Rate Equations for the Vibrational Relaxation of CO2 – N2 or CO2− Noble Gas Mixtures— Application to Comparison of Spectrophone Data with Results from Other Experimental Techniques

Abstract

Macroscopic rate equations are formulated for vibrational relaxation in mixtures of CO2 with either N2 or a noble gas. A model is used that assumes the bending and symmetric-stretching modes of CO2 to be in equilibrium with each other and to have a common vibrational temperature. The asymmetric-stretching mode is taken to be described by a different vibrational temperature, which, in the case of CO2−N2 mixtures, is taken to be common with the temperature of the nitrogen vibrational mode. The rate equations are then derived on a phenomenological basis. The resulting phenomenological coefficients can be interpreted in terms of characteristic relaxation times and energy exchange ratios, which are a measure of the relative amounts of energy exchanged by the different vibrational modes in V—V transitions. The equations can be used for any linearized problem. Here they are applied to a spectrophone. The resulting phase-lag equations are used to reinterpret spectrophone data that had been thought to lead to false conclusions. It is shown that the data is in fact compatible with the results from other experiments. Well done and well interpreted spectrophone experiments can possibly yield new information about the energy exchange ratio (and hence the important V—V transitions) for CO2−diluent collisions. It might also be possible to obtain more accurate values for the long V—T relaxation times for CO2 collisions with the heavy noble gases. These possibilities are discussed.

CO2dissociation using the Versatile atmospheric dielectric barrier discharge experiment (VADER)

“…While these large vibrational excitation rates suggest that a DBD highly excites the vibrational states which lead to a significant portion of CO 2 dissociation in a DBD, it was calculated that vibrational to translational (V-T) relaxation is also relatively high at atmospheric pressures (2.6 × 10 −4 mol/cm 3 s versus a vibrational excitation rate of 3 × 10 −4 mol/cm 3 s). These high V-T relaxation rates suggest that vibrational excitation may only play a limited role in CO 2 dissociation at atmospheric pressures [8,[51][52][53]. A similar modeling result was obtained by Aerts et al [54] and Kozak and Bogaerts [55].…”

CO<inf>2</inf> dissociation using the versatile atmospheric dielectric barrier discharge experiment (VADER)

“…where T g is in K. This reaction rate constant is consistent with other sources and is stated to be a relatively slow process [14,[95][96][97]. However, calculating the relaxation rate using the relaxation rate coefficient, an atmospheric pressure background density (n n = 4.06 × 10 −5 moles/cm 3 ) and a vibrationally excited population of density ∼5×10 −9 moles/cm 3 per discharge (calculated from the vibrational reaction rates at 5 eV in Figure 2.…”

Influence of oxygen on the ro-vibrational kinetics of a non-equilibrium discharge in CO2–O2 mixtures

“…Also, the two-mode approximation usually made for CO 2 , i.e. T 1 = T 2 = T 12 , is justified due to the close proximity of vibrational energy levels for both modes [9][10][11]. It is commonly observed that for these temperatures the following relation persistently applies: T CO > T 3 > T 12 > T gas ∼ = T rot [12][13][14][15][16][17][18][19][20][21][22].…”