Analysis of rovibrational relaxation in nitrogen via direct atomic simulation

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.