7
ISSN 0018151X, High Temperature, 2010, Vol. 48, No. 1, pp. 40–46. © Pleiades Publishing, Ltd., 2010. Original Russian Text © S.A. Losev, V.N. Yarygina, 2010, published in Teplofizika Vysokikh Temperatur, 2010, Vol. 48, No. 1, pp. 44–51. 40 INTRODUCTION The propagation of shock waves, combustion, det onation, and other processes of strong stimulation of gas are known to cause an appreciable disturbance of chemical and thermal equilibrium. If the rotation of molecules is excited as a result of several collisions of particles in gas, the excitation of vibrational degrees of freedom of molecules and of the electron states of atoms proceeds under significantly nonequilibrium conditions and is to be simulated in detail. After many years of investigations, this problem found successful solution in numerous theoretical and experimental studies, for example, in the case of shock tubes and in the theory of relaxation processes (see [1, 2]). It appears to be of most interest at present to consider processes involving molecules and atoms in excited electron states such as the emergence and quenching of these states in chemical reactions of dissociation, recombination, and exchange, as well as electron energy exchange in collisions of particles. The elec tron energy exchange associated with chemical trans formations is defined as an electronchemical reac tion. The results of kinetic calculations [3] reveal that the failure to include excited electron states in the treatment of thermally nonequilibrium processes leads to significant errors in the values of parameters of gas behind the shock wave front and in the assumed values of rate constants of dissociation and recombination in the ground electron state. Lunev [4, p. 518] points out that “…in view of the absence of reliable information, one very seldom takes into account the possible effect of electron excitation of molecules on the reaction rate constants”. All this necessitates further experimental and theoretical activities aimed at thorough investiga tion of the processes of electronchemical kinetics involving excited electron states of reacting atoms and molecules. It is expedient to treat the electronexcited mole cules involved in these reactions as individual compo nents of mixture for each electron state with respective vibrational levels, as is usually the case for molecules in the ground electron states. The course of processes involving electronexcited molecules is considered in a number of published papers, for example, in reac tions with carbon monoxide [5], in describing the motion of space vehicles in the Earth atmosphere [6], during combustion of hydrogenoxygen mixture [7, 8], and so on. PROCESSES INVOLVING MOLECULES AND ATOMS IN EXCITED ELECTRON STATES The basic process of formation of excited electron states of molecules is that of recombination; this pro cess is much more effective than the process of forma tion of molecules in the ground electron state. Such a result was obtained by Aliat et al. [3] in the case of for mation of CO molecules: the value of rate constant of recombination to the state СО(A 1 Π) is twice that in Processes in HighTemperature Air Involving Molecules and Atoms in Excited Electron States S. A. Losev a and V. N. Yarygina b a Institute of Mechanics, Moscow State University, Moscow, 119899 Russia Email: [email protected] b GNPP Bazal’t Federal State Unitary Enterprise, Moscow, Russia Email: [email protected] Received February 16, 2009 Abstract—Analysis is made of kinetic processes involving electron states of atoms and molecules in the air behind the shock wave front. The electron states of atoms and molecules are formed in hightemperature air as a result of dissociation and recombination, in the processes of electron exchange of energy in collisions of particles, and in chemical exchange reactions. The fastest one of these processes is the process of formation of excited electron states under conditions of recombination of atoms and during isenergic transition of vibra tionaltoelectron energy from highly excited vibrational levels. The quenching of metastable particles occurs in collisions of particles, under conditions of dissociation and recombination, and in chemical exchange reactions. The data base for rate constants of electron energy exchange reactions in hightemperature air is demonstrated. Examples are given of description of vibrational energy exchange in electronchemical reac tions. DOI: 10.1134/S0018151X10010074 THERMOPHYSICAL PROPERTIES OF MATERIALS

Processes in high-temperature air involving molecules and atoms in excited electron states

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Page 1: Processes in high-temperature air involving molecules and atoms in excited electron states

ISSN 0018�151X, High Temperature, 2010, Vol. 48, No. 1, pp. 40–46. © Pleiades Publishing, Ltd., 2010.Original Russian Text © S.A. Losev, V.N. Yarygina, 2010, published in Teplofizika Vysokikh Temperatur, 2010, Vol. 48, No. 1, pp. 44–51.

40

INTRODUCTION

The propagation of shock waves, combustion, det�onation, and other processes of strong stimulation ofgas are known to cause an appreciable disturbance ofchemical and thermal equilibrium. If the rotation ofmolecules is excited as a result of several collisions ofparticles in gas, the excitation of vibrational degrees offreedom of molecules and of the electron states ofatoms proceeds under significantly nonequilibriumconditions and is to be simulated in detail. After manyyears of investigations, this problem found successfulsolution in numerous theoretical and experimentalstudies, for example, in the case of shock tubes and inthe theory of relaxation processes (see [1, 2]). Itappears to be of most interest at present to considerprocesses involving molecules and atoms in excitedelectron states such as the emergence and quenchingof these states in chemical reactions of dissociation,recombination, and exchange, as well as electronenergy exchange in collisions of particles. The elec�tron energy exchange associated with chemical trans�formations is defined as an electron�chemical reac�tion.

The results of kinetic calculations [3] reveal thatthe failure to include excited electron states in thetreatment of thermally nonequilibrium processes leadsto significant errors in the values of parameters of gasbehind the shock wave front and in the assumed valuesof rate constants of dissociation and recombination inthe ground electron state. Lunev [4, p. 518] points out

that “…in view of the absence of reliable information,one very seldom takes into account the possible effectof electron excitation of molecules on the reaction rateconstants”. All this necessitates further experimentaland theoretical activities aimed at thorough investiga�tion of the processes of electron�chemical kineticsinvolving excited electron states of reacting atoms andmolecules.

It is expedient to treat the electron�excited mole�cules involved in these reactions as individual compo�nents of mixture for each electron state with respectivevibrational levels, as is usually the case for molecules inthe ground electron states. The course of processesinvolving electron�excited molecules is considered ina number of published papers, for example, in reac�tions with carbon monoxide [5], in describing themotion of space vehicles in the Earth atmosphere [6],during combustion of hydrogen�oxygen mixture [7,8], and so on.

PROCESSES INVOLVING MOLECULES AND ATOMS IN EXCITED ELECTRON STATES

The basic process of formation of excited electronstates of molecules is that of recombination; this pro�cess is much more effective than the process of forma�tion of molecules in the ground electron state. Such aresult was obtained by Aliat et al. [3] in the case of for�mation of CO molecules: the value of rate constant ofrecombination to the state СО(A1Π) is twice that in

Processes in High�Temperature Air Involving Molecules and Atoms in Excited Electron States

S. A. Loseva and V. N. Yaryginab

aInstitute of Mechanics, Moscow State University, Moscow, 119899 RussiaE�mail: [email protected]

bGNPP Bazal’t Federal State Unitary Enterprise, Moscow, RussiaE�mail: vika�[email protected]

Received February 16, 2009

Abstract—Analysis is made of kinetic processes involving electron states of atoms and molecules in the airbehind the shock wave front. The electron states of atoms and molecules are formed in high�temperature airas a result of dissociation and recombination, in the processes of electron exchange of energy in collisions ofparticles, and in chemical exchange reactions. The fastest one of these processes is the process of formationof excited electron states under conditions of recombination of atoms and during isenergic transition of vibra�tional�to�electron energy from highly excited vibrational levels. The quenching of metastable particles occursin collisions of particles, under conditions of dissociation and recombination, and in chemical exchangereactions. The data base for rate constants of electron energy exchange reactions in high�temperature air isdemonstrated. Examples are given of description of vibrational energy exchange in electron�chemical reac�tions.

DOI: 10.1134/S0018151X10010074

THERMOPHYSICAL PROPERTIES OF MATERIALS

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HIGH TEMPERATURE Vol. 48 No. 1 2010

PROCESSES IN HIGH�TEMPERATURE AIR INVOLVING MOLECULES AND ATOMS 41

the case of recombination to the ground stateСО(X1Σ). In collisions of molecules in various excitedvibrational and electron states, the fastest process isthat of vibrational�to�electron energy exchangebetween molecules exhibiting similar stores of vibra�tional and electron energy, i.e., isergic states. Kustovaet al. [9] cite references to relevant experimental inves�tigations and to the acquisition of values of level con�stants of the rate of isergic vibrational�to�electronenergy exchange involving CO molecules. Theseresults emphasize the part played by level kinetics indescribing the processes occurring in high�tempera�ture gas.

The mechanisms of electron�chemical reactionsinvolving electron�excited atoms and moleculesinclude the processes of formation and quenching ofthese states under conditions both of collisional energyexchange and of dissociation and recombination. In sodoing, most effective is the formation of molecules onthe upper vibrational levels of various electron states.

The excited states of atoms and molecules in theair, which are considered below, are largely metastablestates, the quantum transitions from which to states oflower energy are forbidden and have long radiativelifetimes. The main channel of quenching of metasta�ble particles is provided by the transfer of energy toother atoms and molecules in collisions, namely, elec�tron�electron (EE) and electron�vibrational (EV)energy exchange.

As usual, the coefficients in kinetic equations, i.e.,reaction rate constants, are the target function of theprocesses being described. The values of these con�stants in electron�chemical reactions were largelyobtained from the results of experimental studies,because it is very difficult to theoretically obtain thequantitative data about these processes.

ANALYSIS OF PUBLISHED RESULTS

The results of theoretical and experimental investi�gations of electron�chemical reactions in high�tem�perature air at temperatures significantly above 500 Kare given in various publications.

The theoretical treatment of rate constants of elec�tron�chemical reactions involves the use of themethod of transition states for potential surfaces incomplexes of colliding particles using the solution of

equations of quantum mechanics. In the case of high�temperature air, these quantities were obtained in onlytwo studies (Gonzalez et al. [10] and Tully [11]). Theresults of experimental investigations are based onfairly extensive studies of the processes occurring inshock waves and in electric�discharge and other facil�ities. The results of analysis of numerous experimentaland theoretical studies were considered and recom�mended for use in reviews and summarizing publica�tions [6, 12–15]. Gorelov et al. [6] used and evaluatedthe data on electron�chemical reactions involving N2

and NO molecules in describing the processes occur�ring behind the shock wave front under conditions ofmotion of space vehicles in the Earth atmosphere.Demonstrated in [16, 17] are the results of using thedata obtained in view of electron�excited О2 mole�cules for solving kinetic equations in treating the det�onation in supersonic flows. The recommended dataon the results of analysis of concrete studies are givenin [6, 7, 18–26].

DATA BASE FOR THE RATE CONSTANTS OF ELECTRON�CHEMICAL REACTIONS

IN HIGH�TEMPERATURE AIR

High�temperature air, which is considered below,includes the components N2, N, O2, O, and NO in theground and excited electron states in accordance withthe classification of N2(X, A, B), N(4S, 2D), O2(X, a, b,c, C), O(3P, 1D, 1S), and NO(X, A, B, C); M is the gen�eralized designation of all components in the groundelectron states; the components, in which the statesare not indicated, belong to the ground electron statesas well.

The data base includes the description of the fol�lowing processes in high�temperature air:

– the formation of excited electron states underconditions of recombination of atoms (Table 1) and incollisions of particles (Table 2);

– the electron energy exchange in collisions of par�ticles (Table 3) and under conditions of recombinationof atoms (Table 4);

– the quenching of excited electron states of atomsand molecules in collisions (Table 5) and under condi�tions of dissociation (Table 6).

The rate constants of the processes under consider�ation are given by Arrhenius’ formula k(T) =

Table 1. Formation of excited electron states under conditions of recombination

Reactions Tmin Tmax LogA N Ea Reference

N + N + N2 N2(A) + N2 300 30000 –30.68 –0.8 0 [6]

N + O + N2 NO(A) + N2 300 30000 –30.60 –1.24 0 [6]

N + O + N2 NO(B) + N2 300 30000 –30.82 –1.4 0 [6]

O(3P) + O(3P) + O2 O2(X, a, b) + O2 300 2000 –31.57 –0.41 0 [12]

O(3P) + O(3P) + O O2(X, a, b) + O 300 2000 –31.1 –0.41 0 [12]

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HIGH TEMPERATURE Vol. 48 No. 1 2010

LOSEV, YARYGINA

, except for the rate constantmarked with asterisk in Table 5.

These data define the reaction rate constants incm3/s for second�order reactions and in cm6/s forthird�order reactions. The values of are given in

kcal/mol, and kcal/(mol K).

( )−expNaAT E RT

aE−

= ×

31.987 10R

The temperature�independent rate constants givenin this data base describe high�temperature gas in thecase of reactions without potential barrier and reac�tions with forbidden transitions (see examples in [7]),as well as in the cases where the reaction rate constantis high enough and close to the gas�kinetic rate con�stant.

Table 2. Formation of excited electron states in collisions of particles

Reactions Tmin Tmax LogA N Ea Reference

N2(X) + N2 N2(A) + N2 300 30000 –11.74 –0.5 142.2 [6]

N2(X) + N N2(A) + N 300 30000 –6.7 –1.5 142.2 [6]

N2(X) + O2 N2(A) + O2 300 30000 –8.0 –1.5 142.2 [6]

N2(X) + O N2(A) + O 300 30000 –6.92 –1.5 142.2 [6]

N2(X) + NO N2(A) + NO 300 30000 –11.77 –0.5 142.2 [6]

NO(X) + M NO(A) + M 300 30000 –10.8 –0.5 126.1 [6]

N2(X) + N N2(A) + N 300 20000 –10.77 0.5 142.1 [18]

N2(X) + O N2(A) + O 300 20000 –10.77 0.5 142.1 [18]

NO(X) + O NO(A) + O 300 20000 –10.77 0.5 142.1 [18]

Table 3. Electron energy exchange in collisions of particles

Reactions Tmin Tmax LogA N Ea Reference

N2(A) + M N2(B) + M 300 30000 –10.7 0 26.8 [6]

N2(A) + NO(X) NO(A, v) + N2(X) 300 30000 –10.0 0 0 [6]

N2(A) + NO(X) NO(C, v) + N2(X) 300 30000 –9.01 0 0 [6]

N2(A) + N2(A) N2(B) + N2(X, v) 300 30000 –8.91 0 0 [6]

N2(A) + NO(X) N2(X) + NO(A) 300 20000 –10.77 0.5 0 [18]

O2(a) + O2(a) O2(b) + O2(X) 300 3000 –27.15 3.8 –1.39 [13, 16, 19]

O2(b) + O(3P) O2(a) + O(3P) 300 3000 –13.09 0 0 [16]

O2(b) + N(4S) O2(a) + N(4S) 300 3000 –13.09 0 0 [16]

O2(c) + O2(X) O2(b) + O2(X, a, b) 300 2000 –15.0 0 0 [12]

O2(C) + O2(X) O2(X, a, b) + O2(X, a, b) 300 2000 –12.0 0 0 [12]

O(1S) + O2(X) O2(X, a, b) + O(3P) 300 2000 –11.4 0 1.727 [12]

O(1D) + O2(X) O(3P) + O2(a) 300 3000 –11.20 0 –0.133 [16]

O(1D) + O2(X) O(3P) + O2(b) 300 3000 –10.59 0 –0.133 [16]

O(1D) + O2(X) O(3P) + O2(b) 300 2000 –10.3 0 0 [12]

O(1D) + O2(a) O(3P) + O2(b) 300 3000 –10.3 0 0 [16]

O(1S) + O2(X) O(1D) + O2(b) 300 2000 –15.8 0 0 [12]

N(2D) + O2(X) NO(X) + O(3P) 295 5000 –10.9 0 0.63 [10]

Table 4. Electron energy exchange under conditions of recombination

Reactions Tmin Tmax LogA N Ea Reference

O(3P) + O(1D) + O2 O2(c) + O2 300 2000 –32.4 –0.41 0 [12]

O(3P) + O(1D) + O O2(c) + O 300 2000 –33.0 –0.41 0 [12]

O(1D) + O(1D) + O2 O2(C) + O2 300 2000 –32.6 –0.41 0 [12]

O(1D) + O(1D) + O O2(C) + O 300 2000 –32.1 –0.41 0 [12]

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HIGH TEMPERATURE Vol. 48 No. 1 2010

PROCESSES IN HIGH�TEMPERATURE AIR INVOLVING MOLECULES AND ATOMS 43

VIBRATIONAL DISEQUILIBRIUMIN ELECTRON�CHEMICAL REACTIONS

In simulating processes which involve molecules inexcited electron states, one must take into accountvibrational disequilibrium of molecules in these states.It is expedient to use for this purpose well�knownmodels of thermally nonequilibrium reactions in theground states of reacting molecules and generalize

these models for describing excited electron states;examples of such uses are given in [5, 7].

In simulating the reactions which involve electron�excited molecules, for example, in the state О2 (а1Δg),it is recommended to use the α model [7], where thequantity α is the so�called energy utilization factor ofexcited state (see the description of S.19 model in thereference book [27, p. 277]. In considering the disso�

Table 6. Quenching of excited electron states of atoms and molecules under conditions of dissociation

Reactions Tmin Tmax LogA N Ea Reference

N2(A) + M N + N + M 300 30000 –6.44 –0.871 82.6 [6]

N2(B) + M N + N + M 300 30000 –7.55 –0.9 55.3 [6]

NO(A) + M N + O + M 300 30000 –8.14 –0.74 23.8 [6]

O2(a) + M O(3P) + O(3P) + M 300 3000 –5.04 –1 95.3 [16]

O2(b) + M O(3P) + O(3P) + M 300 3000 –5.04 –1 80.4 [16]

Table 7. Formation of electron�vibration�excited O2 molecules in electron�exchange reactions (by Arrhenius’ formula in di�mensions given before Table 1)

Reactions A N Ea Reference

O2(b, v = 0) + O2(X) O2(a, v = 0) + O2(X, v = 3) 3.3 × 10–23 2.4 241.5 [28]

O2(b, v = 0) + O2(X) O2(a, v = 1) + O2(X, v = 2) 2.3 × 10–22 2.4 241.5 [28]

O2(b, v = 0) + O2(X) O2(a, v = 2) + O2(X, v = 1) 9.7 × 10–23 2.4 241.5 [28]

O2(b, v = 0) + O2(X) O2(a, v = 3) + O2(X, v = 0) 8.2 × 10–24 2.4 241.5 [28]

O2(a) + O2(a) O2(b, v = 0) + O2(X) 2.2 × 10–28 3.8 –700 [29]

O2(a) + O2(a) O2(b, v = 1) + O2(X) 2.8 × 10–29 3.8 –700 [29]

O2(a) + O2(a) O2(b, v = 2) + O2(X) 4.5 × 10–28 3.8 –700 [29]

O(D) + O2(X) O2(b, v = 1) + O 1 × 10–11exp(67/T) [28]

Table 5. Quenching of excited electron states of atoms and molecules in collisions

Reactions Tmin Tmax LogA N Ea Reference

N2(A) + N(4S) N2(X) + N(4S) 6000 14000 –2.3 –2.23 0 [20]

NO(A) + M NO(X) + M 300 30000 –11.1 0.5 0 [6]

NO(B) + M NO(X) + M 300 30000 –10.97 0.5 0 [6]

NO(C) + M NO(X) + M 300 30000 –10.90 0.5 0 [6]

O2(a) + NO O2(X) + NO 300 1100 –13.5 0 4.031 [21]

O2(a) + O2 O2(X) + O2 300 3000 –17.8 0 0 [13, 16]

O2(a) + O O2(X) + O 300 3000 –15.15 0 0 [13, 16]

O2(b) + N2 O2(a) + N2 300 2000 –19.2 1.6 –0.85 [13]

O2(b) + O2 O2(a) + O2 300 1000 –21.4 2.4 0.478 [14]

O(1D) + O2(X) O(3P) + O2(X) 300 3000 –10.5 0 –0.133 [15]

O(1D) + O2(X) O(3P) + O2(X) 300 2500 –12.5 0 0 [22]

O(1D) + O(3P) O(3P) + O(3P) 300 3000 –10.5 0 –0.133 [16]

O(1D) + O(3P) O(3P) + O(3P) 1000 1000 –11.0 0 0 [23]

O(1D) + N2 O(3P) + N2 400 2100 see formula* [11]

* k(T) = (–0.0014T + 8.28) × 10–11.

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44

HIGH TEMPERATURE Vol. 48 No. 1 2010

LOSEV, YARYGINA

ciation of diatomic gas, Aliat et al. [5] generalized theMarrone–Treanor model (see the description of S.21model in the reference book [27, p. 287]) to the simu�lation of level constants of dissociation rate undervibrational excitation of molecules in various electronstates. The results of calculation of the dissociationrate constant of molecules of О2 in various electronstates using the Marrone–Treanor model are demon�strated in Fig. 1 for the vibrational level v = 20(in cm3/s), and in Fig. 2—for various vibrational lev�els in the state O2 (a).

At present, the processes of vibrational excitationof electron�excited molecules have been studied only

for low�temperature air. Electron�vibration�excitedparticles may form in electron exchange reactions(Table 7).

The quenching of electron�vibration�excited parti�cles occurs in the so�called fast reactions of EE�exchange, where the quantum of electron excitation istransmitted in collision to the particle in the groundelectron state, and the level of vibrational excitationremains the same. The processes of energy transferbetween isenergic electron�vibrational levels are veryfast. The problems of identifying the end reactionproducts (Table 8) arise when considering the pro�cesses of quenching of upper vibrational levels of elec�

5000450040003500300025002000T, K

10–14

10–15

10–16

10–17

10–18

10–19

10–20

10–21

k, cm3/s

v = 20

1

2

3

Fig. 1. The temperature dependence of dissociation rate

constants of molecules of (1) О2(Х3 ), (2) О2(a1Δg), and

(3) О2(b1 ), calculated by the Marrone–Treanor model.

Σg+

Σg

5000450040003500300025002000T, K

10–14

10–15

10–16

10–17

10–18

10–19

10–20

10–21

10–22

10–23

10–24

10–25

10–26

k, cm3/s

v = 20

v = 10

v = 5

v = 1

Fig. 2. The temperature dependence of dissociation rateconstants of molecules of O2 (a), calculated by the Mar�rone–Treanor model for various vibrational levels.

Table 8. Quenching of electron�vibration�excited O2 molecules (rate constant in cm3/s)

Reactions Rate constants Reference

O2(a, v = 1) + O2(X, v = 0) O2(a, v = 0) + O2(X, v = 1) 5.6 × 10–11 [28]

O2(a, v = 2) + O2(X, v = 0) O2(a, v = 0) + O2(X, v = 2) 3.6 × 10–11 [28]

O2(a, v = 17) + O2(X, v = 0) reaction products 3.2 × 10–13 [30]

O2(a, v = 18) + O2(X, v = 0) reaction products 4.9 × 10–13 [30]

O2(a, v = 19) + O2(X, v = 0) O2(b, v = 8) + O2(a, v = 0) 1.4 × 10–11 [30]

O2(b, v = 1) + O2(X, v = 0) O2(b, v = 0) + O2(X, v = 1) 4.2 × 10–11exp(–312/T) [28]

O2(b, v = 2) + O2(X, v = 0) O2(b, v = 0) + O2(X, v = 2) 2.3 × 10–11exp(–691/T) [28]

O2(b, v = 3) + O2(X, v = 0) O2(b, v = 0) + O2(X, v = 3) 1.5 × 10–14 [28]

O2(b, v = 11) + O2(X, v = 0) reaction products 2.2 × 10–13 [30]

O2(b, v = 12) + O2(X, v = 0) reaction products 1.8 × 10–13 [30]

O2(b, v = 13) + O2(X, v = 0) reaction products 1.1 × 10–11 [30]

O2(b, v = 14) + O2(X, v = 0) reaction products 2.9 × 10–12 [30]

O2(b, v = 15) + O2(X, v = 0) reaction products 2.7 × 10–12 [30]

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HIGH TEMPERATURE Vol. 48 No. 1 2010

PROCESSES IN HIGH�TEMPERATURE AIR INVOLVING MOLECULES AND ATOMS 45

tron�excited particles. Along with reactions of fastEE�exchange, the quenching of electron�vibration�excited particles may occur without the variation ofthe electron state of particle, similarly with the case ofmolecules in the ground electron state (Table 9).

ATOMIC AND MOLECULE RADIATION

The excitation of electron states causes intenseradiation of atoms and molecules in various spectralranges (ultraviolet, visible, and near�infrared regions)as a result of radiative transitions. In so doing, one ofthe important processes is that of recombination ofnitrogen and oxygen atoms with radiation of theseatoms and formation of molecules of N2, O2, and NOin various electron states (see the review [34]).

The nonequilibrium radiation significantly affectsthe population of electron states of atoms and mole�cules; this fact must be taken into account in solvingproblems in physicochemical kinetics [35]. Models ofradiative transfer in gas are exhaustively treated inmonographs by S.T. Surzhikov [36–38], in particular,in describing the physicochemical kinetics and radia�tion in strong shock waves [39].

CONCLUSIONS

In considering reactions which involve electron�excited molecules, it is expedient to treat these mole�cules as individual components of mixture for eachelectron state with respective vibrational levels, as isusually the case for molecules in the ground electronstates.

The data base developed for the rate constants ofelectron�chemical reactions in high�temperature airfacilitates the solution of problems in kinetics.

The failure to include excited electron states in thetreatment of thermally nonequilibrium processes leadsto significant errors in the values of parameters of gasbehind the shock wave front and in the values of rateconstants of reactions in the ground electron state.

The urgency of and demand for the simulation ofprocesses of electron�chemical kinetics cause the needfor further experimental and theoretical investigationsin this field.

The detailed inclusion of processes involving atomsand molecules in excited electron states, along withthe consideration of vibrational excitation of mole�cules, brings the simulation of relaxing and reactinggas behind the front of strong shock wave closer toreality.

ACKNOWLEDGMENTS

This study was supported by the Russian Founda�tion for Basic Research (grant no. 08�08�00765).

REFERENCES

1. Stupochenko, E.V., Losev, S.A., and Osipov, A.I.,Relaksatsionnye protsessy v udarnykh volnakh (Relax�ation Processes in Shock Waves), Moscow: Nauka,1965.

2. Agafonov, V.P., Vertushkin, V.K., Gladkov, A.A., andPolyanskii, O.Yu., Neravnovesnye fiziko�khimicheskieprotsessy v aerodinamike (Nonequilibrium Physico�chemical Processes in Aerodynamics), Moscow:Mashinostroenie, 1972.

3. Aliat, A., Kustova, E.V., and Chikhaoui, A., Chem.Phys., 2005, vol. 314, p. 37.

4. Lunev, V.V., Techenie real’nykh gazov s bol’shimi sko�rostyami (High�Velocity Flow of Real Gases), Moscow:Fizmatlit, 2007.

Table 9. Quenching of electron�vibration�excited particles without the change of electron state (rate constant in cm3/s)

Reactions Rate constants Reference

O2(a, v = 1) + N2 O2(a, v = 0) + N2 1.2 × 10–18 [31]

O2(a, v = 1) + O O2(a, v = 0) + O 1.2 × 10–16 [31]

O2(b, v = 1) + N2 O2(b, v = 0) + N2 <7 × 10–13 [32]

O2(b, v = 2) + N2 O2(b, v = 1) + N2 <9 × 10–13 [32]

O2(b, v = 3) + N2 O2(b, v = 2) + N2 <1 × 10–13 [32]

O2(b, v = 1) + O O2(b, v = 0) + O 1–5 × 10–12 [32]

O2(b, v = 2) + O O2(b, v = 1) + O 1.1 × 10–11 [32]

O2(b, v = 3) + O O2(b, v = 2) + O ~10–10 [32]

NO(A, v = 1) + O2 NO(A, v = 0) + O2 1.48 × 10–10 [33]

NO(A, v = 2) + O2 NO(A, v = 1) + O2 1.99 × 10–10 [33]

NO(A, v = 1) + N2 NO(A, v = 0) + N2 6.1 × 10–13 [33]

NO(A, v = 2) + N2 NO(A, v = 0) + N2 5.9 × 10–12 [33]

NO(A, v = 3) + N2 reaction products 2.3 × 10–12 [33]

NO(A, v = 4) + N2 reaction products 2 × 10–11 [33]

Page 7: Processes in high-temperature air involving molecules and atoms in excited electron states

46

HIGH TEMPERATURE Vol. 48 No. 1 2010

LOSEV, YARYGINA

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