Insight into CO₂ Dissociation in Plasma from Numerical Solution of a Vibrational Diffusion Equation

Abstract

The dissociation of CO2 molecules in plasmas is a subject of enormous importance for fundamental studies and in view of the recent interest in carbon capture and carbon-neutral fuels. The vibrational excitation of the CO2 molecule plays an important role in the process. The complexity of the present state-to-state (STS) models makes it difficult to find out the key parameters. In this paper we propose as an alternative a numerical method based on the diffusion formalism developed in the past for analytical studies. The non-linear Fokker-Planck equation is solved by the timedependent diffusion Monte Carlo method. Transport quantities are calculated from STS rate 2 coefficients. The asymmetric stretching mode of CO2 is used as a test case. We show that the method reproduces the STS results or a Treanor distribution depending on the choice of the boundary conditions. A positive drift, whose energy onset is determined by the vibrational to translational temperature ratio, brings molecules from mid-energy range to dissociation.Vibrational-translational energy transfers have negligible effect at the gas temperature considered in this study. The possibility of describing the dissociation kinetics as a transport process provides insight towards the goal of achieving efficient CO2 conversion. IntroductionPlasma-assisted gas conversion techniques are widely considered as efficient building blocks in a future energy infrastructure which will be based on renewable but intermittent electricity sources. In particular CO2 dissociation in high-frequency plasmas is of interest in carbon capture and utilization process chains for the production of CO2-neutral fuels 1 . In this case, the vibrational excitation of the CO2 molecule plays an important role in the energy efficient non-equilibrium dissociation kinetics, however several aspects of the dissociation kinetics in plasmas are still unclear.Dissociation takes place when collisions between molecules and electrons, as well as intermolecular collisions, provide enough energy to lead an already excited molecule into the continuum region thereby producing CO and O. The state-to-state (STS) approach 2,3 allows to calculate very accurate reaction rates by considering any vibrational state as an individual species.This amounts to solve the so-called Master Equation (ME) for the populations of vibrational states 2,4 : The ME is actually a system of n non-linear ODEs (Ordinary Differential Equations)

Vibrational Kinetics in Plasma as a Functional Problem: A Flux-Matching Approach

“…data and a few differences in the calculation of transport coefficients (see above), our result here is not exactly matching the MC approach in Diomede et al. 7 In particular, we obtain here somewhat different behaviours of the distribution close to the dissociation threshold.…”

“…Furthermore, since a different value of J amounts to a different relation between f and its gradient df/dε at the boundary ε = εdiss, this result confirms the findings in our previous paper 7 that boundary conditions play a fundamental role in continuum formulations of the vibrational kinetics. In agreement with the findings of our previous paper, 7 in Figure 3 which populates the VDF close to the dissociation limit and is consistent with the negative flux: this last result also shows that our approach can be applied also in a recombination regime.…”

“…Rusanov et al 5 ) and summarized in the books by the same author. 3,4,6 The same approach has been considered in our previous paper 7…”

“…[2][3][4][5][6] The difference with respect to previous diffusion approaches is the use of a numerical solution which avoids the approximations of the perturbation techniques used in the past. 3,4 In a previous paper, 7 we have solved the Fokker-Planck (FP) equation numerically using a Monte Carlo (MC) technique based on the short time Green function of the same equation. In this paper, we use a much more effective method and analyse the role of the reactive flux J, which equals the dissociation rate per molecule at the steady state.…”

Overview of Electric Field Applications in Energy and Process Engineering

“…Thus, NTPs are promising for exhaust gas treatment for automotive and industrial applications. Furthermore, they are applied for conversion of carbon dioxide (CO 2 ), methane (CH 4 ) and syngas (consisting primarily of hydrogen (H 2 ), carbon monoxide (CO), and some CO 2 ) into hydrocarbons [61,62]. Thermal plasmas have also been used for plasma gasification, which is already applied in industry, e.g., for waste treatment [63].…”