Evolution times of tropospheric positive ions

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    tiniversite Paul Sabatier. Centre de Physique Atomlyue. Physique des Akrosols et Echanges Atmosph~riques~

    Equipe de recherche associke au CNRS No. 378, 31077. Toulouse Cedex. France

    Abstract A computer program has heen developed to study the evolution times of tropospheric posi- tive ions. Twenty-eight ions have been considered and their evolution times are a function of 79 ran-molcule rate constants. These calculations have shown that the ions NO are created mainly from N and 0. At 760 Torr and water concentration of 10 per cent by vol (or 44,, r.h. at 18 CI the ions H,O.(H,O),. II = I, 2. 3.. ..7 are formed in less than IO 3 ,.


    Identification studies of tropospheric ions by mass spectrometry are fairly new. They have shown the im- portance of polluting gases on the ionic composition (Cohen et al.. 1971; Mohnen, 1972; Huertas pt nl.. 19741.

    About ionospheric D-Region, direct mass spectro- metry observations of the ionic composition have led to numerous laboratory measurements of ion-- molecule rate constants at thermal kinetic energy (McDaniel et cd., 1972; Banks pt al., 1973, and to the development of calculated models derived from these laboratory experiments (Ferguson rt al., 1969; Niles. 1970; Thomas, 1971).

    With the help of methods used for ionospheric model investigations we have developed a theoretical model which describes the evolution times of positive ions in the troposphere. Mohnen has published similar studies (1969, 1970) in which he discusses tht: forma- tion mechanism in these ions and the nature of final ions between 0 and 50 km, in an air without pollut- ing gases. The work presented here is a continuation of the study presented by Huertas (1972). It allows further investigation, and enables us to study the evo- lution times of tropospheric positive ions according to numerous measured reaction rate constants.


    In the atmosphere between 0 and IO km three ionizing agencies must be considered: radioactive gases and their decay products, soil radiations and cosmic rays. Radioactive gases and their decay pro- ducts generate 4.6 ion pairs cmm3s- . (a-ray contribu- tion is cu. 90 per cent). Up to 1 m the @- and ;I-rays. coming from the earth, generate approximately 2 ion pairscmm3 s- : these /IL and II-ray ionizations become

    negligible at heights of up to 2 and IOOm respectively. Cosmic radiations produce I .5- I +3 ion pairs cm- 3 s .~ The energy of cosmic rays may attain 1000 GeV. The beta and gamma rays have a maximum energy of several MeV. The most energetic a-particles reach 7.X MeV.

    These ions are formed directly by ionizing particles or by secondary electrons resulting from the slowing down of these particles in the air. The secondary elec- trons of beta rays have a continuous energetic spec- trum between zero and the energy of the incident par- ticle. The primary ion mass spectra produced by YX- particles show the same fragment ions as those pro- duced by 70 eV electrons; mass spectra created by these electrons show slightly more dissociative ioniza- tions than those produced by 2.2 MeV r-particles (Rudolph et ul., 1966). As mentioned by Kebarle (*r al. (1967) the secondary electrons produced by x-par- ticles are responsible for more than 50 per cent of the total ionization; the energies of these electrons peak in the range 2pt-100 eV, so that again the pri- mary ions will be similar to those produced by 70 eV electrons. In a gas such as N,. these electrons produce N:, N. N. Ni ions are almost at thermal kinetic energy. But where there is a dissociative ioni- zation. i.e. for N+ and N.+. a ionic energy spectrum is observed (Durup et al., 1964: Field tt al.. 1970; Appell et al.. 1972; Stockdale et nl.. 1973). The kinetic energy of ions is a function of the energy of the inci- dent electrons. And the higher the electron energy. the greater the proportion of dissociative ionizations (which is already 18 per cent for 70 eV electrons in Nz).

    I .1 E-w rdution qfprifw2r~~ iorls

    The primary ions undergo many competjtive pro- cesses: recombination with negative ions. charge

    I (I I x

  • Evolution times of tropospheric positive ians 1019

    Table 1. Concentrations and ionization potentials of different corn- ponents of tropospheric air at ground level.

    Concentration fppm) (Junge, 1963)

    --- 9300

    18 5.2 1.1 0.086

    0-4-400. 102 o-5. i0-2


    (2-4). IO1

    (1--2o).1o-2 1.2-1.5

    c-3.10-3 2-6.10-l o-3.10-3 o-2.1o-2

    It20. 1o-3 2-20.10-3

    7.8. IO5 209.10*


    Ionization potential (eV) (McDaniel, 1964)

    (Handbook ajChemistry and Physics, 1973-1974)

    15.7 21.6 24.6 13.9 121

    12.6 I I.7 15.6


    14.1 145

    9.25 12*Q 11 11.2

    13.1 10.4

    IS-51 t 207 1.56

    transfer or chemical reaction. Table 1 gives the pro- portions and ionization potentials of the main com- ponents of the neutral tropospheric gas. The evolu- tion is more complex if the primary ions result form a dissociative ionization. Thus, as they are slowed down, the Of ions created with 3 eV energy may produce NO+ by the reaction:

    0 + N,-+NO+ + N. 1.4 Secondurp i&3

    These ions are formed by a reaction between pri- mary ions and gas molecules (cf. above). Table 2 pre- sents the main ion-molecule reactions of air com- ponents. It must be observed that NO+ ions may result from a charge transfer, as NO a low ionization potential (9.25 eV); but the NO concentration in the air is very low. To understand the high concentrations ofNO+ and its hydrates in the ionic mass spectra of the troposphere (Huertas et al., 1971; Griffin et al., 1973) one must introduce the reactions (66) and (71); these reactions are due to O+ and N+ ions. The formation of NO: and its hydrates* results from reactions similar to (66) and (71).

    These ions result from the clustering of Hz0 around the ions. Two formation processes may be considered: Y+ + H,O+ YH+ + OH YH+ + H,O+H,O+ + Y --

    Y+ = Ar... \ (f) YH+ = H,O+j

    * Knewstubb (1966), Shahin (1967), Varney et nl. (1967) have observed that in glow discharges where E/p is large (E: electric field. P: pressure) there is a large production of nitrogen oxide ions.

    if4 + X + H,O+X+(H,O)

    + MX = O;,NQ. (2)

    Depending on the bonding energy of X+ (H,O), swc- cessive hydrations may be observed: X(H20), X+(HzO) 2 ,..., X+ (H,O),. In some cases X (H,(I), is the final ion; but in other cases, the final reaction in the sequence is: Xs (HH20& + H,O-+H,O+ (H,O),_ 1 -I- X + OH. Many competitive reactions lead to HsO* (HzOfn. The mjor sequences start with O:, Ar+, NO, H20f.0: gives 0; (H,O) by the reactions (15, 16 and 20). The sequence beginning with 0; (H,O) gives HsO+ and two other reaction branches starting with H,O+.OH and 0: (H&I),.


    2.1 Rate equations

    From the reactions listed in Table 2, the equations describing the ionic evolution times are obtained. yi (t): concentration of ions i as a function of time Y,: concentration of mole&es m. Y, is independent oft k,: reaction rate con&& of the ions i with the molecules m (the first index letter always refers to the ion species).

    (a) Loss of the ions i: By recombination with negative ions y-(t):


    ct = ionic recombination coefficient. By reactian with the molecules m: -k,,y,(t) I,.

    (b) Production of the ions i : By charge transfer:j + i+ic +j: + kji yj (t) Yi.

  • IO20 M. L. HUERTAS and J. FONTAN

    By dissociation or addition evolution time lower than a few seconds. recombina- j + 17--+i+ + k

    1 + k j_V,W y,

    tion is negligible, at least for ions created by /I-, ;s-

    I -t ,I-- ;+ and cosmic rays; the ions created by 3: particles un-

    d@) dergo columnar recombination. which leads to

    dt - -xy,J-(t) - _Vi(t) 1 k,,Ym complex mathematical problems. If we assume that

    m recombination may be neglected the equation

    + I:C kji!;j(t) + C kj,J;(f)Y,. becomes: i .; .ff

    in the troposphere, the mean ionic concentration is dyAt) \

    always slightly lower than 10 ions.cm-. For an dr = -i;{t)Z:k*, Ym + I:?.;(t)

    In J ( kiiYz +l;&)_


    Table l(a). Ion-molecule reactions of thermal tropospheric ions for the calculation of the evolution timcs in the Rung- Kutta program. Reaction rate constants are expressed in cm s 3 in the case of bimolecular reactions and in cm- in the case of termolecular reactions. 5( - IO) means 5. IO-. Sometimes differing measured values of the same rate constant have been found in the literature; usually the most recent value has been chosen; but when the choice was

    difficult. WC have taken the average value

    0; + (II - 0; + 20> Hit>. + H,O- H,O + OH

    H,O + 0: +O: + Hz0 Vi) + H,O + y- NO+(H,Ol + h

    NOlti,O), - 4 - NO(H,0)2 + 4 + NO

    fi,OIH,OI + HA0 + .I --+H,0*(H,012 + Y

    t(,O(H,t)t, + Hz0 + X- HJO(H,O), + .\

  • Evolution times of tropospheric positive ions 1021

    34 H,O(H,OI2 -+ X- H,O+(H,O) t x + Hz0

    35 H,O+(H,O), + H,O + X-H,O+(H,O), + X

    36 H,OT(H,O)> + X - H,O+(H,O), c H,O + X

    37 3x







    45 46

    H,O+(HIO)~ + X - H,O+(H,O), -c X + H,O H,O+.OH + H,O-.H~O+(H,O) + OH

    H,O+.H,O.OH + H,O-H,O+(H,O), + OH

    H,O*(HzO), i H10 + X + H,O+(H,Ols + X

    H,O(H~Of, + X- H,O(H,O), + H,O + X

    H,O(H,O), + H,O + X-r H,O(H,O), + X

    HaO+(H20), + X - H,O+(H>O), + H,O + X

    H,O+(H1O)o t Hz0 + X -H,O+(H,OI, + X

    4- H,O.H,O.OH + 0,

    O:tH,O), + H,O -T;~H,O+.H,O+OH+O,

    47 N; + H20-. NlH+ + OH 48 Art + H,O--r ArH+ + OH 49 ArH + H,O-+H,O + AI

    As rate ~on~tmt~ of N; ion have not been measured at 300 K, we assume that they are of the same order as those or h at thermal knetic energy

    50 N: + H,O-+ H,O+ + N + Nz 51 N:+O,-O;tN+Nz 52 N;+01-.NO*+N,+O 53 N+ +0,-O; + N 54 N+O,-iNO+ +0 (5 NcNO-NO+N 56 N++N,+X-.N:+X

    51 N+ + H,O-+H,O + N 58 O+ i N,-NO+ + N 59 o++o~-o~+o 60 0 + NO-. NO+ + 0 61 0 + H,O--rH,O+ + 0 62 OH+ + Oz.-+O: + OH 63 OH+ + H>O- H,O + 0 64 -+ H,O f OH

    x=0> 1.4(-17) X = N, 7 (-18) X = Ar I(-13)

    X = 2{9,1;~129,

    X=0,4(-14) X = N, 3(-14) X = Ar 4 (-14) X=0,6(-12)

    Fast reaction presumed value I (-9) x = aa moiecule

    >, 5. (-31) X = air molecule

    2.lWI X = air molecule

    D 2 (-32) X = air molecule

    2.10-5 X = air molecule

    Huertas et al. (1974)

    Huertas et al. (1974)

    Huertas rr rrl. (1974)

    Huertas rf al. (1974)

    Huertas et al. (1974) I.0 (-32)

    k,,+k4*=6(-ll) Good PZ al. (197Ob)

    WC prcsumc: h,, = L*,, k,, = k, -A, = l.9(-IO) k,. = k, -k, = l(-10)

    lsst reactlo presumed value: I (-9)

    Howard et 41. (1970)

    26 (-9) 5 (-IO) 5 (-10) 5 (-IO) 5 f-10) 8 (-10) X = N, I.8 (-29) X = He M-30) T&6(-9) 3(-12) 2(-II) I.3 (-12) 2.33 (-9) 2 (-IO)

    2 (-9) k,, * k,,

    Good et al. (1970b) Good ef al. (197Oa) Young et al. (1970) Good et al. (197Ob) Young et al. (1972) Good et al. (197OM Good et ni. (197Oa) Young et al. (1970) Good et al. (1970b) Fehsenfeld et al. (1971a) Young et al. (1972) Good et al. (1970b)

    Stebbqs et al. (lY66a) Stebbings PI al. 11966bl Goldan rt al. (1966) Moscley CI ol. (19691 Bohmc et of. (IYW) Howard et al. t 19701 Stebbings et ai: (19&) Stebbings et ol. (1966) Dunkin et al. (197lb) Howard a al (1970) FehsenTeld et of. (1967) Ryan et al. (1970)


    Table I(b). Ion-molecule reactions of energetic ions N+, O+ and OH+ for the calculation of various ionic species created during the slowing down of these ions. These values are extracted from graphical data of papers given in the references.

    (1) When no values were found in the literature, we have presumed that the cross sections of possible charge transfer reactions are about 8 AZ; this value is in accordance with the results of other charge transfer reaction cross sections

    (Stebbinas et ai.. 1963. 1966)

    No. Reaction

    65 N+ +O,-+O; +N 66 N+ + 02-+NO+ + 0 67 N++NO--NOfN 68 N+ +NL-+N; +N 69 N++N,+X+N:+X

    70 N+ + H,O-+H,O+ + N 71 0+ + N,-+NO+ + N 72 0+40,-+0;+0 73 0+ +NO-+NO+ +0 74 0+ + H,O--+O + HtO 75 0 + N,-+N: + 0 76 OH* +02--tO: +OH 77 OH+ + H20+HZO+ + OH 78 +H,O+ + 0 79 OH++N,-N:+OH

    Reaction rate constant as a function of ion energy

    0.05 eV 1 eV 5 eV

    5 (-10) 7 (-10) 12 (-10) 5 (-10) 5 (-10) 5 (-10) 8 (-10) (1) (1)

    X = N, 1.8(-29) 8 (-11)

    X = He8.6(-30) 2.5 (-10) 5.5 (- 10) 1.2 (-9) 3 (-12) 4 (-11) 1.8 (-10) 2 (-11) 2 (-11) 1.3 (- 12) (1) (1) l-3 (- 10) 5.1 (-IO) 15 (-9)

    9.8 (-10) 2 (-10) (1) (1) < k,s 2 (-9) Z9) c 77



    Stebbings et al. (1966) Stebbings et al. (1966) Goldan et al. (1966) Murad et al. (1970) Mosley et al. (1969) Bohme et af. (1969) Turner et al. (1968) Stebbings et nl. (1966) Stebbings et al. (1966) Dunkin rt al. (1971b) Stehhings cf ctl. (1966) Stebbings et ctl. f 1966) Fehsenfeld rr al. (1967) Ryan et al. (1970) Ryan et al. (1970)

  • 1012 M. L. HUERTAS and J. FONIA>

    We can write in matrix form:

    0) = (A)(Y) y(t) is the i element of the column vector (Y) \tXt) is the ,j element of the row vector (Y)

    cl,; = x(kji + Z,k, Y,) is the (j clement of the square matrix (A) uii = -E,;uij is the ii element of the square matrix

    (A) The computed ionic concentrations are obtained by using the Runge-Kutta numerical integration of the simui~neous differential rate equations.

    (a) At t = 0, an instantaneous and homogeneous ionization of N positive ions is created in a gas com- posed of the mixture: N2-02-Ar-HZ&NO. The con- centrations of these various components arc those existing in tropospheric air, with water concentrations of IO3 and lo4 ppm.

    (b) In our calculations we have supposed that the concentration of positive ions is Ri = 10 ions.cn~. If .N is not equal to IO. the results given in Figs. l-3 are still correct and it is only necessary to change the numerical values of the ionic concentration axis.

    (c) Two pressures have been considered: 760 and 10 Torr, i.e. tropospheric pressure and the pressure inside our mass spectrometer source (Huertas rf al., 1971; 1974).

    Time. s

    Fig. I. Ionic evolution times at 10 Torr pressure and a water concentration of ld ppm. Ionic concentrations:

    N = IO ions. cm .- .

    . -. A_._.- - \

    I J

    b-ig. 7. lonlc evolution tunes at 760 lnrr pressure and it water concentration 01 IO ppm. Ionic concentrations.

    N := IO ions.cm .

    (d) The ions are created by 70 eV energy electrons. This is the case of ionization by alpha rays (cf. Section 1.2). Also, in this case. the dissociative ionizations are less numerous, because the electron energy is low.

    (e) The ion molecule reactions studied are presented in Table 2. It should be noticed that:

    Many trace gases (cf. Table I) have been neglected in making the calculations. He, Ne, Kr. Xe are in very low concentrations and their chemical activity is very weak. The action of CO2 is not important because of its high ionization potential. Other gases (03, CH,,. ,. H,S) have concentrations lower than I ppm; so their action will only be significant for evo- lution times greater than I Om 3s at 760 Torr and 10- s at 10 Torr.

    fn order to complete our calculations. we have csti- mated the numericai values of some rate constants. which have not been measured; but in some casts. indications of these values have been given by other authors, reactions (39. 49). etc.

    When the pressure increases, a termolecular ag- glomeration reaction becomes a bimolecular one. For example. this occurs in reaction (30) at 760 Torr; the time between two elastic collisions of the ion hecom- ing less than the stabilization time of the cluster. For the calculations at 760 Torr. it has been assumed that lijo = 1.15. lo- cm3sm1 (elastic collision rate con- stant).

  • Evolution times of tropospheric positive ions 1023

    Time. I

    Fig. 3. Ionic evolution times at 760 Torr pressure and a water concentration of lo4 ppm. Ionic concentrations:

    N = lo3 ions.cm-3.

    No reaction rate constant measurements concern- ing NOi and its hydrates at 300K have so far been found in the relevant literature. These reactions have been studied at 200K by Dunkin et al. (1971a):

    N; +O,+NO+ +Nz+O -0; +Nz+N dN0; + Nz

    Due to this lack of experimental results concerning the formation and the clustering of NO: it was im- possible to introduce these ions in our model.

    (f) The Runge-Kutta calculations concern reaction rate constants at thermal kinetic energy. Primary ions, created by dissociative ionizations have kinetic energies of a few electron volts. In preliminary calcu- lations we have studied the slowing down of energetic ions.

    2.3 Primary ionization

    Doubly charged ions are created in very low con- centrations; by a few charge-transfer collisions, they become singly charged ions. For the purpose of this work they may be neglected. According to the cross section values for simple and dissociative ionizations

    (Laborie et al., 1971) we have taken:

    N; : 078 0: :072

    Nz-+ ;O*-+ ; N+ :022 0+ :0.28

    NO+ :08 Ar-+Ar+:l ; NO-+ O+:@l


    H20+ :0.66 OH+ :0.16

    H,O+ H+ : 0901

    H2 :0.169 Of :O.Ol

    H+ and Hl disappear rapidly by charge transfer; these ions have not been introduced in the calcula- tions.

    2.4 Slowing down of the ions N+, O+, OH+

    Computer calculations have been used in this study.

    The ions are created by 70 eV energy electrons in a gas the composition of which has been indicated in section 2.2.a. The kinetic energy spectra are those given by Stockdale et al. (1973). For an ion of kinetic speed u, the relationship between the rate constant k and the cross section a is: a = k/v. When there is an elastic collision between the ion and an air mole- cule, we have supposed that there is energy isotropy in the laboratory system. Thus for low energy levels, the collision cross section for an elastic collision a, has been calculated by means of the formula given by Giousmousis et al. (1958):

    k, 2~ u a,=-=- _ V V J PL,

    a,: elastic collision cross section k,: elastic collision rate constant ~1: molecule polarizability H: ion-molecule reduced mass u: ion molecule relative velocity.

    For example, the slowing down of 0 ions has been computed in the following way: for an initial energy Eo, we calculated the numbers of ions NO+, Oi,... created during the first collision, and the number n(l) of O+ ions that have undergone a first elastic collision, and their kinetic energy distribution f(1). Then n(1) and f(1) are used as starting points for computing the numbers of ions NO+, O:,. . formed during the second collision and the number n(2) of ions that have undergone a second elastic col- lision and their energy distribution f(2). In all, nine successive collisions were considered, which is suffi- cient if the initial energy Eo is less than about 10 eV. From a knowledge of the energy distribution f(o) of the ions resulting from dissociative ionization, it has been possible to deduce the total numbers of ions NO+, O;,... created during the slowing down of O+ ions. At 760 Torr and a Hz0 concentration of lo4

  • 1024 M. L. HUERTAS and .I. FONTAN

    Table 3. Recapitulation of the ion--molecule reactions considered in our calculations. Italic numbers refer to the reaction numbers of Table 2(b), the others to the reaction numbers of Table 2(a).

    Initial ionic concentrations and concentrations after the corrections due to the slowing down of energetic ions for the following conditions: 760 Torr pressure and a H,O volumic concentration of IO3 ppm

    initial concentration Initial concentration after slowing down f

    Ions Production reactions 1.0~ reactions (x 103) energetic ions (x Iii-) - . -~

    AFL ArH N,H+

    N; NO

    NO+(H,O) NO+(H20), NO+(H,O), 0: N; 0; (H,O) O;fHtO)z H30+ .OH H,O+ .H*O.OH H,O+ H30(HzO)

    H,O+(H,O)z H@+fH&% H#+(H20)4 H3O+(H,O), H,O+(H,O), H,O+(H,O), N+


    OH H

    48 47 6 5-l&14-52 W5s 58 6WHs 67~ 71 73 2427 25-29 26 I6 56-69 15m 20 19 I8 45 I I- i3-22&32-G 78 3&334-38 46 2X 31-3639 33-m37 3S41 4@ 43 42 44

    3C2I so-51-52 17-18 19 45 46 3X 39 30 31 32 33- 34 3S3h 37 40 41-42 4% 44

    6~lO.10 144.lO








    lG4. IO 1.12.10

    644.10 L

    ppm. the following results have been obtained:

    O+:NO+(@lO); 0;(0.21); N;(O.06);

    H,O+(@O5) ; O+,i,,,,,,(OW

    N :N0+(0.23); 0;(0.27); N;(O.lQ);

    H20+(004); N:(OQ6); N&&0.30)

    OH+:O;(O.l8); Nl(O.16); Hz0+(0.05);

    H,0+(0.02) ; OH;,,,,,(@59).

    2.5 Numerical values used in the calculations of slow- ing down and evo~utjon times of the ions. Table 3

    This preliminary study of the slowing down of ener- getic ions has simpi~ed the calculations; thus, we have introduced in the Runge-Kutta program, the numbers of ions resulting from the slowing down of N+, rather than the initial number of N ions, created by dissociative ionization. The same modifica- tions concerns the O+ and OH ions.

    The curves shown on Fig. I may be compared with our experimental results obtained in the air at the same pressure and water concentration (pressure: IO Torr: water concentration: IO ppm), After 2.5. IO- % the ions 0: (H,O)E, !I = 0. I. 2: NO (H,O),. m = 0. I. 2 and H30+ (H,O),, 1 = I, 2. 3 are observed both experimentally and theoretically. After 6.10m4s, H,O (H,O), are the only ions observed in the experiments as in the calculations (Huertas, 1972; Huertas et ul.. 19741. A good accord- ance is also found between the calculations and the mass spectra obtained at 10 Torr and a water con- centration of lo4 ppm. as far as the evolution times of 0: (H,O),, NO (H,O), and H,O+ (H,O), are concerned. NO+ (HZO& has not been detected exper- imentally. According to our calculations. this ion should have appeared in the ionic mass spectra. Therefore it may be presumed that either the reac- tion :

    NO (H,O), + H,O-+ H30+ (H,0)2 + HIJOZ.

    3. RESULTS AND DISCUSSION is more rapid in the air than in pure gases: or that Figures i--3 present the results obtained for various in the air switching reactions transform and accebr-

    water concentrations and at various pressures. ate the simple reaction chain proposed by Fehsenfeld

  • Evolution times of tropospheric positive ions lr)25

    et al. (1971b) or Puckett et al. (1971). This is the opinion of Hiermel (1971) who has considered the switching reaction:

    NO+ + COz + M+NO+ .COz + M

    NO+ .COz + HzO-+ NO+ .H20 + COz.

    A HNOz molecule is produced at the end of the NO+ (H,O), reaction chain. NO+ is formed during the slowing down of energetic N+ and O+ ions and also by the thermal reaction of N with Oz. Per ioniza- tion, 5 per cent of NO+ is created; so 5 per cent of HNO, is generated in each ionization.

    In the 0: (H,O) formation, two additional steps, which may be important in the ionosphere, have been found by Howard et al. (1972):


    0: .N, + Hz04 0: (H,O) + N,

    But in our calculation conditions, this sequence time is slower than the mechanism time resulting from reaction (15).

    Figures 2 and 3 show the evolution of ions at 760 Torr, for two different water volumic concentrations. With a H,O concentration of lo4 ppm, there are high proportions of 0: (H,O) and 02 (H20)2. The differences between Figs. 1 and 2 show that termolecu- lar reactions are more important at 760 Torr and the ions resulting from these reactions (0: (H,O),, H30+ . H20. OH,. .) are in greater proportions. At 760 Torr and a water concentration of 10% vol (or 49% r.h. at 18C), the ions H30f (H,O),, n = 1, 2,.. .7 are formed in less than 10m3s. The rate con- stants that we have determined are lower than the exact values in the troposphere (reactions 3&35); in- deed these rate constants have been calculated at E/p values of about 1 V cm- Torr-. However, using these low values it was found that the H30+ (H,O), evolution time is less than 10w3s. Moreover larger rate constants would also lead to a time shorter than 10e3s. Therefore after 10e3s (the upper limit in the troposphere), the ionic evolution is caused by the clustering of minor compounds other than water vapor.

    For some important reactions there is a lack of exact numerical values. However we think that the values chosen are not incorrect; and the fact that the experimental results are in agreement with the calcu- lated results, confirms this assumption and the vali- dity of our numerical models.

    Acknowledgements-The help of J. P. Patau, maitre as- sistant and of his research group at the U.P.S., has been extremely appreciated in the development of the computer programs.


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