Atomistic modeling of the decomposition of charring

Atomistic modeling of the decomposition of charring ablators Balaji Shankar Venkatachari1, Gary C.Cheng2 University of Alabama at Birmingham, Birmingham, AL, 35294, USA

Ioana Cozmuta3 ELORET corp., Sunnyvale, CA, 94086, USA Abstract The composition of the pyrolysis gases that are injected into the boundary layer gas from an ablative thermal protection system (TPS) has a significant impact on the aerothermodynamics near the TPS surface. Recent analysis revealed that predicted surface response (surface temperature) of the TPS is very sensitive to the initial composition of the pyrolysis gases in the pyrolysis zone and leads to large uncertainties. This sensitivity study used a recently developed high-fidelity numerical model – one that accounts for the transport and reaction of the pyrolysis gases through the char in the surface ablation process, using both equilibrium and detailed finite-rate chemistry. For most carbon (PICA) or silicon (AVCOAT) based ablators the decomposing phase is a phenolic resin for which the underlying mechanism of thermal decomposition is unknown; the by-products of the thermal decomposition have also not been experimentally determined. The current study represents an attempt to obtain an improved fundamental understanding of the thermal decomposition process of phenolic resins, using reactive force field (ReaxFF/LAMMPS) atomistic simulations and characterize the composition of the resulting pyrolysis gas at various temperatures. In this study, decomposition pathways along with the composition of the resulting pyrolysis gases at different temperatures are determined for phenol and one other sub-structure of the PICA monomer, as a precursor for future studies on the thermal decomposition of more complex substances like PICA and other phenolic-resin based ablators. Results from these simulations are outlined in terms of detailing the decomposition pathway and by comparing the resulting composition of the pyrolysis gases against available experimental data. Potential use of these simulation tools in constructing simplified chemical kinetic models, which has wide implications for TPS modeling, is also discussed.

I. Introduction Charring ablative heat shields have been the preferred choice of thermal protection systems for many planetary entry/re-entry vehicles1. In this regard, there have been several studies2-4 investigating the process of ablation and on how it effectively protects these vehicles. A significant component in design of ablative TPS involves the chemical interaction between the ablation system and the boundary-layer flow. This aspect can be further broken down into: (i) surface interaction between the char layer and the boundary layer; and (ii) the influence of the pyrolysis gases (a by-product of the decomposition of the ablators) that get injected into the boundary layer. The exit gas composition is critical to correctly predicting the aerothermodynamics (including chemical reactions) of the boundary layer near the TPS surface and thereby estimate the heat flux experienced by the TPS. As reported in the work of Ahn et al.5, the influence of pyrolysis gas composition in cooling the TPS is quite substantial. Improving the accuracy in predicting the exit gas composition forms the main objective of this study. 1

Graduate Student, Dept. of Mechanical Engineering, Student Member AIAA. Associate Professor, Dept. of Mechanical Engineering, Senior Member AIAA. 3 Senior Research Scientist, Reacting Flow Environments Branch, Member AIAA. 1 American Institute of Aeronautics and Astronautics 2

Given the complex and difficult physics involved in the behavior of ablative TPS systems, as well as the high costs associated with performing flight test, design of ablative TPS often relies on numerical simulations anchored to various types of ground tests that have limited coverage of parameter envelopes relevant to hypersonic flight. A large variety of experimental techniques (determination of material properties, mass loss curves via thermogravimetric analysis, enthalpy curves via differential calorimetry, laser scans to evaluate surface recession, scanning electron microscopy and spectroscopy to determine elemental compositions and distributions) are used along the way to construct and validate parts of the baseline material response model. To build a high-fidelity numerical model to predict the thermal response of a charring ablative TPS, at least three different sub-models are needed: (i) an in-depth heat and mass transfer model; (ii) a pyrolysis model governing the rate of pyrolysis of the virgin ablative material and to predict the composition of the resulting pyrolysis gas; and (iii) a surface energy balance model to calculate the surface recession rate of the TPS. Although much work has been done regarding aspects (i) and (iii),6-10 even in the most modern state-of-the-art ablation codes6, 10 the pyrolysis models still lack important features. Specifically, most codes do not model the transport of pyrolysis gases through the char and their chemical kinetics completely, and hence do not correctly predict the heat absorption effect of the flowing pyrolysis gas as well as their exit gas composition at the ablator surface. Unfortunately, neither experimental nor numerical studies have been performed with sufficient detail, to determine quantitatively the pyrolysis gas species concentrations during ablator thermal decomposition. Hence, most existing surface ablation codes ignore chemical reactions taking place within the: char entirely and often arrive at the gas composition above the TPS surface based on the assumptions that: (i) ejected gases reflect the initial elemental composition of the ablative resin; and (ii) ejected gases come into thermo-chemical equilibrium at the TPS surface temperature. Both these assumptions can lead to significant errors in the prediction of heat-flux experience by the TPS. However, to accurately predict the exit gas composition, one must correctly identify the initial gas composition arising from the pyrolysis of the ablator and also account for the change in their composition - due to them undergoing further thermal decomposition as well as chemical reactions among themselves and with the solid material. In an attempt to account for all the above-mentioned interactions of the pyrolysis gases and to improve the fidelity of existing numerical models, we have developed a stand-alone thermal response code11, 12 that simulates the transport and chemical reactions of the pyrolysis gas as it passes through the char (in the surface ablation process) using both equilibrium and finite-rate chemistry models. Using this code, a sensitivity analyses study13 was performed in which the influence of different parameters and properties associated with the ablation process was estimated. Based on the study, it was inferred that the pyrolysis gas composition entering the char layer of the TPS has a strong influence on the outcome of predicted surface response (surface temperature). The pyrolysis gas composition entering the char is dependent on how the ablator shield material pyrolyzes and needs to be specified as an inlet boundary condition to the developed surface ablation code. However, there is no such data available (from either experimental or theoretical studies) for phenolic-based ablators materials like PICA14 or AVCOAT, that are of importance in relation to on-going/future space exploration missions, and thus the numerical result from our ablation code bear a large uncertainty. To substantially minimize this uncertainty and improve the fidelity of the developed model, there is a need to obtain this missing piece of information through theory or experiments. In this regard, atomistic simulations using reactive force fields are being increasingly used to investigate the thermal decomposition process of many complex polymers and substances15. If utilized to model the pyrolysis of ablative heat shield materials, atomistic simulations by their nature, could help us obtain a more fundamental understanding of the pyrolysis process itself in addition to the decomposition pathways. The current study aims to attempt the same and identify the correct decomposition pathway of phenolic resins, which would then help obtaining a quantitative estimate of the pyrolysis gas composition for a range of temperatures. The current work presents details of the utilization of reactive molecular dynamics (MD) methods to model the thermal decomposition of materials employed as ablators, with the primary emphasis of the study being the identification the major gaseous species formed as a result of pyrolysis along with their composition (and the influence of temperature). This process is applied to model pyrolysis of phenol molecule as well a monomer unit that is characteristic to the PICA - in an attempt to model more complex phenolic–resin based materials in the future - results of which are presented and discussed. Comparisons of simulations data against data available in literature (experimental studies) are also reported. This paper is divided into six major sections with the second section briefly describing the various atomistic simulations available along with details on those employed in this particular work. The third section details the 2 American Institute of Aeronautics and Astronautics

modeling procedure employed in the studies reported herein. Brief experimental studies on pyrolysis of phenol make up section four, while the remaining sections contain details of results from validation of the atomistic simulation procedure, and simulation of the pyrolysis of phenol and the monomer representative of PICA, along with potential future work.

II. Atomistic Simulation Tools Given the challenges in experimentally modeling chemical processes and their prohibitive costs, researchers have increasingly begun to utilize computational methods to understand the theory behind these chemical processes. Quantum mechanics is often the preferred method to model chemical processes. However for most practical systems, the prohibitive computational costs (due to the large size of the system) of ab initio quantum mechanics methods render them unsuitable for studying or predicting dynamical properties of large molecules and solids. In this regard, MD methods are a more practical solution to model such problems and have been gaining popularity. The use of MD methods to study chemical processes can be broadly classified into three major categories: (i) an empirical approach that involves development and utilization of force fields to model the chemical processes; (ii) the hybrid approach that utilizes a combination of quantum mechanics and molecular mechanics methods to model chemical processes, and (iii) ab initio methods involving density functional theory (DFT). Each of these approaches has its own benefits and challenges, details about which can be found in Ref. [16]. In this work, we will however utilize the empirical approach, with the reason being that the utilization of force fields allows one to quickly evaluate the forces and other dynamical properties of a system. As a result, one can obtain highly accurate results that are comparable to those of quantum mechanical calculations, in a fraction of the computer time. Many of the force fields commonly used in chemistry, such as DREIDING17, UFF18 and MM319, are based on molecular mechanics and embody a classical treatment of particle-particle interaction and a rigid connectivity; allowing it to reproduce structural properties and conformation changes accurately but can not describe chemical reactivity. A few of the force fields that can model chemical reactivity include Brenner, Valbond, and BEBO (see Ref. [20]); these however have many shortcomings and often cannot be employed to model complex molecules. In this work we will be utilizing the ReaxFF20 force field that was developed specifically for hydrocarbon systems. Other alternatives to this force field can be found in Refs. [21] and [22]. A. ReaxFF ReaxFF20 is a general bond-order parameterized force field that enables modeling, at atomic level, of bond breaking and formation. The main difference between traditional non-reactive force fields and the reactive ReaxFF is that, in ReaxFF the connectivity is determined by bond orders calculated from interatomic distances that are updated after every MD step. This allows for smooth breaking and formation of bonds during the simulation. ReaxFF has been developed in such a manner that it accounts for non-bonded interactions, such as Van der Wall and Coulomb interactions, from the beginning and utilizes quantum chemistry calculations to obtain the dissociation and reaction curves that are needed to describe bond breaking and formation in molecules. Additionally, ReaxFF accounts for polarization effects through use of a geometry-dependent charge calculation scheme. A more detailed description of ReaxFF can be found in ref. [20]. To date, ReaxFF has been successfully applied to a variety of chemical problems23-26 that include thermal decomposition of polymers. B. LAMMPS The MD code employed in this research was the massively parallel general-purpose open source particle simulation code LAMMPS27 (Large-scale Atomic/Molecular Massively Parallel Simulator) from Sandia National Laboratories. It has a variety of force fields, making it suitable for modeling a wide range of problems. Being an open source code, it is continuously supported and is easily extensible. ReaxFF force field has been recently integrated into the LAMMPS code and is the only available parallel implementation of ReaxFF, making LAMMPS our ideal choice of MD code. More details on LAMMPS and its applications can be found in ref. [27].

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III. Modeling method for studying thermal decomposition of ablators With atomistic modeling of the thermal decomposition of charring ablators being the main emphasis of this work, we will focus on the commonly used ablator material PICA, monomer of which is shown in Fig. (1). PICA14 material is obtained by cross-linking this monomer. In this section, we provide details on how the modeling is performed.

Figure 1: The original PICA monomer, Phenol and the simplified neutral sub-structure modeled. A. Selection of initial molecular models Before we attempt to model the decomposition of a complex organic molecule like PICA, due to lack of experimental data (pyrolysis gas composition of PICA) for comparison and in an attempt to keep the size of the system (number of atoms) being simulated small, the study of decomposition of PICA is split to 3 components. This process is inline with the procedure adopted by Salmon et al. 26 in their study of the thermal decomposition of kerogen. The main tasks involved in the study of decomposition of PICA is as follows: 1) Atomistic simulation of the decomposition of smaller molecules like Phenol and a neutral submonomer shown in Fig.1.Each of these, represent specific sub-structures of the PICA monomer. 2) Modeling of the thermal decomposition of the PICA monomer. 3) Atomistic simulation of PICA itself. In this work, we focus on task (1) alone. One of the primary reasons for studying decomposition of smaller molecules - that make up the sub-structure of the main monomer - is that there often exists experimental or theoretical studies of pyrolysis of these smaller molecules that one could use to compare the results obtained from atomistic simulations. Additionally, the smaller size of system that needs to be modeled offers benefits in terms of computational effort. For the case here, there have been some important studies on the high-temperature pyrolysis of phenol, which could provide us the needed data to compare our simulation results against. The second sub-structure chosen here has no experimental/ theoretical data. However, this sub-structure was chosen under the assumption that the fundamental PICA monomer (that has four similar aromatic structures linked among each other through methyl groups), on decomposition would initially break into 4 aromatic structures; and this chosen sub-structure had the most complex form amongst the four aromatic structures. As a result of this assumption, we expect that the results from decomposition studies of the sub-structure considered would provide details about the decomposition behavior of the main monomer itself. Henceforth in this work, this sub-structure will be addressed as the neutral sub-structure of the PICA monomer. B. MD simulation procedure The thermal decomposition simulations on Phenol and the neutral sub-structure of the PICA monomer were conducted according to the following scheme: 4 American Institute of Aeronautics and Astronautics

1) First the atomistic representation of the molecule of interest is constructed using software like Materials Studio (Accelrys software). Several replicas/copies of this molecule are generated. 2) These replicas are then packed in a unit cell using rotational isomeric state tables and random configurations with random packing to a target predefined density close to the corresponding experimental density.

Figure 2: Procedure used to simulate thermal decomposition of materials. 3) An energy minimization (low temperature MD) to release any internal stresses that could arise from the amorphous build is then performed 4) The minimized unit cells are then equilibrated at the initial pressure and temperature conditions of interest (300K and 1 atm, in this case). This step consists of a fixed volume NVT-MD (NVT stands for fixed number of atoms, volume, and temperature) that is carried out first (for around 20 picoseconds) using the Berendsen thermostat to maintain the system at 300 K. This is then followed by a NPT-MD (NPT: fixed number of atoms, pressure, and temperature) at a pressure of 1 atm and a temperature of 300 K, where the system’s volume is allowed to expand or contract, until the system reaches its actual density at those conditions. 5) A cook-off/ heat up simulation is then performed on the selected system, wherein the temperature of the system is ramped (within a span of ~10-40 picoseconds) from room temperature to a realistically high temperature (~3500K) for various heat up rates. Results from these cook-off simulations are utilized to identify the onset temperature of thermal decomposition at the picosecond time scale of our simulations. 6) Using results from the cook-off simulation, stand-alone molecular simulations at constant temperature conditions (NVT-MD) are conducted for a set of temperatures around which major changes were observed. These simulations are conducted for a large duration of time, and the time history of the various species created or destroyed along with their numbers/concentration are extracted. For conducting these NVT runs, the following procedure is adopted: (i) The equilibrated system’s temperature was first ramped up from the room temperature value to the non-reactive temperature limit (temperature slightly below one at which the onset of thermal decomposition was observed in cook-off simulations) and is equilibrated there using a NVT-MD and Berendsen thermostat (for around 5-10 picoseconds). (ii) Then, a quick ramp up from the non-reactive temperature limit to the target temperature is done within 10000 MD steps (preferred time step = 0.1 femtoseconds). (iii) It is then followed by constant temperature NVT-MD runs at the target temperature for 50 picoseconds or longer. 7) These constant-temperature simulation runs are then repeated several times to increase statistical sampling and then utilized to arrive at a detailed listing of the decomposition mechanism, as well 5 American Institute of Aeronautics and Astronautics

as the components and composition of the pyrolysis gases at those various temperatures. The initial configuration of the system for these additional runs could come either by generating various periodic cell configurations in a software like Material studio or by saving trajectories (along with velocities) at various time steps from a low temperature MD simulation. Steps 3, 4, and 6 are then applied to these unique configurations. 8) These results are then compared against experimental data, if available, to validate the approach and make necessary changes before being applied to materials like PICA for which no experimental data are available. Outline of the entire procedure is indicated in Fig. 2.

IV. Brief overview of experimental/theoretical studies on pyrolysis of phenol Although limited in number, there have been some important studies on the high-temperature pyrolysis of phenol, given its importance in the area of protective heat shields as well as combustion of aromatic compounds. It is of note, however, that most of these studies disagree with one another regarding the initiation step of the pyrolysis of phenol. Cypres and Bettens28, who experimentally studied the pyrolysis of phenol in the temperature range 938K to 1138 K, concluded that the hydroxylic H atom first undergoes a migration to a position within the phenolic ring, resulting in a keto molecule (C6H6O) that decays into cyclopentadiene and carbon monoxide, as shown in Eq. (1). C6H5OH → C6H6O → C5H6 + CO

(1)

On the other hand, Lovell et al.29, and Manion and Louw30, based on their experimental studies on phenol pyrolysis in a H2/N2 atmosphere, arrived at a different initiation step. Herein, the phenol decay begins with the formation of a phenoxy radical + H as shown in Eq. (2), which is then followed by the decay of the phenoxy radical into a cyclopentadienyl radical and carbon-monoxide as given by Eq. (3). C6H5OH ↔ C6H5O* + H

(2)

C6H5O* ↔ C5H5* + CO

(3)

As a result, we have two different initiation reaction mechanisms as shown in Eqs. (1) and (2). In recent times, Horn et al.31 and Brezinsky et al.32 have also investigated this dilemma, without any closure. Horn et al.30 (based on his shock-tube studies and computational work) arrived at the same conclusion as Cypres and Bettens et al.28 while the work of Brezinsky et al.31 agreed with Lovell et al.29 in that the H formation step was the initiation mechanism. However, Brezinsky et al.32 also did predict a scenario, wherein Cyclopentadiene and carbon monoxide could be produced in flow reactor experiments, despite H formation being the initiation step, which could have led Cypres and Bettens27 to conclude that CO formation was the initiation step. Although there is uncertainty regarding the initiation reaction, in most other aspects, many of these studies agree with each other in terms of the major reaction intermediates and minor species. All of them predict carbon monoxide and cyclopentadiene to be the major reaction intermediates, while benzene, acetylene, naphthalene, methylcyclopentadiene, and methane are the minor species. Based on these studies, after the initiation step, some of the key steps that could occur during the pyrolysis of phenol are described below: 1) Abstraction or displacement reaction of phenol:

2)

C6H5OH + H ↔ C6H6 + OH

(4)

C6H5OH + H ↔ C6H5O + H2

(5)

OH produced in the displacement reaction (Eq. (4)) abstracting H from phenol to form water: C6H5OH +OH ↔ C6H5O* + H2O

3)

Phenoxy radical decomposing to produce CO and cyclopentadienyl radical: 6 American Institute of Aeronautics and Astronautics

(6)

C6H5O* ↔ CO + C5H5* and 4)

(7)

Reactions of the resonantly stabilized propargyl radical: 2 C 3H 3 ↔ C 6H 5 + H

(8)

Refs. [31] and [32] have more details on the key reaction steps including details on their rate kinetics, through which the pyrolysis of phenol proceeds. These studies and the decomposition mechanism outlined therein could help us ascertain the validity and accuracy of the atomistic simulation procedure, and thereby refining the simulation approach, before it is adopted to model the pyrolysis of complicated materials like PICA - that have very little or no experimental data.

V. Results and discussion In this section we present results from our study on thermal decomposition of phenol and neutral substructure of PICA monomer, as well one another study of high temperature oxidation of methane (that served as a validation study). Note that, as the time scale of MD simulations are much shorter compared to those in experiments, simulations are often carried out higher temperatures (than those in experiments) in order to observe chemical reactions on the computational time scale. As a result of this difference in time and temperature scale, product distributions may get affected; however, qualitative agreement with the actual mechanism for the initial decomposition process is expected. ReaxFF parameters for carbon, hydrogen, and oxygen used in these simulations were taken from a previously published data set25. A. High-temperature gas phase oxidation of methane As part of our preliminary study, in an attempt to understand the atomistic simulation tools, we conducted simulations of high temperature oxidation of the methane. The primary motivation behind that investigation was to identify the reaction pathway of the combustion process and compare it against other numerical simulations as well as experimental studies. The secondary motivation was to gain an understanding of the use of reactive force field ReaxFF with the LAMMPS software. ReaxFF has only recently been ported into the LAMMPS code; hence, this task serves the additional goal of identifying any issues that may exist in their integration with relevance to this particular study. In this simulation, a periodic cell containing one methane molecule and 100 oxygen molecules was created. After the minimization of the system using low temperature MD, the system was equilibrated at a temperature of 2500K using a NVT-MD (100 picoseconds duration). Following equilibration, an NVT-MD at 2500 K was carried out for a duration of 500 picoseconds using a time step of 0.1 femtoseconds, in order to understand the mechanism behind high-temperature oxidation of methane and to determine the initiation time (time at which the first set of reactions occur coinciding with the disappearance of methane molecule) required for oxidation of methane. Figs. 3 - 4 along with Eq. (9) indicate the possible reaction pathway followed by the system modeled. The initiation of oxidation occurs around 230 picoseconds, starting with the hydrogen abstraction by the oxygen molecule to form a methyl and hydro-peroxyl radicals. This predicted pathway compares well with those results reported in an earlier study25 (the study had utilized a serial version of ReaxFF and compared results against experimental data), thereby validating ReaxFF and its implementation into the LAMMPS code. Although not directly relevant to the thermal decomposition process, which is the focus of this paper, this validation study is still relevant from the perspective of gassurface interactions (key area for TPS modeling) indicating the reaction pathway for methane, released as pyrolysis gas, interacting with molecular oxygen. The reaction pathway indicated here, could then be utilized to build a simplified kinetic model for modeling the gas-surface interaction itself.

(9)

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Figure 3: Evolution of key intermediaries in high-temperature oxidation of methane (lean mixture)

Figure 4: Visualization of the various key intermediates formed during the simulation of the high temperature oxidation of methane

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B. Thermal decomposition of phenol A periodic cell containing 40 units of phenol (system of 520 atoms) was created using molecular modeling software. Five unique configurations of the same were created for use in a statistical study. The periodic cell was minimized using low temperature MD, that was then followed by equilibration at fixed volume (NVT) using the Berendsen thermostat to maintain the system at 300K for 10 picoseconds, as outlined earlier. Following this, the system was allowed to expand or compress, in order to reach its experimental density by subjecting it to NPT equilibration at 300K and 1 atm pressure for another 10 picoseconds. The equilibrated system was then subjected to a heat-up/cook-off simulations, wherein the temperature of the system was ramped up from 300K to 4000K at rates of 46.25, 92.5 and 185 K/picoseconds respectively, in order to determine the onset of the thermal decomposition of phenol at the picosecond time level (Fig. 5). From Fig. 5 it can be seen that the thermal decomposition of phenol at the picosecond time scale begins between 1200 – 2000K.

Figure 5: Determination of initiation temperature using NVT dynamics at different heating rates. Table 1: Products formed at end of cook-off simulations (dT = 92.5 K/ps) Molecular Formula C12H12O2 C12H11O C12H10O C 6H 7O 2 C 6H 7O C6H6O (Phenol) C 6H 5O C 6H 5

No.of Molecules 2 1 1 1 1 25 1 1

Molecular Formula C 2H 2 C 2H C2 H 2O OH H2 H

No.of Molecules 3 4 2 3 2 1 1

In actual experimental conditions27-34, phenol begins to decompose at much lower temperatures. However, because of the picosecond time scale of the MD simulation runs, we observe it only at temperatures higher than those found in experiments, as mentioned at the beginning of the section. Figure 6 shows the evolution of some of the intermediate species during the heat-up simulations for the various heatup rates. Table 1 lists the products from the cook-off simulation for a heating rate of 92.5 K/ps. Based on the results from the cook-off simulation temperatures 1300K, 1500K, 1750K, 2000K, 2500K, 3000K, and 3500K were identified for conducting constant temperature MD runs, in order to gain a more detailed understanding of the decomposition process. The non-reactive temperature limit was identified as being 9 American Institute of Aeronautics and Astronautics

around 1200K. All constant temperature MD runs were carried out for a time period of 50 ps (time step = 0.1 femtoseconds). Based on the results obtained from the constant temperature runs, it was seen that between 1300K – 2500K, not much decomposition of phenol takes place. As a result, OH and C6H5 radicals seem to be the only species that evolve intermediately. At the end of the simulation, most of the original phenol was recovered without any decomposition. Results from the constant temperature run at 3000K, indicates a substantial change from what was observed until then. By the end of the run, the number of phenol units had decreased from 40 to 28 and Table 2, given below, indicates the major species that was observed along with their number of units. Results from the constant temperature run at 3500K (Table 3) also indicate a similar trend. At the end of the simulation, all of the phenol had decomposed and no big aromatic chains were left behind. For comparison, end products of the thermal decomposition of Phenol obtained by experimental studies28-35 is listed under Table 4. The influence of the temperature on the decomposition of phenol is described through Fig. 7. The drastic change in decomposition rate between temperatures 3000 K and 3500 K indicates the need for conducting more constant temperature MD runs at around 3000 K for obtaining a better characterization of phenol decomposition and its rate. Although many of the species observed in experimental studies28-35 have also been observed in the results from the atomistic simulations, there is also some considerable discrepancy. One of it is that, we were never able to isolate the formation of the cyclopentadiene molecule and its radical form, which was predicted, by experimental studies, during the initiation of the decomposition of phenol. It was often only found during the intermediate stages and their formation at those stages could be explained through Eqs. (6) and (7). We did however find instances of co-polymerization and de-polymerization, through which the organic ring eventually breaks down to result in smaller hydrocarbons. Results from the simulation also predicted formation of acetylene (C2H2) and the highly reactive C2H species, both of which act as main precursors for soot formation. Table 2: Major species observed at the end of constant temperature NVT MD (T = 3000K) Molecular Formula C12H11O C12H10O C 6H 6O 2 C6H6O (Phenol) C 6H 5O C 6H 5

No. of Molecules 1 1 1 28 1 1

Molecular Formula C 2H 2 C 2H H 2O OH H2

No. of Molecules 2 3 4 1 1

Table 3: Major species observed at the end of constant temperature NVT MD (T = 3500K) Molecular Formula C 7H 7O C 6H 7O C6H6O (Phenol) C 6H 6 C 4H 6O C 4H 4O C 3H 4 C 3H 6 C 2H 6O C 2H 4 C 2H 3 C 2H 2O

No. of Molecules 1 1 0 1 1 1 1 1 1 2 1 1

Molecular Formula C 2H 2 C 2H C2 CH4O CH2O CH4 CO H 3O 2 H 2O OH H2 H

No. of Molecules 6 26 51 1 1 3 2 1 25 1 22 1

Table 4: End-products of decomposition of phenol as observed in experimental studies Major Products Minor Products

H2O, H2, CO, C2H4, C2H2, C6H6 C6H8, C5H6, C10H8, C3H4, C2H6, C3H6

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Figure 6: Evolution of key intermediates during the cook-off simulations for various heating rates

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Figure 7: Thermal decomposition yield for Phenol at various temperatures

(a) Number of Phenol molecules decomposing during the NVT run at 3500K

(b) Number of different species produced at various instances Figure 8: Results from the NVT run at 3500 K using five independent configurations 12 American Institute of Aeronautics and Astronautics

Although the MD scheme we utilize is deterministic, one still needs to understand that these simulations involve sampling of rare, reactive events. As a result, in order to test the reproducibility of the results and their statistical reliability, we repeat the entire constant temperature MD runs (for all target temperatures) using the five different configurations of the periodic cells constructed. Figures 8 (a) and (b) demonstrate the reproducibility of the results for decomposition of phenol at 3500 K, as well as the number of unique species generated in the process. As can be seen from Fig.8, there is a considerable spread among the results indicating that one needs to run more simulations (with unique configurations) in order to achieve statistical convergence and to accurately capture the rare reactive events. Efforts are currently on towards achieving this. C. Decomposition of neutral sub-structure of PICA monomer The second study, conducted as part of understanding the thermal decomposition of PICA, is the modeling of the thermal decomposition of the neutral sub-structure of PICA monomer (see section III). Here again, five unique configurations of the molecule considered were built, with each of the periodic cell containing 20 units of the molecule. Only 20 units of the molecules were packed into the unit cell, in contrast to the 40 units used in the phenol simulation, in order to maintain a similar system size (520 atoms in both cases).

Figure 9: Progress of cook-off simulations of the modeled neutral subtructure of PICA monomer The MD procedure remains predominantly the same as in the previous case. The periodic cell was minimized using a low temperature MD, that was then followed by equilibration at fixed volume (NVT) using the Berendsen thermostat for maintaining the system at 300K (10 picoseconds simulation). This was followed by a NPT-MD run (300K and 1 atm pressure) for another 10 picoseconds, thereby allowing the system to expand or compress in order to reach its experimental density. The equilibrated system was then subjected to heat-up/cook-off simulations, wherein the temperature of the system was ramped up from 300K to 4000K at two different rates, namely, 92.5 and 185 K/ps. Once again, this was done in order to determine the onset of the thermal decomposition of the neutral sub-structure at the picosecond time level (see Fig. 9). From Fig. 9, it can be observed that the onset of thermal decomposition (at the picosecond time scale) occurs in the range 1000 – 2500K. Temperatures 1000 K, 1500 K, 2500K, 2700 K, 3000 K, and 3300 K were identified as temperatures at which 40 picoseconds duration NVT-MD simulations were to be carried out. The various species that could be expected from the decomposition of the molecule, based on the end products of one of the cook-off simulation runs, is listed as part of Table 5. Comparing these results against those from the cook-off simulation results of phenol, many bigger molecules were found at the end of the cook-off run, indicating strong co-polymerization effects. Even for a moderate heat-up rate of 92.5K/ps, all of the molecules underwent decomposition by the end of the cook-off runs, unlike the phenol cook-off simulation where more than 50% of phenol remained intact. The major end–products found here were water, methane and some other smaller hydrocarbons, while it was mainly water in the 13 American Institute of Aeronautics and Astronautics

Table 5: Products formed at end of cook-off simulations (dT = 92.5 K/ps) Molecular Formula C19H20O2, C19H20 C14H15O C11H16O2 C10H14O2 C10H12 C9H10O3, C9H10O2, C 9H 9O 3 C8H6 , C7H8O, C6H10, C 6H 6O C 4H 3O C3H6 , C3H3O, C3H4 C 3H 3 C 3H 2

No. of Molecules 1 1 1 0 1

Molecular Formula C 2H 4 C 2H 3 C 2H CH4O, CH3O CH4

No. of Molecules 3 2 6 1 6

1

CH3

4

1

CO

1

1 1 2 1

H 2O OH H2

16 2 5

Table 6: Chemical composition observed after 40ps of NVT-MD simulations at 2700 K and 3000 K for the neutral sub-structure

Bigger Hydrocarbons

Medium size Hydrocarbons

Neutral sub-structure 20 × C1014O2 T = 2700 K C20H27O3 C20H25O3 C20H23O2 C19H24O2 C11H14O2 5 C10H14O2 2 C10H14O 2 C10H13O C10H11O C9H12O2 C9H12O

Smaller Hydrocarbons

C 7H 8O C 3H 2 CH2O

Others

8 H 2O OH H2 CO

T= 3000 K C28H32O2 C20H23O2 C11H16O C11H15O C11H14O2 C11H10 C10H16 0 C10H14O2 C10H13O2 C10H13O C10H12O C 6H 9 C 5H 7O C 4H 4O C 3H 2 C 2H 4O 2 C 2H 4 C2HO C 2H 2 4 C 2H 2 CH4O 2 CH4 CH3 2 CH2O 12 C2 16 H2O 8 H2 OH CO

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case of phenol; this in part could be attributed to the additional methyl groups that are attached to the ring here (see Fig.1). As results from all the five independent constant temperature runs (NVT-MD runs at the identified temperatures) were not available at the time of preparing this paper, results from a single run alone are presented here. As a result, these results can only be considered preliminary. Here again, in the temperature ranges 1000 K to 2000 K, very little decomposition of the sub-structure was found to occur. Only beyond 2500 K did substantial decomposition of the molecule occur. As mentioned at the beginning of this section, the small time scale nature of MD runs allow chemical reactions to be observed only at elevated temperatures. Results from the constant temperature MD runs at 2700 K and 3000 K are given in Table 6. As can be observed from Table 6, more number of heavier and moderate sized hydrocarbons was found at lower temperatures, indicating the occurrence of co-polymerization. At 2700 K, 25 % of the molecule remained intact while everything underwent decomposition at 3000 K. With increase in temperature increased concentration of water and hydrogen was also observed. When compared against phenol, more alcohols, ketones and smaller hydrocarbons were produced. Completion of multiple runs will allow us to collect more statistics and ascertain the repeatability of results. In addition, it is also expected to provide more insights into the initiation mechanisms of the decomposition. Based on the preliminary results presented here, the neutral sub-structure considered here seems more reactive than Phenol. It also appears to decompose faster and much lower temperatures (even at 3000K, more than 50% phenol remained intact). Additionally, the resulting pyrolysis gas composition appears to be richer in small hydrocarbons.

VI. Conclusion and future work The potential to use atomistic simulations as a tool for understanding the thermal decomposition of charring ablators and to identify the composition of the resulting pyrolysis gases was demonstrated through this work. MD along with reactive force fields like ReaxFF permit one to understand chemical processes that otherwise could be difficult to reproduce or understood experimentally. Initial studies on thermal decomposition of simpler molecule like phenol and the smaller subset of PICA monomer that were presented here could greatly help us refine the MD simulation procedure - in terms of determining the optimal computational time step, simulation time, system size, and the number of independent runs needed to achieve statistically reliable results – before it can be utilized to achieve our goal of modeling the thermal decomposition of more complex materials like PICA and other charring ablators. Potential future work also involves utilization of atomistic simulation to construct simplified chemical kinetic models for the interaction of pyrolysis gases and the char left behind from the pyrolysis, which has crucial implication in the prediction of soot formation and oxidation within TPS. The pyrolysis of a carbon-phenolic based material, such as PICA, can produce various hydrocarbons including aromatic hydrocarbons, which are main contributors to soot formation. Unfortunately, the detailed mechanism of soot formation and oxidation involve a very complex pathway, which includes hundreds or even thousands of chain reaction steps and makes the numerical simulation extremely computationally expensive. Atomistic simulations (reactive MD) can be very helpful to narrow down the most important pathways for the reactions taking place between char and the pyrolysis gases and thereby easing the procedure to construct simplified kinetic models. These approaches once perfected, can produce results that will greatly benefit TPS modeling codes and help reduce uncertainty in the results obtained from them.

VII. Acknowledgements This work was performed under the NASA constellation university institute project (NASA CUIP) program. The authors would like to acknowledge NASA’s technical help and financial assistance for making this work possible. The authors would also like to thank Dr. Adri van Duin of Penn State University, for sharing his experience and knowledge that was on immense value to this study. This work was made possible in part by a grant of high performance computing resources and technical support from the Alabama Supercomputer Authority.

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