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We present DMS calculations to investigate vibrational excitation and dissociation in molecular nitrogen, including both N 3 and N 4 processes and under strong nonequilibrium conditions. A preliminary constitutive model is also described and parameterized with the available DMS results. The analysis of vibrational energy distributions obtained with DMS shows that high vibrational energy states are immediately populated in the initial stages of the dissociation process, due to the very energetic nature of the molecular collisions. Throughout the excitation process, distributions remain highly nonequilibrium and generally have a strong bimodal character. Quite interestingly, the pre-collision distributions of molecules undergoing dissociation rapidly converge toward the QSS distribution, even in the early portion of the excitation. This may suggest that, once high-v states become sufficiently populated, the dissociation process is effectively initiated. Hence, we introduce the idea of a critical vibrational incubation temperature Tc,v to account for the excitation of the high energy tails of the system distribution f(v). If Tv < Tc,v, little to no dissociation occurs, even at very high translational temperatures. Once high-v states are sufficiently populated (Tv ≃ Tc,v), then dissociation proceeds at a rate controlled by a combination of Tt and Tv (and, in principle, Tr). A preliminary model for nitrogen vibrational excitation and dissociation is proposed here based on the analysis of the DMS results. The new model reproduces particularly well both energy and composition history, including the slower initial dissociation (incubation period), for the vibrational excitation and dissociation process simulated with DMS from several initial conditions. Furthermore, it also describes the QSS state, characterized by Tv < Tt.

We present an atomic-level study of vibrational excitation and chemical dissociation in molecular nitrogen at high temperature. The computational techniques, quasiclassical trajectory calculations (QCT) and classical trajectory calculation direct simulation Monte Carlo (CTC DSMC), solely rely on the specification of a highly accurate ab initio surface for N2-N2 interactions. We show that the simulations accurately reproduce the vibrational relaxation times obtained from the Millikan-White correlation and further support existing high-temperature corrections. Using both QCT and CTC DSMC methods with the same PES, we show that dissociation proceeds 4 to 5 times faster under equilibrium conditions compared to quasi-steady-state nonequilibrium conditions. At high translational energies (20,000 K and 30,000 K), the overall vibrational energy ladder is depleted, and dissociation proceeds at a rate approximately corresponding to a lower vibrational temperature. Conversely, at lower energies (10,000 K), almost no dissociation occurs from low-lying vibrational energy states. In this case, even a slight depletion of the upper-level vibrational energy states, which preferentially dissociate and are not rapidly re-populated due to slow bound-bound energy transfer mechanisms, causes a remarkable reduction of the dissociation rate. The ab initio CTC DSMC method is able to directly simulate rovibrational excitation and dissociation processes without computing the large number of cross-sections required by a state-resolved approach, and can be used directly to form new CFD models.

Pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC) are used to analyze the rovibrational behavior of molecular nitrogen for temperatures greater than 4,000 K. Both techniques are shown to produce statistically identical results at the conditions of interest here. Furthermore, they solely rely on the specification of a potential energy surface (PES). In this work, we used the site-site Ling-Rigby potential, and modeled the N-N bond either as a harmonic spring or an anharmonic spring (for bound states ) or with the Morse potential (to model bond breaking). Selected preliminary results, obtained with a global fit of a quantum-chemistry PES, are also included. We show that the Ling-Rigby molecular model (i) recovers the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predicts well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduces vibrational relaxation times in excellent accordance with the Millikan-White correlation and previous semiclassical trajectory calculations in the low temperature range, i.e., between 4,000 K and 10,000 K. By simulating isothermal relaxations in a periodic box, we found that the traditional two-temperature model assumptions become invalid at high temperatures (> 10, 000 K), due to a significant coupling between rotational and vibrational modes for bound states. This led us to add a modification to both the Jeans and the Landau-Teller equations to include a coupling term, essentially described by an additional relaxation time for internal energy equilibration. The model thus obtained was parametrized by fitting temperature histories obtained with molecular-level calculations. The degree of anharmonicity of the N-N bond determines the strength of the rovibrational coupling, with possible implication on rovibration/chemistry interaction at the onset of N2 dissociation. Initial results for vibrational relaxation times are also obtained with the quantum-chemistry based PES of Paukku and co-workers in the low temperature range (< 10, 000 K) and were found to agree well with the experimental data. Although the bound assumption is largely unrealistic under equilibrium conditions at temperatures above about 10,000 K, high-temperature extrapolations are nonetheless very important for flows characterized by extreme nonequilibrium. This is demonstrated through the direct MD simulation of a reflected shock wave in dissociating N2.

The objective of this study is to use Molecular Dynamics simulation to evaluate the rotational relaxation process in nitrogen from a first-principles perspective. The intermolecular model used in the MD simulations is shown to (i) reproduce very well the shear viscosity of nitrogen over a wide range of temperatures, (ii) predict the near-equilibrium rotational collision number in good agreement with published trajectory calculations done on ab initio Potential Energy Surfaces, and (iii) produce shock wave profiles in excellent accordance with the experimental measurements. The rotational relaxation process is found to be dependent not only on the near-equilibrium temperature (i.e., when systems relax to equilibrium after a small perturbation), but more importantly on both the magnitude and direction of the initial deviation from the equilibrium state. Although this dependence has been previously recognized, it is here investigated systematically. The comparison between MD and DSMC, based on the Larsen-Borgnakke model, for shock waves (both at low and high temperatures) and one-dimensional expansions shows that a judicious choice of a constant Zrot can produce DSMC results which are in relatively good agreement with MD. However, the selection of the rotational collision number is case-specific, depending not only on the temperature range, but more importantly on the type of flow (compression or expansion), with significant limitations for more complex simulations characterized both by expansion and compression zones. Parker’s model, parametrized for nitrogen, overpredicts the magnitude of Zrot for temperatures above about 300 K. It is also unable to describe the dependence of the relaxation process on the direction to equilibrium. Finally, based on the MD data, a preliminary formulation for a novel rotational relaxation model, which includes a dependence on both the rotational and the translational state of the gas, is presented.

The structure of a normal shock waves in dilute gas mixtures of various compositions (Xenon-Helium and Argon-Helium) are studied using Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC). The MD solutions reproduce well the experimental data, with the exception of the parallel temperature profile in the 24.7% Ar-He mixture, despite the satisfactory agreement between the parallel velocity profiles. The Generalized Hard Sphere (GHS) DSMC solutions match almost perfectly the MD data, for all the cases considered. Using textbook parameters for like particles and their arithmetic averages for unlike particles, the Variable Hard Sphere (VHS) model fails to describe the shock wave structure in the Xe-He mixture. For the Ar-He cases, the VHS diffusion cross-section better approximates that obtained with the Lennard-Jones potential. Therefore, the VHS DSMC solutions exhibit less significant differences with those obtained with MD. If the VHS model is properly parametrized, the agreement between DSMC and MD solutions increases significantly. These cases exemplify situations where MD simulations based on a reliable interatomic potential can be used to inform simplified collision schemes used in DSMC.

Atomic-level simulations equipped with a reactive force field (ReaxFF) are used to characterize atomic oxygen adsorption on a Pt(111) surface. The off-lattice Grand Canonical Monte Carlo (GCMC) calculations presented here rely solely on the interatomic potential and do not necessitate the pre-computation of surface adlayer structures and their interpolation. As such, they provide a predictive description of adsorbate phases. In this study, validation is obtained with experimental data as well as other DFT results available in the literature. The use of the GCMC technique based on a transferable potential is particularly valuable to produce more realistic systems (adsorbent and adsorbate) to be used in subsequent dynamical simulations (Molecular Dynamics) to address recombination reactions (via either Eley-Rideal or Langmuir-Hinshelwood mechanisms) on variously covered surfaces. This is demonstrated by simulations to determine the probability of Eley-Rideal recombination on Pt(111), using information provided by the GCMC computations and using the same force field parametrization. The proposed methodology is general, and does not depend on the particular crystal structure of the substrate. A preliminary simulation on Pt(533) is therefore also shown. The (533) facet is characterized by surface defects (regularly spaced steps). It was found that a much higher O coverage is determined compared to Pt(111) under the same pressure and temperature conditions. By using GCMC and Molecular Dynamics simulations, the ReaxFF force field can be a valuable tool for understanding heterogeneous catalysis on a solid surface. Finally, the use of a reactive potential is a requirement to investigate problems where dissociative adsorption occurs, as typical of many important catalytic processes.

Atomistic simulations equipped with the ab initio based classical reactive force fleld ReaxFF are used to study adsorption of oxygen on a Pt(111) surface. Molecular Dynamics (MD) simulations are used to study the adsorption dynamics of O2 on Pt(111) for both normal and oblique impacts, whereas Grand Canonical Monte Carlo (GCMC) calculations are employed to study the surface coverage of atomic oxygen on the same platinum surface. Overall, good quantitative agreement with the experimental data is found. Our MD 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 eV and 0.4 eV, the sticking probability increases, similarly 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 DFT. For oblique impacts, the trapping probability does not scale with the total incident kinetic energy, but is reduced by the non-zero parallel momentum because of the PES corrugation. Furthermore, our simulations predict quasi-specular (slightly supraspecular) distributions of angles of re∞ection, in accordance with molecular beam experiments. With GCMC simulations, a coverage of about 0.25 is determined at ultra-vacuum conditions (» 10 i10 atm), reproducing the experimental observations. Further reflning of the potential parameters will be aimed to improve the agreement of sticking results at high Ei (by including direct dissociation pathways in the training set) and to reproduce the p(2£ 2) adsorbates surface structure at 0.25 coverage (by strengthening the lateral repulsion between adsorbed O atoms).

Molecular Dynamics (MD) simulations, using the Lennard-Jones potential, are used to study the structure of normal shock waves in dilute argon. For moderate free stream densities (�1 = 1 kg/m 3 ), large-scale parallel calculations are required to simulate the full shock flow. At very dilute conditions (�1 � 10 3 kg/m 3 ), a combined Event-Driven/Time-Driven (ED/TD) algorithm is proposed to speed up the MD simulations using realistic spherically symmetric soft potentials. Because of the rarefied conditions, the novel combined scheme identifies the impending interaction (like in Event-Driven MD), however resolves each interaction adequately using Time-Driven MD with small time steps. This method correctly reproduces translational relaxation, and it is further validated by simulating full shock waves. Through detailed comparisons with Direct Simulation Monte Carlo (DSMC) solutions using the variable-hard-sphere (VHS) collision model, MD simulations allow a more sensitive evaluation of the VHS model parameters than possible using available experimental density data. Consistently with Chapman-Enskog theory, at high temperatures (300-8000 K), near-perfect agreement between MD and DSMC solutions is demonstrated and inverse shock thickness predictions reproduce experimental measurements. In the low temperature range (16-300 K), both theory and MD results show that the VHS collision model becomes less valid. At very dilute conditions, the ED/TD algorithm determines a significant speed-up, being up to several thousand times faster than conventional TD MD, depending on the problem. Therefore, with this method, it could be possible to use much more accurate and computationally demanding interatomic potentials, either classical or first principles, to include such physics as chemical reactivity and vibrational nonequilibrium.

A mechanism-based finite-rate wall boundary condition is implemented in a state-ofthe-art finite volume CFD thermochemical nonequilibrium code to study a high enthalpy CO2 flow over blunt bodies. All the relevant surface processes responsible for the catalytic behavior of the wall are accounted for, including adsorption and desorption (both atomic and molecular), and Eley-Rideal and Langmuir-Hinshelwood recombinations. The model only requires the specification of the reaction rates for each of the processes considered, and the law of mass action is used to compute surface coverages and mass fluxes produced or consumed at the wall due to its catalytic activity. The kinetic rates are chosen to describe a platinum surface, with a fairly high degree of catalycity with respect to CO oxidation. As expected, the predicted heat flux is intermediate between the two extrema, namely the non-catalytic and supercatalytic wall assumptions. Because the only input of the model are the reaction rates, which are usually unavailable or affected by a large experimental uncertainty, the use of Molecular Dynamics simulations employing the Quantum Chemistry based reactive force field ReaxFF is proposed as a novel approach to both determine and characterize each of the underlying processes which collectively cause the wall catalytic activity. Because (dissociative) adsorption is a fundamental step leading to surface recombinations, the sticking of O2 on Pt(111) is studied using ReaxFF Molecular Dynamics simulations.