A reactive molecular dynamics simulation study to the

Computational Materials Science 154 (2018) 14–24

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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci

A reactive molecular dynamics simulation study to the disintegration of PVDF and its composite under the impact of a single silicon-oxygen cluster ⁎

Bin Yuana, Fanlin Zenga, , Chao Penga, Youshan Wangb,

T

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a

Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, People’s Republic of China National Key Laboratory of Science and Technology on Advanced Composites in Special Environment, Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, People’s Republic of China

b

A R T I C LE I N FO

A B S T R A C T

Keywords: Silicon-oxygen cluster Erosion Failure mechanism PVDF POSS

With the applications of polymers and their composites in aerospace industries becoming more and more common, it is of great significance to investigate their ultrahigh-speed particle erosion behaviors. Taking poly (vinylidene fluoride) (PVDF) and its composites containing polyhedral oligomeric silsesquioxanes compound (3,3,3-trifluoropropyl)8Si8O12 (FP-POSS) as the research objectives, this paper analyzed the failure process under the impact of a single silicon-oxygen cluster using reactive molecular dynamics simulations. Firstly, in terms of erosion surface morphologies and erosion rates, the influence of FP-POSS on the erosion resistance of PVDF matrix was analyzed. The results indicated that the erosion resistance of neat PVDF is poor, but the addition of FP-POSS can significantly enhance its erosion resistance performance and reduce its impact crater size and erosion rate. Then in order to understand these results, the movement and fracture processes of molecular chains in neat PVDF were investigated. The effect of constraints on the movement of molecular chains was analyzed, and two stages during the chain fracture process derived respectively from the cluster impact and the thermal degradation were also obtained. Finally, by calculating the gyration radii of molecular chains and the strain field distributions, the influence and the inner mechanism of FP-POSS on the erosion resistance of PVDF were further analyzed.

1. Introduction In space, the influence of ultrahigh-speed cosmic dust particles and atomic clusters on a spacecraft cannot be ignored. In 2002–2004, the international space station (ISS) detected the existence of cosmic dust smaller than 10 nm [1]. Cassini-Huygens Cosmic Dust Analyzer (CDA) also detected the particle which velocity is more than 200 km/s and diameter is smaller than 10 nm [2]. If the intelligent structural materials in a spacecraft were subject to ultrahigh-speed dust or dusty plasma erosion, the normal physical and mechanical properties of the materials will change, which will then deteriorate the spacecraft operation performance, accuracy and service life. Many studies using molecular dynamics (MD) simulations to model the particle-surface interaction have begun since 1960s [3]. As the computing performance develops, these studies are focused on not only the properties of inorganic materials [4–9], such as erosion yield, crater size, surface morphology, phase transition, plastic deformation, nucleation and initiation of micro-cracks and so on, but also those of polymers and organic molecular solids [10–12]. At present, many

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research articles about kiloelectronvolt (keV) particle impact have been published. Delcorte et al. [10,13–15] studied the mechanisms of energy transfer and material sputtering of polyethylene induced by keV projectiles using MD simulations. Smiley et al. [16] simulated the bombardment of benzene molecular solid by a series of 5-keV carbon projectiles from C6H6 to C180. In order to enable chemical reactions, Garrison et al. [17] performed the similar simulations using the AIREBO potential and obtained the amount of energy going into reactions, and the number of free and reacted H atoms. Some other articles have studied the atomic oxygen (AO) erosion using the ReaxFF force field. Rahnamoun et al. [18] studied the effects of AO impact on different materials and verified that adding silicon to Kapton can enhance the stability of the Kapton against AO impact. Rahmani et al. [19] showed that the mass loss, erosion yield, surface damage, AO penetration depth, and temperature evolution are lower for the polyimide (PI) systems with randomly oriented carbon nanotubes (CNTs) and graphene (Gr) or PI-grafted polyhedral oligomeric silsesquioxane (POSS) compared to those of the pristine POSS or aligned CNT and Gr systems at the same nanoparticle concentration. However, the impact mechanisms between

Corresponding authors. E-mail address: [email protected] (F. Zeng).

https://doi.org/10.1016/j.commatsci.2018.07.033 Received 7 May 2018; Received in revised form 5 July 2018; Accepted 15 July 2018 Available online 20 July 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.


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Fig. 1. Total six erosion models for neat PVDF and 10%FP-POSS/PVDF. Upper: the side view, lower: the top view. For each model, the clusters are respectively located at different locations and colored differently (green, yellow and pink).

2. Simulation methodology

cluster projectiles and polymers haven’t been completely explained, especially on the basis of the movement and fracture of molecular chains. It is commonly believed that when the kinetic energy of an incident particle is greater than the threshold energy Eth of the substrate material [20], the particle will destroy the surface, otherwise, will deposit or reflect. In other words, by controlling the incident cluster kinetic energy, the cluster-surface interaction can change from soft landing toward implantation [9]. This paper aims at analyzing the failure mechanism of poly(vinylidene fluoride) (PVDF) under ultrahighspeed cluster erosion and the effect of polyhedral oligomeric silsesquioxanes compound (3,3,3-trifluoropropyl)8Si8O12 (FP-POSS) on PVDF erosion resistance. Since the composition of cosmic dust is related to the space environment and silicates are the most common minerals in the solar system [21], the Si5O16 cluster is selected as an incident particle. The cluster velocity is assumed to be 20 km/s (823 eV), which is the common cosmic dust velocity and is much greater than the PVDF threshold energy Eth. In our previous work, several properties of binary mixtures of PVDF and POSS compounds have been researched by using MD simulations, such as miscibility, morphology, crystallization, piezoelectricity, mechanical properties and erosion effects of AOs [22–27]. PVDF is prone to be eroded by AOs, but with the incorporation of POSS, the atomic oxygen resistance of PVDF can be effectively improved [27]. Since the erosion effect of clusters cannot be explained by the summation of individual atoms, which is termed as ‘nonlinear effect’ [28], and the cluster has the properties intermediate between those of individual atoms and bulk material, the study of the cluster erosion is significant. In this work, firstly the substrates of neat PVDF and 10%FP-POSS/ PVDF (mass ratio of FP-POSS is 10%) were constructed, which could be considered as nano-films or coatings. These substrates were eroded once because there was only a single cluster to impact in the periodic boundary condition. Then the erosion results for the two materials were analyzed, and their crater sizes and erosion rates were compared. Finally, by analyzing the movement and fracture behaviors of PVDF molecular chains and the effects of FP-POSS on PVDF, the mechanisms of the erosion results were presented.

2.1. ReaxFF force field By numerically solving the Hamilton’s equations of motion, molecular dynamics (MD) simulations can calculate the motion parameters of atoms or molecules, such as force, position, velocity and acceleration. In order to simulate the bond cleavage and formation in a molecular system, the ReaxFF force field was used. This force field, proposed by van Duin and coworkers [29–33], can describe the reactions and meet the requirements of large molecular systems. It tends to be faster than Quantum Mechanics (QM) based methods and helps to bridge the gap in simulation scale separating QM and classical methods. It defines the relationships between bond lengths and bond orders, as well as bond energies and bond orders. Generally, it consists of nonbonded terms, covalent terms and specific terms. The nonbonded terms include van der Waals energy (EvdW), and Coulombic energy (ECou). The covalent terms include bond energy (Ebond), overcoordination energy (Eover), valence angle energy (Eangle) and torsion angle energy (Etors). For the specific terms (Especific), different versions of the ReaxFF force field can have different contents, depending on the research systems. That is,

Esystem = Ebond + Eover + Eangle + Etors + E vdW + ECou + ESpecific In this work, the 2008 version of the ReaxFF force field [33] was adopted, which is also used in LAMMPS software [34,35]. Its simulation parameters are the same as those in Ref. [27]. The specific terms in the version include lone pair energy (Elp), undercoordination energy (Eunder), penalty for ‘allene’-type molecules (Epen), angle conjugation (Ecoa), C2 correction (EC2), triple bond energy correction (Etriple), torsion conjugation (Econj) and hydrogen bond (EH). That is,

Especific = Elp + Eunder + Epen + Ecoa + EC2 + Etriple + Econj + EH

2.2. Simulation models In order to study the failure mechanism of PVDF and its composites containing FP-POSS under Si5O16 cluster erosion, a total of six erosion models were constructed, as shown in Fig. 1. They were respectively formed by two types of polymer substrates (neat PVDF and 10%FPPOSS/PVDF) and three Si5O16 clusters at different initial locations. For 15


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Fig. 2. Construction progress of the neat PVDF and 10%FP-POSS/PVDF substrates. Structure of (a1) CH3-CF3 monomer to form a PVDF chain, (a2) PVDF chain with a polymerization degree of 100, (a3) initial PVDF cell, (a4) neat PVDF substrate with an estimated thickness of 53.04 Å and PVDF simulation cell with a size of 42.36 × 42.36 × 150 Å3, (a5) expanded neat PVDF substrate with a size of 84.73 × 84.73 × 53.04 Å3, (b1) FP-POSS molecule (R = CH2CH2CF3), and (b2) expanded 10%FP-POSS/PVDF substrate with a size of 85.79 × 85.79 × 53.93 Å3. The gray-white balls represent H atoms, the gray-black balls represent C atoms, the blue balls represent F atoms, the orange balls represent Si atoms, and the red balls represent O atoms.

lengths in X and Y directions. As a result, the PVDF substrate contains 60 PVDF chains (36,120 atoms) with a size of 84.73 × 84.73 × 53.04 Å3, which is shown in Fig. 2a5. Here, the thickness of the substrate is an estimated value due to the uneven surface. With such a thickness, the substrate has a density of 1.680 g/ cm3 in 100 K, which is consistent with the experimental amorphous density of PVDF at 298 K (1.60 g/cm3 [37]). The process of constructing the 10%FP-POSS/PVDF substrate (mass ratio of FP-POSS is 10%) is quite similar. The structure of the FP-POSS molecule was shown in Fig. 2b1. The simulation cell of 10%FP-POSS/ PVDF contains 56 PVDF chains and 36 FP-POSS molecules (37,312 atoms) with a cell size of 85.79 × 85.79 × 150 Å3, which is shown in Fig. 2b2. The estimated thickness of the substrate is about 53.93 Å. With such a thickness, the substrate has a density of 1.684 g/cm3 at 100 K, which is close to that in neat PVDF. Fig. 3 shows the structure of the Si5O16 cluster, which was also geometrically optimized in the COMPASS force field. Since the cluster is instantly neutralized as they approach the polymer surface, there is no need to consider their electrification [12].

the convenience of modeling, Materials Studio software and the COMPASS force field were used during the construction of the substrates. The Compass force field is very powerful to simulate the mechanical and structural properties of polymers [36]. But unfortunately, it is not able to describe the procedure of bond breakage and bond formation. However, the impact process involves a large number of chemical bond cleavage and formation phenomena and the ReaxFF force field is particularly suitable in this case. Thus, LAMMPS software and the ReaxFF force field were used in the impact progress. The construction progresses of the two substrates are shown in Fig. 2. And the intermediate models of the neat PVDF substrate are shown in detail. The polymerization degree of a PVDF chain is 100, shown in Fig. 2a2. For the convenience of achieving a reasonable surface, the initial polymer cell was constructed in the condition that the molecular chains were not permitted to exceed the cell in Z direction. The initial cell is a 40 × 40 × 50 Å3 orthogonal hexahedron structure with a density of 2.0 g/cm3 and contains 15 PVDF chains (9030 atoms), shown in Fig. 2a3. Then a MD simulation using the COMPASS force field was performed on this cell for 100 ps with a time step size of 0.25 fs in the NPT ensemble at 100 K and 1 atm. Due to the application of a three-dimensional periodic boundary condition in the NPT ensemble, the upper and lower surfaces of the substrate will interact with each other and become unclear. Therefore, the following methods were used to reconstruct the surfaces. Keeping atomic positions of the polymer substrate unchanged, the Z direction of the simulation cell was extended to 150 Å, and that is, a 100 Å-high vacuum layer above the surface was added. Thus the size of the simulation cell became 42.36 × 42.36 × 150 Å3, and the substrate thickness became 53.04 Å. The model is shown in Fig. 2a4. After a 5 Å-thick atomic layer in the lower surface was fixed, another MD simulation was performed for 50 ps with a time step size of 1 fs in the NVT ensemble at 100 K to optimize the surface and structure of the system. Finally, in order to alleviate the impact effects from the X and Y periodic boundaries during the impact process, the substrate size was expanded by doubling the cell

2.3. Simulation details This paper simulated the process that a Si5O16 cluster perpendicularly impacts the substrate at an initial temperature of 100 K using the ReaxFF force field. Because the periodic boundary conditions in X and Y directions were applied in the simulation cell, the adjacent impacts would inevitably affect each other. Based on the fact, the number of incident clusters per unit area in neat PVDF and 10%FP-POSS/PVDF can be calculated, i.e. 0.0139 nm−2 and 0.0136 nm−2 respectively, which are quite close. Before the impact process, each model was energy-minimized and then equilibrated for 10 ps with a time step size of 0.1 fs in the NVT ensemble at 100 K. The main reason of re-equilibrium is the change of the force field from COMPASS to ReaxFF. When the surface was relaxed again, the estimated thicknesses of neat PVDF and 16


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terms of the atomic numbers and structures, the identified molecular chains were proved to be identical, which means the assumed cutoff radii are effective. These works were also performed in OVITO. 3. Results and discussion 3.1. Impact crater size Fig. 4 shows the key snapshots of 20 Å-thick slices of the two models (Fig. 3a and d) from 150 fs to 20 ps. Each slice symmetry plane passes through the corresponding cluster center. It can be seen that the impact crater shape and size vary with the simulation time, and the self-healing phenomenon is obvious especially in neat PVDF. Some molecular chains with a fixed end are dangled in a vacuum or adsorbed on the substrate surface. The crater of neat PVDF looks like a cone, which both depth and opening diameter are large. The 10%FP-POSS/PVDF presents a shallow crater since only a small amount of molecular fragments leave from its surface. According to their crater shapes and sizes, it is obvious that neat PVDF is more likely to be eroded and that the addition of FPPOSS can significantly enhance the resistance of PVDF to the erosion of Si5O16 clusters. In order to quantitatively compare the erosion results, the average crater size of three models for each material at 20 ps has been calculated. It is well known that the material volume increases with the temperature commonly. Since the temperatures of the two materials at 20 ps are different, it is not reasonable to compare their impact crater sizes directly. Then for mitigating the effect of temperature, the concept of free volume was used. Therefore, here the calculated crater size is equal to the difference between the total volume V0 actually occupied by atoms at the initial moment and the corresponding volume V at the current moment. The volume V0 and V were calculated by a surface construction algorithm based on the alpha-shape method of Edelsbrunner and Mücke [39], which is developed as a Construct Surface Mesh modifier in OVITO [40]. The average crater sizes of neat PVDF and 10% FP-POSS/PVDF are 11.9 and 3.8 nm3, respectively. The data show that the crater of 10% FP-POSS/PVDF is significantly smaller than that of neat PVDF, which is consistent with the observed results in Fig. 4.

Fig. 3. Structure of the Si5O16 cluster.

10%FP-POSS/PVDF substrates were respectively increased to about 56 Å and 54 Å. The collision simulations were performed in the NVE ensemble. The cluster appeared at a height of about 30 Å from the substrate upper surface with a velocity of 20 km/s. In order to improve the computational efficiency and extend the simulation time to 20 ps, the time step size was set to two values. In the initial 5 ps, the atomic kinetic energy was highly concentrated, so the step size was set to 0.05 fs. In the next 15 ps, the atomic kinetic energy had spread, so the step size was set to 0.2 fs. In addition, the 5 Å-thick atomic layer at the lower surface was still fixed throughout the simulation process. The 6 models in Fig. 1 show the initial impact state where the clusters impact the substrates at three different locations, respectively. All the models were constructed using the Amorphous Cell module in Materials Studio software packages from Accelrys Inc. All erosion simulations were performed in LAMMPS running on a multiprocessor workstation with 128 processors. These models were visualized in the OVITO software [38]. In order to identify the molecular chains and the product molecules at any time, the cutoff radii (or maximum bond lengths) between different atoms were assumed, which were listed in Table 1. Since the distances between atoms can vary with vibration, these assumed radii are greater than the equilibrium bond lengths calculated in Materials Studio. By comparing with the original constructed molecular chains in

3.2. Erosion rate In order to compare the mass loss of the two materials during the erosion process, their erosion rates have been analyzed. Here, the erosion rate (or sputtering rate) refers to the relative atomic mass of material loss per incident particle. Because the substrate is impacted by a single cluster, the erosion rate is the total mass of the atoms having left the material surface. If the distance between a leaving atom and surface atoms is greater than 4 Å, then we assume that the atom has left the surface or been eroded. Since the largest van der Waals force radius among all atoms is the equilibrium radius 2.1 Å between Si-Si atoms and the distance of 4 Å is about two times of this length, we think it is sufficient to consider the influence of Van der Waals force can be ignored. Fig. 5 shows the average erosion rate for each material as a function of time. The sudden increases of these curves are caused by the departures of large molecular fragments. The erosion rate curves show that the erosion starts at the same time (150 fs) as the clusters contact the substrate. The time is earlier than the start time of other simulations [27], which may be derived from the larger size and the higher kinetic energy (20 km/s) of the impact particles (Si5O16) simulated in this paper. Anyway, Fig. 5 shows that both the erosion growth rate and the final result of erosion rate of neat PVDF are greater than those of PVDF with FP-POSS. It also indicates that with the addition of FP-POSS molecules, the erosion resistance of PVDF is improved. Further, the cleavages of carbon bonds (including CeC, C]C, C^C) in molecular chains have been compared. Because the carbon bonds form the skelecton of molecular chains and most of them exist in the

Table 1 Assumed cutoff radii of molecular chains or product molecules. Element

Element

Equilibrium bond length/Å (calculated in the Materials Studio software)

Assumed cutoff radius/Å

C C C C C H H H H F F F O O Si

C H F O Si H F O Si F O Si O Si Si

1.53 1.10 1.39 1.39 1.80 0.74 0.92 0.95 1.46 1.42 1.42 1.59 1.21 1.67 2.19

1.65 1.6 1.55 1.45 2.3 0.8 1.15 1.05 1.5 1.5 1.42 1.85 1.3 1.75 2.2

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Fig. 4. Two 20 Å-thick slice models (Fig. 3a, d). Each slice symmetry plane passes through the cluster center.

perspective views of the entire neat PVDF simulation cell at 0 ps and 20 ps, where the molecular chains are distinguished by different colors. Fig. 7c shows a 20 Å-thick slice at the impact point at 20 ps. The conformations of molecular chains can be clearly observed from the figures. In order to analyze the movement and fracture of molecular chains more clearly, all the chains were divided into two groups, the undamaged (50 chains included) and the damaged (10 chains included).

PVDF chains, the cleavages of carbon bonds can directly characterize the fragmentations of the PVDF chains. Fig. 6 shows the ratio of the number of broken carbon bonds to the total number of initial carbon bonds. The 0 to 5000 fs time range ensures that all carbon atoms are in the simulation cell. It can be seen that the ratio in 10%FP-POSS/PVDF is significantly lower than that in neat PVDF. This indicates that the addition of FP-POSS reduces the cleavages of carbon bonds and improves the strength of the PVDF molecular chains, which is also consistent with the previous results we obtained from the analysis of the crater size and erosion rate.

3.3.1. Analysis of molecular chain movement Because of the molecular entanglements, the movements of the chains are complicated. In order to analyze the effect of intermolecular junction points on molecular movements, the effect of fixed points in a molecular chain on its own displacement has been analyzed. We make the assumption that if a molecular chain had only one atom or a few successive atoms that are fixed, the chain has a fixed constraint point. These fixed constraints originate from the 5 Å-thick atomic layer of the substrate lower surface. Fig. 8 shows the Z coordinates of the center of mass of the 50 undamaged PVDF chains as a function of time. The red, blue, and green curves respectively represent the chains with no fixed constraint point, a fixed constraint point and two or more fixed constraint points. The Z coordinates of the chains with more constraint

3.3. Movement and fracture of PVDF molecular chains The ultrahigh-speed erosion of the Si5O16 cluster can cause severe damage to the material in the impact zone, leading to the emission of substrate atoms inside the impact crater, resulting in the intense movement and deformation of molecules around the crater. For polymer materials, these phenomena are related to the structural parameters of chain lengths and entanglements [13]. Therefore, it is necessary to study the movement and fracture of molecular chains at the molecular level. Here, the total 60 molecular chains in the neat PVDF substrate have been analyzed. Fig. 7a and b respectively show the

Fig. 5. Average erosion rate for each material (neat PVDF and 10%POSS/PVDF). 18


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Fig. 6. Ratio of the number of broken carbon bonds from 0 to 5000 fs to the total number of initial carbon bonds.

points are smaller, which is consistent with the fact that the fixed constraint layer is at the bottom of the substrate. It can be found that the curves rise and then fall during the erosion process because the undamaged molecular chains around the crater initially move upwards because of being squeezed, and then return to the positions near their original positions after the energy released. By comparing the curves with the same Z coordinate of the center of mass at 0 ps (circled in red), it can be seen that the blue curves are flatter than the red ones, indicating that as long as there is a fixed constraint point in a molecular chain, the motion amplitude of a molecular chain will be greatly reduced. These results show that when a molecular chain has more constrained or junction points, its movement will be more restricted and its center-of-mass displacement is smaller.

of the molecular number and the atomic number of product molecules in the simulation cell. Because molecules were identified by the assumed cutoff radii in Table 1 and the atoms were still violently vibrating, the identified product molecules would change continually, resulting in the oscillations of the curve in Fig. 10a. It can also be found in Fig. 10a that most of the product molecules appear at the initial stage from 150 fs to 1200 fs, and the maximum rate of the product generation is about 1.12 molecules per femtosecond. At 150 fs, the number of product molecules starts to increase due to the contact of the cluster and the substrate. After 650 fs, the growth rate of the product gradually decreases and the number of product molecules becomes locally stable. However, the atomic number of the products keeps increasing until 1200 fs, shown in the inset of Fig. 10b. This is because although the kinetic energy of the cluster has almost been transferred to the molecular chains at 650 fs, the free radicals and active atoms generated by the collision will continue to react until 1200 fs. It can also be found from Fig. 10b that the curve gradually falls after 1200 fs because the atoms are gradually leaving the simulation cell. The rapid decline of the curve after 12,500 fs is caused by the departures of some large chain segments. However, during the stage from 1200 fs to 20 ps, the molecular number of products in Fig. 10a still shows an increase. This phenomenon reveals that the chemical bonds are still breaking continuously. By tracking the structural changes of product molecules, we observed that this is mainly caused by the

3.3.2. Analysis of molecular chain fracture Fig. 9 shows the snapshots of the 10 damaged molecular chains at different time. These molecular chains are all concentrated around the impact point, which means that the impact is local and dose not lead to the fracture of molecular chains away from the impact point. In order to understand the molecular chain fracture process, the time evolution of all product molecules is displayed in Fig. 10. Here, the product molecules refer to the products of chemical reactions among the molecular chains and the cluster without considering the 10 longest molecular chains. Fig. 10a and b respectively show the time evolution

Fig. 7. Perspective view of the entire simulation cell of neat PVDF at (a) 0 fs and (b) 20 ps. (c) 20 Å-thick slice at the impact point at 20 ps. Total 60 molecules are colored differently.

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Fig. 8. Z coordinates of center of mass of the 50 undamaged PVDF chains. The red, blue, and green curves represent respectively the chains with no fixed constraint point, a fixed constraint point and two or more fixed constraint points.

transitional intermediates), which occurs after 1200 fs. When a damaged carbon chain is stretched during this stage, the fracture may occur more easily. Based on the above analysis, it can be concluded that the fracture process of molecular chains during the erosion is mainly affected by the following two factors. One is the strength of material itself and the speed of energy dissipation in the system, which corresponds to the first stage. If the molecular chain strength is strong enough at this stage the energy can be dissipated more quickly into the entire substrate, the probability of the molecular chain breaking will be smaller. The other is the number and the length of free segments, which corresponds to the second stage. The depolymerization occurs from the ends of the free segments, and when the segments are longer, the carbon bonds are easier to break. Therefore, at this stage, the lower degree of freedom in the entire material system can help to suppress the thermal degradation process.

depolymerization of carbon chains, which is a thermal degradation of polymer. Fig. 11 shows the fragmentations of two molecular chains from 6200 fs to 6500 fs and from 11,500 fs to 11,900 fs, respectively. It can be observed that the carbon chains (or radical molecules) begin to cleave from its free end. Fig. 12a–e show a complete fracture process of the molecular chain in Fig. 10a. For sake of observation, the six broken carbon atoms have been numbered from 1 to 6, respectively. The chain conforms to the chain reaction mechanism, that is, the monomers are decomposed one by one. The depolymerization phenomenon has been observed in all the three neat PVDF models. After 1200 fs, the thermal degradation reaction is dominant and it mainly occurs in the damaged carbon chain or transitional intermediate. It is also observed that the time of a carbon chain’s thermal degradation is coincided with the time of the chain being straightened, indicating that the tensile state probably aggravate the speed of thermal degradation. According to the contraction behavior of the molecular chain after its end monomer leaves, the stretched molecular chain can be regarded as a spring [41]. A carbon atom or monomer at the free end is only unilaterally constrained by the molecular chain, so if the damaged free chain segment was longer, the free end movement tends to be wider and the tensile stress will be greater, leading to the increase of the probability of carbon bond breaking. Therefore, the fracture process of the molecular chains can be divided into two stages. The first stage is caused by the impact of the cluster, which occurs between 150 fs and 1200 fs. Most of the kinetic energy of the cluster is transferred to the PVDF chains, resulting in the appearance of a large number of active atoms and free radical molecules. The second stage is caused by the thermal degradation of free radical molecules (especially in the damaged carbon chains and

3.4. Effect of FP-POSS To some extent, the radius of gyration of a molecular chain can reflect its deformation ability because the molecular chain with a large radius of gyration is more prone to deform [42]. In order to study the effect of FP-POSS on the deformations of molecular chains, the changes of the gyration radii of PVDF chains without constraints in neat PVDF and 10% FP-POSS/PVDF have been compared, as shown in Fig. 13. It can be discovered that the gyration radii in neat PVDF vary between −4 Å and 4 Å, while those in 10%FP-POSS/PVDF only vary between −1 Å and 1.6 Å. This indicates that the incorporation of FP-POSS molecules hinders the deformation of PVDF molecular chains. Moreover,

Fig. 9. Perspective view of the 10 damaged molecular chains at different times. 20


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Fig. 10. Product molecules of the reactions among the 10 damaged chains and Si5O16 cluster in the simulation cell. (a) Molecular number of the productive molecules. (b) Atomic number of the product molecules.

Fig. 11. Fragmentations of two molecular chains.

chains, as shown in Fig. 14. The gyration radius analysis results show that after adding FP-POSS, the whole system has a smaller degree of freedom, thus the stiffness of the whole system is improved. Moreover, the FP-POSS itself has a stable SieO cage structure, which is expected to bring a higher strength in 10% FP-POSS/PVDF. This can explain why the model has a better erosion resistance and a smaller cracter size after

the curves in Fig. 13b show more obvious crests and troughs when compared to Fig. 13a. By tracing the trajectories of typical molecular chain motions of the two materials, this is because the deformations of molecular chains in 10%FP-POSS/PVDF are mainly derived from the deformations of local segments, whereas the deformations of molecular chains in neat PVDF are mainly derived from the entire molecular 21


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Fig. 12. A complete cleavage process of the molecular chain in Fig. 11a. For ease of observation, the six broken carbon atoms have been numbered from 1 to 6, respectively.

adding FP-POSS. In order to study the effect of FP-POSS on the whole deformation of the substrate, the strain fields along Z direction (the impact direction of the cluster) of the two substrates have been calculated. Here, the local Green strain has been calculated [43,44] according to the relationship between the current displacement dji and initial displacement dji0 of the atoms (total number is Ni0) in a neighboring list of atom i.

ηi =

1 (Ji JiT−I ) 2

where Ji is the local deformation gradient tensor, ηi is the local Green strain tensor. Fig. 15 shows the Z-direction strain field distributions in 20 Å-thick slices at 2500 fs and 20 ps. It can be seen that the distribution in neat PVDF is more chaotic or anisotropic and shows obvious localization characteristics, while the distribution in 10%FP-POSS/PVDF is relatively uniform. The strain analysis results show that unlike neat PVDF, the substrate deformation in 10%FP-POSS/PVDF tends to the entire

−1

⎞ ⎛ ⎞ ⎛ Ji = ⎜ ∑ d ji0T d ji0 ⎟ ⎜ ∑ d ji0T dji⎟ 0 0 ⎠ ⎝ j ∈ Ni ⎠ ⎝ j ∈ Ni

Fig. 13. Changes of the gyration radii of PVDF chains without fixed constraints. 22


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Fig. 14. Trajectories of typical molecular chain motions in the two materials.

Fig. 15. Z-direction strain field distribution at 2500 fs and 20 ps.

results show that 10%FP-POSS/PVDF has a smaller impact crater size and a lower erosion rate, and its erosion resistance is much better than that of neat PVDF. To understand the results, the movement and fracture process of molecular chains in neat PVDF have been analyzed. It is found that the chains' movements strongly depend on the constraints subjected to them. When a molecular chain has more constraints or junction points, its movement is more restricted and the center-of-mass displacement is smaller. The fracture process of the molecular chains can be divided into two stages. The first one is mainly caused by the impact of clusters. During this stage, most of the kinetic energy of the cluster is transferred to the PVDF chains, leading to the fracture of the chains, and a large number of free atoms and free radical molecules. The second one is mainly attributed to the thermal degradation of free radical molecules, resulting in a chain reaction. During the first stage, the strength of the material itself and the dissipation rate of energy in

uniform. Obviously, the latter is more conducive to dissipating the energy and preventing the excessive concentration of heat and stress, which can subsequently improve the erosion resistance. This is mainly because FP-POSS plays an anchor-like role in the PVDF matrix, leading to the increase of intermolecular constraints and the reduction of substrate local deformations. Moreover, the additional constraints imposed by the FP-POSS can also reduce the lengths of the damaged free segments and then at the thermal degradation stage, to some extent, inhibits the cleavages of carbon bonds at the chain ends. 4. Conclusion In this paper, the failure processes of neat PVDF and 10%FP-POSS/ PVDF substrates have been compared under the erosion of a Si5O16 cluster using reactive molecular dynamics simulations. The simulation 23


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the system will affect the fracture of molecular chains. Higher system stiffness and faster energy dissipation are helpful to reduce the probability of chain breakages. During the second stage, when a damaged free segment is longer or stretched, the thermal depolymerization will be accelerated. Therefore, a lower degree of freedom in the entire material system is helpful to inhibit the thermal degradation process. In addition, the effects of FP-POSS on the radii of gyration of PVDF molecular chains and the strain field along the impact direction have also been analyzed. The gyration radius results show that the addition of FP-POSS reduces the degree of freedom and improves the stiffness in the entire system. The strain field distribution results show that FPPOSS can help to make the deformation of the substrate more uniform. The higher stiffness and a stable SieO cage structure of FP-POSS in the system can improve the strength of the system, leading to a better erosion resistance performance. The more uniform entire deformation in the substrate is beneficial to the dissipation of energy and preventing the excessive concentration of heat and stress, also leading to a better erosion resistance. FP-POSS molecule acts like an anchor in the PVDF matrix, on the one hand increasing the intermolecular constraints, and on the other hand reducing the substrate local deformations. Moreover, the additional constraints imposed by FP-POSS also reduces the lengths of damaged free segments and inhibits the cleavages of carbon bonds at chain ends.

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Acknowledgements The authors would like to thank the National Natural Science Foundation of China (51790502) for the financial support of this research.

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