ps for the carbon atom. The direction of the momentum was the same direction as γ-ray.

The second assumption was that we selected the shape of the applied velocity area sphere where collision cascade occurs. The radius of the area was 1.6 Å, which is the C-C bond length. This area was increased by increasing the absorbed dose. We applied this assumption by the equation:

$$D\_n = \frac{N\_d}{N} = \int\_0^t \int\_0^\infty \int\_{E\_d}^{T\_{\text{max}}} \mathcal{Q}(E, t) \frac{d\sigma(E, T)}{dt} \mathbf{y}(T) d\mathbf{T} d\mathbf{E} dt \tag{3}$$

where *Dn* denotes the probability of displacement atoms, *N* denotes number density of the material, *Nd* denotes the number of displaced atoms per unit volume, *t* denotes irradiation time, <sup>∅</sup>(*E*,*<sup>t</sup>*) denotes flux of incident particle, *<sup>σ</sup>*(*E*,*<sup>t</sup>*) denotes scattering cross-section, γ(*T*) denotes the number of atoms displaced from origin position by PKA, *E* denotes the initial energy of the incident particles, *T* denotes transferred energy, *Ed* denotes the energy of the displaced atom and *Tmax* is maximum energy transferred to PKA. In the simulation, the initial energy of the incident particle (*E*) was fixed by the value of conversion energy of γ-ray as the first assumption because the radiation intensity was set by the energy of γ-ray (1332 keV). The flux of incident particle was increased proportionally to the absorbed dose, so we increased the PKA region (collision cascade zone) proportional to the absorbed dose. Because increasing absorbed dose means that increasing the number of atoms displaced from origin position (γ(*T*)) is proportional to the flux of incident particles, including the irradiation time. The number of atoms displaced from the original position and their velocity by PKA are shown in Figure 4.

The absorbed dose of polystyrene and fluorinated polystyrene was 25, 50, 75, 100 kGy in the experiment. We increased the radius of the PKA area proportional to the absorbed dose, and they were 1.6, 2.3, 2.8, and 3.2 Å in the simulation. We optimized the geometry of each material, and the simulation time was one ps. We checked the distance of each atom at 10 cells after the 1 ps-the collision process and compared them with the bond break length (1.8, 1.09, and 1.35 Å for C-C, C-H, and C-F bond) to obtain the scission rate for each bond.

**Figure 4.** Snapshots of the displaced atoms' velocity vector (conversion of γ-ray energy to kinetic energy-collision in the cascade zone) at the polymers @ 1 ps with increasing the PKA radius.
