Ionic mobility of the middle atmosphere

Sac~ .~es.Vol.4, No.6, pp.29—32, 1984 Printed in Great Britain. All rights reserved.

0273—1177/84 $0.00 + .50 Copyright © COSPAR

IONIC MOBILITY OF THE MIDDLE ATMOSPHERE William Swider Air Force Geophysics Laboratory, Hanscom Air Force Base, MA 01731, U.S.A.

ABSTRACT Positive ion mobilities are calculated for 40—75 km by computing the theoretical positive ion composition and combining it with laboratory—determined mobilities. Theoretical determinations for mobility appear to be especially apt for the 40—65 km region since oxonium ions are observed to be the principal positive ions and they should be subject to thermo2/V—s for 40—65 dynamic compute Atmosphere a mean reduced of 2.1 + 0.1 cm of 5 ppmv. The km using equilibrium. the 1976 U.S. WeStandard and a mobility water vapor mixing ratio results are compared with atmospheric data for mobility. Observations of a lower mobility from about 35 km down to ground level are qualitatively compatible with the onset of the so—called non—proton hydrate ions at about this altitude and extending to lower heights. We note that the laboratory determined mobilities for oxonium ions average about 12 % less than the theoretical Langevin values. The total positive ion conductivity is determined also and compared with in—situ results. INTRODUCTION Measurements of positive and negative ion mobility in the upper atmosphere are difficult to make and are few in number. Meyerott et al. /1/ stress three major problems in measuring mobilities: a) the break—up of heavy ions into lighter ions (larger mobilities) during the sampling process due to the electric field of the measuring device, b) for rocket—borne instruments, a similar breakup due to the shock created by the rockets, and c) contamination of the observational data by vehicle outgassing which effect generally leads to heavier ions and hence lower mobilities. Presumably, shock effects inhibit contamination. For rockets, contamination is most likely in a wake configuration. Contamination can be especially troublesome for balloon—borne instruments. Another problem for such instruments, perhaps the major problem, is the accuracy of the intake flow of air /2/. In this paper we compare theoretical calculations of positive mobility with data on positive mobility and mass—spectra. In addition, positive ion conductivity measurements will be compared with our calculations. Negative ion mobility and conductivity will not be considered since the negative ion chemistry of the middle atmosphere is still uncertain. POSITIVE ION DISTRIBUTIONS Kebarle et al. /3/ obtained the data necessary for the computation of the relative distribution of oxonium ions based on the temperature and the partial pressure of water. Mohnen /4/ calculated the equilibrium distribution of oxonium ions, H~0+*(HpO)n...l H~(H~O)~.~ for the altitude region 0—50 km. Reid /5/ has made calculations from 10 to ~O km based on a reaction rate model. (It is now known, as we’ll discuss shortly, that ions other than oxonium dominate below 35 km.) Our calculation of the equilibrium positive ion distribution over the region 40 to 75 km is shown in Figure 1. The 1976 U.S. Standard Atmosphere temperature profile and total concentration profile were used. A water mixing ratio of 5 ppmv was assumed. The dominant positive ions over the altitude span 40 to 70 km are H 7O3+ (55 amu mass) and HQ04+ (73 amu). The mean mass, therefore, varies between these limits and has a value of o~about 64 ±8 amu (Figure 22. However, CO2 may be involved in oxonium ion chemistry /6/ by forming ions like H5O2 .C02, which react with H2O to produce H7O~ ions. Since carbon dioxide is much more a’bundant than water, this mechanism assists tFie formation of oxonium ions and basically shifts the distribution toward somewhat heavier ions. Thus, our value of 64 ±8 amu may need to be revised upward.

29

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~:

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20

30

40

50

60

H703

70

80

POSITIVE ION PERCENTAGES

~

90

.

40

50

I

60

70

80

90

MEAN POSITIVE ION MASS (amu)

Fig. 1. (Left) Altitude plot of the relative oxonium ion abundance as derived from thermodynamic equilibrium data /3/ assuming a 5 ppmv mixing ratio for water. The temperatures and total neutral concentrations were taken from the 1976 U.S. Standard Atmosphere. Fig. 2.

(Right) Mean mass of oxonium ions vs altitude.

MOBILITY VALUES The mobility of ions Is related to other parameters through a complex relationship derived by various workers, especially Langevin, early this century. This relationship breaks down, in the extreme limits, into two cases: (1) the elastic sphere limit, where polarization effects are negligible as compared with those of elastic sphere scattering, and (2) the small ion limit, where polarization forces predominate. The latter case is believed to be most appropriate for atmospheric ions at the altitudes condidered here. The simplest theoretical form for this case is /7/ 0~5 cm2/V—s (1) 359/(aM.~) where the polarizibility of the gas, a, Is measured in units of the radius of the first Bohr orbit (11.5 for air) and Mr, the reduced mass, Is measured in units of proton mass. La~oratory data (not shown in this abbreviated version of this paper) average about 2.7 cm /V—s for the hydronium Ion, H 30+, and about 2.4, 2.2, 2.1 and 2.0 /8,9,10/ for the successively heavier (hydrated) oxonium ions. We note that the laboratory data best fit formula (1) if the rhs of the equation is multiplied by 2! 0.88. V—s (Figure The mean 3) positive since equilibrium mobility calculations oxonium ions at kin yield H for 40 to 65 for km is calculated to 40—75 be about 2.1 +principally 0.1 cm 7O~and H9O4+ ions (Figure 1). according to mobility Meyerott et al. /1/, too small to our calculations. The2/V—s reduced in—situ measured by is Conley /11/ compared and l4iddel et al. /12/, about This 2.7 result implies a predominance of H cm 30+ Ions, an unlikely probability in our judgement. Three—body processes are important below 90 km in the atmosphere and these processes virtually guarantee that the predominant Ions below 90 km are heavier than the principal neutral species, N2(28 amu) and 02 (32 amu). 2/V—s. If CO2 plays an important role in forming oxonium ions as noted in the previous section, the mean Near 65 km mobility and especially of the oxonium with increasing Ions at 40—75 heightkmabove may be this somewhat altitude, higher the than presence 2.1 of cm electrons makes the thermodynamic relationship used here for the oxonium ions Inappropriate. Below 40 km, other positive ions are observed. At 35 kin, these ions constitute about 50% of the total positive Ion population as measured by Arijs et al. /13/ and Arnold and Henschen /14/. Basically, it appears that one or two acetonitrile, CH 3CN, molecules substitute for an equal number of water molecules in the oxonium ion structure below 40 km. The data yield a mean mass of about 92 ±6 amu near 35 km. This observed transition to higher masses at lower altitudes 2/V—s appears forto5—30 be qualitatively km /15/. However, compatible an ion with mass the of deduction 92 ±6 amu 35 kmmobility corresponds to cm a positive Ion mobility nearer to 2.0 ±0.1 amu. A mobilof anear reduced of 1.5 ity of 1.5 cm2fv—s suggests a positive ion mass of several hundred amu. An actual measurement of the mobilIties of oxonium—acetonitrile ions Is needed.

Ionic Mobility

31

POSITIVE ION CONDUCTIVITIES The positive conductivity, &~, Is given by the expression (2) where e is the electronic charge and n+ is the positive particle concentration. Electrons are sufficiently few in number below 65 km, (and fall off rapidly below this height) so that (3) where q is the ion—pair production rate due to galactic cosmic rays and ai is the ion— 3s1 is iO~7 n, where n is ion A nominal value for the q In1976 cm U.S. Standard Atmosphere for the recombination total neutral coefficient. gas concentration in cm3. Using n and the variation of ai given by tude above sea level,

Smith and Adams /16/,

ai (cin3s~)— 1.63 x 10

where z represents the alti-

exp (—z/7.38) + 5.25 x i08

(4)

we calculate positive ion concentrations of 2.6 x iü~ (40 km), 1.7 x ~ (50 km) and 1.1 x ~ cm3 (60 km). These values may be compared with the calculations (heavy curve In Figure 4) based upon a detailed chemical model /17/ which gave 3.75 x ~ 1.90 x 1O3 and 3.87 x 102 cm3 for the same altitudes, respectively. Agreement Is best at 50 km since the three—body portion of the ion—ion recombination coefficient was not included before /17/, allowing n+ to be higher at 40 km than in the present, simpler, calculation, which, however, is probably more accurate at this altitude. The lower positive ion concentration at 60 km /17/ results from the presence of some electrons in the model. Electrons combine with oxonium ions with a rate coefficient about 50 times greater than that for binary ion— ion recombination. In Figure 4, the total positive ion concentration model of Swider /17/ and the conductivity computed from that profile, is compared with the measurements of Bourdeau et al. /18/, Widdel et al. /19, 20/, Hale /21/ and Burt et al. /22/. The theory agrees best with the results of Hale /21/ and Burt et al. /22/, although agreement is poor above 60 km, possibly because the calculations may yield excess electrons. The presence of any “heavy ions” at 60—65 km /19, 20/ seems contrary to other evidence and theoretical expectations. Basically, simple theories appear to give ion concentrations and conductivities which agree fairly well with observations. On the other hand, we cannot categorically exclude the possibility that very heavy positive (negative) ions may exist in the atmosphere which, because of their size, have a passive role. There is no mass—spectrometric evidence to date that positive ions other than oxonium ions dominate the 40—65 km region.

TOTAL ION CONCENTRATION (c”~’) lO~

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I 2.3

I 2.4

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Fig. 3. (Left) The mean reduced mobility of positive ions from 40 uncertainty increases with height above 65 km and exceeds that shown.

to

75

km.

The

Fig. 4. (Right) Experimental total positive ion conductivities and total positive ion profile (one case) versus altitude. The theoretical ion profile is from Swider /17/. The theoretical conductivity Is based on this Ion profile.

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32

W. Swjder

CONCLUS IONS For 40 to 65 kin,

we find (like others) the dominant positive ions to be H 7O~and H9O~ with a mean mass of 64 + 8 amu. This appears to be consistent with mass—spectrometric 2/V—s Coupled is derived this altitude span. Measurements of reduced 1.5 cm2/mobility V—s fromof5 2.1 to 30 km data. with for laboratory mobility measurements, a mean ±0.1 cm /15/ may be compatible with a changeover from oxonlum ions above 40 km to oxonium—acetoni— trlle ions below 35 km as the measured mean positive ion mass at 35 km is about 92 ±6 amu. Laboratory measurements of the mobilities of these ions are needed. Fair comparisons between theory and experiment are obtained for positive ion conductivities. Differences may point up discrepancies in the model, such as excess electrons near 65—70 km. We note that laboratory—determined oxonium ion inobilities appear to have values that on the average lie 12 7, below the classical Langevin results for small Ions. ACKNOWLEDGEMENT

We thank P.M. Bench for programming support. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

R.E. Meyerott, J.B. Reagan, and R.G. Joiner, J. Geophys. Res. 85, 1273 (1980). J.M. Rosen and D.J. Hofmann, J. Geophys. Res. 86, 7399 (1981). P. Kebarle, S.K. Searles, A. Zolla, J. Scarborough, and M. Arshadi, J. Amer Chein. Soc. 89, 6393 (1967). V.A. Mohnen, Pure Appl. Geophys. 84, 141 (1971). G.C. Reid, in Middle Atmosphere Electrodynamics, ed. N.C. Maynard, NASA, CP—2000 1979, p.27. W. Swider and R.S. Narcisi, J. Geophys. Res. 80, 655 (1975). E.W. McDaniel, Collision Phenomena in Ionized Gases, J. Wiley, N.Y., 1964. I. Dotan, D.L. Aibritton, W. Lindinger, and M. Pahl, J. Chem. Phys. 65, 5028 (1976). C.E. Young and W.E. Falconer, J. Chem. Phys. 57, 918 (1972). M.L. Huertas, A.M. Marty, and J. Fontan, J. Geophys. Res. 79, 1737 (1974). T.D. Conley, Radio Sci. 9, 575 (1974). H.U. Widdel, G. Rose, and R. Borchers, J. Geophys. 44, 179 (1977). E. Arijs, 0. Nevejans, and J. Ingels, J. Atmos. Terr. Phys. 44, 43 (1982). F. Arnold and G. Henschen, Planet. Space Sci. 30, 101, (1982). J.M. Rosen, D.J. Hofmann, W. Gringel, J. Berlinski, S. Michnowski, Y. Morita, T. Ogawa, and 0. Olson, J. Geophys. Res. 87, 1219 (1982). D. Smith and N.G. Adams, Geophys. Res. Lett. 9, 1085 (1982). W. Swider, Adv. Space Res. 2, 213 (1983). R.E. Bourdeau, E.C. Whipple, Jr., and J.F. Clark, J. Geophys. Res. 64, 1363 (1959). H.IJ. Widdel, G. Rose, and R. Borchers, Pure Appl. Geophys. 84, 154 (1971). H.U. Widdel, G. Rose, and R. Borchers, J. Geophys. Res. 81, 6217 (1976). L.C. Hale, in Methods of Measurements and Lower Ionospheric Structure, ed. K. Rawer, Academie—Verlag, Berlin, 1974, p.219. D.A. Burt, E.F. Pound, and G.D. Allred, Utah State Univ., DNA 5O39F (1979).