Conventional polymer force-fields, such as COMPASS, CVFF, CHARMM, and AMBER, are inadequate for simulating the breakage and formation of bonds. Hence, they are unsuitable for examining the impact of AO on polyimide materials. In this study, we employed the ReaxFF force-fields proposed by van Duin et al. Compared to conventional force-fields, ReaxFF determines the connectivity between atoms by calculating the bond order based on the interatomic distances. As chemical bonds break and form, the connectivity between atoms is continuously altered, allowing the simulation of bond breakage and formation throughout the process. Similar to empirical non-reactive force-fields, ReaxFF divides the total energy of the system into different energy contributions. The total energy is expressed by the following equation (van Duin et al., 2001): E s y s t e m = E b o n d + E t r i p l e + E C 2 + E v a l + E p e n + E t o r s + E l p + E c o a + E c o n j + E o v e r + E u n d e r + E H − b o n d + E v d W + E C o u l o m b Where, E_system is the total system energy, E_bond is the bond energy term, E_triple is the triple bond energy correction term, E_C2 is the triple bond energy penalty term, E_val is the valence angle energy term, E_pen is the bond angle energy penalty term, E_tors is the torsion angle energy term, E_lp is the lone pair energy term, E_coa is the three-body conjugate effect energy term, E_conj is the four-body conjugate effect energy term, E_over is the over alignment energy correction term, E_under is the under alignment energy correction term, E_H-bond is the non-bonding hydrogen bonding interaction term, E_vdW is the van der Waals energy, E_coulomb is the Coulomb energy.

In this equation, all the connectivity-dependent parameters, such as angle and torsion, are related to the bond orders, which are calculated based on the interatomic distances and updated at each iteration. Compared to non-reactive force-fields, ReaxFF calculates non-bonding interactions between each pair of atoms, regardless of their connectivity. The coulomb and van der Waals energy terms incorporate shielding terms to eliminate excessive non-bonding interactions (van Duin et al., 2001; Rahnamoun and van Duin., 2014). More detailed information regarding the ReaxFF is provided in the article by van Duin et al. (2001).

In the present study, the ReaxFF force-field parameters set (CHONSi-2014) proposed by Rahnamoun and van Duin. (2014), including H, N, C, and O elements, were used to simulate the AO impacts on Kapton and Upilex-S. This ReaxFF parameter set has been applied to successfully simulate AO effects on various polymeric materials, including polyimide, yielding reliable research outcomes (Rahnamoun and van Duin., 2014; Zeng et al., 2015; Kim and Choi, 2021).

Simulation models for Kapton and Upilex-S were established prior to the AO impact simulations. The process of constructing the AO erosion models for Kapton and Upilex-S is illustrated in Figures 1, 2. Specifically, we first created monomeric structures for Kapton (C₂₂H₁₂O₅N₂) and Upilex-S (C₂₂H₁₂O₄N₂). Thereafter, 50 Kapton monomers with a total of 2050 atoms and 50 Upilex-S monomers with a total of 2000 atoms were separately placed in cubic boxes to form amorphous models with an initial density of 0.1 g/cm³. The systems were then subjected to a 2 ns NPT (constant atomic number, N; constant pressure, P; constant temperature, T) simulation at atmospheric pressure and room temperature (300 K). The pressure and temperature were controlled using a Berendsen barostat and a Nosé–Hoover thermostat (Evans and Hoian, 1985), respectively. Using the NPT simulation, the volume of the cubic boxes was gradually reduced to stabilize the densities of the Kapton and Upilex-S models at approximately 1.389 and 1.333 g/cm³, respectively, as shown in Figure 3 (close to the actual material densities). The final dimensions of the Kapton and Upilex-S models were 28.5 Å × 28.5 Å × 38.8Å and 28.1 Å × 28.1 Å × 38.2Å, respectively. Table 1 provides detailed information regarding the two models.

After constructing the initial models of Kapton and Upilex-S, MD simulations of AO impact on Kapton and Upilex-S were performed separately using the LAMMPS software. The main process consists of three steps. First, to allow for the insertion of AO, the dimensions of the models in the z-direction were expanded to increase the vacuum region of the surface. Periodic boundary conditions were set in the x- and y-directions of the simulation box, whereas the z-direction was set as a fixed boundary condition. Second, the system was subjected to energy minimization using the conjugate gradient method (Štich et al., 1989), and run for 30 ps under NVT (constant atomic number, N; constant volume, V; constant temperature, T) conditions at 300 K until a dynamically stable structure with a temperature equilibrium of approximately 300 K was attained for both Kapton and Upilex-S. Third, the system was switched to the NVE (constant atomic number, N; constant volume, V; constant energy, E) simulation, and 150 AOs were randomly inserted at a distance of 74 Å from the material surface at intervals of 200 fs. To simulate the AO impact, the randomly inserted AOs were assigned a velocity of 0.074 Å/fs (∼4.5 eV) in a direction perpendicular to the material surface. The time step is set to 0.1 fs, and a total of 300,000 steps (∼30 ps) are run under NVE conditions. To prevent a downward drift of Kapton and Upilex-S during the AO impact simulation, the bottom layer of the material was fixed at a height of 10 Å and did not participate in the reaction. The output of the disintegration products was obtained using the “reaxff/species” command in LAMMPS. Atoms were visualized using the Ovito software. A Python program was written to statistically analyze the quantity of the surface dissociation products. Notably, owing to the high computational cost of ReaxFF MD, the number of AO impacts and monomers in the model was determined based on prior experience by Rahnamoun and van Duin, as well as the thickness of the non-penetrating model after AO impact.

The reaction simulations in the NVE condition are simulations of a non-equilibrium state, indicating that the system is not in an equilibrium state during the 150 AO impact process. In the NVE condition, a random AO with an energy of 4.5 eV was vertically introduced onto the surface of Kapton and Upilex-S along the z-direction every 200 fs, corresponding to an incident AO dose rate of 5 AO/ps. Each material was subjected to the AO impact for 30 ps (150 AOs). Figures 4, 5 illustrate the structural evolution of Kapton and Upilex-S under the AO impact. During the initial stage of the impact, most AOs are adsorbed onto the surfaces of both materials without undergoing any reaction, and only a few AOs are deflected. In the later stages, the erosion of both materials by AO progresses from the surface toward the interior. The matrix that reacts with the AOs possess a loose structure, whereas the matrix that does not react with the AOs undergoes minimal structural changes. Furthermore, more reaction products separated from the surface of Kapton than from the surface of Upilex-S throughout the AO impact process. The resistance of the two materials to AO was investigated by analyzing the temperature variation, mass loss, decomposition products, erosion yield, and damage propagation depth (DPD) under the AO impact.

In contrast to non-reactive force-fields that can only simulate physical dissociation, reactive force-fields can simulate both chemical and physical dissociation of polymeric materials (Fu et al., 2021). High-speed AO transfers its kinetic energy to the system upon impact, thereby increasing the system temperature. Figure 6A represents the temperature evolution of the Kapton and Upilex-S materials under the AO impact, and illustrates that the temperature of both materials increases almost linearly with the AO impact. The final temperatures of the two materials range from 1,800 to 2,000 K, exhibiting no significant differences. The temperature evolution of AO bombardment on the surface and interior region of Kapton and Upilex-S are respectively illustrated in the Figures 6B, C, which reveals that the temperatures of the interior and surface of the two materials are generally increased in a linear way. However, the temperature of the eroded surface is evidently higher than that in the interior region at any random moment. Figures 7A, B depict the mass changes of the two materials under the AO impact. Within a timeframe of 0–6 ps (0–30 AOs), AO does not chemically react with the surface of either material. Instead, it physically adheres to the material surfaces, increasing their mass. This phenomenon has also been observed in other experimental (Duo et al., 2005) and simulated study (Rahnamoun and van Duin., 2014) on the impact of AO on Kapton. As the number of impacts with AO increases, the surface temperature of the material increases rapidly. This rapid increase in temperature causes strain on the bonds between atoms on the surface, which makes the chemical reactions between the impacting AOs and the surface material more facile. This results in greater release of products and rapid disintegration of the material, leading to rapid mass loss. Both Kapton and Upilex-S exhibit a trend of initial mass increase followed by a decrease. In a similar study where ReaxFF was utilized to investigate the effects of the AO impact on other polymers, Zeng et al. (2015) suggested that in the initial stages of impact, high-energy AO simply transfers energy to the targeted polymer, and as AO continues to collide with the material, the temperature steadily increases. When the surface atoms of the matrix begin to be released, the reaction of the subsequent incident AOs with the remaining matrix is intensified, resulting in accelerated mass loss. The combined observations in Figures 4, 5 and analysis of the data in Figures 7A, B are consistent with the findings of Zeng et al. Under the AO impact, the rate of erosion of both Kapton and Upilex-S accelerates rapidly with increasing temperature because higher temperature promotes the production of more active and reactive atoms, thus facilitating more extensive chemical reactions with the AOs.

Figure 7A illustrates that Kapton undergoes rapid disintegration and exhibits significant mass loss starting at 50 AO impacts. In contrast, Upilex-S begins to degrade rapidly and exhibits mass loss after 85 AO impacts, as shown in Figure 7B. Analyzation on the outcome of “reaxff/species” commands from LAMMPS software shows that, comparing with Kapton, more AOs are physically adsorbed on the surface of Upilex-S during the 6–17 ps impact timeframe. The detached surface products mainly consist of oxygen molecules formed by the interaction of AOs with the Upilex-S surface and other small molecules; therefore, no significant mass loss was observed for Upilex-S. The AO impact simulations utilized the NVE ensemble, representing an isolated system that does not exchange heat with its surroundings. In addition, owing to the limitations imposed by the size of the system and the number of atoms, it is generally accepted that the mass loss during the initial phase of the AO impact (0–20 ps, corresponding to the first 200,000 steps of the simulation) is the best indicator of the material performance under the AO impact. Considering the different initial masses of Kapton and Upilex-S, we normalized the mass of each material at any given time during AO impact by dividing it by the initial mass. This enabled us to compare the mass loss of the two materials, as shown in Figure 7C. Figure 7C reveals that during the initial phase of the AO impact, the increase in the mass of the two materials is approximately identical. However, in the later stages of the initial phase, Upilex-S exhibits a smaller mass loss than Kapton. This indicates that Upilex-S is more resistant to the AO impact than Kapton, which is consistent with the findings of the MISSE 2 experiment (De Groh et al., 2008). Both materials display a nearly linear decrease in the mass loss with the continued AO impact. After 150 AO impacts, the degree of mass loss of Upilex-S is similar that of Kapton. Combining with Figure 6 demonstrate that although the temperature changes of the two materials do not differ significantly, Upilex-S consistently maintains a slightly higher temperature than Kapton, particularly in the later stages, which could potentially explain why the mass loss of Upilex-S becomes similar to that of Kapton in the later stages of the AO impact.

The lower mass loss for Upilex-S than that of Kapton during the initial stage of the AO impact can be explained by the bond-dissociation energies (BDEs) (Luo, 2002). The key structural difference between Kapton and Upilex-S is the presence of an additional oxygen atom in Kapton, forming a “C–O–C” structure between the two benzene rings on the main chain. The BDE of the “C–O” bond in the “C–O–C” structure on the main chain is 313.8 kJ/mol (∼3.25 eV). In contrast, Upilex-S exhibits a “C–C” bond structure connecting the two benzene rings on the backbone, with a high bond energy of 478.6 ± 6.3 kJ/mol (∼5.02 eV). The other bond types in the two materials are identical. Consequently, Upilex-S is more stable under the AO impact than Kapton. Temperature is a macroscopic statistical result of the thermal motion of a large number of microscopic atoms. After the initial phase, as AOs continue to impact the two materials, the temperature increases continuously, leading to highly intense thermal atomic motion in the materials. Atoms with vigorous thermal motion readily react with AO, resulting in a significant mass loss for both materials during the later stages of the AO impact.

After the AO impact, the surface structure undergoes physical disintegration and chemical reactions, with the subsequent separation of the reaction products, resulting in mass loss. Identification and quantification of the reaction products over time present significant challenges in the experiment. However, The determination and quantification of the reaction products are essential parts of the MD ReaxFF research. First, reaction products are directly associated with the mass loss of the material. Furthermore, they provide in-depth insights into the disintegration induced by high-speed AO impacts. In this study, we identified and quantified the substances that were detached from the surface of the materials under the AO impact.

Whether Kapton or Upilex-S, the major small-molecule products that were detached from the surface under the AO impact include HO, O₂, CO, and H₂O. this is because that Kapton and Upilex-S contain the same types of elements and similar atomic bonds. Figure 8 shows the variation in the quantities of the four major products (HO, O₂, CO, and H₂O) over the simulation time. Observation of Figure 8 combined with analysis of reaction trajectory files using Ovito software founded that the hydrogen atoms on the benzene rings of both materials initially dissociate and then combine with AO to form hydroxyl radicals (HO), hydroxyl radicals are the dehydrogenation products of both polyimide materials under the AO impact. Comparison of Figures 8A, D shows that H₂O is generated after the formation of the hydroxyl radicals for both materials, In other words, Upon the impact of AO on both materials, hydroxyl radicals (HO) are initially generated. Subsequently, as AO continues to impact, the hydroxyl radicals combine with other hydrogen atoms released from Kapton and Upilex-S to form H₂O molecules. Hydroxyl radicals are precursors to the formation of H₂O molecules. Such a series of formation mechanisms of hydroxyl radicals and water molecules match with the experimentally observed reaction pathways between the reactive AO and hydrogen-containing polymers (Hansen et al., 1965; Medel et al., 2019).

Figure 8B shows the oxygen molecules generated from the surfaces of the two types of materials. One route involves the reaction of oxygen atoms produced from the C=O bond breaking of the imide rings with AO, resulting in the formation of oxygen molecules. Furthermore, O₂ molecules can be formed from the reaction of AOs on the material surface. The carbon atoms in the CO molecules originate from the decomposition of the imide and benzene rings in both Kapton and Upilex-S, As also deduced from Figure 8C, CO is the major reaction product in the AO oxidation process, which is consistent with the experimental observations (Ozawa et al., 2000; Xiao et al., 2010).

Figures 8A, B, D demonstrate that there is no significant difference in the amount of HO, O₂, and H₂O separated from the surfaces of the two materials under the same AO exposure conditions. However, Figure 8C shows that Kapton consistently produces a larger amount of CO than Upilex-S throughout the AO impact period. At the same time, Comparison of Figure 8C and Figures 8A, B, D shows that CO is generated noticeably later than HO, H₂O, and O₂. Based on these two observations, we conclude that there is a relatively lower oxygen atom content of the monomeric structure of Upilex-S than that of Kapton, leading to a deficiency in the oxygen atoms required for CO generation. With Kapton, the extra oxygen atoms responsible for the higher generation of CO molecules originate from the rupture of the C–O–C bonds in the main chain structure, which further supports the foregoing interpretation. Additionally, the observed order of generation of HO, H₂O, O₂, and CO aligns with the findings of previous studies.

To further analyze the reaction products, we counted the surface separation products of the two materials at the end of the AO impact by major small molecule separations (HO, O₂, CO, H₂O), carbon-chain dissociation products classified based on the carbon content and other dissociation products, and drew a pie chart as shown in Figure 9. The results presented in Figure 9 illustrate that the main small-molecule products, including hydroxyl radicals (HO), oxygen molecules (O₂), carbon monoxide (CO), and water molecules (H₂O), account for 71.5% and 75.4% of the total products from Kapton and Upilex-S, respectively. Upilex-S contains a higher proportion of the main small-molecule products than Kapton, while Kapton has a significantly higher amount of high-carbon-content macromolecular products. As mentioned in previous sections, the backbone of Kapton contains a “C–O–C” bond, while Upilex-S has a higher-energy “C–C” bond that connects the two benzene rings. Under the AO impact, the bond structure of Upilex-S is less prone to breakage, resulting in a lower production of high-carbon-content-macromolecules. Consequently, the mass loss of Upilex-S is insignificant.

The erosion yield is defined as the average mass or volume loss of a material induced by a single AO interaction and serves as an important indicator for studying the effects of AO interactions on spacecraft materials. The data obtained from MISSE 2 (De Groh et al., 2008) reveal that the average AO erosion yield for Kapton is 4.28 × 10⁻²⁴ g/atom, which is ∼3.35 times that of Upilex-S (1.28 × 10⁻²⁴ g/atom). In this study, Upilex-S exhibits a noticeable mass loss after 17 ps of AO exposure. So Table 2 lists the AO erosion yield of Kapton and Upilex-S from 17 to 20 ps. According to Table 2, it can be observed that the average erosion yield of Kapton is 2.6 times that of Upilex-S. Considering that in the low-Earth-orbit (LEO) environment, material degradation is influenced by AO and other environmental factors in space. Meanwhile, heat exchange with the external environment is not considered in this simulation. The stabilized density in the model is slightly lower than the density of the actual material. Additionally, limitations are imposed by the model size and number of atoms. Hence, the simulated erosion yield is deemed reasonable.

It is extremely difficult to experimentally characterize the AO penetration depth and AO-induced damage depths of the materials. However, MD simulations are effective for studying the AO penetration and damage propagation depths. To further analyze the degradation of Kapton and Upilex under the AO impact, we plotted the visual representations of the AO penetration depth using the Ovito software (Figure 10) and the number density distribution of AOs after 150 AO impacts (Figure 11). Figure 10 shows that AO penetration is deeper in Upilex-S than in Kapton. Furthermore, more AOs are retained in the Upilex-S matrix than in Kapton. Figure 11 confirms that the maximum penetration depths of the AOs in Upilex-S and Kapton are 22.9 Å and 15.8 Å, respectively. Additionally, Upilex-S has a higher AO number density and a higher peak value than Kapton. These findings indicate that Kapton is more stable than Upilex-S under the AO impact, contradicting the aforementioned findings in previous sections, while being in line with the notion that deeper AO penetration typically corresponds to more severe damage. Therefore, following the approach adopted by Rahmani et al. (2017), we further analyzed the damage propagation depth (DPD) of Kapton and Upilex-S after 150 AO impacts.

The DPD is determined by the change in the initial and final mass densities along the z-axis (parallel to the direction of the AO impact). It is defined as the distance between the initial surface and the depth where the final mass density starts to remarkably decrease compared with the initial mass density of the material. For the accuracy of the DPD results, we conducted two additional AO impact simulations separately for each material and calculated the average and standard deviation of the DPD based on the three AO impact simulations. Figure 12 presents the DPD of Kapton and Upilex-S induced by 150 AO impacts in the first simulation. Table 3 provides the average and standard deviation of DPD obtained from three simulations. It can be observed that the average DPD is 15.22 Å for Kapton and 12.02 Å for Upilex-S, indicating that Upilex-S is more stable than Kapton under the AO impact, which is consistent with the analysis of the normalized mass loss and major products. The observations in Figures 10, 11 are attributed to the low density of Upilex-S. Although the AO penetration depth is an important indicator, assessment of the AO resistance based solely on this factor may not produce reliable results, which is an interesting finding.