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MOLECULAR SIMULATION OF OXYGEN REACTIONS WITH REALISTIC SILICA AND CARBON SURFACES AT HIGH TEMPERATURE Thomas E. Schwartzentruber, Savio Poovathingal, and Eric Stern Department of Aerospace Engineering and Mechanics University of Minnesota, Minneapolis, MN, USA Email: [email protected] ABSTRACT Recent computational results for gas-surface reactions including atomic level simulations of oxygen-silica recombination and microstructure level simulations of carbon-based ablative surfaces are summarized. Atomic level calculations of oxygen-silica reactions show the main recombination mechanism to be non-activated (associated with no energy barrier). This is in contradiction to current empirical models fit to limited experimental data. For ablative porous and non-porous TPS, where complex microstructure is important, the capability to image a real material with µm scale resolution via x-ray micro-tomography, triangulate the surface, and directly simulate the gas-surface interaction with DSMC is demonstrated. 1. INTRODUCTION During hypersonic reentry, a shock-layer forms in front of the spacecraft where temperatures can reach several thousands of degrees. Such high temperatures lead to the vibrational excitation and dissociation of diatomic and polyatomic molecules. At the low gas densities characteristic of high altitude hypersonic flight, the gas can diffuse through the boundary layer and reach the surface of the vehicle in a partially dissociated state, where reactive species drive gas-surface chemical reactions. There are two main classes of materials used for thermal protection systems (TPS); re-useable ceramics, which often form silica-based oxide coatings, and carbon-based ablative materials. For re-useable ceramics, the surface remains microscopically flat and chemical reactions occur at defect sites. Such surfaces can be precisely characterized at the atomic level and accurate electronic structure calculations can be used to study the reactivity of these surface defects. Recent results are summarized that identify the main defects on realistic silicon-dioxide surfaces that promote exothermic catalytic reactions with oxygen [1]. Most importantly, these calculations show the main recombination mechanism to be nonactivated (associated with no energy barrier). This is in contradiction to current empirical models fit to limited experimental data. Furthermore, the summarized calculations (and recent experimental results [2]) show a significant probability of recombination into the first electronically excited state of molecular oxygen. For ablative materials, complex changes in microstructure occur that have a significant impact on the overall gas surface interaction. It is now possible to use x-ray tomography to image a real TPS material in 3D, triangulate a surface geometry, and directly simulate boundary layer gases interacting with real material microstructure [3,4]. Results are summarized where the DSMC method is used to simulate reacting gas-flow over (and within) porous fiber-based carbon TPS microstructure obtained from micro tomography. 2. OXYGEN SILICA INTERACTIONS A substantial amount of previous research has been conducted regarding computational chemistry studies of oxygen recombination on silica surfaces [5-11]. These studies use computational chemistry techniques to investigate oxygen interactions with a specific crystalline polymorph of SiO2 (called β-cristobalite). The choice of β-cristobalite is motivated by experimental studies from Balat-Pichelin et al. [5,12,13] where silicon-carbide (SiC) surfaces were exposed to high temperature air-plasmas. In contrast to these studies, our research focuses on “defective” silica surfaces. Amorphous SiO2 surfaces inherently contain defect structures. Furthermore, simulations predict that both crystalline surfaces (such as reconstructed quartz surfaces) and amorphous surfaces contain the same defects when exposed to dissociated oxygen [1]. Our computational research has shown that it is only on such defect sites (also referred to “active sites”) where recombination reactions are energetically favored, and that crystalline (nondefective) surfaces are completely non-catalytic. Calculations were first performed using the ReaxFFSiO potential [14], which accurately predicted the bulk structure of amorphous-SiO2 (a-SiO2) and α-quartz, as well as a number of surface defect chemistries that participate in catalytic recombination reactions [15]. Since ReaxFFSiO was not developed for such defects and gas-surface reactions, a study was performed where a large number Density Functional Theory (DFT) energy calculations, spanning a large number of configurations for each defect, were performed [16]. Essentially, all of the surface features predicted by the original ReaxFFSiO potential and interactions with atomic and molecular oxygen were analyzed in detail using DFT. As gasphase atoms/molecules were moved relative to the defect sites, single point energies were computed. These energy curves were compared to the predictions of the original ReaxFFSiO potential, and were then used to fit a new ReaxFFSiOGSI potential; greatly improving the accuracy [16]. However, the ReaxFFSiOGSI potential still exhibited accuracy limitations for binding energies and energy barriers due to the complexity of the energy surface [1,16]. Figure 1. Amorphous SiO2 surface exposed to atomic oxygen. Resulting surface defects are highlighted. The new ReaxFFSiOGSI potential was quite successful in predicting the most stable defect structures. The most dominant are shown in Fig. 1, and shown in more detail in Fig. 2. In fact, the more accurate ReaxFFSiOGSI potential now successfully predicted the dominant defect, the peroxyl defect (Fig. 2c), which lent further confidence to the ReaxFFSiOGSI potential. To further verify this peroxyl structure, more DFT calculations were performed of this defect and found that it is indeed an energetically favorable (stable) defect that would be expected to participate in recombination reactions [1]. (a) (b) (c) (d) Figure 2. Dominant defects in catalytic cycle: (a) Under-coordinated silica defect (≡ Si⋅) (b) Non-bridging oxygen defect (≡ Si-O⋅) (c) Peroxyl defect (≡ Si-O 2 ⋅) (d) Recombination reaction, and return to the nonbridging oxygen defect to continue catalytic cycle There is experimental evidence for the existence of the (≡ Si⋅) and (≡ Si-O⋅) defects on silica surfaces under irradiation and fracture. The (≡ Si⋅) defect has been extensively studied, and has been identified on irradiated and vacuum fractured quartz and amorphous silica using Electron Spin Resonance (ESR) [17,18]. ESR in conjunction with isotope effects have been used to identify the (≡ Si-O⋅) defect on irradiated amorphous SiO2. The (≡ Si⋅) and (≡ Si-O⋅) structures have also been observed in other MD simulations of a-SiO2 surfaces simulated using different interatomic potentials [19,20,21]. Finally, the peroxyl defect (≡ Si-O 2 ⋅) has also been observed experimentally [22]. Thus all of the defects predicted by ReaxFFSiOGSI MD simulations were rigorously verified by DFT calculations and supported by experimental evidence. We therefore concluded [1] that these are the actual defects (Figs. 1 and 2) present on real SiO2 surfaces exposed to dissociated oxygen at high temperature. This was a crucial milestone, which now enabled detailed investigation of reactions pathways that involve these defects, using both MD and DFT. Trajectory analysis (shown in Fig. 3) was performed for oxygen atoms impacting the defect structures, including off-normal impacts. The results indicated a high probability for the formation of an O2 molecule on the surface in a peroxyl configuration. Thus, the ReaxFFSiOGSI MD simulations predict a significant amount of peroxyl defects. When subsequent oxygen atoms impact a peroxyl defect, this leads to an O2 molecule leaving the surface into the gas phase (as shown in Fig. 2d). This can occur in two ways, either the adsorbed O2 is completely replaced by the incoming oxygen atom, or the incoming atom bonds to the terminal oxygen on the peroxyl defect and the resulting molecule leaves the surface. The important result was that there is no energy barrier associated with either process, a conclusion that is fully supported by very recent transition state DFT calculations [23]. As a result, oxygen recombination can readily occur through the catalytic cycle shown in Fig. 2. Specifically, real surfaces have a finite number of defects, including under-coordinated silica defects (Fig. 2a). Oxygen adsorbs onto this site with no energy barrier to form a non-bridging oxygen defect (Fig. 2b). An additional oxygen atom is then able to form a peroxyl defect (Fig. 2c), again with no energy barrier. Finally, as described above, an oxygen atom may then interact with the peroxyl defect to form molecular oxygen (Fig. 2d), leaving a non-bridging oxygen defect on the surface. This completes a catalytic cycle, and again, the computational results (transition state calculations) [23], predict this to be a “barrier-less”, or “non-activated” process. This leads to no temperature dependence in the reaction probability; an interesting result that has ramifications for the behavior of the recombination efficiency (γ) and its temperature dependence. process that readily occurs on any silica surface that contains defects, without a dependence on temperature. Although our results do not explain the increase in γ at high temperatures, they conclude that such a dependence on temperature is not a result of an activated process (i.e. one with an energy barrier), as currently modeled in the literature. Figure 3. Off-normal trajectory analysis. Additionally, a finite-rate reaction model was constructed that included all of the observed defect structures and main reaction mechanisms. Developing such a model is important, as it indicates each mechanism’s overall contribution to the recombination process under the relevant conditions. For example, if the non-bridging oxygen atom were to desorb before an additional oxygen atom was able to hit it, then the above-described catalytic cycle would not actually occur. The finalized rate model formulation was identical to that constructed using the original ReaxFFSiO potential [24]. However, the precise reactions, pre-exponential factors, and activation energies were re-evaluated based on the new results from the ReaxFFSiOGSI potential and direct use of DFT data. After formulating the finite rate model, the dominant reaction pathway that most influenced the rate of recombination was an E-R type reaction on the peroxyl defect. This reaction was found by both MD and detailed DFT transition state analysis to be a nonactivated process (no significant energy barrier). The ramification is that the overall finite rate model predicts almost no temperature dependence for the recombination efficiency (γ). This is in contrast to almost all prior models. These prior models were constructed to fit a weak temperature dependence found in a few (and widely variable) experiments (Fig. 4). Specifically, an LH mechanism was invoked to explain the constant value of γ at low temperatures, and an activated E-R process was invoked to explain increase in γ at high temperatures. In stark contrast, our results indicate that the constant value of γ at low temperatures is a result of a “barrier-less” E-R recombination reaction that occurs through the peroxyl defect (outlined in Fig. 2). That is, recombination is a “downhill” energy Figure 4. Experimental results for the O atom recombination efficiency for SiO2 surfaces. Experiment 1 is Ref. [12]. Experiment 2 is Ref. [25]. Experiment 3 is Ref. [26]. There are a number of alternate explanations for temperature dependence of recombination other than an activated ER process. For example, the experimental measurements were interpreted using simple diffusion models, which varied between experiments, and whose accuracy is questionable for high temperature dissociated air. Inaccuracy in the diffusion model could lead to an apparent temperature dependence of the interpreted recombination efficiency. As another example, the number of surface sites (defect sites) could be increasing with temperature, and this could be the cause of increased recombination at high temperatures (not an activated process). Finally, to generate atomic oxygen, the high temperature experiments required a plasma and so additional surface processes could be occurring in these experiments, beyond interactions with dissociated oxygen as studied in this work. In fact, recent experimental measurements [2] have reconfirmed prior observations [27,28] that recombination of oxygen on silica can form molecular oxygen in its first electronically excited state. The experiments, performed by White, Copeland, and Marschall, quantify that approximately 10% of all recombination reactions produce oxygen in the singlet-delta state. Additionally, the experiments determine that quenching of electronic energy to the silica surface is much more probable. So if the gas or plasma interacting with the surface contains electronically excited molecular oxygen, which many facility environments likely do, then such quenching is an additional factor that could influence the gas-surface interaction. Therefore, our detailed computations predict nonactivated recombination pathways are present on real silica surfaces (on defect sites supported by experimental evidence). Thus, any temperature dependence of the recombination efficiency should not be attributed to an activated ER reaction process, as our results conclude that these are non-activated reaction pathways. 3. REAL CARBON MICROSTRUCTURES Ablation experiments, carried out in high-enthalpy facilities, typically measure macroscopic phenomena such as surface recession, heat flux, surface temperature, and with recent laser-based diagnostics, radiation signatures of certain species can be measured within the boundary layer near the ablating surface. It is important to realize that such measurements (surface recession, heat flux, and species within the boundary layer) are the net result of the following highly coupled processes: (1) The microstructure of the material (effective exposed surface area). (2) The local gas-surface reaction rates on the microstructure surface. (3) The near-surface boundary layer diffusion and gasphase chemistry. These coupled processes, make it very difficult to interpret specific gas-surface reaction rates from experiments (for use in CFD simulations). Reaction rate data inferred from a limited number of experiments span orders of magnitude. Such experiments may have used different “types” of carbon (C-C composites, graphite, HOPG, etc.) and, furthermore, very different gas environments may be present in each experiment. Since processes (1), (2), and (3), are all coupled, it can be difficult to interpret gas-surface reaction rates from experiments. In an attempt to understand the coupled processes individually, this section summarizes recent advances for (1) and (2). A number of experimental results indicate that the local gas-surface reactions, occurring on many types of carbon materials and under a variety of flow environments, have a common mechanism. A variety of experimental images reveal similarities in local etching behavior. Specifically, this data suggests that carbon atoms are most easily removed from “edges” in the atomistic graphitic carbon structure. Such a common mechanism could drastically simplify the problem and enable physics-based modeling of ablation. In effect, the local gas-surface chemistry (< 1µm scale) may be similar for all of these materials, and therefore it could be the microstructure (> 1µm scale) that leads to differing reactivity for different surfaces (i.e. different rates for different types of carbon TPS). Thus an interesting strategy is to directly simulate material microstructure and apply gas-surface boundary conditions only on the microstructure itself (i.e. below the µm scale). New computational research has led to the capability to use x-ray micro-tomography to scan a real material microstructure and directly simulate gas-surface reactions within a boundary layer flow. The gas flow is simulated with the direct simulation Monte Carlo (DSMC) particle method. DSMC is appropriate for such micro scale simulations as it simulates the Boltzmann equation and is thus accurate for flow conditions ranging from continuum to free molecular. The Molecular Gas Dynamic Simulator (MGDS) code is used for the simulations presented here [29,30]. One of the nice features of the MGDS code (and DSMC in general) is that it can accommodate geometry of any complexity using cutcell algorithms [31]. This enables a compelling application for this methodology: simulating real microstructures obtained from doing x-ray computed micro-tomography scans of the materials. Micro-tomography has previously been applied to spacecraft heatshield analysis by Mansour et al. [32] Using high-resolution scans of FiberForm, Mansour et al. characterized some of the parameters of the microstructure. Additionally, they used the random walk approach of Lachaud et al. [33] to simulate the ablation of the microstructure under certain conditions. Taking a similar approach, but using DSMC, allows for more of the relevant physics to be simulated. As a demonstration for this work, we have scanned a small sample of FiberForm using the X5000 highresolution microCT system at the X-ray computed tomography lab at the University of Minnesota. This system has a maximum resolution of approximately 2µm. The output from a tomography scan is typically a stack of grayscale images, each corresponding to a slice of the material. These images are then filtered and a threshold grayscale value is identified that corresponds to the surface, after which the images are converted to binary (black and white). From here we can construct a triangulated surface corresponding to the threshold value. For this demonstration the triangulation was performed using the Avizo software package. Using the triangulated surface obtained from the tomographic scan, we can now simulate the flow through the FiberForm material using the method described in our previous work [3,34]. Figure 5 shows an SEM image of the FiberForm sample, and Fig. 6 shows a rendered image of the tomographic scan. The MGDS DSMC code is then used to simulate gas flow through the FiberFrom geometry (velocity contours are shown in Fig. 7). In these simulations, Dirichlet boundary conditions have been imposed at the inflow and the outflow, with a constant velocity of 1 m/s. These are not proper subsonic boundary conditions and do not correspond to any specific experimental conditions, however our purpose here to demonstrate the viability of the approach for relevant conditions. In the results from the simulation we can see that the flow accelerates through the consolidated pores in the microstructure and stagnates where there are blockages. An important feature of the MGDS code that enables these simulations is that the surface is partitioned across multiple processors just as the flow field grid is. This is necessary due to the extremely large number of triangles required to define these surfaces. The DSMC simulation shown in Fig. 7 contains approximately 0.5 billion particles run for 200,000 timesteps, and the FiberForm geometry consists of more than 12 million surface triangles. The simulation required a few days of run time using a few hundred core CPUs. The most important aspect of this simulation is that it demonstrates that direct simulations of porous microstructure are computationally feasible at the macroscale (the FiberForm sample simulated is 1mm3). This scale is larger than a typical grid cell size within a continuum material response solver, and so results of such large microstructure simulations could feed directly into sub-cell models employed in continuum material response solvers. Another demonstration is presented for the microstructure of a non-porous carbon ablator. A 2D Carbon-Carbon (C-C) composite sample was provided by the Corral Laboratory at University of Arizona. The diameter of the sample is 4mm and the un-ablated height is 2mm. The sample was ablated for 15 min at 1600 C where the O2 partial pressure was 0.29 kPa. The sample was scanned in the x-ray micro-tomography facility at University of Minnesota and 3-D reconstructed using tomographic techniques described above. The reconstructed image is shown in Fig. 8, and the resolution of the triangulated surface can be seen in the inset of Fig. 8. The triangulated surface can now be used in the MGDS DSMC solver and species concentrations that develop due to gas-surface reactions, and ultimately diffuse into the boundary layer can be computed and analyzed. For example, Fig. 9 shows CO2 mass fraction contours for an example simulation. More details can be found in Ref. [4]. This is an ongoing work and will be examined in detail in the future. Figure 5. Scanning Electron Microscope (SEM) image of a FiberForm sample. Figure 6. Rendered image of the FiberForm geometry resulting from the micro-tomographic scan. Figure 7. MGDS DSMC simulation of 1m/s flow through the (1 mm3) FiberForm sample. with DSMC is demonstrated. Such simulations are expensive, but are shown to be computationally feasible at macroscopic scales (mm scale) using state-of-the-art simulation codes combined with high-performance computing clusters. 5. ACKNOWLEDGEMENTS This research is supported by Air Force Office of Scientific Research (AFOSR) under Grants FA9550-121-0486 and FA9550-10-1-0563. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the U.S. Government. Figure 8. Rendered image of the ablated C-C sample resulting from the micro-tomographic scan. A portion of the triangulated grid is shown in the inset. 6. REFERENCES 1. Norman, P., Schwartzentruber, T.E., Leverentz, H., Luo, A., Paneda, R.M., Paukku, Y., and Truhlar, D.G., “The Structure of Silica Surfaces Exposed to Atomic Oxygen”, J. Phys. Chem. C (2013), 117, pp. 9311-9321. 2. White, J. D., Copeland, R. A., and Marschall, J., “Singlet Molecular Oxygen Formation by O-Atom Recombination on Fused-Quartz Surfaces”, Journal of Thermophysics and Heat Transfer, Vol. 29, No. 1 (2015), pp. 24-36. 3. Stern, E.C, Nompelis, I., Schwartzentruber, T.E., and Candler, G.V., “Microscale simulations of porous TPS materials: Ablating microstructures and micro-tomography”, AIAA Paper 2015-1450, Jan. 2015, presented at the 53rd Aerospace Sciences Meeting, AIAA SciTech, Kissimmee, FL. Figure 9. Demonstrative DSMC simulation of species concentrations resulting from gas-surface reactions on the C-C sample microstructure. 4. CONCLUSIONS Recent computational results for gas-surface reactions including atomic level simulations of oxygen-silica recombination and microstructure level simulations of carbon-based ablative surfaces are summarized. Accurate atomic-level simulations are able to identify the main defects on realistic silicon-dioxide surfaces that promote exothermic catalytic reactions with oxygen. Most importantly, these calculations show the main recombination mechanism to be non-activated (associated with no energy barrier). This is in contradiction to current empirical models fit to limited experimental data. For ablative porous and non-porous TPS, where complex microstructure is important, the capability to image a real material with µm scale resolution via x-ray micro-tomography, triangulate the surface, and directly simulate the gas-surface interaction 4. 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