**4. Results**

#### *4.1. Simulation Results*

The bond break lengths of each bond are 1.8, 1.09, 1.35 Å, corresponding to C-C, C-H, and C-F bonds, respectively. We obtained the distance of each bond at 1 ps after applying the velocity, which is shown in Figure 4. The maximum number of bond dissociations (@ 1 ps) for polystyrene and fluorinated polystyrene are listed in Tables 1–3.


**Table 1.** Maximum dissociation number of each bond in polystyrene @ 1 ps.

**Table 2.** Maximum dissociation number of each bond in 1F-PS (poly(4-fluorostyrene)) @ 1 ps.


**Table 3.** Maximum dissociation number of each bond in 5F-PS (poly(2,3,4,5,6-pentafluorostyrene)) @ 1 ps.


The dissociation rate was calculated at the maximum dissociation number. The maximum dissociation rate region was 3 (#/kGy) from 25 to 50 kGy at polystyrene, 1.96 (#/kGy) from 25 to 50 kGy at the 1F-PS (poly(4-fluorostyrene)), and 2.84 (#/kGy) from 50 to 75 kGy at the 5F-PS (poly(2,3,4,5,6-pentafluorostyrene)).

The average dissociation number of each bond at 1 ps in polystyrene for 10 simulations is shown in Figure 5. The dissociation of C-C bonds is less than that of C-H bonds in polystyrene, implying that the scission rate of the backbone in polystyrene is less than that of other bonds.

In 1F-PS (poly(4-fluorostyrene)), the dissociation number of C-C bonds is also less than that of C-H and C-F bonds. The dissociation of C-F bonds occurred, as shown in Figure 6.

The average dissociation number of each bond at 1 ps in 5F-PS (poly(2,3,4,5,6-pentafluorostyrene)) is shown in Figure 7. Dissociation did not occur up to 25 kGy. The dissociation number of C-C bonds was higher than that of C-F and C-H bonds.

We did not compare the dissociation number of each bond in the polymers because the total number of C-H and C-F bonds are different for each polymer. However, the total dissociation number was comparable for radiation resistance according to the same atom number. The 5F-PS (poly(2,3,4,5,6-pentafluorostyrene)) had the lowest dissociation number, as shown in Figure 8.

**Figure 5.** Average dissociation number of each bond in polystyrene at 1 ps.

**Figure 6.** Average dissociation number of each bond in 1F-PS (poly(4-fluorostyrene)) at 1 ps.

**Figure 7.** Average dissociation number of 5F-PS (poly(2,3,4,5,6-pentafluorostyrene)) at 1 ps.

**Figure 8.** Total dissociation number of polymers.

#### *4.2. Comparison with Experiment Results*

We applied the scission rate by considering the mass of each atom for comparison with the gel permeation chromatography results. The results of polymers' average molecular weight (Mn) are shown in Figure 9, and the ratio of differential average molecular weight (Mn) of the irradiated polymers are summarized in Table 4. The values of Mns were different for each polymer. We applied the ratio of changes to compare the radiation resistance of each polymer. The ratio was calculated by standardizing the initial Mns value.

**Figure 9.** The polymers average molecular weight after irradiation (experiment results).



In the process of the experiment (measuring average molecular weight by gel permeation chromatography after irradiation), both the scission and crosslinking processes had happened. The initial average molecular weights of polymers are 25,651.0, 27,468.3, 56,011.0 for PS, 1F-PS, and 5F-PS. The average molecular weight of PS increased to 28,129.0 at 100 kGy. In the case of polystyrene fluoride, the average molecular weight of 1F-PS increased to 29,691.5 at 50 kGy, decreased to 29,540.0 at 100 kGy, and the average molecular weight of 5F-PS increased to 57,630.0 at 25 kGy and decreased to 54,345.5 at 100 kGy. However, the scission process should be done before crosslinking process. So we assumed that the change of average molecular weight was dominant by the scission process. We normalized the difference of average molecular weight by matching the initial average molecular weight to zero, and then we calculated the absolute difference between the initial average molecular weight and after the irradiation as shown in Figure 10 [25–27]. We compared these differential values with the simulation results of the scission rate. Equations (4) and (5) are being applied for comparison.

$$\text{av (scission rate)} = \frac{N}{m} \tag{4}$$

$$
\delta(\text{Ratio of Difference} \mid \text{Mn}) = \left(\frac{1}{M\_0} - \frac{1}{Mn}\right) \times N \tag{5}
$$

where *m* denotes the mass of bonds, *Mn* denotes the number average molecular weight after irradiation, *M*0 denotes the initial average molecular weight, and *N* is the differential

number: the ratio between the average molecular weight of atoms (experiment results) and atom number (simulation value) after irradiation. The scission rates of the bonds which were simulated in the polymers are shown in Figures 11–13.

**Figure 10.** The polymers normalized average molecular weight after irradiation (experiment results).

**Figure 11.** Scission rate of C-C bond of polymers.

**Figure 12.** Scission rate of C-H bond of polymers.

**Figure 13.** Scission rate of C-F bond of polymers.

The scission rate of the C-C bond was the highest in the polystyrene. The value of the scission rate was increased sharply in the region of 25 to 50 kGy for polystyrene and 1F-PS and 50 to 75 kGy for 5F-PS. These results were similar with the maximum dissociation rate region, which were 3 (#/kGy) from 25 to 50 kGy at the polystyrene, 1.96 (#/kGy) from 25 to 50 kGy at the 1F-PS, and 2.84 (#/kGy) from 50 to 75 kGy at the 5F-PS.

This relation was also investigated in the gel permeation chromatography results. The difference of Mn was the highest in the region of 25 to 50 kGy for polystyrene and 1F-PS. However, it is different in the 5F-PS case. This means that the dominant scission happened in the C-C bond for polystyrene and 1F-PS.

The scission rate of the C-H bond was also the highest in the polystyrene. The value of the scission rate was increased linearly in the region of 0 to 50 kGy for polystyrene and 1F-PS and 75 to 100 kGy for 5F-PS. The increment of the scission rate was decreased after 50 kGy for polystyrene and 75 kGy for 1F-PS, 5F-PS.

The scission rate of the C-F bond in the 1F-PS was higher than 5F-PS until 75 kGy. The scission process did not happen until 25 kGy in the 5F-PS. The number of C-F bonds in 5F-PS is 5 times larger than 1F-PS. However, the scission rate of C-F bonds in 5F-PS was similar to 1F-PS.

The total scission rate of PS was higher than 1F-PS, 5F-PS in the simulation. The results of the scission trend of PS, 1F-PS was similar with the measured value, particularly until 50 kGy. The measured value was decreased after 50 kGy.

In the case of 5F-PS simulation, the scission did not happen until 25 kGy in the simulation. However, the measured value was increased until 25 kGy, and the rate of increase was the minimum in the data. The simulation results were compared with the experimental results and shown in Figure 14.

**Figure 14.** Total Scission Rate.

## **5. Discussion**

The radiation enhancement effect with fluorine in the polystyrene has been determined by atomistic simulations to predict the possibility of using this method for modeling and simulation, which is irradiation reactions that occur in these materials.

The fluorinated PS backbone is made up of carbon–carbon bonds and the pendant groups are carbon-fluorine bonds. Both are extremely strong bonds. The basic properties of fluoropolymers from these two very strong chemical bonds. The quantity of the fluorine atom can be affected the crystallinity of PS and continuous covering around the carbon– carbon bonds and protect them from chemical attack, thus imparting chemical resistance and stability to the molecule.

In these polymers, chain scission (scission of C-C) was the primary reaction. The number of dissociation was increased proportionally with the absorbed dose. The ratio of increment of atoms in the simulation was the same with the measured (Mn) value.

5F-PS was found to be more resistant to radiation damage than 1F-PS and polystyrene. The benzene ring can be considered to act as a very efficient trap for F atoms due to the

so-called cage effect. So, the F atoms are formed in an efficient cage of benzene molecules; the reactions (6) and (8) can predominate over reaction (9).

$$
\sim \mathcal{C}\_6 \mathcal{F}\_5 \quad \to \quad \sim \mathcal{C}\_6 \mathcal{F}\_4 \bullet \quad \text{F} \bullet \tag{6}
$$

$$\sim \mathcal{C}\_6 \mathcal{F}\_5 + \text{ F}\bullet \rightarrow \sim \mathcal{C}\_6 \mathcal{F}\_6 \bullet \tag{7}$$

$$\mathbf{R}\bullet + \sim \mathbf{C}\_6 \mathbf{F}\_5 \to \mathbf{R} \mathbf{C}\_6 \mathbf{F}\_5 \bullet \;/\; \mathbf{R} \bullet = \sim \mathbf{C}\_6 \mathbf{F}\_4 \bullet \;/\; \sim \; \mathbf{C}\_6 \mathbf{F}\_5 \bullet \;/\; \sim \; \mathbf{C}\_6 \mathbf{F}\_5 \mathbf{C}\_6 \mathbf{F}\_4 \bullet \;/\; \tag{8}$$

$$\text{R}\bullet + \text{R}\bullet \to \text{ RR} \tag{9}$$

$$\text{R}\bullet + \text{ F}\bullet \rightarrow \text{ RF} \tag{10}$$

$$\rm{F\bullet} + \rm{F\bullet} \rightarrow \rm{F}\_2 \tag{11}$$

The simulation results were reasonable especially calculating the scission ratio, and predicting the radiation resistance of aromatic fluorocarbon. In the simulation, we assumed that the absorbed dose of polystyrene and fluorinated polystyrene relatively increased cascade area 1.6, 2.3, 2.8, and 3.2 Å. In this assumption, we converted the whole energy of γray to the kinetic energy of atoms which were participated in the cascade. We expected that the experiment results were different from the simulation results because of the difference between the average molecular weight of atoms (experiment results) and atom number (simulation value). However, we coupled the simulation results with the scission rate and differential ratio of Mn (the number of molecular weight) and figured out that the trend of scission rate was similar in the results comparing the simulation data and experimental data. In this study, the scission process was only considered to predict the effect of fluorine. We will update this method with the crosslinking process to overcome the unforeseeable circumstances—prediction of radiation enhancement before the irradiation.
