Download molecular simulation of oxygen reactions with realistic silica and

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.
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including atomic level simulations of oxygen-silica
recombination and microstructure level simulations of
carbon-based ablative surfaces are summarized.
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the main defects on realistic silicon-dioxide surfaces
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