Origin of Flexibility of Organic-Inorganic Aerogels; Insights from

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Origin of Flexibility of Organic−Inorganic Aerogels: Insights from Atomistic Simulations Shingo Urata,*,† An-Tsung Kuo,† and Hidenobu Murofushi‡ †

Innovative Technology Research Center and ‡New Product R&D Center, AGC Inc., Yokohama, Kanagawa, 230-0045, Japan

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S Supporting Information *

ABSTRACT: Silica aerogel has a variety of excellent properties, but the mechanical brittleness inhibits the practical applications. Recently, many experimental efforts have been made to improve the compressibility and bendability of aerogels by hybridization with organic materials; however, the reason of the flexibility has not yet been well understood. To identify the intrinsic origins of the flexibility of organic− inorganic hybrid aerogels, polymerization and mechanical responses of tetramethoxysilane (TMOS), methyltrimethoxysilane (MTMS), and 1,2-bis(methyldiethoxysilyl)ethane (BMDEE) polymers were investigated by using reactive molecular dynamics simulations. As a result, cyclic compressive deformation simulations successfully reproduce the experimental results that TMOS is substantially fragile, whereas MTMS and BMDEE are easy to be reshaped. Detailed structure analyses showed that Si−O−Si−O rings in TMOS are collapsed by compressive deformation, whereas any kind of ring structure in BMDEE is maintained even after large compression. Tetrahedral SiO4-based network structure (Q4) in TMOS is found to be the source of the brittleness. On the contrary, the absence of Q4 silicones and the presence of ethylene units, which provide rotatable dihedrals, in BMDEE allow it to deform without disrupting the microscale network. The insightful information provided by the theoretical investigation in atomistic scale is essential to design new composite aerogels.

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INTRODUCTION

aerogels have a potential in the application as window panes and solar collector cover instead of oxide glasses.3 A critical drawback of the silica aerogel is its fragility and inflexibility because of the fragile Si−O−Si network analogous to inorganic silica.7 For example, Moner-Girna et al. have investigated the mechanical property of silica aerogel using microindentation and found that the silica aerogel behaves as an elastic material if the density is low enough, whereas plastic deformation is enhanced in higher-density aerogel.8 Such a fragile characteristic is unfavorable for the processing and production of aerogels and limits their practical applications. To overcome the drawback, recently, a variety of organic− inorganic hybrid aerogels have been proposed. For instance, Rosa-Fox et al. have reported that the addition of poly(dimethylsiloxane) to an aerogel composed of tetraethoxysiloxane (TEOS) improves the latter’s elasticity.9 Kanamori et al. have developed a reformable aerogel against compressive deformation using methyltrimethoxysilane (MTMS) as a monomer.10 Furthermore, insertion of an organic unit in the Si−O−Si network by hybridization of cellulose and polymethylsilsesquioxane,11 or using 1,2-bis(methyldiethoxysilyl)ethane (BMDEE) as a monomer,12,13 successfully improves the bendability of the organic−inorganic hybrid aerogels. These

Silica aerogel is a promising material with extremely high performance as thermal and sound insulators,1−3 thanks to extremely low density as a result of the highly porous structure of silica nanoparticles (Figure 1).4,5 The diameter of the silica nanoparticle is about several nanometers and the size of the pores distributed in the material is around 50−100 nm. The substantially spongy microstructure is useful for catalysis, drug delivery, and biomaterials.6 In addition, optically transparent

Received: July 4, 2018 Revised: August 7, 2018 Published: August 9, 2018

Figure 1. Schematic view of nanoscale morphology of aerogel. © XXXX American Chemical Society

A

DOI: 10.1021/acs.jpcc.8b06409 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

accelerate the dehydration reaction between the Si−OH bonds. Because such an extremely high temperature causes bond dissociation of C−H, Si−C, and C−C bonds, these bonds were constrained by applying a harmonic constrain force with a constant prefactor of 50 kcal/(mol Å2).35 This kind of artificial acceleration is usually employed for sol−gel reaction simulations.36,37 The ReaxFF is a reliable model to simulate reaction without using expensive first principle calculations, such as ab initio or density functional theory.21−23 However, it is still difficult to model a complex reaction by considering catalysis or explicit solutions including acidic, alkaline agents, and surfactants, for example, which are usually used in the experiment to enhance reaction or control the morphology of aerogels. Thus, in this work, we do not study the reaction process of polymerization in detail. Instead, we would focus on understanding the relation between microscale morphology of polymer network and mechanics of the aerogels. To do so, we modeled two different cross-linking density models for each polymer.

enormous progresses promise feasibility of the hybrid aerogels as thermal and sound insulators with machinability. The intrinsic origin of the flexibility for the hybrid organic− inorganic aerogels is not well understood so far. Here, we tried to model hybrid aerogels in atomistic scale and investigate the mechanical response by performing molecular dynamics (MD) simulations of tetramethoxysilane (TMOS), MTMS, and BMDEE. The network structures of the polymers were constructed by polymerization simulations. Conventional classical MD (CMD) simulation method does not allow bond formation and dissociation because harmonic potential is usually adopted between bonding atoms. The CMD method is thus not suitable to simulate polymerization explicitly. Nevertheless, a number of studies have already applied CMD technique to simulate polymerization by employing several artificial techniques.14−20 The most simple method is to create a new bond between two neighboring atoms when they approach within a cutoff distance. Even though simple polymerization technique is useful to construct a cross-linked network of organic polymers, it does not take activation energy and transition state into account, and thus temperature effect is not available. On the other hand, the chemical reaction can be calculated by using ab initio or density functional theory; however, these calculations are only available to investigate the individual reaction step or small clusters.21−23 Instead, several empirical models for chemical reaction have been proposed in the last few decades.24−26 One of the successful models is reactive force field (ReaxFF) proposed by van Duin et al.27 They first developed the model for hydrocarbons and have extended it to a variety of materials, including both organic and inorganic materials.28−31 Several reports have already examined the sol−gel reactions by using the ReaxFF model.32−37 Deetz and Faller have optimized ReaxFF potential parameters with fitting to density functional calculations and applied them to simulate the reaction of TMOS, TEOS, MTMS, and trimethoxysilane in the methanol solution.32,33 In addition, the reactivity and microstructure of tetrahydroxysilane and trihydroxysilane have been studied with the ReaxFF model.34 Furthermore, the ReaxFF has been applied to investigate the silanol reaction on silica surface35 and reaction process of bioglasses.36,37 The ReaxFF also allows us to simulate fracture of polymers because bond dissociation is explicitly represented. Therefore, we applied the ReaxFF model to investigate both polymerization and mechanical properties of the organic− inorganic aerogels in this study.

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RESULTS AND DISCUSSION Polymerization. First, we prepared a relatively small unit cell composed of 200 monomers of TMOS and MTMS each and 100 monomers of BMDEE. As described in the Computational Method section, it is assumed that all the monomers are fully hydrolyzed as hydroxyl group in advance (see Figure 2). For TMOS, the initial configuration was relaxed

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COMPUTATIONAL METHOD All MD simulations were performed by using LAMMPS38 with the ReaxFF potential. Even though Deetz et al. have optimized parameters of the ReaxFF model to simulate sol−gel reaction as mentioned above,32,33 the parameter set has not yet been disclosed in their literatures. Thus, we used the parameters found in the other reference.39 Details of the definitions of inter- and intra-atomic interactions of the ReaxFF model can be found in a recent review.31 Temperature and pressure were controlled by using Nosé−Hoover thermostat and barostat.40 Verlet algorithm was used for time integral with 0.25 fs time step. Initial configurations of the monomers were generated by using Packmol package.41 To make our polymerization modeling simple, each methoxy group (−O−CH3) was presumed to be hydrolyzed to hydroxyl group (−OH) in advance. The polymerization simulations of monomers were carried out at high temperature, 2000 K, to

Figure 2. Hydrolyzed monomers for (A) TMOS, (B) MTMS, and (C) BMDEE.

by 0.4 ns at room temperature under atmospheric pressure by a NPT simulation. The density of the initial model was 1.47 g/ cm3. On the other hand, the initial configurations of MTMS and BMDEE were generated by using Packmol41 with presumed density of 1.16 and 0.92 g/cm3, respectively. During polymerization simulations, the shape of the unit cell was fixed and temperature controlled at 2000 K. Figure 3 displays the change in the number of Si atoms in the largest polymerized network as a function of time. As shown in Figure 3A, the largest cluster size in the TMOS B


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including all Si atoms at about 3.5 ns (green circle in Figure 3A). In cases of MTMS and BMDEE, water molecules generated by the dehydration reaction were eliminated from the unit cell every 1 ns simulation duration. Eventually, these system construct a complete network composed of all Si atoms at about 3 and 5 ns, respectively. For BMDEE, we densified the unit cell by equilibrating the model at 300 K and 0.1 MPa for 5 ns to accelerate the reaction. The constructed polymer models were enlarged by combining the unit cell into 2 × 2 × 2 size of a super cell because the original unit cell is not large enough to perform deformation simulations. The unified model was relaxed at 300 K and 0.1 MPa condition. We name this model as “Coarse model”. Next, the coarse model was heated up to 2000 K again and further polymerization was carried out for 0.5 ns. After removing the water molecules from the extended unit cell, the system was equilibrated at 300 K and 0.1 MPa. The further polymerized model is called “Dense model” hereafter. The snapshots of the dense models of the three polymers are visually illustrated in Figure 4. Because we assumed an anisotropic cell shape when we equilibrated the configurations, the unit cells are rectangular but not cubic. Table 1 summarizes the properties of the coarse and dense models of each polymer. The TMOS models have a relatively high density but lower than that of crystalline and amorphous silica (ca. 2.2 g/cm3). It may be because approximately one hydroxyl group per silicon atom remains in the TMOS models. Densities of the MTMS and the BMDEE models are close to each other and lower than that of TMOS. In MTMS, about 2.6−2.7 Si−O−Si connections per silicon atom are generated, whereas about 1.6 the Si−O−Si connection per silicon atom are generated in BMDEE. Because BMDEE has a Si− CH2CH2−Si unit, the results indicate that the same number of bridging sites for Si atoms are formed in the MTMS and the BMDEE models. The dense models always have larger density than the coarse models owing to the additional Si−O−Si connections. In the following session, we would discuss the effects of the network density and the monomer structure on the mechanical response and suppleness of the three aerogel models. Mechanical Response. Using the six models listed in Table 1, uniaxial stretch, compression, and shear deformation simulations were performed to measure the stress−strain relation (see Figure 5). During the deformation simulations, temperature was controlled at 300 K. Strain rates for uniaxial and shear deformations are 1.0 × 109 s−1. Young’s and shear moduli were evaluated from the initial slope of the stress− strain (S−S) curves and are summarized in Table 2. Comparing the three polymers, the moduli of TMOS are several times larger than those of MTMS and BMDEE. MTMS is slightly stiffer than BMDEE, but its magnitude relation depends on their density. The S−S curves of TMOS in uniaxial stretch and simple shear deformation clearly demonstrate work-hardening after yielding. The S−S curves reach a maximum at approximately 0.3 and 0.5 strain for the uniaxial stretch and shear deformation, respectively. After that, the stress is almost constant. A sharp drop in stress, which corresponds to a disruptive breakage of the polymer network, is seen in the S−S curve of stretching only for the dense model of TMOS (see the Supporting Information). On the contrary, stress of MTMS and BMDEE monotonically increases with increasing strain

Figure 3. Degree of polymerization for (A) TMOS, (B) MTMS, and (C) BMDEE. (A) Three cases, sequential reaction simulation (blue square), water elimination at 2 ns (red circle), and densification at 2 ns with water elimination (green circle), are illustrated. Reversed triangles in red and green indicate water elimination and densification, respectively.

system is almost constant after 2 ns if we did not apply any extra treatment during the reaction. Because water molecules were generated during the polymerization of TMOS, the produced water molecules would disrupt the Si−O−Si network as a backward reaction and as a result inhibit the growth of the TMOS cluster. The constant value of the largest cluster size after 2 ns indicates that the system reaches an equilibrium of the hydration−dehydration reaction. For further polymerization, we eliminate water molecules to avoid the backward reaction (red circle in Figure 3A). However, because the effect of water elimination on accelerating polymerization was not significant, we densified the unit cell by equilibrating the configuration at 2 ns with normal condition (300 K, 0.1 MPa). After that, TMOS makes continuous Si−O−Si network C


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Figure 4. Snapshots of equilibrated polymer structure of dense models for (A) TMOS, (B) MTMS, and (C) BMDEE.

Table 1. Properties of Polymerized Models for Aerogels

monomer

model

no. of atoms

density (g/cm3)

cell size (Å)

TMOS

coarse dense coarse dense coarse dense

7344 6879 11 360 11 192 15 504 15 348

1.69 1.77 1.42 1.58 1.40 1.45

47.8 46.7 50.9 49.1 52.7 52.0

MTMS BMDEE

no. of Si−OH per a Si atom

no. of Si−O−Si per a Si atom

1.06 0.87 0.40 0.33 0.46 0.40

2.94 3.13 2.60 2.67 1.54 1.61

Figure 5. Stress−strain curves of (A) uniaxial stretch, (B) compression, and (C) simple shear deformations for TMOS, MTMS, and BMDEE.

and there is no clear evidence of yielding in both stretch and shear deformations. It may imply that MTMS and BMDEE polymers have elastic-like mechanical characteristic, whereas the TMOS polymer is more fragile against such a large deformation. Comparing the coarse and dense models in Table 2, moduli of the dense model are obviously larger than those of the coarse model in any cases, even though the number of Si−O− Si connections does not increase much as summarized in Table 1. This result suggests that the degree of polymerization

substantially influences the mechanical strength and stiffness of the silica-based polymers. It is worth noting here that the modulus of compressive deformation is more sensitive to the degree of polymerization than those of stretch and shear deformations, although an extended study is necessary to understand the reason of the difference between stretch and compressive deformations. D


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Figure 1). In other words, the suppleness would result from not only nanoscale porous morphology but also atomistic scale network structure of the hybrid organic−inorganic aerogels. To understand the reason of the extraordinary reformability of the BMDEE polymer from atomistic view points, we analyzed variation in the number of Si−O bonds in each polymer model during uniaxial stretch and compression (Figure 7). BO(m) stands for the ratio of silicon atoms

Table 2. Mechanical Properties of Aerogels modulus (GPa)

max. stress (GPa)

monomer

model

stretch

comp.

shear

stretch

shear

TMOS

coarse dense coarse dense coarse dense

12.3 12.7 5.0 6.8 4.0 5.0

13.5 16.8 5.0 8.5 4.8 6.5

4.2 5.9 1.3 2.7 1.9 2.3

4.1 6.2 1.6 2.2 1.1 1.5

2.3 3.2 0.9 1.8 0.5 1.1

MTMS BMDEE

In the case of compressive deformation, the stress−strain curve monotonically increases with increasing strain for all the polymer models. The plastic deformation is not clearly identified from the S−S curve, which is contrary to silicate glasses.42−45 Because previous experimental studies have reported that BMDEE possesses better reformability under compressive condition than conventional silica aerogels,12,13 we here discuss the difference in suppleness of the three polymers by performing cyclic loading/unloading compressive deformation. As shown in Figure 6, the specimen was first compressed down to −0.6 of strain, and the unit cell was reformed to the

Figure 6. Stress−strain curve of compression−stretch cyclic loading/ unloading deformation.

original shape with the same absolute deformation rate. The S−S loop of TMOS is definitely larger than those of MTMS and BMDEE. During the unloading deformation, the curve of TMOS reached zero stress when the specimen was reformed to −0.5 of strain, and the stress increased up to 6 GPa at strain = −0.2. The fact proves that the TMOS polymer performs plastic deformation even though there is no clear yielding point in the S−S curve when compressive deformation is applied. The S−S loops of MTMS and BMDEE are absolutely smaller than that of TMOS, clearly implying that they are more flexible, although plasticity is also identified from the loop. Especially, during the unloading deformation, the stress of BMDEE is almost zero after reaching zero stress. This result enables us to presume that the BMDEE polymer does not suffer from any critical damages under compressive deformation and thus shows higher flexibility and suppleness against compressive deformation. It should be emphasized here that the atomistic simulations reasonably reproduce the bendable behavior of BMDEE and MTMS, even though this study does not take into account the mesoscale aggregate of nanosize particles (see

Figure 7. Variation in the number of Si−O bonds per silicon atom. BO(m) stands for the ratio of silicon atoms bonding to m oxygen atoms.

connected to m oxygen atoms in this figure. In the case of TMOS, the number of silicon atoms connected to four oxygen atoms (BO(4)) decreases, whereas BO(3) increases when the absolute value of strain is larger than 0.2, clearly demonstrating that breaking of the Si−O bond occurs at strain of ±0.2. The breaking of Si−O bond was also found in MTMS, but the extent of bond breakage is less than that in TMOS. Surprisingly, almost of all the Si−O bonds are maintained in BMDEE, even if the specimen suffers from large stretch and E


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Si atom. The TMOS possesses a tetrahedral SiO4 network and thus shows a more rigid mechanical characteristic than MTMS and BMDEE. It should be noted that each silicon atom in BMDEE has one site connecting with CH2−CH2−Si, which should be considered in the practical bridge site for each Si atom. Hence, one can find that around 60 and 30% of Si atoms possess two and three bridge sites, respectively, in BMDEE. The distribution of the practical bridging site in BMDEE is analogous to that in MTMS. Although this may reflect similar network structure in these two polymers, BMDEE is more reformable than MTMS. This might be because the Si−CH2− CH2−Si unit is more rotatable than the Si−O−Si−O unit. In the aspect of the compressed structure at strain −0.6, the Q4 and Q3 species in TMOS decrease, whereas Q1 and Q2 ones increase after compression, describing the disruption of the tetrahedral SiO4 network structure due to the breaking of the Si−O bond. The Q3 specie of MTMS is also found to decrease after compression; however, the extent of the decrease in Q3 specie of MTMS is lower than that of the decrease in Q3 and Q4 species of TMOS. This indicates that the disruption of the network structure is limited in MTMS. This is ascribed by the fact that MTMS has no Q4 silicon atoms and possesses a higher fraction of Q2 silicon atoms to provide a rotatable Si−O−Si−O unit, reducing the collapse of the network structure under compression. Contrary to TMOS and MTMS, the distribution of the Qn species is almost identical before and after the compression for BMDEE. Because BMDEE possesses an extra rotatable Si−CH2− CH2−Si unit in comparison with MTMS, the units can adjust the steric structure under compression and thus prevent the disruption of the network structure. This unique characteristic causes the high bendability of BMDEE. Eventually, we also analyzed the distribution of the ring size of the Si−O−Si network after and before compressive deformation by using R.I.N.G.S.46 with King’s definition47,48 as drawn in Figure 9. Note that the number of rings is defined as the number of silicon atoms in cases of TMOS and MTMS, whereas the total number of silicon, carbon, and oxygen atoms are counted for BMDEE. It is observed that the number of the rings in the TMOS polymer significantly decreases in the range of ring size from 3 to 7 when the specimen is compressed, showing that the small ring is easier to disrupt under compression. The origin of plasticity and poor reformability of TMOS is demonstrated in the deformation simulations. On the contrary, the change in the ring distribution is limited in the case of the MTMS polymer. As mentioned above, MTMS possess a higher content of Q2 silicons, which form rotatable Si−O−Si−O units. The change in the conformation prevents the collapse of the network structure and thus MTMS shows higher flexibility than TMOS. Interestingly, variation in the the ring size distribution of the BMDEE polymer due to compression is almost negligible. This finding supports the hypothesis that the presence the ethylene group can make the structure flexible enough to avoid stress concentration and prevent bond dissociation, thanks to the rotatable torsion angles of Si−C− C−Si together with O−Si−C−C and Si−O−Si−C. As an example, we draw several rings, which are initially aligned to the compressive direction before and after compression for BMDEE as shown in Figure 10. The rotatable network structure due to the absence of Q4 and Q3 and the insertion of a flexible ethylene unit enables the rings to vary the structure from parallel to perpendicular to the deformation axis

compressive deformations. Note here that, in the case of TMOS, a sharp drop in BO(3) at +0.5 strain means that the specimen is disruptively broken, as shown in the Supporting Information. We further analyzed the microstructure using two models. One is an equilibrium structure before compression and the other one is a compressed structure at strain −0.6. Figure 8

Figure 8. Distributions of O−Si−O angle in aerogels. Solid line is equilibrium structure and dashed line is compressed structure at strain −0.6.

displays the distribution of the O−Si−O angle for the two cases. The distributions were averaged over 0.1 ns of constant volume MD run at 300 K. After compression, the distribution of TMOS gets broader symmetrically, indicating that a threedimensional-like network of the tetrahedral SiO4 is pressed in the TMOS polymer. In comparison with TMOS, the distribution of the Si−O−Si angle in the compressed BMDEE spreads toward a larger angle but not much to a smaller angle. This is because there is no tetrahedral SiO4 branching in the polymer. MTMS is categorized as intermediate between TMOS and BMDEE. In addition, according to the fact that the monomer of BMDEE has a Si−CH2−CH2−Si unit, we can infer that BMDEE possesses a more rotatable chain network to adjust the steric structure during the compression and thus shows the narrowest distribution of the Si−O−Si angle after compression. To confirm the hypotheses, we analyzed the fraction of the bridging silicon atom (Qn), which is bound to n bridging oxygen atoms, in an equilibrium and compressed the structures as listed in Table 3. In the equilibrium structure, about onethird of silicon in TMOS bridges the polymer network as a tetrahedral SiO4 structure, whereas MTMS and BMDEE have no Q4 silicon atoms due to an additional methyl group on each Table 3. Qn Distribution in Dense Models of the Aerogels before and after Compression at Strain = −0.6 polymer

model

Q0

Q1

Q2

Q3

Q4

TMOS

equib. comp. equib. comp. equib. comp.

0.1 1.1 0.3 0.6 3.6 3.9

2.5 10.4 3.8 7.7 31.4 33.0

17.4 30.4 29.2 38.0 61.5 60.2

45.7 40.0 66.8 53.5 3.4 2.8

34.3 18.2 0.0 0.2 0.0 0.0

MTMS BMDEE

F


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Figure 10. Examples of shape change in rings before (shadowed) and after (bright) compressive deformation for BMDEE. Yellow, red, and blue beads are silicon, oxygen, and carbon atoms, respectively.

uniaxial stretch, compression, and simple shear deformation simulations, we can summarize the following remarks. 1. Young’s and shear moduli of MTMS are about half of those of TMOS, and BMDEE is less stiff than MTMS. Increase in Si−O bonding increases the moduli for all polymers. 2. Although there is no clear yielding point in stress−strain curve of uniaxial compression for all polymers, loading/ unloading cyclic deformation simulation draws large hysteresis of the S−S curve for TMOS. On the other hand, the loops of S−S curves of MTMS and BMDEE are substantially smaller than that of TMOS. Especially, BMDEE maintains almost zero stress on the reforming process, indicating that the aerogel is fairly reformable. 3. According to the microstructure analyses, such a variation in the bond order of Si−O, distribution of O−Si−O angle, Qn species, and ring size distribution, it was revealed that BMDEE can change the shape without disrupting the network structure. On the contrary, the Si−O−Si network is substantially damaged in TMOS. Absence of Q3,4 and also more rotatable networks due to an ethylene unit connecting two silicone atoms prevents destructive bond breakage and results in substantially bendable nature of BMDEE. These results of atomistic simulations successfully explain the reasons of improved bendability of the organic−inorganic hybrid aerogels, MTMS and BMDEE. Even though aerogels

Figure 9. Ring size distribution: equilibrium condition (dark blue) and compressed structure at strain −0.6 (orange). Ring size is the number of silicon atoms in a ring for TMOS and MTMS, whereas it is number of silicon, carbon, and oxygen atoms for BMDEE.

without bond dissociation. These microstructure analyses allow us to conclude that the organic−inorganic hybrid aerogels possess rotatable torsion angles to decrease the stiff structure of the Si−O−Si network and thus construct a flexible network. This results in the specifically bendable nature of the BMDEE aerogel.

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CONCLUSIONS To evaluate the mechanical properties of three kinds of aerogels, reactive molecular dynamics simulations employing the ReaxFF model were performed to build polymer models of TMOS, MTMS, and BMDEE. Two different density models were compared for the three polymers. According to the G


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have a very porous structure composed of several nanometersized particles, the mechanical property of the structural unit in an atomistic scale is also essential to gain reformable flexibility of the aerogels.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b06409. Snapshots of the dense model of TMOS during uniaxial stretch (Figure S1); snapshots of the dense models of TMOS, MTMS, and BMDEE at strain 0.6 by uniaxial stretch (Figure S2); LAMMPS input files for BMDEE polymerization; Supporting Information of ref 39 for ReaxFF parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81 (0)45 3747450. Fax: +81 (0)45 3748856. ORCID

Shingo Urata: 0000-0001-6878-345X Notes

The authors declare no competing financial interest.

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REFERENCES

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