Mobilities of thermal cations in oxygen gas: Temperature dependence

Rndiat. Phys. Chem. Vol. 32, No. I, pp. 59--63, 1988 Int. J. Radlat. Appl. Instrum. Part C Printed in Great Britain. All rights reserved

0146-5724/88 $3.00 + 0.00 Copyright © 1988 Pergamon Joumah Ltd

MOBILITIES OF THERMAL CATIONS IN O X Y G E N GAS: TEMPERATURE DEPENDENCE'[" NORMAN GEE and GORDON R. FREEMAN Chemistry Department, University of Alberta, Edmonton, Alberta, Canada TOG 2G2 (Received 21 April 1987)

AImlract--Cation mobilities, /z, in oxygen were measured at fields E/n < 4Td, 103 ~< T / K ~<594 and 2.53 ~ 300 K, n/~ increased with increasing T, and at > 350 K became larger than n# for O~ in 02 reported in the literature. The energy dependence of the momentum transfer cross section 0= was estimated both for 04+ and O~" in O 2. At ~ < 0.01 eV both a m sets were merged into the polarization cross section op~ for 0 2. At ~ > 0.1 eV, om(Of-O2)> O'm(O4+~)2).

I. INTRODUCTION The density-normalized mobilities of thermal cations 02+ and O~" in oxygen gas have been reported. °-5) At 126 K the mobility for 02+ in O2 was 25% larger than that o f O2-. °) As the temperature was increased the mobility of 02+ decreased c5) while that o f O~ was nearly constant, (('S~ and at 300 K the mobility of 02+ was only 6% larger than that o f O~. On further increasing T towards 600 K the mobility of O~" continued to decrease. °'S~ Data for 02" at T > 300 K seem to be lacking, In this work we re-investigated the mobility of O~" in O2 at low temperature and then extended the temperature range up to 594 K. Our mobility values were used to estimate the energy dependence of the cation-molecule m o m e n t u m transfer cross section o=. W e also estimated the 0 ~ - 0 2 O'm values from the published mobility data for 02+ in O r " 5) 2. EXPraIMENTAL (a ) Sample preparation

The oxygen was Matheson Research grade ( > 9 9 . 9 9 % ) with possible impurity of ~ I ppm nitrogen and 5 ppm hydrogen. (° The cylinder was fitted to a Linde oxygen regulator which was welded to a 32 crn length of flexible stainless steel. The steel was in turn welded to a K o v a r - P y r e x seal and connected through similar seals to a H o k e Inc. (model 4251N6Y) valve then to a Pyrex side line o f a greasefree vacuum system. The conductance celF ~) was connected by its 3 mm i.d. Pyrex capillary to 8 cm piece of 7 mm i.d. Pyrex joined in turn by a P y r e x - K o v a r seal to a second H o k e valve leading into the same side line as the oxygen cylinder. The volume of the cell to the midpoint of the 3 m m Pyrex capillary was measured t This paper is dedicated to the memory of Milton Burton.

to +0.1 crn 3 as the volume o f water from a calibrated syringe required to fill the cell to that point. A typical volume was 45 cm 3. The syringe had been calibrated to _+0.3% by weighing ejected water volumes on a Stanton Instruments (model C.L.I) analytical balance. Similarly the volume of the remaining capillary plus the 8 crn length of Pyrex and the valve tube on that side of the plug had been calibrated before the section and valve were attached to the vacuum line; a typical volume was 5 cm 3. A mercury manometer composed o f an 80 em length of 3 m m i.d. capillary joined to a reservoir was connected through a third H o k e valve to the same vacuum system sideline as the cell. This manometer was used to measure the gas pressure introduced into the sideline when the sideline was isolated from the rest of the high vacuum system. The height of the mercury column could be read to 0.01 cm but might only be reliable to 0.1 cm due to surface tension effects of the capillary. At the average pressure used to fill a sample, 0.1 cm corresponds to a possible 0.6% error. A fourth H o k e valve connected the entire side line to the main vacuum system. Before filling the cell, it was heated to > 600 K for at least 6 days, including > 620 K for 2 days, while pumping to < 10-( Pa (valves to manometer and gas cylinder closed). The cell was then cooled to r o o m temperature (usually 295 K) while still pumping and with the valves to manometer and cylinder opened. The section to the cylinder was pumped out up to the final stopcock of the pressure regulator. The stopcock was closed but the regulator itself was opened to the cylinder pressure (4.8 MPa). The sideline was then isolated, the regulator stopcock opened to let ,,, 15 kPa of oxygen into the sideline, cell and manometer section, and the stopcock re-closed. After 10 min the sideline, cell and manometer section were re-evacuated, re-isolated and filled with a second 15.kPa portion of oxygen for another 10min. The 59

NORMAN GEE and GOP.DONR. FREEMAN

60

sideline section was re-evacuated, re-isolated and the desired pressure of oxygen introduced into the section, and the valve connecting the cylinder to the sideline was closed. After 5 rain the valve connecting the cell to the sideline was also closed. The cell was quickly ( < 4 5 s ) sealed off at the midpoint of the Pyrex capillary using a small, hot flame (total flame length ~ 5 cm, hottest portion ~ I cm). To check for heating effects on the gas density in the cell during sealing, for one filling (6.08 x 10u molecule/m3) the cell was surrounded with a water bath at room temperature. The mobility normalized for density agreed to 0.3% with that obtained at 6.04 x 1024 molecule/m3, sealed without the water bath. All other samples in this work were prepared without the water bath. The temperature of the cell during filling, and of the section up to the Hoke valve joining the side line, was taken to be that measured on the cell body by a copper--Constantan thermocouple in combination with an Omega Engineering digital thermometer. This device gave the temperature to + 0 . 5 K , as verified against a Fluke 2189A platinum resistance thermometry system, which is accurate to 0.01 K at 273.15 K [checked by ice-water(S')], 0.07 K at 76.80 K (liquid nitrogen at 94.9 kPa) and hence likely to <0.03 K at 295 + 2 K. (gb) The 0.5 K uncertainty in the Omega digital thermometer reading at the typical filling temperature of 295 K would add a possible error of 0.2*/0 to the filling density. As the filling pressure might have an e[ror of 0.6% (s¢¢ above) the density by our filling method has a possible error of 0.8%. At all filling conditions of this work the oxgyen gas density could be calculated using the ideal gas equation. This was confirmed by checks against the Van der Waals equation. (9)The same filling procedure was used in our earlier work with argon and xenon gas"°~ but was not described,

(b ) Cation production Oxygen in the conductance cell was ionized with 100 ns pulses of X rays from a Van de Graaf acceler-

ator, producing ~ 106 ion-electron pairs per cm;. The transient conductance signal consisted of a fast electron component followed by the slower ion component: ") The drift distance was 10.58 ram. Cations were not mass identified in this work but at the densities used, 2.53 ~
[O~ (%)= + ,] K,~ = [O~ (O:)=1 lOs]

where the square brackets in equation (2) indicate concentrations. For m = 0 at 295K, K ~ = (1.8 + 0.7) x 10 -23 m3/moleculd4"12)so that [O~ ]/[O~] varied from 46 at n = 2.53 x 10u molecule/m~ to 143 at n = 7.94 x l024. At lower T and higher n, further clustering (m I> i) might occur. (4:2)

(c ) Other methods Temperature control and measurement, the voltage source and signal amplifier, and the time of flight method for obtaining th~mt~oitity ~t in ReL (11). The experimental current against time signals were like that in Fig. I of Ref. (1 !). Four copper-Constantan thtrmocouples were used to monitor the temperature at the top, two sides at the level of the plates, and bottom of the ceil; they had been calibrated in combination with a Fluke 2100A digital thermometer at 77 ~< T/K <~371 against the Fluke 2189A thermometry system. As noted in Section (a), the uncertainty of the 2189A system was < 0.07 K at 77-273 K, and that at 273-469 K would be about the same. (sb) Hence over the calibration range our temperature uncertainty is that set by the spread in the four thermocouple readings, so ATe< + 0 . 3 K . In the uncalibrated range at T > 371 K the spread in thermocouple readings increased with increasing temperature. The largest -

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T (K) Fig. I. Plot of density-normalized mobility of 02" in 02 against temperature. Present work unless otherwise indicated. The symbols arc (n/10~ moloculc.m-3): Q, 2.53; O, 3.16; @, 4.05; A, 6.04; V, 6.08; I'q, 7.94; /X, 0,026-0.86;(4~ V, ~0.05; ~s~ <), 0.1-0.2;(I) ~, not specified:2) The • is (5.66:t:0.08) x1021 moltcules]m.V' s at 295 + 1 K. The solid and dotted lines were calculated from equation (4) using the corresponding a m curves from Fig. 3. The error bars indicate + 2%. The - - - indicates the decrease towards the n# at 144 K because of clustering.

THERMAL

CATIONS IN OXYGEN

spread was A T = -+0.8 K at 594 K. The temperatures in our earlier works had all been measured using calibrated thermocouples, but in two studies t7'~3~A T for uncalibrated thermocouples were cited by error.

7.0 2.5 _~

6.5

AND

DISCUSSION

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0

o

% v-

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61

GAS

3 o o

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each temperature more than I0 current-time

signals were recorded at voltage V over a 5-10-fold range. The time of flight td was obtained from each record tin' and the mobility /~ = (12/td " V) was calculated. Half of the signals were measured using positive and half with negative applied voltage. The fields used, normalized for density, were E/n < 4 T d (Td=lO-2~V.m:/molecule) where the mobilities were field independent within a mean deviation of _+2%. The cations were therefore essentially in thermal equilibrium with the gas molecules.

-~ 2.0

200

4OO

T or Te. (K)

Fig. 2. Plot of ,~u of 02+ in O z against 7", except ~ which is against Tdr. Measurements were at ,/lO 22 molecule-m -~ of: A, 0.084-2.0; I" ~7, ~ 0. I;a~ ~), 47-74;t3~I-l, 0.032-0.86; ~4~ C), 0.65-3.9. °~ The solid line was calculated by equation (4) using a m from Fig. 3.

such an extent that it decreased from the O~ n/~ curve defined by the Ref. (4) and (5) results. Values of K~q with m = 1 only extend down to 133 K. c~z'~ Extrapolation of the van't Hoff plot to (a) Mobility 103 K lead to an estimated [O~ ]/[O~" ] > 105, or com(i) At room temperature. At low gas densities plete O [ formation, although our value is in agreewhere three-body interactions are not important the ment with the mass identified O~ values of Ref. (5). mobility is inversely proportional to n the n u m b e r The Ref. (5) n/~ values should be considered as density of the neutral gas molecules, t|~') Hence we anchoring the low T range of the O~ n/~ values, as our present our results as the density normalized mobility value at 103 K might be affected by O~" formation. n~. Often cation mobility results are reported as At > 3 0 0 K the n/~ curve increased continuously K0 (cm2/V's) which is the mobility adjusted to the with T. The behaviour of n/~ for O f in 02 is different: density at STP, 2.69 x 10~s molecule/m ~. The two , p decreased as T increased (Fig. 2). The O~" curve forms are related by n/~ ( m o l e c u l e / m . V . s ) = increased above the Oz+ curve at near 350 K. This 2.69 x 10~ K0 (cm2/V.s). We obtained six mobilities difference at T > 350 K indicates that declustering of at 2.53 ~< n/202~ molecule.m -~ ~< 7.94 and at 295 _+ O~ did not occur in our measurements. 1 K which, normalized for density and averaged, gave For O~ in O2~3~ results obtained at low E/n as a ,/~ = (5.66_+ 0.08) x 10~ molecule/m.V.s. This is function of T > 532 K agreed with those obtained at in good agreement with previous experiments at 300 K as a function of high E/n when compared using similar temperatures: (5.81 _+ 0.22) x 1021 at 300 K, ~'~ Tcfr given by the Wannier relation, ~2~ (5.60 _+ 0.22) x l0 ~ at 300 K, t2) and (5.58 _+ 0.04) x Te~ = T + Mv~ (l + fl)/3k a (3) l02~ at 294 K. ~ The Ref. (l) value was obtained with direct mass identification of 04+ . where M is the molecular mass of the gas, ka is (ii) Temperature dependence. The effect of tem- Boltzmann's constant, vd = n/~ x E/n is the ion drift perature on np for O + in 02 is shown in Fig. I. At velocity, and fl is a correction often set to zero. t2~This IO0<~ T/K ~< 300 the temperature dependence was can be seen in Fig. 2 by comparing Ref. (2) (,/~ small, in agreement with earlier work. At t00 K n/~ against T~) and Ref. 3 (n/~ against T). The agreement was still smaller than that of the polarization limit, t~4~ is surprising because collisions of the molecular 02+ which would be 6 . 4 x 1021 molecule/m.V.s [see with O2 should be inelastic and exert a cooling effect Section 3(b)], calculated using the polarizability from on the cation heating by the field, even discounting Ref. (I 4c). the thermalizing effect of charge transfer, t4~Hence the At T < 200 K the ,/~ values might be affected by energy gained from the field by the cation at high E/n further clustering of the O~ cation. (*'m2)From K~q with should be less than indicated by equation (3). tlS,16)As m=l, measured at 134-196K, t~) [O~]/[O~+]= a result, for O~ in O2 where dnp/dT < 0 it might have (1.7 _+ 0.2) at 184 K and 4.05 x l0 :~ molecule/m 3 and been expected that n/~ obtained at low E/n and at 191 K and 6.08 x 102. molecule/m 3. If the values of varying T would have been lower than n/~ at T~ K~ are correct our values of n# cannot be assigned obtained at high E/n. to purely O~+, although they agree with the Ref. (4) (b ) Momentum transfer cross section value for O~ at 194K. With K,q ( r e = l ) = 2.0 x l0 -2s ma/molecule at 194 K, t~u) at the density of The energy dependence of the cation-molecule Ref. (4), 2.1 <~n/lOu molecule.m-~-..< 17, they had m o m e n t u m transfer cross section o m is related to the 0.004 ~< [O~ ]/[O~ ] ~<0.03. Our np values also agree temperature dependence of n/~.~2'1'~ Values of o m for with the mass identified O~ results of Ref. 5. At 04+-02 were estimated as a function of the collision 144 K the np value seemed affected by clustering to energy ~ by fitting the experimental (n/~, T) values in R.PC 32;I- -E

62

Norman Gee AND Gordon R. Freeman I

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(eV) Fig. 3. Momentum transfer cross section against relative collision energy for 0+-02 ( . - and .. -) and 02+--02 ( . . . . ), obtained by fitting the results of Figs I and 2 to equation (4). - - - , a ~ using~, equation (6), I e V ~ 1.60 x 10-19 J.

Fig. 1 to equation (4). (2.'~) 3e

n# =--8 (keT)

5/2 /' 27t'~112/ ["~ 2

k-~J/Jo ~ a m e x p ( - - ~ ) & ( 4 )

where e is the charge on the ion and Mr is the ion-molecule reduced mass. The cross section was arbitrarily anchored to that expected from the polarization potential (17) at very low energies, ~ < ! x 10 -2' J (6 meV); in SI units it is

(2.2, e} \M,} (aT2

a~, = \ ~

(5)

(Fig. i). The structure at ¢ ~ 0 . 1 eV in the dotted curve and the low value o f ¢ = at ~ ;~ 0.2 eV in the full curve each offer a problem in interpretation, which remains to be resolved. Values o f a , (O~-O2) were obtained by fitting the (n/~, T) data of Fig. 2 to equation (4). The value o f nl~,ol for O~ in 02 is 7.4 x 1021 molecule/m-V.s, which is greater than the observed values. Thus :> apoI at T >/100 K, but we arbitrarily anchored a= to ~r~ at very low energies (Fig. 3). As in nitrogen ('9) the m o m e n t u m transfer cross section for the m o n o m e r ion is greater than that for the dimer ion, because o f resonance charge transfer.~t~)

where ~. is the permittivity of vacuum, v = (2~/M,) ~/2 is the relative collision velocity, and a is the polarizability of O2, Substitution of equation (5) into equation (4) gives the polarization limit ngpo, Acknowledgement--We thank the staff of the Radiation Research Center for maintaining the equipment. (molecule/m. V. s) as n/z~j = 1.60 x 10-H/(~M,) v2

(6)

where M, is in kg/molecule. Using the mean polarizability ~ = 1.78 x 10 -4o C-m2/V (equivalent to 1.60x 10-3°m 3 in non-SI units TM) one obtains n / ~ = 6.4 x 1021 m o l e c u l e / m . V . s for O~" in 02. The observed value of n/~ was lower than this at T < 4 1 5 K (Fig. 1), so > at these temperatures. At T > 415 K the reverse is true. Cross sections represented by the full line in Fig. 3 give n/~ values represented by the full line in Fig. I. However, these values of a~ (O~-O2) at ~ > 0.16 eV are lower than the Lennard-Jones cross section for neutral oxygen molecules a u ( 0 2 - 0 2 ) = 3.8 x 10-19m2. (ls~ At ~ > 0.25 eV the full curve shows am ( O ~ - O 2 ) ~ 0 . 3 a u (O2-O2), which seems too small (Fig. 3). An attempt to fit the experimental n# values with am ~ a u at ~ > 0.25 eV gave the somewhat structured dotted curve in Fig. 3. The corresponding n/~ curve does not fit the experimental values quite so well

REFERENCES

I. R. M. Snuggs, D. J. VOIz, J. H. Schummers, D. W. Martin and E. W. McDaniel, Phys. Rev. A. 1971, 3, 477. 2. H. W. Ellis, R. Y. Pai, E. W. McDaniel, E. A. Mason and L. A. Viehland, At. Data Nucl. Data Tables 1976, 17, 177. 3. M. D. Perkins, F. L. Eisele and E. W. McDaniel, J. Chem. Phys. 1981, 74, 4206. 4. H. B. Milloy, Aust. J. Phys. 1975, 28, 307. 5. H. B6hringer and F. Arnold, Int. J. Mass Spectrom. ion Phys. 1983, 49, 61. 6. Catalogue 86, p. 54. Matheson Gas Products Canada, Whitby, Ont. 1986. 7. M. A. l=loriano, N. Gee and G. R. Freeman, J. Chem. Phys. 1986, 841, 6799. 8. 2189,4 Thermometry System Instruction Manual, (a) p. 6-8, (b) p. 1. John Fluke Manufacturing Company Inc., Mountlake Terrace, WA, 1981. 9. Handbook o f Chemistry and Physics (Edited by R. C. Weast) 64 edn, p. D-191. CRC Press, Inc,, Boca Raton, Fla. 10. N. Gee and G. R. Freeman, Can. J. Chem. 1986, 64, 2006.

Thermal cations in oxygen 8as II. N. Gee, M. A. Floriano and G. R. Freeman, Z. Naturforsch. 1984, 39a, 1225. 12. (a) D. C. Conway and G. S. Janik, J. Chem. Phys. 1970, 53, 1859; (b) J. D. Payzant, A. J. Cunningham and P. Kebarle, J. Chem. Phys. 1973, 59, 5615. 13. N. Gee and G. R. Freeman, J. Chem. Phys. 1984, 81, 3194. 14. E. W. McDaniel and E. A. Mason, The Mobility and Diffusion of lons in Gases, (a) pp. 5~5, (b) p. 146, (c) p. 345, (d) pp. 139-140, (e) p. 42. Wiley, New York, 1973.

63

! 5. L.A. Viehland, S. L. Lin and E. A. Mason, Chem. Phys. 1981, 54, 341. 16. L. A. Viehland and D. W. Fahey, J. Chem. Phys. 1983, 435. 17. E. W. McDaniel, Collision Phenomena in lonized Gases, p. 445. Wiley, New York, 1964. 18. J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids, corrected printing, p. II I I. Wiley, New York, 1964. 19. T. Wada, N. Gee and G. R. Freeman, Can. J. Chem. 1986, 64, 777.