Quasi-classical trajectory analysis of three-body collision induced recombination in neutral nitrogen and oxygen.

We present theory and a simulation framework to model three-body collisions and gas phase recombination in dilute atom/diatom mixtures of pure oxygen (O/O2) and nitrogen (N/N2) using the Quasi-Classical Trajectory method. We formulate a three-body collision rate constant based on the lifetimes of binary collisions and initialize three-body collisions by sampling the arrival time of a third body within the lifetimes of pre-simulated binary collisions. We use this method to calculate distributions of recombined product energies, probabilities of recombination, and recombination rate constants through different collision pathways. Long-lived binary atom-diatom collisions are observed, but are too rare to play a dominant role in the recombination process for shock-heated air near the equilibrium conditions studied. The resulting recombination rate constants are within an order of magnitude of the predictions of detailed balance. Notably, the recombination simulation framework does not appeal to the principle of detailed balance and could be useful for studying conditions far from equilibrium.

On the Utility of Coated POSS-Polyimides for Vehicles in Very Low Earth Orbit.

The environment encountered by space vehicles in very low Earth orbit (VLEO, 180-350 km altitude) contains predominantly atomic oxygen (AO) and molecular nitrogen (N2), which collide with ram surfaces at relative velocities of ∼7.5 km s-1. Structural, thermal-control, and coating materials containing organic polymers are particularly susceptible to AO attack at these high velocities, resulting in erosion, roughening, and degradation of function. Copolymerization or blending of a polymer with polyhedral oligomeric silsesquioxane (POSS) yields a material that can resist AO attack through the formation of a passivating silicon-oxide layer. Still, these hybrid organic/inorganic polymers become rough through AO reactions as the passivating layer is forming. Surface roughness may enhance satellite drag because it promotes energy transfer and scattering angle randomization during gas-surface collisions. As potential low-drag and AO-resistant materials, we have investigated POSS-containing films of clear and Kapton-like polyimides that have an atomically smooth AO-resistant coating of Al2O3 that is grown by atomic layer deposition (ALD). Coated and uncoated films were exposed to hyperthermal molecular beams containing atomic and molecular oxygen to investigate their AO resistance, and molecular beam-surface scattering studies were conducted to characterize the gas-surface scattering dynamics on pristine and AO-exposed surfaces to inform drag predictions. The AO erosion yield of Al2O3 ALD-coated films is essentially zero. Simulations of drag on a representative satellite structure that are based on the observed scattering dynamics suggest that the use of Al2O3 ALD-coated POSS-polyimides on external satellite surfaces have the potential to reduce drag to less than half of that predicted for diffuse scattering surfaces. These smooth and AO-resistant polymer films thus show promise for use in an extreme oxidizing and high-drag environment in the VLEO.

State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N2-N System.

We present a detailed comparison of two high-fidelity approaches for simulating non-equilibrium chemical processes in gases: the state-to-state master equation (StS-ME) and the direct molecular simulation (DMS) methods. The former is a deterministic method, which relies on the pre-computed kinetic database for the N2-N system based on the NASA Ames ab initio potential energy surface (PES) to describe the evolution of the molecules' internal energy states through a system of master equations. The latter is a stochastic interpretation of molecular dynamics relying exclusively on the same ab initio PES. It directly tracks the microscopic gas state through a particle ensemble undergoing a sequence of collisions. We study a mixture of nitrogen molecules and atoms forced into strong thermochemical non-equilibrium by sudden exposure of rovibrationally cold gas to a high-temperature heat bath. We observe excellent agreement between the DMS and StS-ME predictions for the transfer rates of translational into rotational and vibrational energy, as well as of dissociation rates across a wide range of temperatures. Both methods agree down to the microscopic scale, where they predict the same non-Boltzmann population distributions during quasi-steady-state dissociation. Beyond establishing the equivalence of both methods, this cross-validation helped in reinterpreting the NASA Ames kinetic database and resolve discrepancies observed in prior studies. The close agreement found between the StS-ME and DMS methods, whose sole model inputs are the PESs, lends confidence to their use as benchmark tools for studying high-temperature air chemistry.

Non-Boltzmann vibrational energy distributions and coupling to dissociation rate.

In this article, we propose a generalized model for nonequilibrium vibrational energy distribution functions. The model can be used, in place of equilibrium (Boltzmann) distribution functions, when deriving reaction rate constants for high-temperature nonequilibrium flows. The distribution model is derived based on the recent ab initio calculations, carried out using potential energy surfaces developed using accurate computational quantum chemistry techniques for the purpose of studying air chemistry at high temperatures. Immediately behind a strong shock wave, the vibrational energy distribution is non-Boltzmann. Specifically, as the gas internal energy rapidly excites to a high temperature, overpopulation of the high-energy tail (relative to a corresponding Boltzmann distribution) is observed in ab initio simulations. As the gas excites further and begins to dissociate, a depletion of the high-energy tail is observed, during a time-invariant quasi-steady state. Since the probability of dissociation is exponentially related to the vibrational energy of the dissociating molecule, the overall dissociation rate is sensitive to the populations of these high vibrational energy states. The non-Boltzmann effects captured by the new model either enhance or reduce the dissociation rate relative to that obtained assuming a Boltzmann distribution. This article proposes a simple model that is demonstrated to reproduce these non-Boltzmann effects quantitatively when compared to ab initio simulations.

Consistent kinetic-continuum dissociation model. II. Continuum formulation and verification.

In this article, we implement a recently developed non-equilibrium chemical kinetics model [N. Singh and T. Schwartzentruber, J. Chem. Phys. 152, 224302 (2020)] based on ab initio simulation data and perform verification studies. Direct molecular simulation data are used to verify the predictive capabilities of the model. Using the model, dominant physics, such as the need for a rotational energy equation, and the quantitative role of non-Boltzmann effects are identified. Based on the analysis and reasonable assumptions, a simplified model for implementation into large-scale computational fluid dynamic simulations is proposed. Without incurring additional computational cost, the model can be used in existing flow solvers to analyze hypersonic flows.

Consistent kinetic-continuum dissociation model I. Kinetic formulation.

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results.

Comparison of potential energy surfaces and computed rate coefficients for N2 dissociation.

Comparisons are made between potential energy surfaces (PES) for N2 + N and N2 + N2 collisions and between rate coefficients for N2 dissociation that were computed using the quasiclassical trajectory method (QCT) on these PESs. For N2 + N we compare the Laganà's empirical LEPS surface with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For N2 + N2 we compare two ab initio PESs (from NASA Ames and from the University of Minnesota). These use different methods for computing the ground state electronic energy for N4, but give similar results. Thermal N2 dissociation rate coefficients, for the 10,000K-30,000K temperature range, have been computed using each PES and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the Direct Molecular Simulation of Schwartzentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones and the thermal and QSS values bracket the results of shock-tube experiments. We conclude that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.

Nonequilibrium internal energy distributions during dissociation.

In this work, we propose a model for nonequilibrium vibrational and rotational energy distributions in nitrogen using surprisal analysis. The model is constructed by using data from direct molecular simulations (DMSs) of rapidly heated nitrogen gas using an ab initio potential energy surface (PES). The surprisal-based model is able to capture the overpopulation of high internal energy levels during the excitation phase and also the depletion of high internal energy levels during the quasi-steady-state (QSS) dissociation phase. Due to strong coupling between internal energy and dissociation chemistry, such non-Boltzmann effects can influence the overall dissociation rate in the gas. Conditions representative of the flow behind strong shockwaves, relevant to hypersonic flight, are analyzed. The surprisal-based model captures important molecular-level nonequilibrium physics, yet the simple functional form leads to a continuum-level expression that now accounts for the underlying energy distributions and their coupling to dissociation.

An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions.

Accurate modeling of high-temperature hypersonic flows in the atmosphere requires consideration of collision-induced dissociation of molecular species and energy transfer between the translational and internal modes of the gas molecules. Here, we describe a study of the N2 + N2⟶N2 + 2N and N2 + N2⟶4N nitrogen dissociation reactions using the quasiclassical trajectory (QCT) method. The simulations used a new potential energy surface for the N4 system; the surface is an improved version of one that was presented previously. In the QCT calculations, initial conditions were determined based on a two-temperature model that approximately separates the translational-rotational temperature from the vibrational temperature of the N2 diatoms. Five values from 8000 K to 30,000 K were considered for each of the two temperatures. Over 2.4 × 10(9) trajectories were calculated. We present results for ensemble-averaged dissociation rate constants as functions of the translational-rotational temperature T and the vibrational temperature T(v). The rate constant depends more strongly on T when T(v) is low, and it depends more strongly on T(v) when T is low. Quasibound reactant states contribute significantly to the rate constants, as do exchange processes at higher temperatures. We discuss two sets of runs in detail: an equilibrium test set in which T = T(v) and a nonequilibrium test set in which T(v) < T. In the equilibrium test set, high-v and moderately-low-j molecules contribute most significantly to the overall dissociation rate, and this state specificity becomes stronger as the temperature decreases. Dissociating trajectories tend to result in a major loss of vibrational energy and a minor loss of rotational energy. In the nonequilibrium test set, as T(v) decreases while T is fixed, higher-j molecules contribute more significantly to the dissociation rate, dissociating trajectories tend to result in a greater rotational energy loss, and the dissociation probability's dependence on v weakens. In this way, as T(v) decreases, rotational energy appears to compensate for the decline in average vibrational energy in promoting dissociation. In both the equilibrium and nonequilibrium test sets, in every case, the average total internal energy loss in the dissociating trajectories is between 10.2 and 11.0 eV, slightly larger than the equilibrium potential energy change of N2 dissociation.

Large scale computational chemistry modeling of the oxidation of highly oriented pyrolytic graphite.

Large scale molecular dynamics (MD) simulations are performed to study the oxidation of highly oriented pyrolytic graphite (HOPG) by hyperthermal atomic oxygen beam (5 eV). Simulations are performed using the ReaxFF classical reactive force field. We present here additional evidence that this method accurately reproduces ab initio derived energies relevant to HOPG oxidation. HOPG is modeled as multilayer graphene and etch-pit formation and evolution is directly simulated through a large number of sequential atomic oxygen collisions. The simulations predict that an oxygen coverage is first established that acts as a precursor to carbon-removal reactions, which ultimately etch wide but shallow pits, as observed in experiments. In quantitative agreement with experiment, the simulations predict the most abundant product species to be O2 (via recombination reactions), followed by CO2, with CO as the least abundant product species. Although recombination occurs all over the graphene sheet, the carbon-removal reactions occur only about the edges of the etch pit. Through isolated defect analysis on small graphene models as well as trajectory analysis performed directly on the predicted etch pit, the activation energies for the dominant reaction mechanisms leading to O2, CO2, and CO product species are determined to be 0.3, 0.52, and 0.67 eV, respectively. Overall, the qualitative and quantitative agreement between MD simulation and experiment is very promising. Thus, the MD simulation approach and C/H/O ReaxFF parametrization may be useful for simulating high-temperature gas interactions with graphitic materials where the microstructure is more complex than HOPG.

Molecular dynamics simulation of O2 sticking on Pt(111) using the ab initio based ReaxFF reactive force field.

The molecular dynamics technique with the ab initio based classical reactive force field ReaxFF is used to study the adsorption dynamics of O(2) on Pt(111) for both normal and oblique impacts. Overall, good quantitative agreement with the experimental data is found at low incident energies. Specifically, our simulations reproduce the characteristic minimum of the trapping probability at kinetic incident energies around 0.1 eV. This feature is determined by the presence of a physisorption well in the ReaxFF potential energy surface (PES) and the progressive suppression of a steering mechanism when increasing the translational kinetic energy (or the molecule's rotational energy) because of steric hindrance. In the energy range between 0.1 and 0.4 eV, the sticking probability increases, similar to molecular beam sticking data. For very energetic impacts (above 0.4 eV), ReaxFF predicts sticking probabilities lower than experimental sticking data by almost a factor of 3 due to an overall less attractive ReaxFF PES compared to experiments and density functional theory. For oblique impacts, the trapping probability is reduced by the nonzero parallel momentum because of the PES corrugation and does not scale with the total incident kinetic energy. Furthermore, our simulations predict quasispecular (slightly supraspecular) distributions of angles of reflection, in accordance with molecular beam experiments. Increasing the beam energy (between 1.2 and 1.7 eV) causes the angular distributions to broaden and to exhibit a tail toward the surface normal because molecules have enough momentum to get very near the surface and thus probe more corrugated repulsive regions of the PES.