A Reactive Dynamics Simulation Study on the Pyrolysis of Polymer

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A Reactive Dynamics Simulation Study on the Pyrolysis of Polymer Precursor to Generate Amorphous Silicon Oxycarbide Structure Hong-fei Gao, Hongjie Wang, Zihao Zhao, Min Niu, Lei Su, and Yin Wei J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12287 • Publication Date (Web): 21 Feb 2018 Downloaded from http://pubs.acs.org on March 2, 2018

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The Journal of Physical Chemistry 1 / 25

A Reactive Dynamics Simulation Study on the Pyrolysis of Polymer Precursor to Generate Amorphous Silicon Oxycarbide Structure Hongfei Gao,† Hongjie Wang,*,† Zihao Zhao,† Min Niu,† Lei Su,† and Yin Wei† †

State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong

University, Xi’an, Shannxi 710049, People’s Republic of China

ACS Paragon Plus Environment

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ABSTRACT: Amorphous silicon oxycarbide (SiOC) ceramics have extensive applications as structural and functional materials due to their unique properties. Preparation of SiOC from pyrolysis of polymer precursors involves a complicated process of chemical reactions, various bond redistributions and so on. With the aim to gain more insight on this and obtain a SiOC structure model, a series of molecule dynamics (MD) simulations integrated with a shell programming of gas removal scheme were implemented.

Here

we

chose

hydridopolycarbosilane

(HPCS)

and

polymethylhydrosiloxane (PMHS) as polymer precursors, and constructed a rational polymer atomic model by using reactive force field ReaxFF derived from elsewhere, which has been tested and verified to be applicable to our C/Si/H/O system. MD simulation of pyrolysis of the polymer indicated H2 and CH4 were the major gas products, which were deleted through NVT-MD simulations cooperated with the script code mimicking the experimental process. Atomic model of the dense SiOC was obtained after compressed and further equilibrated of the solid structure. The final SiOC structure was analyzed by computing its radial distribution function. It contains C-C, Si-O, Si-C, and Si-Si bonds, which agrees well with the experimental data. These results confirm the accuracy of the MD simulations and the atomic model of SiOC ceramic.


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1. INTRODUCTION Amorphous silicon oxycarbide (SiOC) ceramics have received extensive attention as structural and functional materials in the fields of radiation-tolerance,1 energy storage,2–5 biomedicine,6 and optics7,8 due to its excellent mechanical strength and toughness, high-temperature stability (up to about 1500 ℃), and resistance to oxidation and corrosion. SiOC is X-ray amorphous at large scale, but heterogeneous at the nanometer length scale, mainly consisting of SiO2 domains, free carbon phase, and silicon-centered mixed bond tetrahedrons at their interfaces. SiOC ceramic can be prepared via melting,9 sol-gel pyrolysis,10–12 radio frequency (RF) sputtering technique,1,13 and chemical vapor deposition (CVD).14 The melting method shows limitation to synthesize true SiOC ceramic and it is difficult to control the final compositions.15 RF sputtering and CVD techniques are usually confined to fabricate thin films and coatings. In contrast, the sol-gel pyrolysis method has advantages to prepare bulk ceramic (dense or porous), powders and composites. But until now, how stoichiometry and properties of the pyrolysis products relate to their initial polymers remains still unclear. Building an atomic model for the polymer derived SiOC provides an efficient way to design materials for different applications, such as in the mechanical, electrical, thermal, and chemical fields. Computational methods, especially reactive molecule dynamics (RMD) simulation, provide an opportunity to deeply clarify the polymer precursor pyrolysis at an atomistic scale, which is not able to be realized by experiments. Chenoweth16 and Naserifar17–19 have studied the pyrolysis of



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poly(dimethylsiloxane) (PDMS) and hydridopolycarbosilane (HPCS) by using the reactive force field ReaxFF, respectively. ReaxFF potential developed by van Duin, Goddard20 allows for accurate description of bond formation and dissociation, which bridges the gap between the computational methods based on empirical force fields and quantum chemical (QC). Therefore, MD calculations of large-scale reactive chemical systems can be carried out by using ReaxFF. It has the advantage of high accuracy comparable to QC at a relative low simulation cost. To generate amorphous structure, melt-quench technique21 and fast algorithm method22 have been used in the atomistic simulations. However, amorphous structures constructed from these two methods correspond to those from melting and RF sputtering techniques. The aim of our paper is to form SiOC structure starting from polymer pyrolysis through RMD simulations, exploring theoretical stoichiometry relationships between initial polymers and amorphous phase. In consideration of carbon atoms existed in silicon carbide and/or free carbon phases will give rise to enhanced mechanical properties,13 electrical and thermal conductivities.23 Here we used

polymethylhydrosiloxane

([CH3(H)SiO]n,

PMHS)

mixed

with

HPCS

([SiH2CH2]n) as polymer precursors, where Si-H and Si-CH3 groups in PMHS could decrease the amount of free carbon.24 HPCS is added as polymer precursor to increase free carbon content, and its pyrolysis behavior has been investigated by RMD simulations17,19 and experiments.25 In this work, atomic model of the dense SiOC ceramic has been constructed by pyrolyzing PMHS and HPCS polymer. The ReaxFF potential derived from


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elsewhere26 was validated and model of the initial PMHS/HPCS mixed polymer was constructed. Then, we performed pyrolysis simulations to determine the gas products. A series of NVT-MD simulations integrated with a script code of gas removal scheme were implemented. Finally, atomic model of the dense SiOC ceramic was generated by structure relaxation under ambient conditions. 2. ESTIMATION OF THE REACTIVE FORCE FIELD ReaxFF potential for C/Si/H/O system26 has been successfully developed, and its validity needs to be tested against quantum mechanical (QM) calculations before using. Some force field parameters, such as Si-C bond, Si-C-O angle, and state equation of the SiC crystal, have been tested. In consideration of good transferability of the ReaxFF, only a few parameters need to be further validated, including dissociation energies of Si-C single bond in H3Si-CH3, Si=C double bond in H2Si=CH2,

and

angle-bending

energies

of

Si-O-C

and

C-Si-O

in

H3Si-Si(CH3)2-O-CH3. They were checked by performing minimization of geometries with the bonds and angles of interest fixed. QC data were computed by using Gaussian 09 software,27 B3LYP functional28,29 and 6-311++G (d, p) basis set. All MD simulations in this paper were carried out by LAMMPS package.30 The dissociation and angle-bending energies obtained by the DFT and ReaxFF are compared in Figure 1, and the results are in good agreement, suggesting accuracy of the ReaxFF.



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Figure 1. Comparison of the energies computed by DFT and ReaxFF for (a) Si-C single bond, (b) Si=C double bond, (c) Si-O-C angle, and (d) C-Si-O angle.

To date, Si-C-O crystalline phase whether existed in nature or synthesized in experiment has not been reported. Therefore, a predicted SiCO-based stable crystal structure (SiC2O6)31 was used to test the ability of ReaxFF for descripting its equation of state. In order to acquire the equation of state for the SiC2O6 crystal structure, DFT computations were performed with Quantum-Espresso code.32 According to a verification approximation

effort,33

Perdew-Burke-Ernzerhof

(GGA)34

and

(PBE)-generalized

local-density

approximation

gradient (LDA)35

exchange-correlation functionals were utilized to expand the wave function into a plane wave basis set with a kinetic energy cutoff of 80 Ry and charge-density cutoff of 560 Ry. The core electrons were described by using ultrasoft pseudopotentials


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(USPPs) generated from GBRB potential library36 and pslibrary.1.0.037 for C and Si atoms

respectively,

and

projector

augmented-wave

(PAW)

plane-waves

pseudopotential method referenced from pslibrary.0.3.138 for O atom. All of our first-principles calculations were ran on an 8 × 8 × 8 k-point density according to the Monkhorst-Pack method39 with 0.002 Ry Marzari-Vanderbilt40 smearing. The results of state equation from ReaxFF against those from first-principles calculations are shown in Figure 2. Compared to the compression conditions, there is about 9% deviations between the stable structures computed by the DFT and ReaxFF, indicating ReaxFF describes the equation of state for the predicted SiC2O6 structure correctly to some extent.

Figure 2. DFT and ReaxFF equations of state (compression and expansion) for the predicted SiC2O6 crystal structure. Blue, yellow and brown spheres correspond to Si, C and O atoms.

3. ATOMIC MODEL OF THE POLYMER To obtain equilibrium structures for the PMHS/HPCS mixed polymer, MD simulations were performed as follows. Four PMHS and four HPCS chains were constructed in a cubic simulation cell with periodic boundary conditions upon the three dimensions. In our simulations, n equals to 28 and 30 for PMHS ([CH3(H)SiO]n)



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and HPCS ([SiH2CH2]n) molecular chains, respectively, namely molecular weights of each PMHS and HPCS molecular chain are 1846 and 1326 g/mol. There are totally 1628 atoms in the initial simulation cell. In order to avoid undesired ring spearing and catenations, initial density of the mixed polymer was set to be 0.15 g/cm3 and then minimized using the conjugate-gradient (cg) method. The relaxed structure was then compressed using MD simulation in the NPT ensemble at 10 K and 0.11 GPa to densify the structure and make its density close to the experimental value. The pressure used in the NPT simulation was determined from the densities of the PMHS and HPCS polymers obtained from the final step in the same way. Energy minimization and short-duration MD calculations in the NVT ensemble were further carried out at 300 K. Finally, MD simulations were performed in the NPT ensemble at 300 K and 0.1 MPa for 3 ns, so as to gain the true equilibrium structure. The time step was set as 1 fs. The temperature and pressure were controlled by employing the Nosé-Hoover thermostat and barostat, respectively. The final equilibrium configuration of the PMHS/HPCS mixed polymer with the density of 0.997 g/cm3 is presented in Figure 3(a). It is obvious that the chain backbones and branches of the mixed polymer remain intact through our multi-step MD calculations. In order to further confirm whether the generated polymer has the true equilibrium structure, the radial distribution function g(r) was computed and is illustrated in Figure 3(b). The locations of the various peaks marked in the Figure 3(b) correspond to the different types of chemical bonds in the mixed polymer, and the results are in good coincidence with the experimental values25 and previous reported


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data.17 Therefore, the ReaxFF force field is applicable to our C/Si/H/O polymer precursors, and the multi-step MD simulations can accurately form an equilibrium structure of the PMHS/HPCS mixed polymer.

Figure 3. (a) Equilibrium structure and (b) computed radial distribution function g(r) of the PMHS/HPCS mixed polymer.

4. PYROLYSIS SIMULATIONS In general, polymer-to-ceramic conversion comprises steps such as crosslinking, pyrolysis and sintering. Although the crosslinking process is necessary for the conversion during experimental sol-gel pyrolysis, it has been omitted in our cook-off simulations for its negligible effect compared to other processes. Before pyrolysis calculations, cook-off simulations were performed to attain an indication of thermal decomposition by heating the polymer from 10 K to 5000 K. The polymer generated in Section 3 was further equilibrated as a result of MD simulation in the NVT



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ensemble at 10 K for 10 ps after energy minimization. Then the calculations were carried out in the NVT ensemble with the temperature heating from 10 K to 5000 K using a rate of 0.1 K/fs. The simulation parameters were the same as before expect for the time step was 0.1 fs. Details of the atomic model of the mixed polymer are listed in Table 1. The theoretical and simulated coordination numbers for each atoms are well coincident, suggesting the accuracy of our atomic model. Table 1. Details of the Atomic Model of the PMHS/HPCS Mixed Polymer, Including Number of Atoms (Na), Theoretical Coordination Number (Nt), Simulated Coordination Number (Ns), Relative Error (RE) C

Si

H

O

total

Na

256

240

1008

116

1620

Nt

1024

964

1008

232

3228

Ns

1091

848

1116

239

3294

RE (%)

6.5

-12.0

10.7

3.0

8.2

Figure 4 presents variations of the total number of molecules/radicals during the heating simulation. The Nosé-Hoover thermostat can well control the temperature in terms of small fluctuation during the cook-off simulations. From Figure 4, the mixed polymer begins to decompose above 1000 K, which agrees well with the previous pyrolysis simulations.16,17,19 Variations of the number of bonds during cook-off simulations are supplied in Figure S1 (see Supporting Information). At 1000 K or below, Si-H, C-H and Si-CH3 bonds are broken forming H and CH3 radicals. The number of Si-Si bonds increases as a result of crosslinking of the mixed polymer. C-C


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bonds begin to form at about 1800 K (18.45 ps), resulting from the formation of C2 hydrocarbons. As the temperature increase, there is also an increase in the number of H-H bonds for the formation of H2.

Figure 4. Time-dependence of the total number of molecules/radicals during the cook-off simulation of the PMHS/HPCS mixed polymer.

Figure 5 shows the time evolution of some products from decomposition of the mixed polymer. H and CH3 radicals are observed as intermediate products during the pyrolysis, and they form more stable CH4 and/or H2 by a fast secondary reaction, leading to large fluctuations on the numbers of H and CH3 radicals. In addition, more H2 and C2 hydrocarbons (e.g. C2H4) may be formed due to CH4 decomposition at high temperatures, which will be shown in the later section. Other products are not discussed because H2 and CH4 are the main gas products.



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Figure 5. Time evolution of the compounds formed during cook-off simulation of the PMHS/HPCS mixed polymer.

It usually takes several hours to complete the pyrolysis of polymer precursor in the experiments, but the time is limited to nanosecond at the most for the MD simulations. Therefore, it is crucial to determine the temperature at which of pyrolysis are to be carried out in the simulations. A series of time-dependent MD calculations at various temperatures of 600, 900, 1200, 1400, 1600, 1800, 2000, and 2200 K were performed to further confirm the appropriate pyrolysis temperature. Each MD simulation lasted for 20 ps was carried out in the NVT ensemble with the time step of 0.1 fs. Other parameters were the same as before. The results are shown in Figure 6. C-H bond increases with increase of temperature up to 1800 K, shows in Figure 6(a), mainly because of the formation of CH4 from H and CH3 radicals, while it begins to decrease above 2000 K. From Figure 6(b), Si-H bond tends to increase up to 2000 K owning to the breaking of C-Si and/or Si-O bonds and forming silane and methylsilane. The number of Si-Si and Si-O bonds have barely increase from 2000 K to 2200 K, and the bonds break and form frequently due to large volatilities above 1200 K, see Figures 6(c) and (d). With the above in mind, 1800 K was selected as the pyrolysis


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temperature in our MD simulations of gas removal later, so as to keep the backbone of the precursor polymer (-C-Si- and -Si-O-) as intact as possible, meanwhile to make sure the Si-H, C-H and Si-CH3 bonds break readily. Higher temperatures are required in the pyrolysis simulations than in the actual experiments of 1175 K, which is mainly for the time scale of a few nanoseconds in the MD simulations and several hours in the actual experiments.

Figure 6. Time-dependence of the number of bonds at various temperatures during the pyrolysis. (a) C-H, (b) Si-H, (c) Si-Si, and bonds.

5. GAS REMOVAL SCHEME TO FORM SiOC In this section, we will introduce a gas removal process, illustrated in Scheme 1. This scheme mimics gas escaping process during the experimental pyrolysis and was carried out by a series of NVT-MD simulations implemented with our own script code.



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Since H2 and CH4 are the major gas products from the pyrolysis analysis, it is crucial to determine the deleted atom list. As pointed earlier, H radical is in high energy state and have a strong tendency to form H2,18 while this process consume too much time for RMD simulations. In order to accelerate the simulations, H radicals were deleted, which equals to deleting H2. Moreover, according to our previous analysis, some CH4 molecules was eliminated as gas products, and others were decomposed into C2 hydrocarbons and H2, as shown in Figure 7. Therefore, additional C and H atoms need to be deleted when forming CH4 products in each iteration. As can be seen in Figure 7, CH4 molecules are degraded into C2 hydrocarbons (e.g. C2H4), and C2 hydrocarbons decomposed into residual carbon in turn. This may lead to more residual carbon in the SiOC structure and help us to gain more insight into the relationship of the stoichiometry and properties between polymer precursor and pyrolysis products.

Scheme 1. The shell script of gas removal scheme for removing the H2 and CH4.


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Figure 7. Time evolution of the PMHS/HPCS mixed polymer observed during NVT-MD simulations integrated with the gas removal scheme.

In order to implement the abstractions mentioned above, a series of NVT-MD simulations carried out by LAMMPS package were integrated with our shell programming to evaluate the atoms to be deleted. In Scheme 1, it is necessary to identify whether H2 and CH4 are generated: 1) for H2 molecule, H atom is appended to the deleted atom list if the distance between H atom and its neighboring C, Si, and O atoms exceeds their corresponding bond length; 2) for CH4 molecule, H and C atoms are added to the deleted atom lists when the C atom not only coordinated with four H atoms but also the lengths of the C atom between its neighboring atoms of C, Si, and O are larger than their bond length. Cutoff distance of the neighbor list is set to be 10.0 ℃. Here the bond length is sum of van der Waals radiuses of the atoms by a factor of 0.6, which is 2.064, 2.292, 1.692, 1.872, 1.920, and 1.500 ℃ for the C-C, C-Si, C-H, C-O, Si-H, and O-H bonds, respectively.



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As described in Section 4, 1800 K was selected as pyrolysis temperature in the gas removal MD simulations. The calculations were performed at a heating rate of 0.1 K/fs. The time step was set to be 0.1 fs in this section. Six periodical gas removal simulations were performed at 600, 900, 1200, 1400, 1600, and 1800 K for 10 ps, respectively. 9 H and 1 C atoms were removed from the system after these six stages. Then, extensive MD calculations integrated with the shell script were carried out by using NVT ensemble at 1800 K. It must be stressed that the total number of atoms (N) is held fixed when the NVT ensemble is used for a MD simulation. The effect on the dynamics of the system should be noted when eliminating an atom throughout the calculations. Thus, there is enough time to readjust the potential and kinetic energies after each removal step. The NVT-MD simulations were lasted for 10 ps during the first 88 cycles, while after that 3 ps was used for the running time. It takes 1343 calculation cycles (about 4.7 ns) to eliminate all the 1008 H and other 117 C atoms. After that, the system consisted of 495 atoms, including 139 C, 240 Si, and 116 O atoms, respectively. Volume of the system after the last step of the gas removal process equals to the relaxed atomic model of the PMHS/HPCS polymer. Therefore, the simulation box was further shrunken to form amorphous SiOC ceramic with a rational density. To obtain the most stable amorphous structure, it is necessary to make the system climb energetic barriers for searching a conformations with the lowest energy. On the basis of extensive pre-calculations, the system was first heating up to 3000 K at 0.1 K/fs, followed by compression at 1.2 GPa in a short time using NPT-MD simulation. Then, the amorphous structure was equilibrated by using of


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NVT-MD simulation for 100 ps, followed by adjusting the temperature and pressure to ambient conditions. The amorphous SiOC conformation was further relaxed at 300 K and 0.1 MPa by NPT-MD calculations to achieve a true equilibrium structure. The final SiOC structure with the density of 2.829 g/cm3 is shown in Figure 8(a).

Figure 8. (a) Final equilibrium structure and (b) computed radial distribution function g(r) of the amorphous SiOC ceramic.

The equilibrium structure of SiOC was verified by calculating its g(r), as shown in Figure 8(b). The peaks corresponding to C-C, Si-O, Si-C, and Si-Si bonds are marked in Figure 8(b), and are well consistent with the previous report.18,41 This indicates good accuracy of the dense amorphous SiOC structure generated from pyrolysis of polymer precursors. Molar ratios of the Si, O, and C atoms in the dense amorphous SiOC structure model can be further adjusted by using this MD simulation method, which makes it possible to simulate composition/structure dependence of their unique



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properties. 6. CONCLUSIONS An atomic model of dense amorphous SiOC ceramic was obtained from pyrolysis of PMHS/HPCS polymer precursor using a series of RMD simulations integrated with a shell programming of gas removal scheme, and the scheme mimics gas escaping process in experiment well. The referenced ReaxFF potential is confirmed to be applicable to our C/Si/H/O system after validation tests. From pyrolysis analyses, 1800 K was selected as pyrolysis temperature in our MD simulations, and H2 and CH4 were the main gas products. The decomposition of part of CH4 molecules into C2 hydrocarbons and H2 affects the residual carbon content and further affects the final SiOC structure. The final atomic model of dense SiOC ceramic was generated by using a series of NVT-MD simulations cooperated with our script code to removing the H2 and CH4. The g(r) peaks of the final SiOC structure were computed and found to be in good accordance with the previous report. These results suggest the accuracy of the MD simulations and the atomic model of SiOC ceramic. ASSOCIATED CONTENT Supporting Information Three additional files associated with this paper are included: (1) Time evolution of the number of bonds during cook-off simulation of the PMHS/HPCS mixed polymer, (2) PMHS_HPCS.cif file, (3) SiOC.cif file. AUTHOR INFORMATION Corresponding Author *E-mail:

[email protected].

Tel.:

+86-029-82663453.


Fax:

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A Reactive Dynamics Simulation Study on the Pyrolysis of Polymer

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