NBS TECHNICAL NOTE

:

484

A Review of Rate Constants of

Selected Reactions of Interest in

Re-Entry Flow Fields in the Atmosphere

m

:':'

":;.. mV

. .. m

<*** ° F *o4

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 484

ISSUED MAY 1969

Nat. Bur. Stand. (U.S.), Tech. Note 484, 62 pages (May 1969)

CODEN: NBTNA

A Review of Rate Constants of Selected Reactions of

Interest in Re-Entry Flow Fields in the Atmosphere

M. H. Bortner

Office of Standard Reference Data

National Bureau of Standards

Washington, D.C. 20234

This review was supported by the Advanced Research Projects Agency

of the Department of Defense under

Project DEFENDER

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C, 20402 - Price 60 cents

TABLE OF CONTENTS

Page

1. Introduction- --------- — __________------- 1

2. Neutral Reactions _____ _____ ______________ _s

+ M -» + M

2 N + N

2

-> N + N + N

N + N+N + N + N

N + Ar->N + N + Ar

NO + M -*-N M

N + N--^NO + N

N + + Ar-*NO + Ar

+ 0- + M->0

3 + M

N + NO * N

2 +

N +

2 * + NO

+ VV°2

3. Ionization -------------------------------- 23

N + * NO* + e

4. Collisional Ionization --------------------------25

N_ + e * N

+

+ 2e: 0~ + e *

+ 2e

2 2

2 2

5. Electron Attachment and Detachment ____ __ ___ — 27

0- + e + M-»-0"+M

2 2 0" + +

3 e

0_ + e * 0" + 0-

6. Negative Ion Charge Exchange Reactions ___ __________ _29

0" + * 0- + 0"

2 2 0" + 0_ + o + o"

2 3 2 3 0" + 0- -* + 0"

0" + * 0" +

3 2 2 0" + N -> 0" NO

2 0" + NO * NO" +

2 2 0" •+ 0" + 0,

3 2 2 iii
TABLE OF CONTENTS (Cont.)

Page

0" C0„ » CO" + 0_

3 2 3 2 0" + NO - NO3 +

NO' + + NO" + 0„

3 2 2 CO" + •> O" + CO

7. Ion-Pair Neutralization. 31

X* + Y" * X + Y

8. Positive Ion Charge Exchange Reactions 33

N* + 0_ - N +0*

2 2 2 2 N

+ + NO * N. + NO*

2 2 N

+

+ -»• N0++ N

2 0* NO » NO*

_. __ CO- + M •+ CO M

9 . References 38

IV
A Review of Rate Constants of Selected Reactions of

Interest in Re-Entry Flow Fields in the Atmosphere*/

M. H. Bortner

The major reactions normally encountered in flow

field re-entry calculations for the oxygen nitrogen

system are reviewed and a rate constant value for each

reaction is recommended. Collisional ionization processes,

charge exchange reactions and attachment- detachment

reactions are included. Rate constant coefficients

to fit the equation k = aT" e" ^ are reported in tabular

form for the selected rate constant. The data are also

graphed as log k vs T(K). In all, over twenty forward

and reverse reactions are reviewed. Additionally, a large

number of rate constant values for reactions which also

effect flow field calculations are given.

Key words: Attachment- detachment reaction; Charge

exchange reaction; Collisional ionization reaction;

Evaluated rate constants; Flow field kinetics; O2-N2 systems.

1. Introduction

In flow field calculations, a number of reactions play a significant role. During the

past several years, a concerted effort has been made to obtain the chemical kinetic data

needed for such calculations. This study has been an effort to review all such data in

detail and thus provide a set of data which would be the best available for calculations. A

2/ review carried out a short time ago (Ref. 1)— endeavored only to present an opinion which

was a concensus among workers that have been using such data over the last few years. Little

study was given to the rate constants although, of course, much thought had been given by

the individuals originally selecting the values. The present study is an effort to select

a set of rate constants based upon a thorough consideration of all available information.

The objective was to obtain the best rate-constant expression for each single reaction

with emphasis on data obtained in studies of that isolated reaction. In applied calculations,

it may be better to employ those obtained for a complex system of similar application since,

to use the rate constants obtained individually, the chemical system must be complete and

1 This work was performed for the National Bureau of Standards on Contract CST-373.

2 References indicate literature citations at the end of this paper.
have accurate rate constants. Otherwise, the somewhat empirical data may be a better

representation of the system. Many reviews on these and similar reactions are available,

several of which are also specifically applied to re-entry flow fields.

A rate constant may be defined by k in the expression

:nrI = kCA) (B)

for the rate of the reaction A + B+. . . The units used are such that they be used with

•i concentrations in molecules cm , time in seconds, and temperatures in degrees Kelvin. The

rate constants are given here in the form k » a T^ e" c' . This form can usually be made to

fit available data as well as any simple form. The value of c is related to the activation

energy. The activation energy of an exothermic reaction may be negligible. If an exothermic

reaction has an appropriate activation energy, the reverse endothermic reaction will have an

activation energy equal to that of the exothermic reaction plus the heat of the reaction.

Although negative activation energies have been reported, these can, at least, be represented by a preexponential negative temperature dependence (negative value of b) . The rate

constants of reverse reactions are related to the equilibrium constant, K, by

., forward

K = r^reverse

providing the states of each reactant and each product is the same for the reverse as for

the forward reaction. If different states are involved, the above reaction does not hold.

For most of the reactions considered here, the relation has been applied since it, somewhat

surprisingly, appears that the data available make its use reasonable. With the rate

constants in this foim, the equilibrium constant must be in this form. However, the

equilibrium constant is a function of the heat capacity which is commonly expressed by a

polynomial. Thus, the equilibrium constant is only approximated by an expression of the

form

K A T

B e'C/1

With available data, however, this form is suitable. In some cases, the value of B is

negligible. Equilibrium constants for reactions involving ozone were obtained by fitting

data from JANAF tables (Ref . 48). Those for the other neutral reactions were taken from

Wray (Ref. 23). 2
The available data for each reaction are discussed in detail. From consideration of

these data, a suggested rate constant has been obtained for each reaction. These are given

as an expression of the form

k =» (a A a) T

(b 1 Ab) e " (c 1 Ac)/T

and in graphical form. Data, with little regard for quality are given in tables, but some

selection of data was made for the figures. In the graphs, the data considered are also

shown together with the suggested rate constant (solid line from 100 to 10,000 K) and upper

and lower limits for it (dotted lines). All graphs show the exothermic reaction since it

can be shown more accurately. The amount of data on the different reactions varies considerably. One of the major areas of uncertainty is the temperature dependence of the rate

constants. For most reactions there are data available at low temperatures for the reaction

in the exothermic direction. For a number of the most important reactions, endothermicdirection data are available at high temperatures. For most the the important reactions

there are little or no data at intermediate temperatures (from about 500 to 2500 K). The

uncertainties in the rate constants are accordingly greatest at the intermediate temperatures.

This is difficult to express when the uncertainty in a rate constant is expressed. In

fact, this can probably not be done in a reasonable manner when a mathematical expression

is given. It can, however, be shown graphically. Thus, while limits are given for each

rate constant expression, a more exact and detailed estimate of the uncertainty as a function

of temperature could be best seen by an examination of the graphical expression. However,

since there is no way to assess the uncertainty accurately, the graphs show the same

uncertainty as given by the expression.

The reactions considered in detail include the major reactions usually used in flow field

calculations together with collisional ionization processes, ion charge exchange reactions,

and attachment and detachment reactions, all for the nitrogen- oxygen system. Also discussed

are a few reactions of other species.

The usual major reactions are:
0. + M •* u r u + M M = , N

2

, 0, N, NO

N-+M + N + N + M M =

2

, N

2

, 0, N, NO

NO + M -> N + + M M =

2

, N

2

, 0, N, NO

+ N + N + NO

+ NO * N +

2 N + -»- N0

+

+ e

The neutral formation of ozone:

+

2 + M +

3 + M M = , N2

, 0, N, NO

is also included as is the subsequent reaction

+ + o

2 + o

2 Under certain conditions, collisional ionization can be important. This is mainly the

ionization of N

2 and 0_ by collision with these same molecules or with free electrons,

leading to the formation of N and ot .

N

2 M * N* e M M = N

2

, 2, e

2 + M -»• 0* e + M M - N

2

, 2

, e

Once these molecular ions are formed, they may recombine with free electron by dissociative

recombination. However, they are much more likely to undergo charge exchange reactions.

The term charge exchange is used here to include both charge transfer and charged rearrangement (ion-molecule) reactions. The most important of these appear to be

^VN

2 + °2

N* + NO -» N

2 NO*

N* + * NO* + N

0* + NO *

2 + NO*

Other reactions of these types could play some role but these four should reasonably

represent the system.

In cool portions of the wake, negative ions are important. Hence, attachment and

detachment reactions were considered. These included:

0- + e + M-+-0"+M M-0ot N

^ 2 2' 2 Other reactions involving negative ions are discussed later.

Nothing is considered on the role of vibrational and electronic excited states.

4
Vibrationally excited nitrogen persists long after the kinetic temperature has fallen in

some cases. This effect is included in some codes on wake calculations but is missing in

many. Likewise, some metastable electronic states, such as O-^Ag), may be important.

2. Neutral Reactions

0- + M - M AE = 5.12 eV

The dissociation of oxygen and the reverse three-body atom recombination are probably

the most studied of the reactions of interest to re-entry. The collision partners for which

the most work has been done and which are of most interest are

2

, 0, N

2

, and Ar. The dissociation process with 2 as the collision partner has been studied at high

temperatures by Mathews (Ref. 2), Byron (Ref. 3), Rink (Ref. 4) Wilson (Ref. 5),

Schexnayder (Ref. 6) , Chesick (Ref. 7) , fleneralov (Ref. 8) , and Eckerman (Ref. 9) . The data

obtained are shown in (fig. 1) and are listed in (table 1).

In this and succeeding tables, the names of the authors who have studied the reaction

in the direction given are underlined.

A recent review by H. S. Johnston considered the available data somewhat differently

with slightly different results. It is believed that the present revision put more stress

on the high temperature data as seemed appropriate to the application.

The temperature dependence has been studied in several of the high temperature

dissociation investigations. While some of these find or suggest a T"^ ,s dependence, there

is by no means general agreement on this. But most serious is the wide difference between

the low temperature recombination rate constant values obtained by exnrapolating the

dissociation data (and using the equilibrium constant) and the values obtained by studies

of the recombination at low temperatures. The dissociation data give values which are an

order of magnitude or more higher than obtained in the direct recombination studies. This

is opposite of what would be most expected of effects of excited electronic or vibrational

states unless the reactant excited states are overpooulated in the dissociation studies.

This indicates a more complex mechanism than the simple reverse reaction.

In view of the appreciable disagreement in the values, and somewhat the temperature

dependencies, obtained in the various high temperature studies, it would seem reasonable

not to require a suggested rate constant to fit any of these temperature dependencies, but

rather to have it agree reasonably with the most acceptable of the absolute values. Use of

such values and those of the low temperature data will give a usable expression for the entire

temperature range. It will not agree with any temperature dependence but will fit the
values given by the best data. Since the experimentally determined temperature dependencies

can only be said to be approximate or in some cases only guessed because of the lack of any

real indication, it is not deemed necessary to use such dependencies. However, it must be

noted that all of these dependencies found showed a steeper dependence than that which is

suggested to fit both high and low temperature data.

The suggested values are:

k

d

(0

2

) = 1.37 x 10" 5 T"* 83

e" 59400 /1 cm

3 particle" V1

k

r

(0

2

)

«= 1.9 x 10" 32 T"* 33 cm

6 particle-V 1

The use of one such expression with the above mentioned shortcomings seems preferable

to using two expressions, one when the dissociation predominates and one when the recombination

predominates. Either is an empirical solution and the suggested values fit the most

acceptable data well, although obviously more work is needed especially at intermediate

temperatures. A polynomial form may be needed for some rate constants.

For Cu as the collision partner, the rate constant is probably accurate to a factor of

three at high temperature and at least that accurately, or perhaps a factor of two, at low

temperature. However, at intermediate temperatures, the uncertainty is greater, perhaps

a factor of five. Thus, the stated uncertainty of the suggested rate constant of a factor

of three may be optimistic at the intermediate temperatures.

Kith atomic oxygen as the collision partner, only high temperature data are available.

These data, obtained by Byron (Ref. 3) , Camac (Ref . 10) , Rink (Ref. 4) , and Wilson (Ref. 5)

,

are shown in figure 2. The data were obtained in shock tubes by density measurements or by

U-V absorption measurements. Wray has evaluated the various data and has selected a

compromise value for this. The compromise is reasonable and agrees well with the absolute

values at the high temperatures and compromises the temperature dependencies. These rate

constants are:

k,(0) = 1.5 x ID"

4 r1 e" 59400/1

a

k

d

(0) = 2.1 x 10" 31 r1/2

Data for the case of argon as the collision partner have been obtained by Byron (Ref. 3),

Camac (Ref. 10), Rink (Ref. 4), Wray (Ref. 11), Schexnayder (Ref. 6), and Generalov (Ref. 8),

all dissociation studies at high temperature studies, and recombination studies by Wray at

intermediate temperatures and by Campbell and Thrush (Ref. 12) and by Marshall (Ref. 13) at

6
low Temperatures. These data are shown, in figure 3. The temperature dependencies found by

the various studies disagree as do some of the absolute values.

A reasonable average curve can be drawn through these data which is in reasonable

agreement with most of these. The expression 3.3 x io" 30T

_1 * 3 fits in this way. It is a

reasonable compromise of the data with most weight being given to the data of Wray (Ref , 11)

.

Since this reaction is of little importance itself and the application of the data to other

collision partners is questionable, the expressions fitting the data as shown is suggested:

kd(Ar) - 2.4xl0- 3 rl' 8 e- 5940

^

k (Ar) » 3.3 x l(f

30 T" 1,3

With nitrogen as a collision partner, most of the available data (fig. 4) are low

temperature recombination data. These are from the work of Campbell and Thrush (Ref. 12)

whose data over the range of 196 to 327°K predict approximately aT' dependence. Morgan's

data (Ref. 14) at 300°K agrees well with these data. The only high temperature data are

those of Generalov (Ref. 8). For want of any more suitable data, they are used to obtain a

temperature dependence. The suggested values are:

k

d

(N

2

) = 2.2 x 10- 3 r1 * 7 e" 59400^

k (N 7

) - 3 x 10-20 t"

1 * 2 r

It is obvious that more data are needed. This case (N-) appears to have a rate constant as

high as that for CL as the collision partner, at least at low temperatures. It is probably

of more importance and many less data are available for it.

For these dissociation rate expressions, the preexponential term is, at low temperatures,

higher than the collision frequency CIO-10

). This can not be explained. Their use is

justified only by the data fit.

Table 1. O + O+M + O+M

M Author

Barth

Ref.

15

f\ -2

k (cm. particle sec.

- 1

) T(K)

°? 8.2 x 10" 33 300

Byron 3 4.54 x 10" 30 T" 1 2800 - 5000

Camac 10 42.5 x 10" 32 T"

1/2 6000 - 7000

Chesick 7 -33

3.3 x 10 -r 3100

Chesick 7 1.3 x 10" 33 3500

Eckerman 9 3.72 x 10" 30T-1

7

4000 - 7000
Table 1. + M *

2 + M—continued.

M

N

Author Ref.

16

ft m7 «1 k

r

(can. particle" sec." )

Elias

-33

<1.1 x 10

Generalov 8 1.33 x 10" 22 rp — «J

Golden 17

-33

3.3 x 10

J-i

Hall (Byron data) 18 8.3 x 10" 34

T*

1

Kiefer 19

-29 -1.22

2.3 x 10 zy T

Kretschmer 20 5.55 x 10"34

Krongelb 21 1.39 x 10" 32

Losev 22 5.55 x 10" 34

Marshall 13 2.2 x 10" 33

Mathews 2 2.53 x

10" 26 ep* Z,

Rink 4

-3fl 4.44 x 10

M) T"

1

Schexnayder 6 2.08 x

10" 37 T .5 22000/T

1 e

Wilson 5 6.94 x

10" 30 T"

1

Wray 23 7.5 x 10' 32 T"

1/2

Langan 24 2.44 x 10" 33 T

-.44

Byron 3 2.71 x 10" 33

Camac 10 1.47 x 10" 27 T

-1.5

Hall (Byron data) 18 4.9 x

10" 33

Rink 4 1.33 x 10" 29 T"

1

Wilson 5 -29

2.08 x 10

^y T"

1

Wray 23 2.08 x 10' 31 T

-l/2

Campbell 12 4.44 x

10" 26

T

-2,9

Campbell 12 2.78 x 10" 34 713/T

e

Generalov 8 8.33 x

10"33 T"

1

Kaufman 25 4.60 x 10" 26

T

-2.9

Baurer 26 6.08 x 10 T

-2.5

293

2600 - 7000

300

2800 - 5000

1500 - 2800

350

300

300

300

3000 - 5000

3000 - 6000

5000 - 10000

2700

Review

Review

2800 - 5000

5000 - 7000

2800 - 5000

3000 - 6000

2700

Review

196 - 327

196 - 327

3700 - 7000

Review

Review
Author

Table 1. + + M •+ 2 + M—continued.

*L Ref. kr (cm. particle" 2 sec." 1) T(K)

N

2 Morgan 14 3.23 x 10-33

300

Wray 23 1.67 x 10" 32 T

-

- 5 Review

Ar Anderson (by Wray) 27 1.4 x 1(T 33 T- 5 300 - 3000

Byron 3 1.18 x 10-34 2800 - 5000

Camac 10 8.35 x 10-33 T"- 5 3300 - 7500

Campbell 12 6.05 x 10-33 196

Campbell 12 1.67 x 10-33 300

Generalov 8 1.56 x 10-23 T" 3 2600 - 7000

Marshall 13 1.8 x 10" 33 300

Rink 4 1.30 x 10" 30 T" 1 3000 - 6000

Schexnayder 6 4.44 x 10" 38 T- 5 e 21800/T 5000 - 10000

Schexnayder 6 5.09 x 10" 37 T- 5 e 7600/T 5000 - 7500

Wray 11 5.8 x 10" 35 1340 - 2920

Wray 23 6.7 x 10" 37 T- 5 5000 - 11000

Wray 28 2.5 x

10" 30

T"

1 * 5 5000 - 11000

Wray 29 5.83 x 10" 35 5000 - 11000

M Author Ref.

°2 Byron 3

Camac 10

Chesick 7

Chesick 7

Eckerman 7

Generalov 8

Hall (Byron data) 18

Langan 24

Mathews 2

Table 1. 2 +M-»0 + + M

k^ (cm. 3 particle"* sec."*)

3.27xl0- 3 T-1.5 e

- 59400/r

1.80 x 10- 5 T-l e' 59400/1

2.3 x 10" 16

6.8 x 10" 16

2.68 x 10" 3 T-l-5 e-59400/T

9.55 x 104 T- 3 - 3 e-59400/T

6.3 x 10" 3 T-l-5 e-59400/T

4.17 x 10- 8 r -5 e- 59400/T

1.82 x 101 I" 2 - 5 e

- 59400/T

TOO

2800 - 5000

6000 - 7000

3100

3500

4000 - 7000

2600 - 7000

2800 - 5000

Review

3000 - 5000
Table 1. 0+M + + + M—continued.

M

Ar

Author

Rink

Schexnayder

Wilson

Wray

Ref.

4

6

5

23

Byron 3

Camac 10

Hall (Byron Data) 18

Rink 4

Wilson 5

Wray 23

Generalov 8

Baurer 26

Wray 23

Anderson (by Wray) 27

Byron 3

Camac 10

Generalov 8

Rink 4

Schexnayder 6

Schexnayder 6

Wray 23

Wray 23

k (cm. particle" 1 sec. )

3.2 x

10" 3 T"

1 - 5 e- 5940°/T

1.5 x 10' 10e" 3740°/T

5.0 x IO"

3 T" 1 - 5 e

- 59400/T

5.4 x 16" 5 I" 1 e

- 5940°/T

1.95 x io"

6 r - 5 e1 -59400/T

1.06 x 10° T"

2 e- 5940°/T

3.5xl0-6 T--

5 e- 5940°/T

9.6 x IO"

3 T"

1 ' 5 e" 59400/T

1.5 x IO"

2 I"

1 ' 5 e- 59400/T

1.5 x IO'

4 T"

1 e

- 5940°/T

1.68 x IO

4 I'

35

e- 5940°/T

4.37 x IO"

1 I'

3 e -59400/T

1.2 x IO'

5 T"

1 e" 5940°/T

3.0 x IO'

6 I'

1 e- 5940°/T

8.52xl0- 8 T-'

5 e- 59400/T

6.01 x IO"

6 I'

1 e

- 5940°/T

1.12 x IO

4 I'

3 ' 5 e- 594°°/T

9.4 x IO'

4 I"

1 ' 5 e- 59400/T

3.2 x IO'

11

e- 37600/T

3.06 x IO'

10

e

- 5180°/T

4.2xl0- 8 T-'

5 e- 59400/T

4.83 x IO" 10e- 5940°/T

10

T(K)

3000 - 6000

5000 - 10000

2700

Review

2800 - 5000

5000 - 7000

3000 - 5000

3000 - 6000

2700

5000 - 7000

2000 - 7000

Review

Review

350 - 3000

2800 - 5000

3300 - 7500

2000 - 7000

3000 - 6000

5000 - 10000

5000 - 7500

1340 - 2920

5000 - 11000
N

2 + N

2 Z N + N + N

2 AE - 9.76 eV

This reaction has been studied in both the dissociation and recombination directions.

The considerable disagreement among the various results is evident in figure 5. The results

on the dissociation reaction are from the work of Cary (Ref. 30) and of Byron (Ref . 31)

,

each of which used a shock tube following the reaction by interferometric measurements. In

the original statements of results, there was only approximately a factor of up to 1.4 disagreement in the rate coefficients in the temperature range covered but a major disagreement

in the temperature dependence. Byron reinterpreted Cary's data and improved this situation

slightly. Byron's analyses of his and Cary's data are marked Byron/Cary in the figures.

Although the source of this disagreement in the absolute values is difficult to determine,

it is not serious enough to be of great concern. However, that of the temperature

dependence is serious. In order to further investigate this, the recombination data must

be considered.

The low temperature values stretch over an order of magnitude of 300 K (from 2.2 x

10" 33 to 1.7 x 10-32 ^6 particle" 2 sec"*). Two studies have reported temperature

dependences, one of T" 2

, the other of T°. Most of the low temperature data have been

obtained from flow discharge systems. In a recent study, Evensen and Burch (Ref. 32)

used both a flowing and a static system. The more reliable results were obtained in the

static system from which they obtained a value of 1.12 x 10" 32 at 300 K. They used an

electron spin resonance technique and found no evidence for the formation of excited atoms

in the afterglow during the measurements although ground state atoms may be formed then.

Campbell and Thrush (Ref. 33) in another recent study using titration techniques studied

the reaction from 196 to 327 K and found a rather steep decrease in rate with increasing

temperature. With these data, they expressed the rate constant by 3.33 x 10" 27 and by

8.33 x 10" 34 e490 /1 . These both fit their data well but give drastically different values

at high temperatures. The expression with the negative activation energy fits both their

data and the high temperature data within a factor of two but shows practically no

temperature dependence at the high temperatures. It would in all likelihood be a poor

expression to use at intermediate temperatures. Herron (Ref. 34) found no effect of

temperature on this rate constant over a range of 273 - 453 K. He did, however obtain a

value of 1.7 x 10" 32 at 197 K. Although he believes this to be in error, it may indicate

11
a temperature dependence similar to Campbell's at low temperatures. Other low temperature

data lie above the Campbell and Thrush data by a factor of 2 to 4. These data, all at 300 K,

give recombination rate constants, shown in Table II along with the expressions obtained

using the dissociation rate constant and the equilibrium constant. Data for He and Ne as

collision partners are also available in the work of Cary (Ref. 30), of Campbell and Thrush

(Ref. 33), and of Herron et al (Ref. 34). The other interesting collision partner is the

7 8 free electron which Bradt (Ref. 35) reports to be 10 to 10 times as effective as N_ in the

recombination. If so, this may be of some importance to re-entry.

It is difficult to reconcile the high temperature and the low temperature data and their

temperature dependences. It appears that the processes change as the temperature changes and

that quite possibly in the obtention of certain of the data, the distribution of excited

states did not follow the Boltzmann distribution appropriate to the kinetic temperature.

Since there are drastically differing data in each range, it would appear reasonable to

select a temperature dependence which goes through the data at each end rather than agreeing

-31 - 75 with one of the stated temperature dependences. A rate constant of 7.7 x 10 T

'

has been chosen. This fits all data within a factor of two (although it is not thought that

such is necessary since not all data available are thought to be that accurate) except the

data of Campbell and Thrush (Ref. 33) which are within a factor of three. It seems likely

that these data show the large temperature dependence because of certain effects which make

it different from the reverse of the high temperature dissociation. It seemed preferable

to use the data of Evensen and Burch (Ref. 32) and at the same time to come closer to such

data as that of Marshall (Ref. 13), of Herron et al (Ref. 34) (as well as closer to others).

A factor of three appears reasonable for the uncertainty although it may be larger in the

500 - 3000 K range.

This recombination rate constant when used with the equilibrium constant gives a

dissociation rate constant of

W- 8.3 x Hf 6 1

- 5 T-" e- U320°/T

This, of course, agrees with the high temperature dissociation data in the same way that the

recombination rate constant agrees with the high temperature recombination data obtained

from the dissociation data.

12
N+N-+N + N + N AE = 9.76 eV

There are many fewer data for the dissociation or recombination with atomic nitrogen

as a collision partner than for the case of molecular nitrogen. Once again, Byron (Ref . 31)

and Gary (Ref. 30) obtained data. The only other data are that of Allen (Ref. 36) at 6400.

These data are shown in Table II and Figure 6 along with the compromise suggested by Byron

(Ref. 31). The last is a result of Byron's reinterpreting Cary's data considering it as well as his own. Wray and Byron (Ref. 37) suggested that Cary's data might be looked at in more detail but no such action has been reported. Until this is done and the two investigations once again considered jointly, it is suggested that Byron's compromise be used for

this rate constant. For dissociation and recombination, this would be

. r

. n

_ in -2 + .6 -1.5 '-113200/T

kj(N) = 5 x 10 - T e

k (N) = 4.6 x

10" 27 -

* 6 T" 1,S

N+Ar-»-N + N + Ar AE = 9.76 eV

This reaction with argon as the collision partner is not important in itself. However,

the rate constants are usually applied to the cases of all collision partners except N and

N - i.e., for , 0, NO, etc. There is no direct justification for this other than that

such has been done and to the limited extent that it can be determined, it seems to fit

calculations when a particular set of rate constants are used. There is, of course, no

basis for supporting this to be correct and that a fit would be obtained when different

rate constants are used for other reactions. Nevertheless, it appears that calculations

would not have been successful if the rate constants for the cases of 0, 2

, and NO are much

higher than that of argon. If they are lower they would have little effect. Thus, the use

of the argon rate constant seems reasonable although somewhat on the empirical side.

There are both dissociation and recombination data with argon as the collision partner,

the former being obtained by Byron (Ref. 31) and by Cary (Ref. 30), the latter by Herron,

Franklin, Bradt and Dibeler (Ref. 34) (at 300 K) , by Campbell and Thrush (Ref. 33) (196-327 K)

and by Ilarteck, Reeves and Mannella (Ref. 38) (at 300 K) . These data are shown in fig. 7

13
all in terms of the recombination rate constant. Once again there are disagreements in

both absolute values and temperature dependences in both the high and low temperature data.

The suggested value is a compromise of the high temperature data in that range and agrees

with Herron's and with Campbell's data at 300 K. It does not agree with Campbell's temperature

dependence or with Harteck's results. The suggested rate constants are

k,(Ar)=4.8xl0- 6 ^°- 5 T--

82

e- 113200/T

a

k (Ar) = 4.4 x

10~ 31 -

0,5

T"'

82

r

Table II. N + N + M + N +M

2

M = N„ Ref.

Allen 36

Barth 15

Campbell 33

Evenson 32

Harteck 38

Herron 34

Kretschmer 39

Marshall 13

Mavroyannis 40

Went ink 41

Byron 31

Cary 30

f\ - ? -

1

k (cm particle sec )

< 1.4 x 10

7.0 x 10

•33

•33

-27 -2 3.33 x 10 T

c

1.12 x 10

32

1.72 x 10

32

7.9 x 10

2.2 x 10

7.5 x 10

1.4 x 10

33

33

33

32

1.7 x 10

-32

Byron $ Cary (Byron) 31

-\7 - 5 7.73 x 10

0L

T

3.45 x

10~ 27 T"

1 - 7

-28 _i 5 7.4 x 10 T

T (K)

6400

300

197 - 327

300

300

273 - 453

350

300

300

300

6000 - 9000

6000 - 10000

6000 - 10000

M = N Ref.

Byron $ Cary (Byron) 31

f\ 1 k (cm particle s )

36

r *

Allen 1.8 x

10" 32

Byron 31 6.6 x

10" 27 T"

iS

Cary 30 2.5 x

10" 29 T"

1

4.6 x 10" 27 T"

1 ' 5

T (K)

6400

6000 - 9000

6000 - 10000

6000 - 10000

14
M = Ar Ref.

Byron 31

Cary 30

Byron $ Cary (Byron) 31

Campbell 33

Harteck 38

Herron 34

kr

(cm particle s" )

2 .84 x 10

-32

T

-.5

1 .6 x

10" 30

T

-l

9 .3 x

10" 33

T

-.5

3 33 x 10

-27

T

"2

1 72 x 10

-32

3 9 x

10" 33

T (K)

6000 - 9000

6000 - 10000

6000 - 10000

197 - 327

300

273 - 453

N+M + N + N + M

M = N, Ref.

Byron 31

Cary 30

Byron § Cary (Byron) 31

Appleton 119

3 -1 -1 k, (cm particle s )

8.0 x

10- ? T- 5 e- 11320° /T

3.73 x

10" 2 T"

1 ' 7 e

" 113200/T

8.0 x 10" 3 T"

1 ' 5 e" 113200/T

6.2 x 10

3 "1.6 -113200/T

T (K)

6000 - 9000

6000 - 10000

6000 - 10000

8000 - 15000

M = N

Byron 31

Cary 30

Byron 5 Cary (Byron) 31

Appleton 119

M = Ar

Byron 31

Cary 30

Byron § Cary (Byron) 31

Appleton 119

7.17 x

10" 2 T"

1 ' 5 a" 113200/1

2.71 x 10" 4 T"

1 e" 11320°/T

5.0 x lO"

2 T"

1 ' 5 e

- 113200/T

2.7 x 10" 2 I"

1 ' 6

e

" 113200/T

T

-.5

e -113200/T

3.17 x

10" 7 T"*

5

1.73 x

10" 5 T" 1 e

" 113200/T

1.0xlO- 7 T--

5 e" 11320°/T

2.3 x 10" 3 T"

1 - 6 e

" 113200/T

6000 - 9000

6000 - 10000

6000 - 10000

8000 - 15000

6000 - 9000

6000 - 10000

6000 - 10000

8000 - 15000

15
NO + M-N + + M AE = 6.51 eV

Data for the dissociation of NO with NO as the collision partner have been obtained by

Freedman (Ref. 42), by Wray (Ref. 43), and by Allport (Ref. 44). Freedman and Allport each

obtained a temperature dependence which he expressed as an activation energy which was

considerably less than the reaction energy, and which when combined with the equilibrium

constant gave a large negative activation energy for the recombination reaction. These data

shown in figure 8 are probably for a more complex chemical system than given by the straight

dissociation reaction. Expressing the temperature dependence as a negative preexponential

temperature dependence would also not appear realistic. Wray's results are used as the

suggested rate constants.

The three-body formation of NO with nitrogen as a catalyst has been studied as low

temperatures by Campbell and Thrush (Ref. 12), by Mavroyannis and Winkler (Ref. 40) and by

Kretschmer and Petersen (Ref. 39). Campbell obtained data from 197 to 327 K. He interprets

his data in terms of two different temperature dependences. No high temperature data are

available. Wray (Ref. 43) has assumed that his data obtained for the case of argon as the

collision partner hold for N_ as the collision partner and has found a fit in calculations

using it this way. These data indicate a T temperature dependence which, if extrapolated,

would be orders of magnitude higher than the Campbell data at low temperatures. Since the

high temperature data were not obtained with N

2

, it is suggested that the temperature

-32

dependence be ignored and a constant value of 1.1 x 10 be used although it is not likely

that there is no temperature dependence. The available data are shown in fig. 9.

For other third bodies of interest, mainly O2 and 0, it is suggested that these same

rate constants be used. It is very difficult to correlate the dissociation and recombination

data for argon as the collision partner (fig. 10). The data of Campbell and Thrush (Ref. 12)

at low temperatures and of Wray and Teare (Ref. 43) at high temperatures are shown in fig. 10.

Recommended values for the rate constants are: M k

d

k

r

NO 1.32 x i

- 2*- 6

T-1.5e -75400/T 9.1 x ur^i-V1 - 5

N

2 1.5 x 10 -9i'V75400/T 1.1 x

10- 32i' 5

Ar 3.5xl0-^V-6e- 75400/T 2.4xlO- 31i-V' 6

16
+ 2 + M + O3 + M AE - - 1.05 eV

This reaction has been investigated in detail for various collision partners. Both

the recombination and the dissociation reaction have been studied, often together with the

reaction +

3

-> 2 + 03. Data are shown in figures 11-13 and Table III. Some of the

data have been obtained at ratios of rate constants and some involve use of the equilibrium

constant. There is uncertainty enough in the heat of formation of ozone to cause a factor

of two uncertainty in the rate constants acquired by use of the equilibrium constants.

Glissman and Schumacher (Ref . 45) obtained ozone dissociation data over thirty years

ago over a temperature range of 343 - 383 K which may still be regarded as reliable. Their

data were O3, O2, N2, Ar, CO2 and He as collision partners. More recently Benson and

Axworthy (Ref. 46) analyzed these data and added their own data at one temperature, 373 K.

They also treated several collision partners, obtaining data in good agreement with the

earlier work. High temperature (689 - 910 K) data were obtained in a shock tube by Jones

and Davidson (Ref. 47) using N2 and Ar as collision partners. These dissociation data have

been used (for the temperature ranges over which the data were obtained) in this study

together with equilibrium constant data from the JANAF Tables (Ref. 48) to obtain recombination rate constants. Their agreement with the recombination reaction data as such indicates that there are no large effects of metastable states in these data.

Zaslowsky and coworkers (Ref. 49) obtained dissociation rate data with O3 as a

collision partner and also obtained data which they interpreted in terms of recombination

with O2 as a collision partner. (Ref. 50) From the latter data, a rate constant of

4.0 x 10" 34 e" 150 /^ was obtained for the temperature range of 213 - 243 K.

Data have been obtained on the recombination reactions using oxygen atoms generated in

several ways. One of the most serious problems is the possibility of creating excited atoms

and molecules when creating atoms. Another problem is the presence of impurities which

react rapidly with the oxygen atoms.

A very careful experiment was carried out by Kaufman and Kelso (Ref. 51, 52) at 300 K

with N2 and O2 as collision partners. They obtained values of 5.5 and 6,5 x 10" 34 cm6

molecule" 2 s"l respectively. Although some of their experiments were carried out using

oxygen from a discharge, they regard their results obtained using atomic oxygen from the

thermal decomposition of ozone as much more reliable and the quoted result is from those

data. The problem of excited 2 and N2 is considered by Schiff and coworkers (Ref. 16, 53-55)

17
who obtained a rate constant for the dissociation of ozone by excited nitrogen.

Clyne, McKenney, and Thrush (Ref. 56) obtained recombination data over the temperature

range 188 - 373 K for Ar as the collision partner. Their data can be fitted over this range

by the expression 1.48 x 10*25 T" 3 * 4 cm6 particle-2

s _1 Sauer and Dorfman (Ref. 57) obtained

a rate constant of 2.36 x 10" 34 at 296 K with Ar forming the atomic oxygen by pulses of high

energy electrons. They present arguments for the lack of effects of electronically excited

species but the arguments are not conclusive.

In re-entry, the formation of ozone is of more interest than its dissociation. The

most reliable data appears to be that of Kaufman for N2 and O2 as collision partners. For

other collision partners, the data of Benson and Axworthy and Glissman and Schumacher may

be used. The high temperature data of Jones and Davidson are usable to obtain a temperature

dependence. Figure 11 shows the various data for + O2 + N2 * O3 + N2 together with a

recommended rate constant of kr(N 2

) - 4.5 x 10" 29 .6 j-2 and figure 13 shows the data

for Ar as the collision partner with the recommended k

r

(Ar) = 2.9 x 10" 29 * » 6 T" z

#

Data are listed in Table III.

Table III. +

2 M * O3 + M

M Author Ref kr (cm6 particle" 2 s"

1

) TOO

N

2 Benson § Axworthy 46 2.53 x 10" 34 373

N2 Glissman § Schumacher 45 3.9 x 10" 31 T" 1 * 24 343 - 383

N

2 Kaufman 51,52 5.5 x 10" 34 300

N

2 Jones § Davidson 47 1.15 x 10- 29 T-1.80 689 - 963

Ar Glissman § Schumacher 45 2.46 x 10" 31 T" 1,24 343 - 383

Ar Clyne, McKenney $ Thrush 56 1.48 x 10" 25 T" 3 * 4 188 - 373

Ar Sauer § Dorfman 57 2.28 x 10" 34 296

Ar Jones § Davidson 47 2.15 x 10" 27 T" 2 * 64 769 - 910

°2 Kaufman 51,52 6.5 x 10" 34 300

°2 Benson § Axworthy 46 2.71 x 10-34 373

°2 Glissman § Schumacher 45 4.3 x 10" 31 T" 1 * 24 343 - 373

2 Hacker 58 7.0 x 10" 34 300

18
Table III. + 2 + M + O3 + M—continued

M Author Ref. kr (cm6 particle" 2 s" 1

) T(K)

2 Dickens 59 3.0 x 10"34 283

2 Krongelb f, Strandberg 21 3. n x 10-34 35n

2 Urbach § Zaslowsky 49,50 4.0 x 10" 34 e" 150 /1

213 - 243

N NO -* N2 AE = - 3.25 eV

This reaction has been studied at about 300 K by Phillips and Schiff (Ref. 60) , by

Herron (Ref. 61,62), by Verbeke and Winckler (Ref. 63), by Harteck and Dondes (Ref. 64),

by Kaufman and Kelso (Ref. 65, 66) and by Kistiakowsky and Volpi (Ref. 67, 68) at somewhat

elevated temperature by Clyne and Thrush (Ref. 69, 70) and in the reverse direction at high

temperatures by Click, Klein and Squire (Ref. 71). The results of these studies are listed

in Table IV and are shown in figure 14. The earlv studies by Kaufman and by Kistiakowsky

obtained lower limits. Phillips and Schiff used a mass spectrometer for species

determination in a flow system. They obtained a rate constant of (2.2 0.6) x 10" 11

cm3 molecule" 1 sec" 1

. The data of Clyne and Thrush over the temperature range of

476 - 755 K were fit by (5.0 + 1.0) x 10 -11 e(" 100 - 350) /T

# The data were obtained

indirectly from a ratio of the rate constant of this reaction to that of the N +

2 reaction. The data of Click were obtained for the reverse (0 + N2

) reaction in shock tube

studies. Their data have been re-examined by Duff who suggests a rate constant of

8.2 x 10" 11 e" 3800°/T to fit them. The available data show that there is no significant

temperature dependence for the rate constant of the N + NO reaction. The rate constant

suggested for use is that of Phillips and Schiff which may be assumed to hold at all

temperatures. This fits the data of Clyne and Thrush and those of Click, Klein and Squire

with the equilibrium constant well. Thus the recommended rate constants for the reverse

and forward reactions are:

+ N 2

-+ N + NO k « 1 x 10" 10 -* 3 e" 380n°/T cm^ol'^ec" 1

and

N + NO + + N 2 k = 2.2 x 10" 11-* 3

19
Table IV. N + NO > N +

Author Ref k (cm particle sec ) T(K)

Clyne 69,70 5 x lO'

11 e- 100/T

476 - 755

Kaufman 25 2.22 x

10" 11 Review

Harteck 64 3 x 10" 13 300

Herron 61,62 1.7 x

10" 11

300

Kaufman 65,66, 74 6.7 x 10" 12 1572 - 1690

Kistiakowsky 67,68 7.67 x

10" 12

394 - 517

Phillips 60 2.2 x

10" 11

298

Verbeke 63

-12

4.3 x 10 ^ 300

+ N„ NO + N

Click, Klein, Squire 71

Wray (Glick data) 23

-12 .5 -37000/T

1.8 x 10 " T e

_ in -ll -38000/T

8.2 x 10 e

2000 - 3000

N + 0, + NO AE = 1.39 eV

This reaction has been investigated most often together with the N + NO * + N

reaction. The exothermic reaction has been studied at temperatures ranging from 300 to

755 K while the reverse reaction has been studied at higher temperatures. The data are

shown in Table V.

The data of Clyne and Thrush (Ref. 69,70), of Kistiakowsky and Volpi (Ref. 67) and

of Mavroyannis and Winkler (Ref. 72) agree well and cover the temperature range of 394 -

755 K. The more recent data of Wilson (Ref. 72a) also agree. These cover a wider range

(300 - 910 K). These can be seen in figure 15. The data of Harteck $ Dondes (Ref. 64) and

of Kretschmer and Petersen (Ref. 39) are uncertain. At high temperatures, the data of Wray

^ Teare (Ref. 43) obtained from 3000 to 8000 K by analysis of a complex system in an NO

shock tube study is more accurate at about 5000 K. The data of Sulzmann § Ludwig (Ref. 73)

require the use of several other rate constants that were not well established at the time

of their work. The data of Kaufman $ Decker (Ref. 74) provide reliable intermediate

20
temperature data. It appears that the data for the rate constant for this reaction are

dependable and a fit of these data is accurate to a factor of two over the temperature

range. Kaufman has obtained a slightly better fit (Ref. 25) to the low temperature data

than given by the suggested expression but the latter is used since there is also much

importance to this pair of reactions at high temperatures. The suggested value for the

exothermic reaction is:

k = 3 x l(f

16 1

- 3 T

1 ' 5 e- 3000/T

and for the reverse reaction, + NO * N + 2

k - 7.2 x

10- 17 *

- 3 T

1 ' 5 e- 19100/T

N + -» + NO

Author

Clyne $ Thrush

Harteck § Dondes

Kistiakowsky $ Volpi

Kretschmer $ Petersen

Wilson

Ref. k (cm particle sec J T(K)

69,70 1.4 x

10" 11

e- 357°/T

412 - 755

64 1 x

10" 16 300

67

_ _ in-12 -3120/T

3.3 x 10 e 394 - 517

39

-17

8.3 x 10 350

72a i «i i ft 17 -3980/T

1.41 x 10 e 300 - 910

+ NO •* N + 0„

2

Kaufman $ Decker

Kaufman § Kelso

Wray f, Teare

Sulzmann § Ludwig

74

65

43

73

6 x

10- 12

e- 199°°/T

l^xlO-^e" 20400/1

5.3 x

10- 15

T e- 19680/T

3A-U T

l/2

e -19200/T

1572 - 1690

1170 - 1530

5000

2250 - 3450

+ VV°2 AE = - 4.06 eV

This reaction lias been studied in conjunction with ozone dissociation and its threebody formation. + M * O + 0„ + M. In most cases the data obtained have been for a ratio

7 3 2 of the 0+0 rate constant to that of one of the others or to the equilibrium constant for

the above reaction. Since the heat of formation of ozone is in doubt by about 0.4 kcal/mole

(Ref. 48) , the rate constant of the + is uncertain by about a factor of two because of

21
this. Data were obtained for this reaction together with data for the dissociation by

Benson and Axworthy (Ref. 46), by Glissman and Schumacher (Ref. 45) with further evaluation

by Castellano and Schumacher (Ref. 75), by Zaslowsky and co-workers (Ref. 49,50), by

Pshezhetskii and co-workers (Ref. 76), and, at higher temperatures, by Jones and Davidson

(Ref. 47). Data were obtained in a recombining system by Clyne and co-workers (Ref. 56).

In a flow discharge system, Phillips and Schiff (Ref. 60) obtained direct data on the

+ 0, reaction. Harteck and Dondes (Ref. 77) obtained a match for data in a complex system

using assumed rate constants. The data are shown in figure 16 and listed in table VI.

Some of the comments made about certain investigations on the 0_+M-«-0 + CL + M reaction

apply here.

The most reliable data are probably those of Schumacher with their various interpretations

(Benson, Castellano) . These are taken together with those high temperature data of Jones

and Davidson to get the suggested rate constant. It is interesting that the extrapolation

of the Schumacher data, using their temperature dependence, gives excellent agreement with

Jones' data. Other data do not agree too well with this and it is rather perplexing that

Phillips data fall this far out of line although there is a possible effect of water vapor.

These considerations lead to a recommended value for the rate constant of the

exothermic reaction, + CL +

? + Cu.

. , , , n -ll + .7 -2750/T

k = 3.6 x 10 — e

which leads to a rate constant of

k=2.7xl0-9 i- 7 T--

5 e- 50190/T

for the reverse reaction. Considering the uncertainties in the experimental data and that

in the equilibrium constant, the uncertainty is estimated as a factor of five although it

may be somewhat lower at low temperatures.

It is quite possible that much of the ozone data involves excited or 0_ and, thus,

is not applicable for much of the manipulations among the various rate constants which are

required to obtain the rate constants of individual reactions. The data were used here,

however, since excited states are in all likelihood present in the reentry system although

admittedly in much different amounts.

22
Author Ref.

Benson § Axworthy 46

Campbell § Nudelman 78

Caste llano § Schumacher 75

Clyne, McKenney § Thrush 56

Clyne, Thrush § Wayne 79

Harteck § Dondes 77

Jones § Davidson 47

Kaufman 25

Phillips § Schiff 60

Pshezhetskii et. al. 76

Urbach, Zaslowsky et. al. 49,50

N + - N0+

+ e E

T(K)

373

Review

278 - 298

180 - 1000

300

295

769 - 910

Review

298

303 - 443

273 - 353

Table VI. Data on +

3 -2 + O2

k(cm3 particle" s~l)

5.6 x 10-1 1 e" 287°A

9.0 x 10-12 e-2133A

5.62 x 10- 11 e-2870/T

1.0 x 10" 11 e- 4 300/T

8+lx 10-14

2.0 x 10- 10 e" 3n8°A

4 x 10" 11 e" 2800 ^

1.4 x 10-12 e-iSOO/T

2.5 x 10" 14

3.83 x 10-12 e-2500A

7.1 x 10-12 e-1600/T

3. Ionization

E » 2.76 eV. The reaction in the ion-electron recombination direction has been studied at room

temperature by a number of workers including Weller (Ref. 80) , Hunton (Ref. 81) , Doering

(Ref. 82) , Young (Ref. 83) , Van Lint (Ref. 84) , and Bascombe (Ref. 85) , over a temperature

range at low temperatures by Gunton (Ref. 81); and at high temperatures by Stein (Ref. 86).

The reaction in the ionization direction has been studied at high temperatures by Lin

(Ref. 87) . There have also been a number of analyses of atmospheric data, such as that of

Donahue who made a complex analysis of atmospheric kinetics over a large altitude range.

The data given consideration here are shown in figure 17. dunton obtained data at

196, 298, and 318 K creating the ions by photoionization with the ions being in low

vibrational levels of the ground electronic state. The data of the several other investigators are in agreement with these data considering the uncertainties involved. Data are

listed in Table VII.

At high temperatures, the data of the ionization reaction are weighed most heavily since

that is the more important at such temperatures. It is, of course, possible that a different

rate constant should be used when the ion-electron recombination reaction predominates from

that used when the ionization reaction predominates. This is one way to allow for the effect

of excited states - the combination into them and the non-Boltzmann distribution among the

23
states of the reactant. But, it would seem that a single rate constant would fit the data

accurately enough. It is, therefore, suggested that the rate constant

k- 2.4 x lO

-3!- 47

T

-1 ' 5

be used for the recombination reaction and

v o a , n -13+0.5 -31900/T k = 8.6 x 10 — e

be used for the ionization reaction. A factor of three is suggested for the uncertainty

although it is certainly less at low temperatures.

Table VII. N0+

+ e •* N +

Author

Bascombe

Biondi

Daiber

Doering

Donahue

Gunton

Stein

Van Lint

Weller

Young

3f k(cm3 particle s

1 TOO

85 2 x io- 7 2000

88 4.7 x

10" 4 T

-1.2

Review

89 6 x

-4 - 10 ^ T

3/2 4900 - 7700

82 3 x

10" 7 tc• 2 x IO

-6

300

90 5.2

1.0

x

10" 7

x

10-6

(S

1.4 Tr = T (130 km)

196

81 4.6 x io

- ; 298

3.5 x 10

_/ 358

86 4 x io"

8 2900

84 3.7

-7 x 10 300

80 6 x IO' 7 300

83 5 x IO"

7 300

N + O * NO + e

Lin 87 5 x IO" 11

I' 172e- 32500/T

24
4. Collisional Ionization

N + M + N* + e + M M = N , 0- AE = 15.58 eV

0+M + 0* + e + M M = N

2

, 2 AE = 12.06 eV

Before the shocked gas has had much opportunity to dissociate and hence to ionize by

associative ionization, some appreciable ionization may occur by molecule-molecule

collisions. This will only occur to a significant extent if the translational temperature

is very high. Ionization of atoms by this mechanism will be unimportant since once

appreciable numbers of atoms are available, associative ionization will occur and the

temperature will have dropped enough to reduce collisional ionization probabilities

drastically. The probability of molecular ionization will be greatest before any relaxation

other than translational occurs, since then, the kinetic temperature is high. The only

available data are for just such conditions. The data of Utterback and co-workers (Ref. 91),

from a study of molecular beam colliding with molecules at room temperature, is of crosssections for collisions with high kinetic energy with the molecules in the ground electronic

state and almost entirely in the ground vibrational state. This is reasonably like the case

of the earliest collisions in the shock layer. The data do not apply as well to the

molecules once they have acquired significant vibrational energy, but no other data are

available and its use is still the best approximation. Utterback has suggested that more

appropriate data could be obtained by a complex reinterpretation of his data.

The data for an N beam with

2 target gas were essentially the same as for an beam

with N_ target gas. It was difficult to separate the formation of N from that of . Data

below the N ionization threshold is, of course, for the formation of . Because of the

distribution of energy of collisions, all of the data in the N - system was attributed

to formation although this is only for convenience. It introduces little error.

The rate constants obtained for the above reactions from Utterback 's data are given in

Table VIII. It should be noted that Utterback obtained no NO from N

2

- 2 collisions and

his data should not be interpreted in that way. The rate constants given apply to a system

with a Boltzmann distribution of kinetic energy and with the molecules in the ground

electronic and mainly ground vibrational states.

It is practically impossible to assign an uncertainty for these rate constants.

Sources of error include the data extrapolation to lower energies, the uncertainty and

25
spread in collision energy, the application to vibrationally excited states. The

uncertainty is at least an order of magnitude and could more conservatively be given as two

orders of magnitude. It is certainly greater at comparatively low temperatures and small

at very high temperatures. Data were obtained from 20 to 500 ev.

It should be mentioned that ion-pair formation could be of some importance but data

on this for the nitrogen-oxygen are lacking. However, the lack of any ions at the

appropriate energies in Utterback's work indicates the process may not be significant.

Table VIII. Collisional Ionization Rates

m . m m

+ A ^ XT v r m-20 + 2 „2 -181000/T

N111 + I\L -» N + e + N_ k = 3xl0 — Te 2

+ -20+2 1.5 -140000/T

2 + N2 + + e + N k = 1 x 10 - T e

0. -Q, * 0% . 0, k - 2 x lo"

20 1

2 T

1 ' 5 e

- 140000/T

2 2 2 2

Cross-section data are available for electron collision ionization. Again, these

processes are most important for the very early times, before much relaxation has occurred.

Thus, the data from electron beams passing through a stationary target gas are most

appropriate since the only appreciable energy is the kinetic energy. There have been

many studies on these two reactions. These data have been critically evaluated by

Kieffer and Dunn (Ref. 91a, 91b) . In general, the agreement is very good among the various

studies. For use here, data in the low-energy range of the study by Eng lander -Golden

(Ref. 92) and of Tate (Ref. 93) have been used for N . The data on ? obtained in these

same studies and that of Assundi (Ref. 94) have been used to obtain that rate constant.

The rate constants so obtained are:

N,.e.N--Ze k-=5.3xlO- 11 * 1 T°-

5 e- 181000/T

2 2*

, -11 + 1 0.5 -140000/T

+ e - + 2e k = 2.2 x 10 - T e

2 2

The major source of uncertainty here is probably the application of data obtained for

unexcited molecules to a system when at least some vibrational excitation enters. Thus,

before any vibrational relaxation, the uncertainties are less than a factor of two, but a

larger factor is applicable when the excitation state is considered.

26
Rate constants for the ionization can also be obtained from those of the reverse threebody recombination process. Those reverse rate constants have been obtained by theory such

as by the Thomson Theory. Dunn (Ref . 94a) has reviewed the various theories and presented

rate constants for the Thomson Theory. These are:

kj. (N

2

) = 6.1 x 10" 22 T" 2 ' 5

k

r

(02

) = 2.4 x 10" 21 T" 2 - 5

From these and the equilibrium constants, the ionization rate constants are:

k. (N

2

) = 5.9 x 10" 6 r1 e

- 181000/T

k. (0

2

) = 1.5 x 10- 5 r1 e- 140000/T

These are obviously much different from the rate constants from the electron collision data.

Since those from ionization are more applicable until the electronic excitation reaches a

distribution nearing that corresponding to the kinetic temperature, it is suggested that the

first set be used for the early ionization. The use of the recombination rate constant

obtained from the theory would be advisable when the recombination step is important but the

three-body recombination probably does not compete with dissociative recombination

(XY + e -* X + Y) for conditions of interest here. Therefore, the use of the rate constants

from electron collision ionization cross-section data is advised.

5. Electron Attachment and Detachment

2 + e + M * 0~

2 + M AE = 0.43 eV

The three-body attachment of electrons to 0. nas been most thoroughly studied by

Phelps and co-workers. The attachment is fast with

2 and certain other less-abundant

species as collision partners and relatively slow with N

2 as the third-body. Phelps

(Ref. 102) has recently reviewed the data on this reaction and has suggested the values

27
°2

N

2

co

2

HjD

M k (an

6 particle" 2 s"

1

)

(4.2 + 0.6)x 10" 27 T" 1 e

" 600/T

(1 + 0.5) x 10" 31

(3.3 + 0.7) x

10" 30

(1.4 + 0.2) x 10" 29

The data of Chanin, Phelps and Biondi (Ref . 103) and of Pack and Phelps (Ref . 104) , most

heavily relied upon, were obtained in a drift tube system in which the electrons were found

to be thermalized with average energies of .023 to 1 ev, the distribution being different

from any standard distribution. The gas temperatures were varied from 195 to 583 K and

these data were used at average electron energies of the corresponding temperature. Other

data (Ref. 105-108) at or near 300 K agreed well with these data for and N . The threebody collision may be either a two-body formation of CL in an excited form which is subsequently stabilized by a collision or a two-body formation of an 0. complex which then

undergoes dissociative attachment in a collision with an electron. The data may be for

either of these or possibly a combination of them. At higher temperatures there are few

data. Chatterton and Craggs (Ref. 169) have obtained data for average electron energies of

0.6 to 1.1 ev. The values fall about a factor of three above the extrapolated curve of

Phelps. However, the gas temperatures are low so that the mechanism of formation, the

possible occurrence of excited states, the conversion of kinetic energy, and any other

uncertainties inherent in the non-thermalization of their system are involved.

Since at high temperatures the rapid detachment makes the attachment of little

importance, the extrapolated curve is suitable for use. Therefore, a rate constant of

4.2 x

10" 27

+

ml T"

1 e

" 600/T

is suggested for

2 as the third-body and 1 x

10~ 31 -

* 3 for

N-. Other collision partners are unimportant because of low rates and competing reactions.

It is concluded that the values suggested by Phelps are the most suitable numbers for

use here, being reasonably accurate for the temperature range of interest.

°2

+ ° "*" °3 + e AE = "°- 62 eV

Fehsenfeld and coworkers (Ref. 110,111) have the only reliable data on this reaction.

They report a value of 2.5 x 10 , this being a slight revision of previously reported

28
values (Ref. 112). No temperature dependence is given. T]\e uncertainty is estimated

as not more than a factor of two.

Curran's data (Ref. 113) could be used to obtain a temperature dependence, the shape

of the cross-section curve indicating a variation of T or T . However, the threshold

shown by these data is in considerable error (about .4 instead of .6 ev) , so that the data

do not seem suitable for use. .no + 0.5)

A value of 2.5 x 10

is suggested and nothing can be said about the temperature dependence.

+ e + + AE = - 0.43 eV

For this reaction the only reliable data are from the work of Fehsenfeld and coworkers (Ref. 110). Their latest published value is 4 x 10 cm particle s . Limits

of the uncertainty are given as 10 to 10 . Data were obtained at only room temperature,

300 K. Curran (Ref. 113) gives some cross-section data but there is a question about

1 75 these data. They have been used to obtain a temperature dependence of T . This, with

Fehsenfeld* s value, would give a rate constant of 4 x

10

~

U

r-I_ 1.75 or 1.85 x

10~ 15

T

1 ' 75

, L 300 J but it is thought that the data and this temperature dependence are both suspect. It is

probably better to use no temperature dependence at this time. Thus a rate constant of

4 x 10 *• — ' > is recommended with no meaningful temperature dependence information.

Using the equilibrium constant, K = 1.67 x 10 T e" ' obtained from data in

the JANAF tables (Ref. 48), the rate constant for the reverse reaction is 6.7 x 10 -

T

.83 -4700/T

6. Negative Ion Charge Exchange Reactions

The reactions of this type which are of possible importance are:

0" + * o

2 + 0"

°2 * °

3 +

°2 * °j

0" +0*0 +

0"

0" + 7 + 0~ + 0_

3 2 2 0" + N - 0" + NO

29
0„ + NO -> NO +0

2 2

0" o + o- + o

2

o" co

2 * CO" o2

O" + NO -» NO" +

3 3

no" + * no" + 0,

3 2 2

CO" + * 0~ + C0„

3 2 2

The data on these reactions are limited. There are room temperature data on several of

them, mainly from the work of Ferguson et al. In addition, there are data at energies of

several eV and above, some of which are on the reverse reaction.

For the o" + + + 0" Fehsenfeld (Ref . 110-112) gives a value of 3 x

10" 1

.

This is the only usable value for this. The temperature dependence is unknown and it is

best to assume none. Since, because of electron detachment from , the reaction is

2 unimportant at high temperatures, the temperature dependence is of little consequence. A

-10 + .3 rate constant of 3.0 x 10 — is recommended.

The reaction + + 0_ + competes with the associative detachment reaction

+ •* + e, both in the wake and in the laboratory system. Its influence is thereby

limited. This also makes it difficult to obtain a value of the rate constant. Fehsenfeld

et al (Ref. 112) have obtained a combined rate constant for the two reactions of 5 x 10

cm particle" s . He later (Ref. 110) gave a rate constant of 3.3 x 10 for the

associative detachment but the difference in this and the previous value should not be

attributed to the charge transfer but rather to a more accurate and lower total value for

the two reactions. Still more recently, Ferguson (Ref. Ill) gives a value of 2.5 x 10

There are no data which can be attributed directly to the change transfer reaction. It is

now thought by Ferguson (Ref. 114) that the charge transfer is slower than the associative

detachment so that its influence on the OZ or concentration is relatively unimportant.

It may be of some importance to the concentration and in this way affect the electron

density.

The reverse attachment reaction has been studied at energies above the endothermicity

(0.62) by Paulson (Ref. 115). By extrapolating this, integrating for a Maxwellian

30
distribution, and using the equilibrium constant a rate constant of 3 x 10" T

can be obtained. This would be 6 x 10 at 300 K. It is probable that such an

extrapolation is not reasonable although it is only from 4 eV down to 3.7 eV. It is

interesting to note that he finds the charge transfer reaction to be three times as fast

as the charged rearrangement giving the same products.

Woo, Branscomb, and Beaty (Ref. 116) obtained rate constants at elevated temperatures

for the endothermic reaction. Use of the data would give much too low an endothermicity

and they concluded that their distribution was non-Maxwellian and unknown and these data

cannot be used. +1

-11 -3

With this limited information, a reasonable rate constant is 1 x 10

No temperature dependence will be used since at higher temperatures will be unimportant.

The reactants 0+0 can form 0+0 , + 0_, or 0. + 0. + e by exothermic reactions.

3 3 Z L / ^ The charge transfer reaction giving the first of these sets of products is apparently the

fastest. Fehsenfeld (Ref. 110) found a rate constant of 7.0 x 10 cm particle s .

The reaction + NO * + NO" has evidently not been studied. If large concentrations

of NO persist in parts of the wake where attachment has become important, data on this can

well be important.

7. Ion-Pair Neutralization

X

+ + Y" -* X + Y

Data on ion- ion neutralization are very limited. However, because this is a major

mechanism for the removal of both positive and negative ions and hence appreciably affect

the electron density it should be included here. It should be noted that the simple

mechanism noted is not necessarily that which occurs. If the positive ion is diatomic

(or larger) it may well dissociate (Ref. 117) since the exothermicity is great enough, i.e.

XZ

+ + Y" •> X + Z + Y. A three-body process, e.g. X

+

+ Y~ + M * X + Y + M (or various other

products), may be important. The information on the ion-ion recombination has been reviewed

recently by Biondi (Ref. 88). The rate constants suggested there are listed in Table IX.

The same rate constants are given for all ions since no data are available to determine

different ones for different ions. Theory does provide distinctions for different species

in the three-body ion- ion recombination.

31
Thus for the more important reactions involving negative ions, the following rate

constants are suggested:

Table IX. Rate Constants for Reactions Involving Negative Ions

k(cm particle s )

e CV 0" +

? 4.2 x

10" 27 1

- 1 T"

1 e' 600^

2 111

2 + e + N2 + 0" + N

2

1 x

10" 31 -

' 3

o

2 .o

3 ,o2 .o- !l .»-"--3 (l. °- 1

0" + + + e 2.5 x10~ 10 -

* 5

3

+ e + 0" +

2 4 x

10" 11 -

* 5

X

+

+ Y" + X + Y 6x 10" 5 -

* 5 T"

1

X

+

+ Y"+Mh-x + Y + M 3x 10" 19 -

' 5 T"

2 - 5

The most stable negative ion will probably only disappear by ion-ion recombination. The

most stable negative ions are probably CO" and NO . These are formed directly from 0_

by charged rearrangement reactions. If it is desired to simplify the chemical system by

omitting CO and N0_, the conversion of 0" to a less stable negative ion by + * + 0_

may be included with a pseudo rate constant reduced by multiplying it by the fraction taking

that path, i.e.

true

\o3* 0)

N

pseudo

k - = true

(°3 + °^ k

(0- + 0)

N + k

(03

^ CO

2

) NC02

+ \03 + N0)

N

N0

Other terms may be included in the denominator which convert 0" to other negative ions

which in turn are stable or convert to CO or NO". This pseudo rate constant would then

have to be calculated at each iteration. If the 0" + reaction is negligible, the 0"

•^ 3 can be regarded as the final negative ion and it may be taken as disappearing only by

ion- ion recombination. 32
8. Positive Ion Charge Exchange Reactions

These are more than twenty exothermic reactions in the nitrogen-oxygen system which

could logically be expected to change the identity of the positive ions in the re-entry flow

field. Consideration of all of these indicates that those which are important and have

most effect on the flow field are:

N

2 + °2 * N

2 + °2

N* + NO * N

2 + N0

+

N* + * N0

+

+ N

0* + NO - o

2 + N0

+

Data are given in table X. All of these studies were carried out at about 300 K. No

usable information is available on temperature dependence. Hence, the factors suggested

for uncertainty hold only for room temperature. At high temperatures, these may be orders

of magnitude in error. This is expressed as an uncertainty in the temperature dependence

°^ 300^ where the exponent 1.5 is merely an estimate.

N

2 + °2 * N

2 + °2

Several investigations of this reaction are in good agreement. Fite (Ref. 95), in a

stationary afterglow obtained a value of 2 x 10" while Fehsenfeld (Ref. 96) and co-workers

and Warneck (Ref. 97), in flowing afterglows, obtained 1 x 10 and 1.1 x 10 respectively.

Fehsenfeld 's value will be accepted here with a factor of two uncertainties at room

1 i m-10 + -3 temperature, i.e. k = 1 x 10 —

N^ + NO •* N + NO

+

The results of Ferguson (Ref. 98) et. al. and of Warneck (Ref. 97) are in excellent

agreement (5 x

10" 10 and 4.8 x 10). The value of 5 x 10" with an uncertainty of a

factor of two at 300 K is suggested here, i.e. 5 x 10 - '

.

33
N + N0

+

+ N

2

The only available data is that of Ferguson (Ref. 99) et. al. This value of

-10

2.5 x 10 at 300 K is acceptable but probably has somewhat more uncertainty than the

others since atomic oxygen is involved. A factor of five uncertainty is suggested. Thus,

k = 2.5 x 10 — .

0* + NO - + NO

+

The results of Ferguson (Ref. 98) and co-workers and of Warneck (Ref. 97) are again in

excellent agreement (8 x 10 and 7.7 x 10" ). The value of 8 x 10 with an uncertainty

of a factor of two is suggested, i.e. 8 x 10

10 + .3

N

+

+ NO * N + NO

+

2 2

Table X. N

+

+ o

-»• N_ + 0*

2 2 2 2

Author Ref. k(cm particle s"

1

) TK

Fite et. al. 95

-10

2 x 10 300K

Fehsenfeld et. al. 96 1 x Itf

10 300K

Warneck 97

-10

1.1 x 10 300K

Poppoff 100 2 x

10" 10

(E Region)

Aquilanti § Volpi 101 6.5 x

10" 11 300K

Ferguson et. al.

Warneck

98

97

5 x 10

10

4.8 x 10

-10

300K

300K

N* + +• NO

+ + N

Ferguson et. al. 99 2.5 x 10

-10

300K

0* + NO - 0„ + N0

+

2 2

Ferguson

Warneck

98

97

8 x 10

-10

7.7 x 10

10

300K

300 K

34
CO. + M + CO + + M AE = 5.45 eV

The dissociation of carbon dioxide has been studied by Steinberg (Ref. 120), by

Brabbs (Ref. 121) and by Davies (Ref. 122). Data are shown in figure 18. Very different

rate expressions are obtained by the three workers. These investigators each fit their data

with an activation energy much lower than the endothermicity . The higher the temperatures

of the studies, the lower the determined activation energy. It appears that the major

dissociation is from the upper vibrational levels which are nearly in equilibrium with the

dissociation products, CO and 0. It is chosen here to consider the data of Steinberg and

of Davies more than that of Brabbs since the last is at a lower temperature range than that

of major interest and because of the method of analysis employed therein. The data can

then be fit reasonably well by an expression employing the endothermicity although the use

of this as the activation energy is only for convenience. This is also a compromise since

the individual studies indicate a lower value, the composite of all the studies indicate

a higher value. Thus, a suggested rate constant is:

k

d

(N

2

) = 1.8 x 10

8 I"4 ' 5 e- 63800/T

for N as the collision partner while for Ar, the suggested value is

k

d

(Ar) = 1.6 x 10

8 T4 - 5 e- 63800/T

No attempt has been made to consider or include the data from the reverse reaction.

These data vary widely, probably bear little relation to the dissociation reaction, and are

difficult to interpret.

h -c/T *^ Table XI. Suggested Rate Constants (k = a T

D e )

°2 + M + + + M

M =« 2

N

2 N, NO, Ar

Forward Reverse

a b c a b c

1.37(-5+.5) -.83 59400 1.9(-32+.5) -.33

1.5(-4+.7) -1 59400 2.1 (-31+. 7) -.5

2. 2(3+. 7) -1.7 59400 3.0(-30+.7) -1.2

2.4(-3+.5) -1.8 59400 3.3(-30+.5) -1.3

35
Forward Reverse

N+M-N + N + M

M = N

2

, 0, NO, Ar

NO + M-N + + M

M = NO, 0, N

2

, N

2 Ar

+ M -> + + M

M = N

2

2

, N, 0, NO

Ar

+ N

2

->- N + NO

+ NO + N +

2

°2 + °2 * °

+ °3

N + - N0

+

+ e

N + M + N

? + e + M

M = N„

+ M-»-0- + e+M

2 2 M = N„

8.3(-6+.5)

5.0(-2+.6)

4.8(-6+.5)

2.1(-5+.6)

2.3(-5+.6)

1.4(-5*.6)

l(-10+.3)

7.2(-17+.3)

2.9C-11+.7)

8.6(-13+.5)

-.75 113200

1.5 113200

-.82 113200

1.32(-2+.6) -1.5 75400

1.5 (-9+. 5) 75400

3.5C-8+.5) -.6 75400

-1.35

-1.35

-1.35

1.5

12300

12300

12300

38000

19100

50190

31900

2 + e+M-*02 +M

M = 0„

3.0 (-20+2) 2.0 181000

5.3(-ll+l) 0.5 181000

1.0(-20+2) 1.5 140000

2.0 (-20+2) 1.5 140000

2.2(-ll+l) 0.5 140000

4.2(-27+.3) -1.0 600

l(-21+.3)

7.7

4.6

4.4

9.1

1.1

2.4

4.5

4.8

2.9

2.2

3.0

3.6

2.4

3.0

5.3

1.6

3.2

3.5

-31+.

5

-27+.

6

-31+.

5

-26+.

6

-32+.

5

-31+.

-29+.

6

-29+.

6

-29+.

-11+.3

-16+.

3

-11+.

7

-3+.5)

-36+2)

-27+1)

-.75

-1.5

-.82

-1.5

-.6

-2.0

-2.0

-2.0

1.5

-1.5

0.5

-1

-36+2)

-36+2

-27+1) -1

3000

2750

1.2(-ll+.3) 0.5

3(-16+.3) 1.5

(see text)

(see text)

5700

5700

36
Forward Reverse

°2

+ (W 3 0- + -

3

+ e

0_ + e -* 0" +

2 X

+ + Y" -*• X + Y

X

+ + Y~ + M-*X + Y + M

N

2 + °2 * N

2 + °2

+ N* + NO + N

2 + N0

+

N* + + NO + N

0* + NO -> 2 + N0

+

a b c a b c

3 (-10+. 3) T/300 3 (-10+. 3) 2800

2. 5 (-10+. 5) T/300 2.5(-9+.5) 7200

4(-ll+.5) T/300 6.7(-21+.5) .83 4700

6(-5+.5) -1

3 (-19+. 5) -2.5

K-10+.3) T/300 3(-ll+.3) 40900

5 (-10+. 3) T/300 1.5(-9+.3) 73100

2.S(-10+.7) T/300 4.5(-10+.7) 35400

8(-10+.3) T/300 4.2(-10+.3) 32200

-3

*Rate constants are in units to be used with concentrations in particles cm and time in

seconds. The number in parenthesis are the powers of ten by which the preceedmg figure

is to be multiplied.

# For the exothermic reaction rate constants, the data cited are intended for general use

in the temperature range of app. 100-5000 K.F or the endothermic reaction rate constants

the data cited are intended for general use between temperatures of app. 1500-10,000 K. Individual exceptions to the above are discussed in the text.

37
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42
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