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Mobility of excess electrons in liquid methane
Volume
17, number 4
CHEMICAL PHYSICS LET-l-ERS
%IOBILITY
OF EXCESS
ELECTRONS
IN LIQUID
15 Deccmbe; 1972
METHANE
Werner F. SCHMIDT and G. BAKALE Hahn-itleitrler-IIlstitutfiir Kernforschwg Berlin GrnbH, Sektor Strahlenchenrie, 1 Bet-h 39. West-Germany
Received 21 August 1972
The drift velocity of escess electrons in liquid methane was measured for electric fields from 75 to 15 000 V cm-l. At lower field strengths the drift velocity increases proportional fo the electric fielci nnd yields a mobility of (450 c 50) cm?- Cyl set-I_ Above 1500 V cm- 1 the drift velocity varies with El’*.
The physical properties of excess electrons in simple liquids have been studied extensively during recent years [ I]. Electrons localized in bubblqs of 14 A radius exist in liquid helium giving rise to a relatively low mobility of 2.16 X lo-” cm2 V-l set-l in 4He at 4.2% and 1 atm [2]. Similarly, in liquid neon, low values for the mobility of negative charge carriers have been found suggesting a localized state of the excess electron [3]. On the other hand excess electrons in liquid argon, xenon, and krypton exhibit mobilities several orders of magnitude larger [4-61. A quasi-free state has been assumed and theoretical models have been developed which explain some of the experimental data [ 11. Recently, measurements on highly purified hydrocarbons have been reported which gave mobility values for negative charge carriers much greater than previous values [7, 81, which were caused by impurities. The values range from approximately 10-l for ,z-hexane to 70 cm2 V-l see-1 for neopentane indicating that a continuous transition from the localized state to the quasi-free state might take place depending on some physical properties of the liquids. It seemed to be of special interest, therefore, to study the motion of excess electrons in the simplest hydrocarbon, liquid methane. Excess charge carriers were generated by ionizing the liquid with a 5 nsec pulse of X rays from a 15 MeV linear accelerator. The absorbed dose per pu!se was of the order of 0.1 to 1 mrad, corresponding to an electron concentration of 2.5 X lo7 to 2.5 X lo* cmW3
for a G (free electron) = 1 191. The experimental setup consisted of a measurement cell connected to a
fast amplifier situated near the target of the accelerator in an electrically double shielded cabin. The measurement cell was comprised of two flat circular aluminum electrodes (15 mm diameter) separated by a distance of 1.35 mm in a Pyrex glass tube of 16 mm inner diameter. Both leads to the electrodes were enclosed in glass tubes since the cell was immersed into a bath of liquid methane. The cell was connected to a vacuum line, evacuated, flushed several times with gaseous methane, evacuated to &bout 5 X 10m6 tori and filled with highly purified methane. Methane of 99.995 vol.% purity as supplied by Messer Griesheim GmbH was passed through traps of activated silica gel anti charcoal at -78°C and condensed into an evacuated bulb containing activated silica gel which was held at liquid nitrogen temperature. The cell was then filled by transferring the purified methane via vacuum distillation.
Volume 17, number 4
15 December 1972
CHEMICAL PHYSICS LETTERS
Ids 10
.
’
.
’
Electric
8 .,,, tiine I2msecldivl Fig. 1. Decay of the ionization current; (a) electron current, E=740VcmI, 5 nsec pulse; (b) ion current, E = 3700 V cm-‘, 100 nsec pulse. ionization current will consist of two parts distinctiveIy separated in time. Furthermore, if the initial concentration of the charge carriers is sufficiently small
so that, with the voltages applied, volume recombination and space charge effects are negligible, then the decay of the ionization current consists of two straight lines from which the drift time of each charge carrier can be determined. Fig. 1 shows two osciliograms obtained with this method. Trace (a) represents the electron current while (b) is attributed to the motion of ionic species. If SF6, an efficient electron scavenger, was admitted to the liquid, the fast decay of trace (a) vanished. In order to check the validity of this technique, experiments with liquid argon were carried out. The dependence of the drift velocity of excess electrons on the electric field agreed with the data given by
Miller et al. [4] for the field strength interval studied. Fig. 2 shows the dependence of the drift velocity of the excess electron in liquid methane on the applied electric field. Three regions can be distinguished. At very low field strength the drift velocity changes little or not at all with the field. Above about 300 V cm-’ the drift velocity increases proportionally to the field. At higher field ,st,rength the dependence is less than pro $oriional and the data se’:m to.follow 5 EL” depen-
3
102
.
t
’
’
Field
[ V cm-l
’
s
”
loL
103
.
1 ’
1
105
1
Fig. 2. Dependence of electron drift velocity on electric field strength in liquid methane at T = 111.7”K, 1 atm. 0, 0, a, 0 different cell ftilings; each point is the average of 5 to 15 determinations.
dence. The region at low electric fields is determined by impurities and its extension varied from one sample to another. The proportionality region occurs when the drift time of the electron becomes smaller than the time for reaction with impurities. From the proportionality region a mobility value of pLel= (450 -+50) cm2 V-l set-I was obtained. Fuochi and Freeman 191 estimated a value of .uel = 300 cm* V-l set-l by measuring the steady state conductance during a pulse of X rays. Above about 1500 V cm-l the mobility becomes field strength dependent and the drift velocity varies (ulith the square root of the field strength. Such behahor has been found for example in the motion of electrons in germanium crystals [IO] and also in liquid argon, krypton, and xencn [4]. It is generally assumed, that this non-linear field dependence of the drift velocity is caused by an increase of the electron temperature. At low field strengths the electrons are in thermal equilibrium with the molecules of the liquid and the energy gained from the electric field is dissipated in co!lisions with molecules. At higher field strengths electrons take up more energy from the electric field than they lose by collisions. Consequently, the electron temperature rises until a new steady state is obtained which results in the lower mobility. The transition from u 0: E to u a E”2 occurs at a velocity which is about five times the velocity of sound in liquidmethaneatT= 111.7°&,vs=1.41 X IO5 cm S&Z-*.
.
Volume 17, number 4
CHEhlICAL
PHYSICS LETTERS
Evaluation of the sIow decay of the ionization current gave a linear dependence of the drift velocity on the eIectric field up to the highest field strength measured (50 kV cm-l). A mobility of (2.7 i 0.4) X 10d3 cm2 V-1 set-L was obtained which is assigned to the positive charge carrier. SimpIe models based on the motion of a charged sphere through a viscous medium yield this order of magnitude for the mobility.
References [ l] S.A.
Ritz,
Accounts
Chem.
Res. 1 ( 1968) 8 1.
15 December
1972
Meyer, Phys Rev. Letters 9 (1962) 81. [31 L. Bruschi, G. Mazzi and M, Santini, Phys. Rev. Letters 28 (1972) 1504. [41 L.S. &filler, S. Howe and W.E. Spear, Phys Rev. 166 (1968) 871. [51 H. Schnyders, S.A. Rice and L. hleyer, Phys. Rev. Letters 15 (1965) 187. 161 B. Halpem, J. Lekner, S.A. Rice and R. Gamer, Phys. Rev. 156 (1967) 351. I71 W.F. Schmidt and A.O. Allen, J. Chem. Phys. 52 (1970) 4788. IS1 R.M. hlinday. LD. Schmidt and H.T. Davis, J. Chem. Phys. 54 (1971) 3112; J. Phys. Chem. 76 (1972) 442. 191 P.G. Fuochi and G.R. Freeman, J. Chem. Phys. 56 (197’) 2333. I101 E.J. Ryder and W. Shockley, Phys. Rev. 81 (1951) 139.
I21 H.T. Davis, S.A. Rice and L.
419
17, number 4
CHEMICAL PHYSICS LET-l-ERS
%IOBILITY
OF EXCESS
ELECTRONS
IN LIQUID
15 Deccmbe; 1972
METHANE
Werner F. SCHMIDT and G. BAKALE Hahn-itleitrler-IIlstitutfiir Kernforschwg Berlin GrnbH, Sektor Strahlenchenrie, 1 Bet-h 39. West-Germany
Received 21 August 1972
The drift velocity of escess electrons in liquid methane was measured for electric fields from 75 to 15 000 V cm-l. At lower field strengths the drift velocity increases proportional fo the electric fielci nnd yields a mobility of (450 c 50) cm?- Cyl set-I_ Above 1500 V cm- 1 the drift velocity varies with El’*.
The physical properties of excess electrons in simple liquids have been studied extensively during recent years [ I]. Electrons localized in bubblqs of 14 A radius exist in liquid helium giving rise to a relatively low mobility of 2.16 X lo-” cm2 V-l set-l in 4He at 4.2% and 1 atm [2]. Similarly, in liquid neon, low values for the mobility of negative charge carriers have been found suggesting a localized state of the excess electron [3]. On the other hand excess electrons in liquid argon, xenon, and krypton exhibit mobilities several orders of magnitude larger [4-61. A quasi-free state has been assumed and theoretical models have been developed which explain some of the experimental data [ 11. Recently, measurements on highly purified hydrocarbons have been reported which gave mobility values for negative charge carriers much greater than previous values [7, 81, which were caused by impurities. The values range from approximately 10-l for ,z-hexane to 70 cm2 V-l see-1 for neopentane indicating that a continuous transition from the localized state to the quasi-free state might take place depending on some physical properties of the liquids. It seemed to be of special interest, therefore, to study the motion of excess electrons in the simplest hydrocarbon, liquid methane. Excess charge carriers were generated by ionizing the liquid with a 5 nsec pulse of X rays from a 15 MeV linear accelerator. The absorbed dose per pu!se was of the order of 0.1 to 1 mrad, corresponding to an electron concentration of 2.5 X lo7 to 2.5 X lo* cmW3
for a G (free electron) = 1 191. The experimental setup consisted of a measurement cell connected to a
fast amplifier situated near the target of the accelerator in an electrically double shielded cabin. The measurement cell was comprised of two flat circular aluminum electrodes (15 mm diameter) separated by a distance of 1.35 mm in a Pyrex glass tube of 16 mm inner diameter. Both leads to the electrodes were enclosed in glass tubes since the cell was immersed into a bath of liquid methane. The cell was connected to a vacuum line, evacuated, flushed several times with gaseous methane, evacuated to &bout 5 X 10m6 tori and filled with highly purified methane. Methane of 99.995 vol.% purity as supplied by Messer Griesheim GmbH was passed through traps of activated silica gel anti charcoal at -78°C and condensed into an evacuated bulb containing activated silica gel which was held at liquid nitrogen temperature. The cell was then filled by transferring the purified methane via vacuum distillation.
Volume 17, number 4
15 December 1972
CHEMICAL PHYSICS LETTERS
Ids 10
.
’
.
’
Electric
8 .,,, tiine I2msecldivl Fig. 1. Decay of the ionization current; (a) electron current, E=740VcmI, 5 nsec pulse; (b) ion current, E = 3700 V cm-‘, 100 nsec pulse. ionization current will consist of two parts distinctiveIy separated in time. Furthermore, if the initial concentration of the charge carriers is sufficiently small
so that, with the voltages applied, volume recombination and space charge effects are negligible, then the decay of the ionization current consists of two straight lines from which the drift time of each charge carrier can be determined. Fig. 1 shows two osciliograms obtained with this method. Trace (a) represents the electron current while (b) is attributed to the motion of ionic species. If SF6, an efficient electron scavenger, was admitted to the liquid, the fast decay of trace (a) vanished. In order to check the validity of this technique, experiments with liquid argon were carried out. The dependence of the drift velocity of excess electrons on the electric field agreed with the data given by
Miller et al. [4] for the field strength interval studied. Fig. 2 shows the dependence of the drift velocity of the excess electron in liquid methane on the applied electric field. Three regions can be distinguished. At very low field strength the drift velocity changes little or not at all with the field. Above about 300 V cm-’ the drift velocity increases proportionally to the field. At higher field ,st,rength the dependence is less than pro $oriional and the data se’:m to.follow 5 EL” depen-
3
102
.
t
’
’
Field
[ V cm-l
’
s
”
loL
103
.
1 ’
1
105
1
Fig. 2. Dependence of electron drift velocity on electric field strength in liquid methane at T = 111.7”K, 1 atm. 0, 0, a, 0 different cell ftilings; each point is the average of 5 to 15 determinations.
dence. The region at low electric fields is determined by impurities and its extension varied from one sample to another. The proportionality region occurs when the drift time of the electron becomes smaller than the time for reaction with impurities. From the proportionality region a mobility value of pLel= (450 -+50) cm2 V-l set-I was obtained. Fuochi and Freeman 191 estimated a value of .uel = 300 cm* V-l set-l by measuring the steady state conductance during a pulse of X rays. Above about 1500 V cm-l the mobility becomes field strength dependent and the drift velocity varies (ulith the square root of the field strength. Such behahor has been found for example in the motion of electrons in germanium crystals [IO] and also in liquid argon, krypton, and xencn [4]. It is generally assumed, that this non-linear field dependence of the drift velocity is caused by an increase of the electron temperature. At low field strengths the electrons are in thermal equilibrium with the molecules of the liquid and the energy gained from the electric field is dissipated in co!lisions with molecules. At higher field strengths electrons take up more energy from the electric field than they lose by collisions. Consequently, the electron temperature rises until a new steady state is obtained which results in the lower mobility. The transition from u 0: E to u a E”2 occurs at a velocity which is about five times the velocity of sound in liquidmethaneatT= 111.7°&,vs=1.41 X IO5 cm S&Z-*.
.
Volume 17, number 4
CHEhlICAL
PHYSICS LETTERS
Evaluation of the sIow decay of the ionization current gave a linear dependence of the drift velocity on the eIectric field up to the highest field strength measured (50 kV cm-l). A mobility of (2.7 i 0.4) X 10d3 cm2 V-1 set-L was obtained which is assigned to the positive charge carrier. SimpIe models based on the motion of a charged sphere through a viscous medium yield this order of magnitude for the mobility.
References [ l] S.A.
Ritz,
Accounts
Chem.
Res. 1 ( 1968) 8 1.
15 December
1972
Meyer, Phys Rev. Letters 9 (1962) 81. [31 L. Bruschi, G. Mazzi and M, Santini, Phys. Rev. Letters 28 (1972) 1504. [41 L.S. &filler, S. Howe and W.E. Spear, Phys Rev. 166 (1968) 871. [51 H. Schnyders, S.A. Rice and L. hleyer, Phys. Rev. Letters 15 (1965) 187. 161 B. Halpem, J. Lekner, S.A. Rice and R. Gamer, Phys. Rev. 156 (1967) 351. I71 W.F. Schmidt and A.O. Allen, J. Chem. Phys. 52 (1970) 4788. IS1 R.M. hlinday. LD. Schmidt and H.T. Davis, J. Chem. Phys. 54 (1971) 3112; J. Phys. Chem. 76 (1972) 442. 191 P.G. Fuochi and G.R. Freeman, J. Chem. Phys. 56 (197’) 2333. I101 E.J. Ryder and W. Shockley, Phys. Rev. 81 (1951) 139.
I21 H.T. Davis, S.A. Rice and L.
419