A microwave afterglow mass spectrometer apparatus is used to determine the dependence on electron temperature T sub e of the recombination coefficients alpha sub n of the dimer and trimer ions of the series CO+.(CO) sub n. It is found that alpha sub 1 = (1.3 + or - 0.3)x 0.000001 (T sub e(K)/300) to the -0.34; and alpha sub 2 = (1.9 + or - 0.4)x 0.000001 (T sub e(K)/300) to the -0.33 cu cm/sec. These dependences on T sub e are quite different from those obtained previously for polar-cluster ions of the hydronium and ammonium series but are similar to that for simple diatomic ions

Biondi, M. A.

Johnsen, R.

Whitaker, M.

English

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Electron-temperature dependence of dissociative recanbination of 
.~ 
electrons with CO • (CO )n -series ions 
Marlin Whitaker, Manfred A. Slomi and Rainer JohnSen 
Department of Physics and Astronany, University of Pittsburgh 
P1ttsburgh, PA 15260 
Abstract 
A microwave-afterglow mass-spectraneter apparatus has been used to 
determine the dependence on electron temperature Te of the recanbination 
+ 
coefficients an of the d1mer and tr:1mer ions of the ser~.es CO • (OO)n' We 
find al = (1.3 ! 0.3) x 10-6 [Te(K)/300J-O.34 and a2 = (1.9 ± 0.4) x 10-6 
[TeCK)/300]-O.33 cm3/sec. '!hese dependences on Te are quite different from 
those obtained previously for polar-cluster ions of the hydronium and anmon1mn 
series but are similar to that for simple diatomic ions. 
(NASA-CR-163572) ELECTRON-TEMPEHATURE N80-33187 
UEPENDENCE OF DISSOCIATIVE RECOMBINAT~ON OF 
ELECTRONS ~rTH CO(+)-(CO)n-SERIES IONS 
(Pittsburgh Univ. , Pa.) 16 p HC A02/11.r A01 Unclas 
CSCL 20H G3/12 28188 
• 
2 
I. Introduction 
'!be capture of electrons by ions of the carbon l\1)noxide series, 
00+ • (CO) n' where n ::: 0, 1 J 2 J ••• is of interest for several reasons. 
'lllese ions nsy be important 111 ionized media where CO or CO2 are arrDng the 
neutral constituents, as in some laser plasmas or in the ionospheres of 
certa:in planetary atll1C1spheres. Thus, determinations of the electron-ion 
recombination coefficients for the appropriate ions provide needed inputs 
to lOOdel calculations of the behavior of these plasmas. r.bre fur¥:1anentally, 
previous studiesl - 3 have shown that recombination coefficients for ions to 
which strongly polar !lX>lecules are clustered exhibit a very different 
variation with electron temperature than that observed for dissociative 
recombination of unclustered l\1)lecular ions 4• 'llle present study e:diends 
the cluster-ion work by eX8udning recombination of ions cl\h~tered with 
weakly polar toolecules, 1. e., the d1mer and. tr:1mer ions, CO + • ro and 
+ CO • (00)2' where the recombination reaction is JOOst probably 
+ - I I I CO • (CO) + e ~ CO • (CO) ... C + 0 + n(CO) 
n n 
. , (1) 
the asterisks indicate that the products !MY be electronically excited. 
II. Me.thad of Measurement and Data Ana;tYsiS 
The microwave-afterglow mass-spectrometer apparatus 1s the same as 
that used previously in a study of the polar-cluster lons3 and has been 
described in some detai15• A microwave discharge lasting typically 0.1 ms 
and repeated at a lO-Hz rate is generated :in 5-20 Torr of neon containw 
an admixture of 8 few tenths percent of carbon rronoxide. '!be "microwave-
averaged" electron density n during the af'terr).ow is obtained from 
!lW 
measurements of the resonant- frequency shift of the high-Q 'lMolO cavity 
rrode1 J while steady elcctl'On heat1ne 1s achieved by application of 
microwave pcwter via a 10\,/-Q ('" 10) 'rElll cavity rrxxie. The time histoPies 
~~·~ .. ·~~.~.~--,~·~~,,,~·._~. __~,~-~_c-~~~r~,-~-~=-,,-,~,~~#~~~_~~,~~ __ ~_--~~~~ __ ~_~~-~~-~~_~ __ ~~_~~_~_~~~ __ -~_--~.~~-~_~=_~_~~.~.~~--~----~--~--~-.~. __ ~_~~-~ .. ~_---~~~~~~~~~~~~~~=~=~~-~,-~$~~~ __ ~_~_~~~_-~~-~--~--~-__ 
of the various afterglow ions are determined by sampling the ions which 
diffuse to the cavity wall and effuse through a small orifice into a 
differentially pumped quadrupole mass filter. 
'Dle principal steps in the formation of the ions of interest are 
thought to be: (a) electron-1 rpac4; excitation of neon to a metastable 
state Nem, (b) Penning ioni ... d.tion of CO molecules via 
Nem + CO + Ne + a/ + e- (2) 
am (c) clustering and breakup reactions, 
a/ + CO + Ne ~ 00+'00 + Ne (3) 
and 
+ - + ( ) CO ·CO + CO + Ne - CO • 00 2 + Ne • (4) 
'!be relative abundance of ions in the afterglow is controlled by varying 
the gas temperature fran '" 250 to 300 K and the partial pressure of CO 
from '" 20 to 100 rriI'orr, thereby affecting the equilibria of reactions 3 
3 
and 4. + (Under the conditions of the present reasurements the CO ion was 
never a significant ion throughout the afterglow, so that its recombination 
coefficient was not determined.) 
Under the conditions obtaining in the present study, that is, the 
ions present in significant concentrations decay together during the 
afterglow, it has been shown3 that the electron continuity equation can be 
written as 
• 
(5) 
where Qeff' the effective r~combination coefficient, is given by 
Q
eff = E Qj f j , in wtlich the fj are the fractional concentrations (essentially 
time-independent) of' each at't(!rglow ion and Da is the amblpolar diffusion 
·1 
.. 
coefficient appropriate to a mixture of positive iOO85, whose separate 
Da values are est1IMted from the Langevtn (polarization) IOObllities 7 of 
ions moving in neon. Usually only two ionic species are present in 
significant concentrations during the afterglow (e.g., the d1nm' and 
trimer ions); therefore Cleff may be written as 
(6) 
with Cll the d1mer and Cl2 the trimer ion recombination coefficient. 
A cClTlputer solution8 ,9 of Eq. (5) with appropriate values of Cleft 
and Da yields the predicted spatial and temporal variation of the electron 
density, from which predicted values of n
l1W 
(t) can be obtained. Since 
the meas~nts of the microwave cavity's resonant frequency shift during 
the afterglow directly yield n
llW 
(t), the value of Cl
err 
may be determined 
from these measurements by obtaining a best fit to the data of conputer-
genel'ated solutions of Eq. (5), using the knO\m values of Da and treat:lng 
Cleff as a parameter. 
III. Results 
+ The reccmbination coefficient for the d1mer ion, CO ·CO, was inferred 
from those data runs in which the d1mer was the only ion of significance, 
representing greater than 90% of the total ion count. Referring to Fig. 1, 
it will be seen that in this exarrple of our measurements the electron 
density decay tracks the CO + • CO wall current decay (the dashed lines ~ 
- + < renormallzed nllW values) and that the CO concentration is - 5% of the d1mer 
ion concentration during the '" 12 msec of the afterglow used. to determine Cl. 
Fig. 2 shows examples of the ~asured electron-density decays for several 
electron temperatures displayed in the "recombination-decay" fonn of 1/ n
llW 
5 
!!. t. '!be solid lines are corrputer solutions of Eq. (5) which provide 
the best fit to the data. ''Dle neasured variation with electron terrp!rature 
for a for the diner ions is shown in Fig. 3. '!be different symbols (circles, 
triangles, squares) indicate separate sequences of runs taken sane days 
apart am suggest that the Te variation f'ran one run to the next is rrm'E: 
reproducible than is the absolute value of 0.(00+ -CO) at a given value of 
Te' '!be + symbols indicate the reproducibility of a values detenn1ned 
fran several runs all at Te = 300 K. 
+ In those runs where the trimer ion, CO '(00)2' was dominant, it 
was necessary in many cases to correct for the presence of s1gnif1cant 
fractions of the dimer ion. An exant>le of the tracking of the electron 
density decay with the decays of the trinm' and. d1rner ions is given in 
Fig. ,.. Electron denslty decays measured at various electron temperatures 
for the case where both trimer (at 84%) and dimer (at 16%) ions were 
present are sho\\'ll in Fig. 5. 'lbe solid lines represent best-fits of the 
computer solutions of Eq. (5) to the data to obtain a
eff vs. Teo When 
the Cl
eff data were corrected via Eq. (6) for the dlrner lon contribution 
using the appropriate values of 0.1 ' the inferred variation of the trimer 
ion recombination coefficknt 0.2 with Te shown in Fig. 6 was obtained. 
Again the different symbols represent different runs. 
If one fits the data of Figs. 3 and 6 to simple power law variations 
of the form a '" Te -x, the results of the studies can be represented by the 
following expressions: 
• 
where the stated uncertainties reflect our estimates of the systematic and 
6 
random errors associated With the detenn1nations. While the data of Fig. 3 
show no systenatic deviation fran the expression given in Eq. (7). the data 
of Fig. 6 suggest that initially a[CO+. (CO)2] may decrease nr::>re slowly with 
increasing Te than the expression of Eq. (8) suggests am then, above 1000 K, 
nr::>re rapidly. .. 
rI. Discussion and Conclusions 
'lhe present studies of recombination of electrons with the carbon 
DDnoxide f'amily of cluster iO!'lS 1ndicate a dependence of the recanbmation 
coefficient on electron tenperature which is quite like that found for 
lmclustered IOOlec.u1Ar ions. '1h1s result" 1s in sharp contrast to the 
virtually electron-tenpera.ture-independent recombination exhibitP.d by the 
clustered ions of the anmmium2 and hydronium3 series. 'Ihus. the d1mer 
+ 
and trimer ions of the CO • (CO)n series exhibit some properties of both 
unclustered and po1ar-cluster roolecular ions; i. e., they have large 
coefficients at Te "" 300 K (sonewhat greater than 10-6 cm3/sp'c), as do 
+ + 
carpara.bly clustered NH4 • (NH4)n and H30 • (~O)n series ions; however, 
the dependence of a on Te approaches that predicted (Te -112) am 
obs",rved ("" T -0.4 to T -0.8) for the direct dissociative process for 
e e 
s1nple diatanic ions". 
'!be substantially larger a values for the d1mer and trimer ions 
compared to that expected 10 for the monomer ion CO + probably result f'ran 
increased likelihood of electron capture via an inelastic energy loss to 
• the canp1ex during the initial Coulomb collision. If the probability of 
such inelastic losses varies slowly with electron ene~gy owing to the many 
closely spaced rotational and vibrational levels in the complex, then the 
Coulomb cross section'e. 1/E energy variation (£ is the electron energy) 
, 
J 
i 
7 
dom:lnates the capture. If, in addition, the stabilization by dissociation 
of the core (refer to reac4;ion (1» is highly probable, one then expects a 
variation or~ a near T
e
-l/2. Although this argument makes plausible the 
+ CO • (CO)n data, it appears that a s1.'TI11ar argument should apply to the 
hydronill1l and anm:mitm1 series ions. '!hus, the observed lack of dependence 
of a on Te in the latter cases2 ,3 is difficult to understan1. 
Farlier studies 11_13 of electron-ion recatbination in CO discharge -
afterglows did rot ~loy mass identification of the recombining ions. 'lhus, 
the attribution of a meast.n'eCl recombination loss rate to a particular 
ionic species is, in our view, rather speculative. <An- mass analysis of 
ions in discharge-afterglows in 00 indicate the presence of a mixture of 
+ + + ions, e.g. 00 , 00 '00 and CnOm, at CO pressures above 0.1 Torr. 
r·1entzoni and Donohue interpreted the lack of a pressure dependence 
< < 
over the range 0.2 - P (00) - 2 Torr in their recombination coefficient 
detenninations12 as evidence that CO was the dominant afterglow ion, 
+ concluding that a[CO ] !I! 4 X 10-7 crn3/sec at Te = 775 K. !n their earlier 
workll they found a constant value, a=:7 X 10-7 cm3/sec, even when the 
electron temperature was decaying to Te = 300 K during the afterglow; 
oowever, in their second paper 12 they use this value for Te -= 300 K and, 
on the basis of these two Te values, infer a T
e
-
O
.6 dependence for a[oo+]. 
While this Te dependence is reasonable, the absolute value appears to be 
about a factor 2 too h1eh 10 , and may result from the presence of d1mer or 
+ triJoor ions along with the CO rwnomer. • 
Centerl3 studied electron loss by recombination in high pressure 
afterglows (100 oS p(oo) s 700 Torr) where cluster ions w:~re almost certainly 
present (as he noted). His values of "a" for the unknown ionic mixture 
are comparable to our values for the dimer or trimer ions at Te ~ 1000 K 
but decrease rruch rrore rapidly with increasing Te t differing from our results 
'''''',#-l~~r~pR;.m?_-,-. jkktS _;-,,¥-441L .. ~_ .,<,.-,,!., .. 
, 
I 
\ 
I 
r , 
I , 
8 
by a factor'" 3 at Te '" 5000 K. In our view, this d1scretWlcy points out 
the difficulty of making quantitative deterrn1nations of recombination 
coefficients for specified ions in mlecular gases in the absence of ionic 
mass identification. 
~knowlecJeme.nt: 'lhls research was supported, in part, by the NASA 
Planetary Atnx>spheres Program under Grant No. NGL-39-011-l37 and the 
U. S. Arn\v Research Off1celONA under Grant DAAG-29-8o-c-0075. 
- - -=--~~ =-~=-- -~r « r- n • 
• 
·-:::-'-.,..,....-:: --'-,--~_-_:~:';7'=:;;;;-=~-·~tt~'''-¥'''~·:-:·=-~~,;: - ~.=5"l'_-_-,~~.:)i'F~.:'$?~_~ . ..:: -~---·-·i~i-}-~3± .... ·-A,# ..... _,@=-:¥ .....rw~ __ ,...1 _"""= ~~~""" .. ~~-o~?~-,>~.~~~_:::e-=-3""""-.-:' 
! 
9 
References 
1. M. T. lat, M. A. Biondi, ard R. Johnsen, Phys. Rev. A 1, 292 (1973). 
2. C. M. Huang, M. A. Biondl, am R. Johnsen, Phys. Rev. A!!t. 984 (1976). 
3. C. M. Huang, M. Whltaker, M. A. Biondl, ~!Xl R. Johnsen, Phys. Rev. A 
J&, 64 (1978). 
4. J. N. Bardsley and M. A. Biondi, in Advances in Atanie am ftblecular 
!'!Vsles, edited by D. R. Bates (Academie, New York, 1970), Vol. 6. 
5. F. J. Mehr and M. A. Biondi, Phys. Rev. 181, 264 (1969). 
6. A. V. Phelps and ~. C. Brown, Phys. Rev. ~, 102 (1952). 
7. P. langevin, Ann. Chim. Phys. 5, 245 (1905). 
8. L. Framlho1d am M. A. B1a1d1, Ann. Phys. ~ 407 (1968). 
9. L. F'ronrnl'x:>ld, M. A. Blondi, and F. J. Mehr, Phys. Rev. 165, 44 (1968). 
10. M. A. B1on:l1, Conrnents on M:x1. Phys. ~ 85 (1973). 
li. M. H. Mentzoni and J. Ibnohoe, Phys. lett. 26A 330 (1968). 
12. M. H. Mentzoni and J. Donohoe, Can. J. Phys. ~ 1789 (1969). 
13. R. E. Center, J. Appl. Phys. ~, 3538 (1973). 
• 
t 
I 
Figure captions 
Fig. 1 r.Q11)8r8.t1ve decays of volume elec~~ dens1ty i\.w ard ion wall 
currents during the aftEtrglow. '!be dashed l1nes represent 
renonnal1zed values of I\.W. 
Fig. 2 1/ nllw !!. time "recanb:1nat1on decay" plots tor various electra'l 
Fig. 3 
Fig. 4 
Fig. 5 
Fig. 6 
t~tures under the same con:litions as Fig. 1. '!be solid lines 
represent best-fit c~er solutions of Eq. (5) to the data. 
'!he zero times for the d1f'ferent Te runs are displaced tor clarity. 
Variat10n with electron teJ11'erature of the d1mer 10n recall-
b1nation c~fficient with T+ • Tn III 300 K. Each type of symbol 
1nd1cates a run taken with a given gas ruling on a given day. 
'!be dashed line represents a T
e
-
O
.34 power law depeBience for Qr 
Cooparative decays of nl1W and ion wall currents in an afterglow 
in which trimer and d1mer ions are the principal posit1ve ions. 
11 n vs tiIoo curves for the same condit1ons as Fig. 4. The 
lJW -
solid lines are best-fit caqmter solutions of Eq.(5) to the data. 
'!he zero t1.'1leS of f'uccessive runs are displaced for clarity. 
Variation of the trimer 10n recombination coefficient with 
Te for T+ • Tn • 250 K. While the dashed line represents a 
power-law variation of the form (12 '\0 Te-O• 33. the dotted 11ne 
may better represent the actual variation. 
• 
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en 
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c 
o 
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)( 
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o 
T = T = T. = 300 K e + n 
)( 
Peo = 25mTorr 
PNe = ISTorr )( )( 
x 
- )/ n,.,.w.( rei. )( x x x 
• 
........... . . 
""6 ..... ../J. ..... 6 I 6 
--
---
• 
o o 
10 O~~~~~~~~~~~~~~~ 
5 10 15 20 
afterg low time (m 5 ) 
Fig. 1 
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E 
u 
en 
10 
-
~ 
:s.. 
Ie 
" -
15 
10 
5 
T+= Tn= 300K 
Pee = 25mTorr 
p. = 15 Torr Ne 
o 5 10 
x 
afterglow !ime (ms) 
Fig. 2 
-- -=' --~~~- -----~ -~--' -~- -- ~--
• 
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0 
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Te = 2520K 
! 
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f, = 0.16, f2 = 0.84 
10 ' 68+,....0 0 0 0 
A A 
A 0 oA A A 
AA 0 0 00 
0 AA 0 o 0 
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1 0 5 10 
afterglow time (ms) 
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+ CO • (CO)n 
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afterglow time (ms) 
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Electron-temperature dependence of dissociative recombination of electrons with CO(+)-(CO)n-series ions

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