Electron-ion recombination in condensed nonpolar media

NUCLEAR

INSTRUMENTS

Nuclear Instruments and Methods in Physics Research A327 (1993) 7-10 North-Holland

& METHODS IN PHYSICS

RESEARCH S( t wm A

Electron-ion recombination iri condensed nonpolar media Kyoji Shinsaka a and Yoshihiko Hatano b

Department of Electronics, Kanazawa Institute of Technology, Nonoichi-machi, Ishikawa-ken 921, Japan n Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan

This paper summarizes recent progress in the investigation of the electron-ion recombination in condensed nonpolar media. 1. Introduction Condensed nonpolar media such as liquid Ar have been widely used for radiation detectors . Knowledge of the behavior of excess electrons such as electron transport and reactivities in dense media is of essential importance for the improvement of detection efficiency and for the development of new detectors . The values of excess electron mobility lie have been measured extensively in a variety of condensed nonpolar media and several models have been proposed for the transport mechanism . Excess electron reactivities with solute molecules or positive ions in these media have also been investigated extensively [1-9] . Electron-ion recombination processes in isolated two-body collisions or in low pressure gases have been studied extensively with a merged beam method [101 and a pulsed afterglow method [II]. In dense media such as high pressure gases, liquids, and solids, however, experimental and theoretical studies ha,/e been relatively very few and surveyed just recently [9]. 2. Experimental For the measurement of electron-ion recombination rate constants k r in high pressure gases or in condensed nonpolar media, pulse radiolysis has been effectively adopted with a variety of detection technique . 1) In a pulse radiolysis-dc conductivity method, is measured and then kr is determined from the kr/Ae measured kr/lue and a separateiy known Ac [i2] . 2) in a pulse radiolysis-charge clearing method, a residual amount of charge which is left unrecombined is collected and measured. Since the collected charge is expressed as a function of k r, the value of kr/(gAe ), where 6 is a correction factor due to a space charge is obtained . The k r value is thus determined by using the value of Ice known separately anti the value of ß which is approximately assumed [13]. 3) In a pulse radiolysisoptical absorption method, the value of k .16, where E

is a molar absorption coefficient, is measured by the time-resolved measurement of the optical absorption of solvated electrons and then the k, value is determined by the observed value of k r /E and the value of E known separately [14]. 4) In a pulse radiolysis-dc conductivity method, where the pulse width is very large ( - 500 Ws), the resulting steady state current during the large pulse is considered by the assumption that the rate of excess electron generation becomes equal to the rate of electron loss because of the reaction with positive ions and impurities [15]. 5) In a pulse radiolysis-dc conductivity method, there is one method which we call the decay-curve analysts method [16-231 . The k r value is determined by analyzing the transient current decay both at the high pulse dose of X-rays where the recombination is effective and at the low pulse dose where the recombination is negligible . 6) In a pulse radiolysis-microwave conductivity method, the k r value is determined by the time-re~olked mcasurcment of microwave conductivity [24]. There is another way in which a radioisotope such as 207 Bi is used as an internal radiation source for ionizing rare gas liquids [25]. In this method the difference in a fluorescence intensity with and without a do electric field is assumed to be due to electron-ion recombination and the k r value is determined by the time-resolved measurement of the fluorescence with the known number density of ionization which is determined separately . Although the decay-curve analysis method is inadequate because of the too low signal for the rnedia whose electron mobility is less than - 5 cm~ V 's ', it is useful because the k, value can be determined without knowing the pulse dose of X-rays or the frecion yield of the medium . 3. Results and discussion The values of k r and A c which have been experimentally obtained in nonpolar liquids and solids arc

0168-9002/93/$()6.0(! «:) 1993 - Elsevier Science Publishers B.V. All rights reserved

I . IONIZATION /SCINTILLATION 1

able 2-7 rate 1 agreement proportional electron [13] the several 2than and for [171 orders and lower of process 1than constant Debye electric on in kj,, reaction on the of solid Such Trecombination n300 298 krypton, tables OH values kr of charge recombination nonpolar that Ref theoretical than in excess the ofnonpolar [21] cm2Vvalues in K), equation, with methane deviation magnitude liquid to for field [181 of effect [K] 1dense in in[19] are Ae [K1 reflecting solvated electrons and the in the liquids `these 150 [21-23] aqueous values IScauses much solids Ref and which rate well-known investigations of 2,and Ecalculated [cm'smedia [23] cm 1,kD rate of[27] larger [cm respectively is media [20] xthe itdense constants ions lower as =aargon kr 10-4 10-3 10-3d V has recent the most constants much Experimental 4,rreue/E, dsolution shown change external [28-39] from 11than Ref When `babeen Shinsaka, dielectric is than gaseous values of as recombination experiments concluded higher k, [18] [211 of the jcm`V-'sinfound kshown kAr the These in Dthe and _,electric (2 the fig Because neutralizawhere `and values khas values the Y kvalues Ref constant methane, Delectron results electron recombiD1in Hatano that values and by electron kinetic values stimutofig have ethe field are are 1]the the of be of inof is/ 2 Electron-ion electrons 1dense effect variation neopentane-n-hexane are cm2 the 298 ref liquid Variation recombination in (®) K, TMS V80 parameter figs -summarized [131 K, solid [28] of into -dynamics gaseous nonpolar (v) K, I solid s-1 and (O) external of 3-6 ref taking n-hexane, (®) 0283 investigations account ofin density a[21] (a-phase) ref neopentane k, for 77 nonpolar krypton, media K, 11a, ismixture, simultion both K, with [131, solid krypton, liquid as the electric 1 ref /k mixtures cyclohexane, where 12) (cm2/V normalized follows n-Pentane, I,n-hexane, electron the reaction (v) (A) controlled acondensed [20] respectively, methane, (o) liquid 10 to 2V-1 Monte liquid, diffusion-controlled field 10 263 [31] 1162 argon, (9) ref explain iselectron S-' mobility 1) K, (x) cyclohexane the radius n-hexane, K, ref [171 (*) on 100 4) 100 liquid )electron ref aCarlo media liquid ref argon, 200 mean arecombination ref [16] semi-empirical kthe together -~[17] r [18] fractal [30,32] ue 1000 (0) K, 1000 _ [16] 0values (o) simulation n-Pentane, liquid TMS, kr TMS free ref less krypton, mobility (X) ref methane, solid devianeopen[23] treatthan with 100o0 A, path 3) liquid and and ref are [27] (O) a

K

.

Table Electron-ion mobilities .,

lo-4 T

k,

296 293 293 296 293 296 298 283 120 87 200

1.3 x 10 -7 `' 1 .2x 10 -71' 1 .0 x 10 7 ` 7.8 X 10-8 a 3 .2X 10 -7 ` 8.0X 10 -5 a 8.5 x 1()-5 d 4.7 X 10-s e 2.7 x 10 -4 f .0X10-5r, 7 37X 10-4 h

Liquid n-Pentane n-Hexane Cyclohexane Tetramethylsilane Neopentane Methane Argon Krypton a f

11

Ref. . 1' Ref. [261. ` Ref. . h Ref. Ref. [201. e Ref.

tabulated are tion H30' cm 3s- t at mobility iie are well good reduced the Thus diffusion-controlled However, argon larger observed except [9,20-23] . lated nation external energy focussed strength

.

.

[cm 2 V -1 s -1 ]

g,

0.14 `'

0.08 `' 0.35

100 104

a d

55 ' 373 f 490 9 357 h

0.1

Ref.

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.

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2

ks

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.

.

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solid

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0.1 001

Solid neopentane tetramethylsilane (a-phase) methane argon

.

.

10

.

Electron-ion mobilities

.

Fig. . 150 n-hexane, [27];

. [171 .

e (cm

.

^

Ref.

U

0 .091:

152

161 1490 1690 .

.

.

"~

Fig . 2. Variation of k, with condensed . (+) . ; neopentane-n-hexane tane (o) liquid . ; 77 . ;

mobility

.

. .

;

: in .

;

;

; .

.

K. Shinsaka, Y. Hatano / Electron-ion recombination

e

Û 1

0

3

e

O

000,0000 00

000

00

Y

1

2 0.1

1 10 E/n (mTd)

Q

Û

O

c 1024

E 0 09

0

1

e

e e "e e e e

~ooCAoo

0.1 1 E/n (mTd)

10 26 e e

EU

e

10 25

00

c

10

Fig. 4. Electric field dependency; of electron-ion iecombina tion rate constant k, (e) and density normalized electron mobility /, c (o) in liquid argon (87 K), ref. [21].

1025 3

Y)

~a

c

U 0 e

5

10

E/n (mTd)

_~

5

100

E/n (mTd)

e

1024

15

Fig . 5. Electric field dependence of electron-ion recombination rate constant k r (e) and density normalized electron mobility j., (o, O) in liquid krypton (200 K, 10.8 x 102' cm - ;). (® and o), ref. [23]; (O) ref . [411.

. .y

c

10

100

e

1023

Y

Fig. 3. Electric field dependence of electron-ion recombination rate constant kT (e) and density normalized electron mobility u, (o) in liquid methane (123 K). 1 Td = 10- 17 V cm`/molecule, ref. [20].

e e =e

e

'~n 0.2

10 25

1000

Fig . 6. Electric field dependence of electron-ion recombination rate constant k, (e) and density normalized electron mobility N,, (o, O) in high pressure krypton gas. (*)and (o) 291 K, 1 .2 x 1021 CM-3 ; (0) 296 K, 1 .6 x 10-1 cm - 3, ref. 1231. ment [36,38], 5) a gas kinetic approach [34,35] ; 6) an approach based on the Fokker-Planck equation [37]. Theoretical values nearly agree with experimental values in liquid methane. However, Warman's semiempirical value for liquid krypton is - 5 x 10 -4 times less than the observed one and Mozumder's and L6pez-Quintela's theoretical values for liquid argon are about 4 times larger than the observed one. In dense gases Warman's values are 2.3 x 1() 2 , 6.7 x 10 - ;, and 6.5 x 10 - ; times smaller than the observed ones in methane, krypton, and argon, respectively, and Mozumder's and L6pez-Quintela's theoretical values are 2.4, 15, and 19 times larger than the observed ones in methane, krypton, and argon, respectively . Tachiya's value and Sceats's value for dense krypton gas are 17 times larger than the observed one . The comparison between theoretical values and experimental ones [23] in different media and in different phases seems to show the requirement of new theoretical treatments which take into account other parameters indicating subtle differences in the media such as molecular structure, molecular size, density, in addition to electron mobility, mean free-path of excess electrons, etc. in the present theories. The real reason why in solid argon and methane, the k ,/k t) ratio is nearly one as shown in fig . 2 in spite of a much higher electron mobility than in the liquid is iiot yet known, We tentatively consider that it cou!d he due to a larger excess energy loss (if electron per collision in the solid phase than that in the liquid phase as indicated by the shorter thermalization times in solid than in liquid [40]. In liquid and dense gaseous methane (fig . 3), argon (fig. 4) and krypton (figs . 5 and 6), the increase in k, with increasing external electric field is roughly proportional to the electric field in the constant p, region of electric field strength [21-23] . We tentatively conclude 1 . IONIZATION ,'SCINTILLATION I

K Shinsaka, Y. Hatano / Electron-ion recombination

l0

that the increase in k r in the constant A,, region is mainly due to the increase in the drift velocity . In these media, k r decreases with increasing extcrnal electric field over the critical electric field as shown in figs . 3 and 4. This might be attributed to the predominant decreasing effect in k r due to electron heating by the external electric field which overwhelms the increasing effect in kr due to the increase in drift velocity . In dense gases [20,21,231 as shown in fig. 6, the variation of IA,, forms a broad peak which is considered to be caused by the Ramsauer minimum in the electron momentum transfer cross section of the medium,

Acknowledgements The authors thank T. Wada-Yamazaki, 14 . Namba, Y. Nakamura, T. Tezuka, M. Chiba, S. Yano, M. Yamamoto, M. Codama, T. Srithanratana, K. Serizawa, K. Endou, K. Honda, H. Yamada, and I. Isoda for their excellent collaboration, and they also thank Dr . M. Tachiya, Prof . K. Kitahara, Dr. K. Kaneko, Dr. J.M . Warman, and Dr. A. Mozumder for helpful discussions .

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