PLASMA ASSISTED CO 2 DISSOCIATION MODELS FOR ENVIRONMENT, ENERGY AND AEROSPACE APPLICATIONS

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1 PLASMA ASSISTED CO 2 DISSOCIATION MODELS FOR ENVIRONMENT, ENERGY AND AEROSPACE APPLICATIONS G. Colonna, L. D. Pietanza, G. D Ammano, A. Laricchiuta, an M. Capitelli CNR-IMIP, via Amenola 122/D, Bari ABSTRACT In the present work, we compare ifferent mechanisms of CO 2 issociation by calculating their corresponing rates through the solution of the electron Boltzmann equation, accounting for elastic, inelastic, superelastic an electron-electron collisions. In particular, electron impact issociation rates are compare to pure vibrational ones, obtaine by supposing issociation from excite vibrational normal moes of CO 2. This point is of funamental importance to unerstan the role of excitation of vibrational moes in enhancing CO 2 issociation. Key wors: CO 2 ; issociation; vibrational moes; Boltzmann equation. 1. INTRODUCTION Plasma-processing of CO 2 uner non-equilibrium conitions is nowaays consiere a promising substitute to conventional routes to specifically tackle the rate-limiting issociation into CO (Taylan & Berberoglu 2015; Goee et al. 2014; Kozàk & Bogaerts 2014; Silva et al. 2014). The iea to use col, i.e. non equilibrium plasmas, for the CO 2 issociation has a long history starte with the works of Russian (Friman 2012; Legasov et al. 1977) an Italian groups (Capezzuto et al. 1976; Capitelli & Molinari 1980), at the beginning of plasma-chemistry activities. The basic iea was the impossibility to rationalize experimental issociation rates of CO 2 by using the irect electron impact issociation process. On the contrary, especially at low electron temperature (T e of the orer of 1 ev), the input of electrical energy goes through the excitation of vibrational moes of CO 2 (in particular the asymmetric one) followe by VV energy exchange processes able to sprea the low lying vibrational quanta over the whole vibrational laer of CO 2, ening in the issociation process. The upper limit to the issociation rate of this mechanism, calle pure vibrational mechanism (PVM), can be obtaine by the following equation = 1 υ max k ev ( ) (1) where k ev ( ) is the rate of the resonant vibrational excitation process an υ max the number of vibrational quanta containe in the vibrational laer of CO 2 (to a first approximation we can imagine to pump vibrational energy selectively on the asymmetric moe of CO 2 ), as in the case of nitrogen (Capitelli et al. 2014; Sergeev & Slovetsky 1983). This rate can be several orers of magnitue higher than the corresponing issociation process inuce by electron impact. These simple consierations are at the basis of the numerous experimental attempts to use vibrational energy in the issociation process rather than the irect electronic process with the belief that the activation energy of the vibrational excitation process is much less than the corresponing electron impact process. Unfortunately, the situation is much more complicate than that given by Eq. 1, which completely isregars the relaxation of vibrational energy by VT energy exchange processes. Moreover the possible enhancement of the irect electron impact issociation process ue to the presence of excite molecules shoul be taken into account. The last has a twofol effect on the irect issociation process: it enlarges the electron energy istribution function (eef) through the effect of superelastic vibrational an electronically excite state collisions, increasing at the same time the irect issociation rate; it increases the issociation rate ue to the lowering of the energy threshol of issociation, ecreasing with vibrational quantum number. The first point has been consiere in the past to unerstan the issociation of CO 2 in laser mixtures (Capitelli et al. 1981), this aspect being reiterate more recently for the same aim (Kumar et al. 2013). The secon point has been recently reinvestigate in the case of nitrogen plasmas (Capitelli et al. 2013). To better unerstan these points, we have solve the electron Boltzmann equation for CO 2 plasma taking into account superelastic vibrational collisions an superelastic electronic collisions. From the resulting eef, electron impact issociation rates an upper limit rates of pure vibrational mechanism have been calculate an compare both in ischarge an post-ischarge conitions.

2 2. THE BOLTZMANN EQUATION The electron Boltzmann equation can be written in the following compact form f(ɛ, t) t = J E ɛ J el ɛ J e e ɛ + S in + S sup (2) The first three terms on the right han sie of Eq. 2 correspon to fluxes in the electron energy ue to the electric fiel, elastic electron-molecule (e-m) collisions an electron-electron (e-e) collisions, while the last two terms are source terms ue to inelastic an superelastic collisions. A very simplifie CO 2 vibrational energy laer is consiere (see Table 1). Table 1. Channels in CO 2 kinetics. notation state energy [ev] channel CO 2(v 0) (000) CO 2(v 1) (010) vib-excitation CO 2(v 2) (020)+(100) vib-excitation CO 2(v 3) (030)+(110) vib-excitation CO 2(v 4) (0n0)+(n00) vib-excitation CO 2(v 5) (0n0)+(n00) vib-excitation CO 2(v 6) (0n0)+(n00) vib-excitation CO 2(v 7) (0n0)+(n00) vib-excitation CO 2(v 8) (001) vib-excitation CO 2(e 1) irect issociation CO 2(e 2) electronic excitation CO ionization We inclue the groun vibrational level v 0 (000), the first excite level v 1 (010) of the ouble egenerate symmetric bening moe, the first level of the asymmetric moe v 8 (001) an other six Fermi resonance symmetric energy levels (v 2 -v 7 ). The inelastic an superelastic collisions consiere are the electron impact vibrational excitation/e-excitation from the groun vibrational level v 0 towars all the other v i with 1 i 8, the electronic excitation from groun level v 0 towars e 2, the issociation an the ionization process e + CO 2 (v 0 ) e + CO 2 (v i ) 1 i 8 (3) e + CO 2 (v 0 ) e + CO 2 (e 2 ) (4) e + CO 2 (v 0 ) e + CO + O (5) e + CO 2 (v 0 ) e + e + CO + 2 (6) The corresponing cross section ata entering the Boltzmann equation have been taken from the Phelps atabase (Lowke et al. 1973). The reverse cross sections have been erive by etaile balance principle. Note that in the corresponing atabase (Lowke et al. 1973) the 7-eV threshol process is consiere as a issociative channel, while the electronic excitation is limite to a process with energy threshol of 10.5 ev. The aition of further excitation an issociation levels (Friman 2012; Kozàk & Bogaerts 2014) can improve the accuracy of the present results, without altering their qualitative valiity. The time epenent Boltzmann solver is use taking the reuce electric fiel E/N, the vibrational temperature of the ifferent moes an the ionization egree as free parameters. In particular, we consier T v as the vibrational temperature of the asymmetric level v 8 (001) an the other vibrational levels corresponing to the other two moes (v 0 v 7 ) are characterize by a T v temperature, with T v > T v following what observe in CO 2 laser physics. Moreover the concentration of the CO 2 (e 2 ) electronically excite state has been estimate from Boltzmann istribution at T v, while, only in the post ischarge regime, a fixe concentration of 10 5 has been impose. The ionization egree has been fixe to DISSOCIATION RATES In this section, we woul like to focus on ifferent mechanism of CO 2 issociation. Besie irect electron impact rates, upper limit rates obtaine in the framework of a pure vibrational mechanism can be calculate. Moreover, the effect of excite vibrational states can be also taken into account. To sum up, the following kins of issociation rate can be efine: 1. the irect electronic excitation-issociation from the CO 2 (v 0 ) groun state, k (000); 2. the irect electron impact issociation rate incluing the effect of vibrational levels υ max [ ( ε00v 1 K (all) = exp 1 )] k (000) k v B T e T v (7) where v max being the maximum value of vibrational levels in the asymmetric stretching laer, i.e. 21 accoring to (Kozàk & Bogaerts 2014). This equation results from the crue assumption of a shift of cross section threshol for excite vibrational levels an eef at T v an T e temperatures, respectively, reucing to K (all) = υ max k (000) for the case T v = T e, as reporte by (Park 2008); 3. accoring to Eq. 1, which correspons to the upper limit of issociation in a pure vibrational mechanism; 4. incluing the effect of vibrational levels in the pure vibrational mechanism (all) = 1 υ max 8 n=1 ε vn ε v8 k ev (0 v n ) (8) where v n are the excite vibrational levels belonging to ifferent normal CO 2 moes, as reporte in

3 Table 1. Note that Eq. 8 normalizes the input of vibrational quanta to the asymmetric moe. k (000) an k ev (0 v n ) are calculate irectly from the stationary eef an the issociation an vibrational excitation cross sections, respectively, through the following equation k = ɛ th f(ɛ)σ(ɛ)v(ɛ)ɛ (9) where σ(ɛ) represents the corresponing cross section, v(ɛ) the electron velocity an ɛ th the collision threshol energy. eef(ev -3/2 ) K K 500 K K 1000 K K 2000 K K 3000 K K 4000 K K 5000 K K 6000 K K 4. RESULTS 4.1. Discharge Conitions Fig. 1 an 2 reports the eef behavior as a function of electron energy at two ifferent values of the electric fiel E/N (15 T an 30 T) for ifferent couples of T v an T v vibrational temperatures, with an ionization egree of 10 3 an by incluing e-e collisions. For T v = T v = 0 K, only elastic an inelastic collisions from the groun vibrational state affect the eef, while superelastic vibrational an electronically collisions enter the calculations only for T v an T v > 0. As alreay shown in literature, superelastic (vibrational) collisions strongly enlarge the eef, affecting in particular the highenergy part of the istribution, with an apparent minor effect on the boy. Moreover, superelastic effects ecrease when E/N increases, since the importance of the vibrational energy exchange between electrons an CO 2 molecules ecreases when the electron energy (gaine by the electric fiel) becomes sufficiently high. The eef of Fig. 1 an 2 are characterize by nearly a Maxwell tren thanks to the action of e-e collisions, with the only exception at lower vibrational temperatures. By neglecting e-e collisions, the resulting eef shows larger eviation from the Maxwell istribution also for higher vibrational temperatures, as it is shown in Fig. 3, where the eef with an without e-e collisions are compare in the case of E/N=30 T an for three couples of sample vibrational temperatures. The eefs calculate by neglecting e-e collisions show a characteristic wavy tren with small peaks in corresponence of the collision process threshols. E-e collisions, by reistributing electron energy, smooths the peaks an prouce higher eef tails. Fig. 4 shows the fractional power transferre from electrons to ifferent channels of CO 2 vibrational excitation, issociation, electronic excitation an ionization as a function of E/N for T v = 500 K an T v = 1500 K. In Fig. 4 results obtaine by incluing (full lines) or neglecting (ashe lines) superelastic collisions are reporte. These fractional powers have been calculate as Figure 1. Electron energy istribution function in ischarge conitions with E/N =15 T reporte at ifferent selecte values of vibrational temperatures of symmetric/bening (T v) an asymmetric (T v ) normal moes. The electron molar fraction is χ e =10 3 an electronelectron collisions are inclue into calculations. eef(ev -3/2 ) K K 500 K K 1000 K K 2000 K K 3000 K K 4000 K K 5000 K K 6000 K K Figure 2. Electron energy istribution function in ischarge conitions with E/N =30 T reporte at ifferent selecte values of vibrational temperatures of symmetric/bening (T v) an asymmetric (T v ) normal moes. The electron molar fraction is χ e =10 3 an electronelectron collisions are inclue into calculations.

4 T v '=6000 K, T v =8000 K 0.8 vibrational excitation eef(ev -3/2 ) T v '=1000 K, T v =2000 K Fractional Power Losses issociative excitation electronic excitation ionization E/N (T) Figure 3. Electron energy istribution function in ischarge conitions with E/N =30 T an for ifferent selecte values of the temperatures of symmetric/bening (T v) an asymmetric (T v ) normal moes with the inclusion (full lines) an neglection (ashe lines) electronelectron collisions. the ratio between the energy transferre per unit time an volume from electrons to ifferent channels of CO 2 excitation (Q vib, Q iss, Q electr, Q ion ) an the total energy per unit time an volume gaine by the electrons from the electric fiel (Q E ). In particular, if we consier, as example, the vibrational energy channel, the energy transferre into the vibrational excitation per unit time an volume can be written as: A = v i B = v i Q vib = N e N tot (A B) (10) v j χ CO2 χ CO2 (v i )K (v i, v j )ɛ v i,v j (11) v j χ CO2 χ CO2 (v j )K r (v j, v i )ɛ v i,v j (12) where N e, N tot are the electron an total ensity, χ CO2 the CO 2 molar fraction, χ CO2 (v i ) an χ CO2 (v j ) the level fractions of CO 2 into the vibrational levels v i an v j (with v i v j ), K (v i, v j ) an K r (v j, v i ) the electron impact vibrational excitation an e-excitation rate coefficients, ɛ v i,v j the threshol energy. The electron energy per unit time an volume gaine from the electric fiel is, instea, given by: Figure 4. Fractions of electron energy per unit time an volume transferre to ifferent channels, i. e. vibrational excitation, issociation, electronic excitation an ionization, as a function of the reuce electric file (E/N), for T v = 500 K an T v = 1500 K, with (full lines) an without (ashe lines) superelastic collisions Q E = N e v q e E (13) where v is the rift velocity, q e the electron charge, E the electric fiel strenght. The results shown in Fig. 4 confirm what alreay state in literature (Friman 2012; Kozàk & Bogaerts 2014), that is, for reuce electric fiels up to 40 T, which correspon to electron temperature of aroun 1-2 ev, the major portion of the ischarge energy is transferre from plasma electrons to vibrational excitation of CO 2 molecules. The issociative, the electronic excitation an the ionization channels are activate soon after by increasing the reuce electric fiel. This results have suggeste in the past the iea to fin the better experimental ischarge conitions to exploit the vibrational excitation mechanism of CO 2 in promoting CO 2 issociation in plasma (Friman 2012). Moreover, inspection of the results in Fig. 4, shows the great importance of superelastic collisions in affecting the energy transfer rates. In particular, the superelastic vibrational losses reuce the power losses of the vibrational channel an consequently moify the power losses in the other channels. It is clear that, superelastic collisions, by pumping electrons at higher energy, promote issociative an electronic excitation energy channels, whose rates epen strongly on the eef tail. In Fig. 5 an Fig. 6, previous efine issociation rates (see Eq. 1, 7, 8) an the electron impact issociation rate from the groun state k (000) are shown as a function of vibrational temperature T v for two values of reuce electric fiel 15 T an 30 T, respectively.

5 issociation rates (cm 3 s -1 ) E/N=15 T k (000) K (all) (all) The calculate issociation rates epen strongly on the form of the eef reporte in Fig. 1 an Fig. 2. In particular, the electron impact issociation rate from groun state k (000) increases as a function of T v ue to the enlarging of the corresponing eef ue to superelastic collisions (see Fig. 1 an Fig. 2). The irect electron impact rate of eq. 7, obtaine by incluing all vibrational levels, becomes more important than the corresponing v 0 contribution as the vibrational temperature increases. The upper rates calculate in the pure vibrational mechanism (Eq. 1 an Eq. 8), instea, with the only exception at low vibrational temperatures an at low reuce electric fiel (E/N=15 T), are nearly constant over the T v range an ominate the irect electron impact mechanism at low E/N value. By increasing the reuce electric fiel value, instea, issociation ue to pure vibrational mechanism become less important T v (K) Figure 5. Dissociation rates in CO 2 plasma as a function of vibrational temperature of asymmetric moe T v, at E/N=15 T. k (000) is the electron impact issociation rate from groun state, K (all), an (all) are taken from Eq. 7, Eq. 1 an Eq. 8, respectively. The above test cases applies mainly in the low-electron temperature plasmas ominate by the excitation of vibrational moes, a situation which can occur in microwave (Mw) ischarges operating at moerate pressures. Microwave riven CO 2 plasma at sub-atmospheric pressures can reach energy efficiencies as high as 60% at low specific injecte energies (aroun 1 ev/molecule CO 2 ) thus confirming the importance of vibrational excitation in the issociation process (Silva et al. 2014). The use of atmospheric DBD pulse ischarges reveale an energy efficiency of about 10% (Silva et al. 2014; Kozàk & Bogaerts 2014). issociation rates (cm 3 s -1 ) E/N=30 T T v (K) k (000) K (all) K (ulpvm) (all) Figure 6. Dissociation rates in CO 2 plasma as a function of vibrational temperature of asymmetric moe T v, at E/N=30 T. k (000) is the electron impact issociation rate from groun state, K (all), an (all) are taken from Eq. 7, Eq. 1 an Eq. 8, respectively Post ischarge conitions Another interesting case is the post ischarge conition (E/N=0 T) obtaine after the use of nanosecon highvoltage ischarges operating at atmospheric pressure. After the pulse, electrons can reach very elevate temperatures, able to excite CO 2 electronic states rather than vibrational states. For this reason, in post ischarge test cases, the concentration of CO 2 (e 2 ) electronically excite state has been fixe to Fig. 7 shows the time epenent eef calculate in the post ischarge with T v = 500 K an T v = 1500 K an with an initial eef, corresponent to that obtaine by terming off a reuce electric fiel of E/N=100 T after several ms resience times. As we can see, the eef cools own reaching a stationary conition very soon at approximately t=10 8 s. Only when it is col enough, the peak ue to the superelastic electronic collisions from the CO 2 (e 2 ) level appear at the threshol energy of the corresponent excitation process, i. e ev. However, elastic an inelastic collisions together with e-e collisions smooths out such peak transforming it in a plateau. Fig. 8, instea, shows the stationary eef in post ischarge at ifferent vibrational temperatures. As it can be seen, the length of the plateau at 10.5 ev ecreases as the vibrational temperature increases since the effect of the superelastic electronic collisions at 10.5 ev is overcome by vibrational superelastic collisions. The corresponing rate coefficients for the issociative channels in the post-ischarge regime

6 10 0 T v '=500 K, T v =1500 K eef(ev -3/2 ) t(s)=0 t(s)=10 11 t(s)= t(s)= t(s)= t(s)= t(s)=5 t(s)= t(s)= Figure 7. Time epenent electron energy istribution function in the post ischarge (E/N=0) for T v= an asymmetric (T v =) normal, by incluing electron electron an by imposing an ionization egree of 10 3 an a concentration of CO 2 (e 2 ) electronic excite states of are reporte in Fig. 9. As it can be seen, the pure vibrational mechanisms ominate the irect issociation channels in the whole T v vibrational temperature range. We shoul remember, however, that pure vibrational issociation rates are essential upper limit ones an that, in any case, the irect issociation channels cannot be neglecte into the escription of post-ischarge regime. eef(ev -3/2 ) K K 500 K K 1000 K K 2000 K K 3000 K K 4000 K K 5000 K K 6000 K K Figure 8. Stationary electron energy istribution function in the post ischarge (E/N=0) for ifferent selecte values of the temperatures of symmetric/bening (T v) an asymmetric (T v ) normal moes by incluing electron electron an by imposing an ionization egree of 10 3 an a concentration of CO 2 (e 2 ) electronic excite states of CONCLUSIONS In this paper, we have investigate ifferent mechanisms of CO 2 issociation in ischarge an post-ischarge conitions. In particular, electron impact issociation rates have been compare to upper limit issociation ones obtaine in the framework of a pure vibrational mechanism. This mechanism is base on experimental an theoretical observations that, at low electron temperature (T e 1 2 ev) an reuce electric fiel (E/N 40T ), most of the electron energy is transferre towars the excitation of vibrational moes, which, followe by vv collisions, ens in CO 2 issociation. Such vibrational excitation energy coul be exploite to increase CO 2 issociation efficiency since the necessary power to excite the vibrational levels of CO 2 molecule is much lower than that one requeste for thermal issociation as well as for electron impact issociation. These ieas epen on the correct evaluation of the input of vibrational energy of CO 2 manifol an on the corresponing activation of electronically excite states. The shown results confirm what alreay iscusse in literature, giving attention over the importance of consiering vibrational an electronic superelastic collisions in affecting the electron energy istribution both in ischarge an in the post ischarge plas- rate coefficient (cm 3 s -1 ) T v (K) k (000) K (all) K (ulpvm) (all) Figure 9. Rate coefficients for issociation channels in CO 2 plasma, as a function of vibrational temperature of asymmetric moe, in the post ischarge (E/N=0 T). k (000) is the electron impact issociation rate from groun state, K (all), an (all) are taken from Eq. 7, Eq. 1 an Eq. 8, respectively.

7 mas. However, the presente results are still qualitative, at this stage, an the moel nees further future improvements. First of all, a more realistic vibrational energy laer of CO 2 molecules is necessary. Symmetric an asymmetric vibrational energy levels up to the threshol of issociation shoul be consiere in the moel. Moreover, a complete ab initio ynamic moel for ev resonant process, electron impact excitation an issociation cross sections shoul be built up for the whole vibrational laer. Also bimolecular reactions processes an eactivation processes involving vibrationally excite CO 2 molecules shoul be treate. Finally, self consistent coupling of the electron Boltzmann equation an excite state kinetic in CO 2 reacting mixture shoul be evelope, since non equilibrium excite state population can occur expecially in col plasmas. Silva, T., Britun, N., Gofroi, T., & Snyers, R. 2014, Plasma Sources Science an Technology, 23, Taylan, O. & Berberoglu, H. 2015, Plasma Sources Science an Technology, 24, ACKNOWLEDGMENTS This work receive funing from the project Apulia Space, PON 03PE from DTA Brinisi (Italy). REFERENCES Capezzuto, P., Cramarossa, F., D Agostino, R., & Molinari, E. 1976, The Journal of Physical Chemistry, 80, 882 Capitelli, M., Colonna, G., D Ammano, G., Laporta, V., & Laricchiuta, A. 2013, Physics of Plasmas, 20, Capitelli, M., Colonna, G., D Ammano, G., Laporta, V., & Laricchiuta, A. 2014, Chemical Physics, 438, 31 Capitelli, M., Gorse, C., Berarini, M., & Braglia, G. 1981, Lettere Al Nuovo Cimento Series 2, 31, 231 Capitelli, M. & Molinari, E. 1980, in Topics in Current Chemistry, Vol. 90, Kinetics of Dissociation Processes in Plasmas in the Low an Intermeiate Pressure Range (Springer-Verlag) Friman, A. 2012, Plasma Chemistry (Cambrige University Press) Goee, A., Bongers, W. A., Graswinckel, M. F., et al. 2014, XARMAE Workshop, Barcelona, January 2014 Kozàk, T. & Bogaerts, A. 2014, Plasma Sources Science an Technology, 23, Kumar, M., Biswas, A., Bhargav, P., et al. 2013, Optics & Laser Technology, 52, 57 Legasov, V. A., Givotov, V. K., Krashennikov, E. G., Rusanov, V. D., & Friman, A. 1977, Sov. Phys. Doklay, 238, 66 Lowke, J. J., Phelps, A. V., & Irwin, B. W. 1973, Journal of Applie Physics, 44, 4664 Park, C. 2008, AIAA Sergeev, P. & Slovetsky, D. 1983, Chemical Physics, 75, 231