ISSN 1990�7931, Russian Journal of Physical Chemistry B, 2009, Vol. 3, No. 4, pp. 641–645. © Pleiades Publishing, Ltd., 2009.Original Russian Text © S.A. Losev, V.N. Yarygina, 2009, published in Khimicheskaya Fizika, 2009, Vol. 28, No. 7, pp. 70–74.

641

INTRODUCTION

Shock waves in a gas strongly disturb chemical andthermal equilibria. Whereas rotation is excited in sev�eral collisions of particles in a gas, the excitation ofvibrational degrees of freedom of molecules and elec�tronic states of atoms and molecules occurs under sub�stantially nonequilibrium conditions and need bemodeled in detail. During many years, this problemhas been successfully solved in many theoretical andexperimental works, in particular, with the use ofshock tubes and the theory of relaxation processes (see[1, 2]). Interrelations between elementary processesand gas�phase chemical kinetics in shock waves wereconsidered in [3]. A model of physicochemical kinet�ics behind the strong shock wave front in the absenceof vibrational equilibrium of molecules was consideredby us in [4]. Processes with the participation of mole�cules and atoms in electronically excited states arecurrently most topical. These processes include theformation and quenching of such states in chemicaldissociation, recombination, and exchange reactionsand electron energy exchange in collisions of particles.

The results of kinetic calculations [5] show that, ifexcited electronic states are ignored in considerationof thermally nonequilibrium processes, this leads tosubstantial errors in gas parameters behind the shockwave front and supposed rate constants for dissocia�tion and recombination in the ground electronic state.According to the author of monograph [6, p. 518],“because of the absence of reliable information, possi�ble influence of electronic excitation of molecules onreaction rate constants is very rarely taken intoaccount.” It follows that detailed experimental andtheoretical studies of electron chemical kinetics of

processes with the participation of excited electronicstates of reacting atoms and molecules are necessary.

It is reasonable to take into account electronicallyexcited molecules as separate mixture components foreach electronic state with the corresponding vibra�tional level, as is usually done with molecules inground electronic states. Processes with the participa�tion of electronically excited molecules were studiedfor reactions with carbon monoxide [7], in describingthe motion of spacecraft in the atmosphere [8], forcombustion of hydrogen–oxygen mixtures [9, 10], etc.

1. PROCESSES WITH THE PARTICIPATIONOF MOLECULES AND ATOMS

IN EXCITED ELECTRONIC STATES

Excited electronic states are largely formedthrough recombination; this process is much moreeffective than the formation of molecules in theground electronic state. This conclusion was drawn in[5] for the formation of CO molecules. The rate con�stant for recombination into the CO(A1Π)state wastwo orders of magnitude larger than the rate constantfor recombination into the ground state CO(X1Σ).When molecules collide in various excited vibrationaland electronic states, vibrational�electronic energyexchange between molecules with similar energy con�tents, isoenergy states, occurs most rapidly. In [11],original works are specified in which the correspond�ing experimental studies were performed and level�to�level rate constants for isoenergy vibrational�elec�tronic energy exchange with the participation of COmolecules were obtained. These results emphasize the

PHYSICAL METHODSFOR STUDYING CHEMICAL REACTIONS

Electronic Energy Exchange in High�Temperature AirS. A. Loseva and V. N. Yaryginab

a Institute of Mechanics, Moscow State University, Michurinskii pr. 1, Moscow, Russiab Federal State Unitary Enterprise “State Research and Production Enterprise ‘Bazalt’”

e�mail: vika�yarygina@yandex.ruReceived April 24, 2008

Abstract—Kinetic processes with the participation of electronic states of atoms and molecules in air behindthe shock wave front were analyzed. All metastable levels of molecular and atomic oxygen and nitrogen andnitrogen oxide molecules situated below the dissociation energy were analyzed. In high�temperature air, atomand molecule electronic states are formed in dissociation and recombination, electronic energy exchange incollisions of particles, and chemical exchange reactions. The formation of excited electronic states in therecombination of atoms and isoenergy vibrational energy transfer from highly excited vibrational levels intoelectronic energy is the fastest process. The quenching of metastable particles occurs in collisions betweenparticles, dissociation and recombination, and chemical exchange reactions. A database on electronic energyexchange rate constants in high�temperature air is presented.

DOI: 10.1134/S1990793109040204

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LOSEV, YARYGINA

role played by level�to�level kinetics in the descriptionof processes in a high�temperature gas.

The mechanisms of electronic chemical reactionswith the participation of electronically excited atomsand molecules include the formation and quenchingof these states in collisional energy exchange and dis�sociation and recombination. Molecules are mosteffectively formed at high vibrational levels of variouselectronic states.

The excited states of atoms and molecules in airconsidered below are largely metastable; quantumtransitions from these states to states with lower ener�gies are forbidden, and they have long radiative life�times. The main channel for quenching metastableparticles is energy transfer to other atoms and mole�cules in collisions (electron�electron (EE) and elec�tron�vibrational (EV) energy exchange).

The objective function of the processes describedis, as usual, kinetic equation coefficients, rate con�stants for reactions. Their values for electronic�chem�ical reactions were largely obtained in experimentalworks, because theoretically obtaining quantitativedata about these processes is a very difficult task.

2. DATABASE ON THE RATE CONSTANTSOF ELECTRONIC�CHEMICAL REACTIONS

IN HIGH�TEMPERATURE AIR

High�temperature air considered below containsthe N2, N, O2, O, and NO components in the groundand excited electronic states according to the classi�fication: N2(X, A, B), N(4S, 2D), O2(X, a, b, c, C),O(3P, 1D, 1S), NO(X, A, B, C); M is the commondenotation of all components in their ground elec�tronic states. Components for which states are notindicated are also in the ground electronic states.

The rate constants for electronic�chemical reac�tions in air characterize two temperature regions, lowclose to room temperatures (T ≤ 500 K) in more detailand high temperatures, much higher than T = 500 K,less thoroughly.

The database presented in the table includes thedescription of the following processes in high�temper�ature air:

(1) the formation of excited electronic states in therecombination of atoms and collisions of particles;

(2) electronic energy exchange in collision of parti�cles and recombination of atoms;

(3) quenching of excited electronic states of atomsand molecules in collisions and dissociation;

(4) electronic�chemical exchange reactions.

The table presents temperature�independent con�stants describing high�temperature gas in barrierlessreactions, reactions with forbidden transitions (seeexamples in [9]), and reactions with fairly high con�stants close to gas�kinetic rate constants [12].

The rate constants for the processes under consid�eration are described by the Arrhenius equation

The data presented in the table determine reactionrate constants in cm3/s for second�order reactions andin cm6/s for third�order reactions. TheEa values are inkcal/mol, and R = 1.987 × 10–3 kcal/(mol K).

The above database on the rate constants of elec�tronic�chemical reactions in high�temperature air isbased on the results obtained in studies of processes inshock waves and electric discharge and in otherdevices. The results of many experimental and calcu�lation works were considered and recommended foruse in reviews and summarizing publications [8, 22,26, 29, 30]. For instance, the authors of [8] used andverified data on electronic�chemical reactions withthe participation of the N2 and NO molecules in thedescription of processes behind the shock wave frontwhen spacecraft moved in the atmosphere. In [24], thedata obtained taking into account electronicallyexcited O2 molecules were used to solve kinetic equa�tions for detonation in supersonic flows. The recom�mended data obtained in an analysis of separate workswere given in [23, 25, 27, 28, 31–33].

3. THE SIMULATION OF PROCESSESIN MIXTURES WITH ELECTRONICALLY

EXCITED MOLECULES

Simulations of reactions with the participation ofelectronically excited molecules, for instance,O2(a

1∆g), are recommended to be performed using theα model [9], where α is the coefficient of excited stateenergy utilization as a generalization of the contribu�tion of vibrational energy (see the description of theS.19 model in handbook [13, pp. 277–283]). Theauthors of [7] considered the dissociation of adiatomic gas and generalized the Marrown–Trinormodel (see the description of model S.21 in handbook[13, pp. 287–289]) to level�to�level dissociation rateconstants for vibrationally excited molecules in vari�ous electronic states. The rate constants for the disso�ciation of O2 molecules in different electronic statescalculated using the Marrown–Trinor model over thetemperature range 2000–5000 K differ by severalorders of magnitude, which is demonstrated in the fig�ure for the vibrational level v = 20.

At moderate temperatures (T < 500 K), separaterate constant values for electronic�chemical reactionsdepend on the vibrational state of the reacting mole�cules (see examples in [14, 15]). At high temperaturesin shock waves, rate constants are averaged [16, 17]and cannot be written in the form of particular tem�perature dependences.

The excitation of electronic states results in intenseemission of light by atoms and molecules as a result ofvarious radiation transitions. Nonequilibrium radia�

k T( ) ATN Ea/RT–( ).exp=

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 28 No. 4 2009

ELECTRONIC ENERGY EXCHANGE IN HIGH�TEMPERATURE AIR 643

Table

Reactions Tmin Tmax logA N Ea Refs.

Formation of excited electronic states in the recombination of atomsN + N + N2 N2(A) + N2 300 30000 –30.68 –0.8 0 [8]N + O + N2 NO(A) + N2 300 30000 –30.60 –1.24 0 [8]N + O + N2 NO(B) + N2 300 30000 –30.82 –1.4 0 [8]O(3P) + O(3P) + O2 O2(X, a, b) + O2 300 2000 –31.57 –0.41 0 [22]O(3P) + O(3P) + O O2(X, a, b) + O 300 2000 –31.1 –0.41 0 [22]

Formation of excited electronic states in collisions of particlesN2(X) + N2 N2(A) + N2 300 30000 –11.74 –0.5 142.2 [8]N2(X) + N N2(A) + N 300 30000 –6.7 –1.5 142.2 [8]N2(X) + O2 N2(A) + O2 300 30000 –8.0 –1.5 142.2 [8]N2(X) + O N2(A) + O 300 30000 –6.92 –1.5 142.2 [8]N2(X) + NO N2(A) + NO 300 30000 –11.77 –0.5 142.2 [8]NO(X) + M NO(A) + M 300 30000 –10.8 –0.5 126.1 [8]N2(X) + N N2(A) + N 300 20000 –10.77 0.5 142.1 [23]N2(X) + O N2(A) + O 300 20000 –10.77 0.5 142.1 [23]NO(X) + O NO(A) + O 300 20000 –10.77 0.5 142.1 [23]

Electronic energy exchange in collisions of particlesN2(A) + M N2(B) + M 300 30000 –10.7 0 26.8 [8]N2(A) + NO(X) NO(A, v) + N2(X) 300 30000 –10.0 0 0 [8]N2(A) + NO(X) NO(C, v) + N2(X) 300 30000 –9.01 0 0 [8]N2(A) + N2(A) N2(B) + N2(X, v) 300 30000 –8.91 0 0 [8]N2(A) + NO(X) N2(X) + NO(A) 300 20000 –10.77 0.5 0 [23]O2(a) + O2(a) O2(b) + O2(X) 300 3000 –27.15 3.8 –1.39 [24–26]O2(b) + O(3P) O2(a) + O(3P) 300 3000 –13.09 0 0 [24]O2(b) + N(4S) O2(a) + N(4S) 300 3000 –13.09 0 0 [24]O2(c) + O2(X) O2(b) + O2(X, a, b) 300 2000 –15.0 0 0 [22]O2(C) + O2(X) O2(X, a, b) + O2(X, a, b) 300 2000 –12.0 0 0 [22]O(1S) + O2(X) O2(X, a, b) + O(3P) 300 2000 –11.4 0 1.727 [22]O(1D) + O2(X) O(3P) + O2(a) 300 3000 –11.20 0 –0.133 [24]O(1D) + O2(X) O(3P) + O2(b) 300 3000 –10.59 0 –0.133 [24]O(1D) + O2(X) O(3P) + O2(b) 300 2000 –10.3 0 0 [22]O(1D) + O2(a) O(3P) + O2(b) 300 3000 –10.3 0 0 [24]O(1S) + O2(X) O(1D) + O2(b) 300 2000 –15.8 0 0 [22]

Electronic energy exchange in the recombination of atomsO(3P) + O(1D) + O2 O2(c) + O2 300 2000 –32.4 –0.41 0 [22]O(3P) + O(1D) + O O2(c) + O 300 2000 –33.0 –0.41 0 [22]O(1D) + O(1D) + O2 O2(C) + O2 300 2000 –32.6 –0.41 0 [22]O(1D) + O(1D) + O O2(C) + O 300 2000 –32.1 –0.41 0 [22]

Quenching of electronically excited states of atoms and molecules in collisionsN2(A) + N(4S) N2(X) + N(4S) 6000 14000 –2.3 –2.23 0 [27]NO(A) + M NO(X) + M 300 30000 –11.1 0.5 0 [8]NO(B) + M NO(X) + M 300 30000 –10.97 0.5 0 [8]NO(C) + M NO(X) + M 300 30000 –10.90 0.5 0 [8]O2(a) + NO O2(X) + NO 300 1100 –13.5 0 4.031 [28]O2(a) + O2 O2(X) + O2 300 3000 –17.8 0 0 [24, 26]O2(a) + O O2(X) + O 300 3000 –15.15 0 0 [24, 26]O2(b) + N2 O2(X) + N2 300 2000 –19.2 1.6 –0.85 [26]O2(b) + O2 O2(X) + O2 300 1000 –21.4 2.4 0.478 [29]O(1D) + O2(X) O(3P) + O2(X) 300 3000 –10.5 0 –0.133 [30]O(1D) + O2(X) O(3P) + O2(X) 300 2500 –12.5 0 0 [31]O(1D) + O(3P) O(3P) + O(3P) 300 3000 –10.5 0 –0.133 [24]O(1D) + O(3P) O(3P) + O(3P) 1000 1000 –11.0 0 0 [32]

Quenching of electronically excited states of atoms and molecules in dissociationN2(A) + M N + N + M 300 30000 –6.44 0.871 82.6 [8]N2(B) + M N + N + M 300 30000 –7.55 –0.9 55.3 [8]NO(A) + M N + O + M 300 30000 –8.14 –0.74 23.8 [8]O2(a) + M O(3P) + O(3P) + M 300 3000 –5.04 –1 95.3 [24]O2(b) + M O(3P) + O(3P) + M 300 3000 –5.04 –1 80.4 [24]

Electronic�chemical exchange reactionsN(2D) + O2(X) NO(X) + O(3P) 295 5000 –10.9 0 0.63 [33]

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LOSEV, YARYGINA

tion substantially influences the population of theelectronic states of atoms and molecules, whichshould be taken into account in solving physicochem�ical kinetics problems. Models of radiation transfer ina gas are considered in detail by Surzhikov in mono�graphs [18–20] and in [21], where physicochemicalkinetics and radiation in strong shock waves aredescribed.

CONCLUSIONS

The following conclusions can be drawn from thedata presented above:

(1) In consideration of reactions with the participa�tion of electronically excited molecules, it is reason�able to take them into account as separate mixturecomponents for each electronic state with the corre�sponding vibrational levels, as is usually done withmolecules in ground electronic states.

(2) The database on the rate constants of elec�tronic�chemical reactions in high�temperature aircontributes to solving chemical kinetics problems.

(3) When electronically excited states are ignoredin considering thermally nonequilibrium constants,this results in noticeable errors in gas parametersbehind the shock wave front and in supposed rate con�stants for reactions in the ground electronic state.

(4) Current interest in and demand for modelingelectronic�chemical kinetics processes necessitateadditional experimental and theoretical studies in thisarea.

Detailed consideration of processes with the par�ticipation of atoms and molecules in excited elec�tronic states and taking into account vibrational exci�

tation of molecules make modeling of relaxing andreacting gas behind the strong shock wave front morerealistic.

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2000 2500 3000 3500 4000 4500 5000T, K

10−14

10−15

10−16

10−17

10−18

10−19

10−20

10−21

k, сm3/s

1

2

3

Temperature dependences of the rate constants for the dis�

sociation of the (1) O2(X3 ), (2) O2(a1∆g), and

(3) O2(b1 ) molecules calculated according to the Mar�

rown–Trinor model for the vibrational level v = 20.

Σg–

Σg+

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