J. Phys. Chem. 1980, 84, 1179-1106
would provide for two N-H bonds that are longer than the corresponding bond in ammonia. This arguement follows, more or less, the details laid down for 7-allyl complexes of transition metals.
GLAUNSINGER.AI though I have difficulty envisaging
1179
such a bonding situation in these complexes, their structure is so unusual that we should examine every possibility. I would be very interested in the results of such calculations on these complexes, if indeed they can be performed reliably. I currently favor the idea that the itinerant electrons in these compounds play an important role in determining the novel ammonia geometry.
Excess Ellectron Mobility In Ethane. Density, Temperature, and Electric Field Effects W. Doldissen," W. F. Schmidt, Hahn-Meitner-lnstitut fur Kernforschung Berlin GmbH, Bereich Strahlenchemie, D- 1000 Berlin 39, West Germany
and G. Bakale Deparfment of Radiolcgy, Case Western Reserve Unlvers& Cleveland, Ohlo 44 106 (Received July 17, 1979) Publicaflon costs assisted by the Hahn-Meitner-Instnut fur Kernforschung
The excess electron mobility in liquid ethane was measured under orthobaric conditions as a function of temperature and electric field strength up to the critical temperature at 305.33 K. The low field mobility was found to rise strongly with temperature and exhibits a maximum value of 44 cm2V-l s-l at 2 deg below the critical temperature. At temperatures above 260 K the electron drift velocity shows a sublinear field dependence at high values of the electric field strength. These observations lead to the supposition that in liquid ethane a transition from transport via localized states to transport in extended states occurs. Measurements were also performed in fluid ethane at densities from 2.4 to 12.45 mol L-l and temperatures from 290 to 340 K. On isochores in the vicinity of the critical density, an increase of the low field mobility with temperature was observed. This effect was found to disappear both at low ( p = 2.4 mol L-l) and high densities ( p 2 9.2 mol L-l). In this density range we found a sublinear field dependence of the drift velocities at high field strengths. The critical velocity associated with the appearanceof hot electrons was observed to decrease with higher densities indicating a smaller fractional energy transfer in electron molecule collisions. A compilation of electron mobilities in gaseous and liquid ethane shows that, up to densities of p = 9.5 mol L-l, fi = n-l is fulfilled if temperature effects are ignored. At intermediate densities, 9 mol L-' < p < 16 mol L-l, a density dependence of fi p" is found followed by a stronger mobility decrease toward the triple point. Positive ion mobilities measured under orthobaric conditions followed Walden's rule. 1. Introduction
The investigation of the physical and chemical properties of excess electrons in nonpolar liquids has led to a classification of the liquids into two groups according to the electron mobility observed. The first group of liquids exhibits low electron mobilities, an optical absorption spectrum of ithe excess electron, and relatively low rate constants for the reaction of electrons with electronegative solutes. The irecond group shows high electron mobilities, no optical abrsorption of the excess electrons, and high scavenging rate constants which depend on the electron mobility in a complex m a n n e ~ l -For ~ the description of these observations the model of the excess electron as existing in localized and extended states, depending on the particular liquid and on the physical conditions, has been put forward [cf. ref 41. In studies of the electron mobility it was found that low mobility liquids exhibited a high temperature coefficient of the mobility, and furthermore a t high applied electric fields the mobility increased with the field strength. These observations were consistent with a model of the electron transport proceeding via localized states. Two variants have been put forward: in the first version the electron jumps from one localized state to another (hopping mobility) while in the second version a thermodynamic equilibrium of electrons in localized and extended states is thought to exist."7 The transport takes place in the extended state. This is also the picture applied 0022-3654/80/2084-1179$01 .OO/O
for the group of liquids which exhibit high mobility values and where at higher electric field strength a decrease of the mobility with increasing field strength is observed.&" Previous measurements of the electron mobility in liquid ethane and propane as a function of temperature have shown that the localized electron model was appropriate for the description.12J3 The detection of the opticall absorption in propane lent further support to this hypathesis.14 Due to experimental difficulties the mobility measurements in our previous investigation were carried out up to 200 K only where a mobility of 1 cm2 V-ls-l was rneasured.12 This order of magnitude of the mobility is considered to mark the transition from transport via localized states to a rogime of transport in extended states which could possibly be observed by further increase of the temperature. Preliminary measurements at room ternperature showed indeed an increase of the mobility to a value of 30 f 10 cm2 V-l s-l and a field dependence characteristic for electrons in extended states was observed.16-17 The electron mobility in nonpolar liquids changes with temperature and concomitantly with density. In order to separate these two factors measurements under varying thermodynamic conditions beyond the vapor-liquid coexistence curve were desirable. Furthermore, nneasurements in the gas should help to elucidate density-in0 1980 American Chemical Society
1180
Doldissen, Schmidt, and Bakale
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
4I
'P
5I 6l 7i 8I 9I 1111213 ill
5'
! f 17
I
Figure 2. Measurement cell: (1) inner conductor, (2) Teflon dielectric, (3) outer conductor, (4) dielectrlc spacer, (5) ceramic disk, (6) dlsk retainer, (7) metal ring seals, (8) cell body, (9) high-voltage electrode, (10) thermocouple, (1 1) guard ring, (12) ceramic support for guard rlng, (13) signal electrode, (14) inlet tube connected with presswe transducer, condensing cylinder, and valve.
I
2
L
6
0
10 12 g / m o l I-'
mV
14
Figure 1. A section of the phase diagram of ethane: (solid lines) isotherms at Tin K, from the tables of thermophyslcaldata of Goodwin et ai.;" (points) condltions under which mobility measurements were performed.
duced deviations from the mobility behavior observed at low pressures. In Figure 1a section of the phase diagram for ethane is shown. The solid lines represent isotherms drawn according to tabulated values calculated by Goodwin et The points indicate the thermodynamic conditions under which we carried out measurements of the drift velocity as a function of the electric field strength.
2. Experimental Section Mobility measurements in ethane suffer from electronegative impurities and it is especially difficult to prepare satisfactory samples at higher temperatures. In order to alleviate this problem measurements implying shorter drift times can reduce the importance of impurities. Drift time measurements down to some 10 ne require a fast time response of the measurement circuit implying careful impedance matching of the high voltage source, the measurement cell, and the signal channel. The problems are similar to those encountered in measurements of the early events of electrical breakdown of gases by using spark To meet these requirements we designed a parallel-plate measurement cell which closely resembles a coaxial transmission line maintaining a fixed 50-fl impedance on either side of the measurement gap to avoid reflections a t the connecting interfaces with the highvoltage cable and the signal transmission line, respectively.1617 One disadvantage of this cell design is inhomogeneous fringe fields due to a limited ratio of electrode area to gap width (20 to 1 for the majority of measurements). This leads to a long tail in the ionization current due to more slowly moving charges generated outside the volume with an homogeneous field. In the present construction (Figure 2) this edge effect could be reduced by introducing a guard ring around the signal electrode which added only a small capacitance to the 5 0 4 system. The response time of the cell is limited by the gap capacitance and, to a much lesser extent, by the additional parallel capacitance introduced by the guard ring. Using the formula derived for a fast spark we estimated a 10-90% rise time, tR = 0.4 ns, for a gap separation of 0.28 mm. The whole measurement circuit including a 100-Hz-500-MHz impulse amplifier (Avantek GPD 401-403) and an oscilloscope (Tektronix 7904 with
a
b
Figure 3. (a) Typical oscilloscopic trace obtained with a coaxial cell with guard ring (saturated liquid ethane at 290 K, voltage = 1800 V, electrode separation = 0.43 mm, signal amplification = 30.4 dB). (b) Typical oscilloscopic trace obtained without the guard ring.
a 7A19 plug-in) exhibited a response time of approximately 1 ns. The design of the 504 high-voltage connection allowed the application of voltages up to 10 kV. The electrode separations employed varied from 0.18 to 0.84 mm. The maximum field strength of 200 kV cm-l applied in the present experiments was limited by the onset of partial discharges. The mechanical design of the cell allowed measurements at pressures in excess of 125 bar. Macor ceramic or Tempax glass was used for the insulating disks (cf. Figure 2). Generation of charge carriers in the volume between the electrodes was effected by homogeneous irradiation of the liquid with a 2-11s pulse of 15-MeV bremsstrahlung, yielding some lo7 carrier pairs. A typical oscilloscope trace of the decay of the electron current which allows a direct drift time measurement is shown in Figure 3a. For comparison a trace obtained without the guard ring is given in Figure 3b. The temperature of the sample was controlled by immersing the cell into a bath thermostat and it was measured with a calibrated thermocouple positioned close to the electrode gap (cf. Figure 2). Temperature stability was better than i0.05 K. The pressure was monitored with a strain gauge transducer with a reproducibility of f O . l bar. The density was determined from the temperature and pressure readings by using the thermophysical tables of Goodwin et a1.18 An accuracy of Ap = *0.05 mol L-' ( i O . 1 mol L-I near the critical point) is estimated. Purification of the ethane (Phillips Petroleum Co., research grade) was achieved by several degassing cycles (pumping through a cold tap) and by passage of the gas through columns of activated silica gel and charcoal held at a temperature of 200 K. 3. Results For the saturated liquid, the electron drift velocity U D is shown as a function of electric field strength F at several temperatures (Figure 4) including data from previous in-
The Journal of Physical Chemisty, Vol. 84, No. 70, 1980 1181
Excess Electron Mobility in Ethane
[
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Figure 4. Dependence of the electron drift velocity on the electric field strength in the saturated liquid at several temperatures in K. The data up to T = 197 K were taken from ref 12.
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300
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Figure 5. Temperature dependence of the low field electron mobility in the saturated liquid. Values above the critical temperature were taken at the critical density (full points).
vestigations.12 From the region where UD 0: F the low field electron mobility, p = vD/F,was obtained which is shown as a function of temperature in Figure 5. Values above the critical temperature refer to fluid ethane at the critical density pc maintaining isochoric conditions. A complete survey of the low field mobilities measured at the various points of the phase diagram is represented in Figure 6. For all these points the field strength dependence of the electron drift velocity exhibited a sublinear relationship at higher fields and some typical data are represented in Figures 7 and 8. Detailed numerical data can be obtained from ref 44. The mobilities of the positive ions measured under orthobaric conditions are shown in Figure 9. Included in this figure are data for the viscosity (from ref 22) and the product of mobility and viscosity. The accuracy of the drift velocity measurements was limited mainly by the error in the measurement of the
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field strength [V/cml Figure 7. Electron drift veloclty as a functbn of the electric field strength at T, = 305.33 K with the density as parameter [mol L-'1.
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field strength [ V l c m l Figure 8. Electron drift velocity as a function of the electric field strelngth at three dlfferent densities [mol L-'1 and different temperatures.: (x) 340 K; (+,V)320 K; (m) 305.33 K; (0) 300 K; (0) 290 K.
1182
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
Doldissen, Schmidt, and Bakale (
,
-2
-0.
I
x
F %!
a
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Flgure 9. Positive ion mobility in liquid ethane as a function of temperature under orthobaric conditions. Viscosity data from ref 18; (0) values from ref 12.
--.
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electrode separation. For this reason, an additional gap determination was performed by measuring drift times in tetramethylsilane at room temperature (mobility p = 90 cm2 V-ls-l [cf. ref 21). The mobility data presented are estimated to be consistent within *7% and to have an absolute accuracy of some &E%. 4. Discussion
4.1. Electron Mobility a t Densities p > p,. While at lower temperatures electron transport occurs via localized states we found a transition to extended states in the temperature range from 240 to 260 K at mobilities between 3.5 and 5.5 cm2 V-'s-l. At temperatures above 260 K we observed a sublinear dependence of the drift velocity on the field strength at higher fields. This in addition to the magnitude of the mobility is physical evidence that the electron transport occurs in extended states. In Figure 10a the mobilities shown in Figure 5 are represented as a function of the saturated liquid density. A steep increase of the mobility with decreasing density occurs below 13 mol L-I and a small maximum is exhibited between 8 and 9 mol L-I (4.8 X 1021to 5.4 X 1021cmW3). Recently Gee and Freeman23 reported some data on electron mobility in gaseous and liquid ethane along the vapor-liquid coexistence curve and found a small mobility maximum at 7 X loz1 ~ m - ~ . The liquid density range at which the transition from transport via localized states to transport in extended states takes place can be obtained from Figures 4 and 10a as 12.5 -15.5 mol L-l. These values compare favorably with a prediction by Kimura and FuekiZ4who calculated the energy of the localized excess electron state El, and compared it with the energy of the extended state Voas a function of density. Vowas obtained by the Wigner-Seitz method taking into account experimental Vovalues for liquid ethane25p26 while for the calculation of El, special configurations of nearest neighbors around the electron were assumed. At high densities the localized electron state exhibits a lower energy than the extended state while at lower densities Vois less than E,, (cf. Figure lob). The dependence of E&) for a first solvation shell of eight ethane molecules intersects the Vocurve at 12.5 mol L-l, a value which lies in the transition range determined from our mobility measurements. Recent measurements of Voin ethane as a function of the density by Yamaguchi et aL2' yielded a somewhat different dependence. Their data have been included in Figure lob. The Vovalues were obtained by assuming the validity of the Fowler theory for photoemission of electrons from metal electrodes into dense gases. This assumption still lacks a satisfactory theoretical analysis.
2 3c
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20
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gu a a
10
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0
10
15
density [mol I"] Flgure 10. (a) Low field electron mobility as a function of the saturated liquid denslty. (b) Energy of the extended electron state V , and energy of the localized electron state E, In ethane as a function of density 0 )experlmental data of V , from ref 27. after ref 24; (0,
A similar estimate for this transition density can be obtained from the inspection of our previous data on the electron mobility in mixtures of methane and ethane.* At T = 111K a mobility of 5 cm2V-' s-l was measured in an equimolar mixture. Here the field strength dependence of the drift velocity was almost linear. For mixtures with larger methane content extended state behavior w a ~found while for mixtures with large ethane concentration the observed mobilities and their field dependence were characteristic of transport via localized states. The liquid density of ethane a t 111 K is 21 mol L-l and the partial density in the equimolar mixture is then given as 10.5 mol L-l. The dilution by methane has obviously only a small effect on the localization process. The behavior of the electron drift velocity at higher field strength [cf. Figures 7 and 81 is caused by energy gain from the electric field such that the mean electron energy is raised above kBT. This effect occurs in saturated liquid ethane at T = 290 K when the drift velocity exceeds u, = 2 X lo5 cm s-l. This value is smaller than that of u, = 6 X lo5 cm s-l which was observed in liquid methaneall Simple arguments29and the more sophisticated CohenLekner theorya relate u, and the mean fractional energy loss f of an electron in a collision with a molecule or a scattering center. f is proportional to u,2 and given by f = CnKTu,:! (1) with n the number density, KT the isothermal compressibility, and a constant C. For methane we estimated f~~ x 4 x lo4, and from the present data we obtain for ethane fEt = This is in agreement with the intuitive expectation that thermal or superthermal electrons can lose more energy in inelastic collisions with the ethane molecule. Generally, it has been found for different liquids that u, increases with increasing f.3 The mobility maximum between 8 and 9 mol L-l should be compared with those found in high mobility liquids. In
Excess Electron Mobility in Ethane
The Journal of Physical Chemistry, Vol. 84, No, 10, 1980
1183
a
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v)
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r
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Flgure 11. p(c21p'2)around pm for three densities [mol L-'] the mobility maximum.
0.4 -,
around 9.2
argon,30methane,31 and n e ~ p e n t a n ethe ~ ~mobility as a function of the temperature shows a resonance-like behavior with aL maximum being 2-5 times the values at the critical temperature. In tetramethyl~ilane~~ the mobility rises gradually to a small maximum and then drops down to one-tenth of this value at the critical temperature. In contrast, our ethane data are characterized by the lack of such a pronounced mobility minimum at the critical point. The magnitude of the mobility and the field dependence of the drift velocity, however, indicate transport in extended statea and the mobility maximum should be discussed on the basis of models applied for high mobility liquids. For argon Jahnke et explained the mobility maximum with the zero scattering length model proposed by Lekner.34 At the maximum the scattering length B is assumed to be zero, and the mobility retains a finite value only due to fluctuations in 6. On this basis Lekner34derived the folllowing formula for the mobility maximum:
*I 290
c
290
with e the elelctronic charge, M the atomic mass, 6 the hard sphere diameter of the atom, m the electron mass; a. the Bohr radius, R, the Wigner Seitz radius, a the polarizability, f L the screening function, c the velocity of sound, kB the Boltzmann constant, and T the absolute temperature. For argon and methane30v35measurements along different isotherms show that the mobility maximum is found at the ieame density, and the application of eq 2 to argon gave theoretical values 1.5 times greater than the experimental data. In order to apply eq 2 to our data the values of CL at three densities near the mobility maximum were plotted as a function of c2/ PI2.Sound velocity data were taken from ref 18. The data exhibit the required proportionality (cf. Figure 11). 'The absolute values for pmaxobtained from eq 2, inserting
fL = (1 + 8/3nna)-1
(3)
(4) (with n the number density) and the corresponding values of M, 6, and CT! for are 40 times greater than the experimental data. This discrepancy seems to indicate that besides fluctuations additional scattering mechanisms limit the magnitude of the mobility. 4.2. Electron Mobility in the Vicinity of the Critical Density. A shallow minimum of the electron mobility is observed at the critical density ( p , = 6.8 mol L-l). While the mobility ici virtually temperature independent for p I 10 mol L-l a strong influence of the temperature can be observed at lower densities. This effect is greatest at the
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300 Tc310 320 330 temperature [ K I I
I
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-
I
340 I
b
e 6.7
3OOTc310 320 330 temperature [ K 1
340
Figure 12. Effect of temperature on low field mobility for various lsochores. p r o = mobility at the critical temperature T:, (a) p : 1 p,, (b) P 5 Pc.
critical density. Figure 12 shows the relative increase of the mobility for several densities. After Lekner'O the mobility in the extended state is given by
with 6 the scattering length and S(0) the structure factor:
s(0)N- kBTnKT (6) where n is the number density and KT the isothermal compressibility. When the critical point is approached S(0) becomes infinite (cf. ref 38) and a minimum in the mobility ie expected. For this regime Lekner and Bishop39estimated the mobility with an expression containing the direct correlation length R of the liquid which varies only slowly in passing through the critical point: 8kBTcmR2/h2 (7) h = h / 2 r is Planck's constant, T,is the critical temlperature, and pc i s the mobility according to Lorentz's forniula obtained from eq 5 by setting S(0) = 1. Inserting for R the hard-sphere diameter, R = 6 = 4.4A, and taking B = 0.5 A (see below), we obtain p c = 57 cm2 V-' 5-l which is in close agreement with the experimental value. It should be noted, however, that Lekner's estimate of p, in argon p, =
1184
Doldissen, Schmidt, and Bakale
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
.
-5 IO6 1 3 c21T3'2 [105cm2s - ~K-3'2]
0.3
FI ure 13. p n as a function of c2/T3'* for various isochores in mol L- (V)2.4,(e)3.7,(0)4.7, 5.8,(0) 6.7,(A)7.2,(V)7.8,(X)
8..
(m)
8.35,(a)9.2,( 0 ) 10.0,
failed to give the experimental value by one order of magnitude and that our value for R may be too rough an approximation. In the vicinity of the critical density the decisive influence of the compressibility on the mobility as expressed in eq 5 and 6 is apparent. If the temperature is raised from 310 to 340 K at p = 6.7 mol L-l the compressibility decreases by a factor of 7.4 while a decrease of only 2% is observed when the temperature is increased form 300 to 330 K at p = 10.0 mol L-l. This strong temperature dependence of the compressibility along isochores near the critical density is qualitatively reflected by the relative increase of the mobilities with temperature shown in Figure 12, a and b. While the mobility rises by more than a factor of 2 in going from T = T, to T = 340 K on isochores between 5.8 and 7.2 mol L-I, it was found to be practically independent of temperature in the high density liquid with p I 9.2 mol L-I) (cf. Figure 12a). A similar density effect of the dependence of the mobility on temperature was observed at densities less than critical, where at p = 2.4 mol L-' p changes less than 25% in going from 290 to 340 K. For small densities corresponding to small pressures, KT approaches the value of p-l = (nkT)-' and S(0) = 1 results. Accordingly, temperature effects mediated by the structure factor disappear. We may try to evaluate the data according to eq 5 and 6 on an absolute scale. The isothermal compressibility is related to the velocity of sound c as follows:
where Cp and Cv denote the specific heats at constant pressure and volume, respectively, and d is the density in g cm-3. Cp/Cv is of tthe order of 1 and inserting eq 8 into eq 5 and 6 we obtain for the product of mobility and number density
where M = d / n is the molecular mass. Plotting p n as a function of c2/1'3l2 should yield a straight line. In Figure 13 the experimental data are shown on logarithmic scales. A line with a slope of I is in reasonable agreement with the data. From eq 9 we obtain 6 = 0.5 A. This value is considerably smaller than that of ii F= 1.5 A, calculated from V, data applying the Wigner-Seitz method in ref 25-27. 4.3. Hot Electron Effects. Proportionality between drift velocity and electric field strength is an indication that the electrons are in thermal equilibrium with the molecules of the liquid or dense gas. At higher values of the electric
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10-18 ~
j
'
'
10-l~ n[ v c d
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'
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Flgure 14. Electron drift velocity as a function of F I n (Fis the field strength and n the number density). Data at T = 320 K and different densities in mol L-'.
field strength F the drift velocity becomes a sublinear function of F. The electrons pick up more energy from the electric field than they can lose due to collisions. As a consequence the electron mean energy rises above thermal and the collision frequency increases. The drift velocity value u, and the field strength F, at which the deviation uD E F occurs are intimately connected with this process.40 From a theoretical analysis8*29 it follows that u, is related to the mean fractional energy loss f = AE/E which an electron undergoes in a collision by u,2
0:
fc2
(10)
in which c represents the velocity of sound in condensed matter, whereas it should be replaced by the thermal velocity of the electrons in gases.41 The high field data presented in Figures 7 and 8 and those at T > 260 K in Figure 4 can now be discussed in a qualitative way. At the ethane density of p = 2.4 mol L-l, u, = 2 X lo6 cm s-l at F, = 12 kV cm-l was observed. At still larger values of the field strength the drift velocity saturates at 4 X lo6cm s-'. These values are in good agreement with drift velocity data at 100 torr published by McCorkle et al.42 With increasing density u, decreases to a value of u, = 2 X IO5 cm s-l (F, = 15 kV cm-l) at p = 12.45 mol L-l. In the density region around the critical density the low field data show the relatively strong influence of the t,emperature while at higher field strengths the various curves merge (cf. Figure 8). This reflects the vanishing influence of the temperature once the electrons have gained superthermal energies. At low ethane pressures single scattering determines the transport properties. The energy loss is governed by the electronic properties of the isolated ethane molecule. A possible mode of energy loss is the excitation of rotational vibrations. H ~ b e r made * ~ a detailed study of the electron drift velocity in ethane gas at 298 K up t o pressures of 4 x lo4 torr. A careful analysis of the high field drift velocities revealed a resonance energy loss at 80-meV electron mean energy. He attributed this energy loss to excitation of rotational vibrations of the ethane molecule. Our gas phase data in the density range from 2.4 to 6.7 mol showed the same resonance energy loss.44 The electron mean energy is at low ethane densities a function of F l n only. For comparison we assume that this dependence is also applicable for the liquid densities. Electron drift velocities at T = 320 K are plotted as a function of F l n in Figure 14. At p = 11.5 mol L-' the F J n is one-fifth of the value at p = 2.4 mol L-l, corresponding to a mean energy of 20-30
Excess Electron Mobility in Ethane
The Journal of Physlcal Chemistry, Vol. 84, No. 10, 1980 11185
i
!
c
‘ 4
i 10
density [mol I-’] Flgure 15. Electron mobility as a function of density: (+) value at T = 295 K, taken from ref 43; (e)values in the saturated liquid, data above 18 mol L-’ taken from ref 12; (a, 0,X, 0,A) isothermic measurements at T = 340, 330, 320, 310, and 305.33 K, respectively.
characteristics of a thermally activated and electric field enhanced transport. 4.5. Positiue Ions. The mobilities of the positive ions as a function of temperature (cf. Figure 9) seem to obey Walden’s rule p + q = constant within the accuracy of the measurement. The transport properties of positive charge carriers have been the sub,ject of much discussion in the literature. Adamc~ewski~~ carried out extensive research in this field and found that for many liquid hydrocarbons p + q x = constant with x = 1.5 held. Dodelet and Freemana reported values of x = 1.1-1.3 for different hydrocarbons. Walden’s rule is based on the simple assumption that the ions can be represented by a sphere which carries out a viscous motion in the liquid under the influence of the electric field. Due to polarization forces the positive parent ion will drag a solvation shell along. Increase in temperature will not only change the viscosity but also the size of the solvation shell. At present no detailed theoretiical description of the transport properties of positive ionri in liquid hydrocarbons is available.
5. Conclusion The study of the electron mobility in fluid ethane EM a function of density, temperature, and electric field strength has revealed at least three different regimes of transport: Transport via localized states (16 5 p 5 21 mol L-l), transport in extended states (band mobility) (9 5 p 5 16 mol L-l), and transport as in a low density gas ( p 5 9 mol L-l) with a marked influence of temperatue near the vapor-liquid critical point. A more detailed description of the electron dynamics requires additional physical information in the various domains of the thermophysical states.
meV. It should be noted that at the low densities u 0: F changes into u 0: P6while at higher densities u a F with n > 0.5 is observed, Condensation introduces the action of intermolecular forces which may give rise to smaller energy loss quanta in the collision process. A somewhat different explamation may be inferred by the assumption of a Ramsauer-Townsend minimum in the scattering cross section. Christophorou and McCorkV observed that the Acknowledgment. The authors thank Dr. A. 0. Allen R-T minimum1 is shifted to lower electron mean energies of Brookhaven National Laboratory, Upton, N.Y., for with increasing ethane density. It would follow then that helpful criticism and comments. We also acknowledge in liquid ethane hot electron effects should show up at stimulating discussions with Professor Tagashira of Hoklower F / n values. kaido University, Japan. The realization of the mea4.4. Electron Mobility as a Function of Ethane Density. surement cell was greatly facilitated by the expertise of Although in the present experiments density and temprecision mechanic Mr. E. Klose, central workshop. G. B. perature could be varied independently of each other only thanks the U.S.Department of Energy for partial support a t p 5 12.45 mol L-l, a plot of the low field mobility as a of this work under Contract No. EP-7843-02-4746. function of density reveals three major mobility regimes References and Notes (cf. Figure 15). At low ethane densities the mobility is inversely proportional to the density. This region extends H. 1.Davis and R. G. Brown, Adv. Chem. Phys., 31, 392 (1975). A. 0. Alien, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 58 up to 9 mol L-I although a marked temperature influence (1976). is apparent from 3 to 9 mol-1 L-l. As a first-order apW. F. Schmidt, Can. J . Chem., 55, 2197 (1977). proximation this may be considered a perturbation that K. Funabastii in ”Advances in Radlation Chemistry”, Vol. 4, M. Burton and J. Magee, Ed., Wiley, New York, 1974, p 103. is superimposed on the general trend. Above 9 mol L-l the 8. N. Rao, FI. L. Bush, and K. Funabashi, Can. J . Chem., 55, 1952 mode of transport changes and p a p-5 is observed up to (1977). approximately 16 mol L-l. The mobilities are greater than R. M. Minday, L. D. Schmidt, and H. T. Davis, Chem. phys., 50, 1473 (1969). 1 cm2V-’ s-l and from the field dependence it is inferred R. Schiller, J . Chem. Phys., 57, 2222 (1972). that the transport occurs in extended states. In their M. H. Cohen and J. Lekner, Phys. Rev., 158, 305 (1967). deformation potential theory Bardeen and S h ~ c k l e y ~ ~ L. S. Miller, S. Howe, and W. E. Spear, phys. Rev., 166, 871 (1968). J. Lekner. Phys. Rev.. 158, 130 (1967). derived a mobility formula yielding fi 0: m,-5f2,with mI the G. Bakaie and W. F. Schmidt, Z . Natorforsch. A , 28, 5 (1973). effective electron mass. The large density variation in the W. F. Schmidt, G. Bakale, and U. Sowada, J. Chem. phys., 81,5275 liquid phase asi compared to the solid should be accom(1974). panied by a change of the exchange integral and thus of U. Sowada, G. Bakale, and W. F. Schmidt, Hlgh Energy Chem. (USSR), 10, 323 (1976). the effective mass. A m, a p2 dependence would yield the H. A. Giliis, N. V. Kiassen, G. G. Teather, and K. H. Lokan, Chem. observed variation of the mobility with density. A t denPhys. Lett., 10, 481 (1971). sities greater than 16 mol L-l a sharp drop of the mobility W. Doldissen, G. Bakale, and W. F. Schmidt, Chem. Phys. Lett., 56, 347 (1978). over three orders of magnitude is observed. The main W. DoMlssen, G. Bakale, and W. F. Schmidt, “Proceeding of the 6th factor determining the mobility in this domain seems to International Conference on Conductor Breakdown in Dielectric be the temperature. The electron transport exhibits the Liquids”, July 1978, Rouen, France, Editlons Frontieres, p 197.
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J. Phys. Chern. 1980, 84, 1186-1189 W. Doidissen, G. Bakaie, and W. F. Schmidt, J. Nectrostatics, 7, 247 (1979). R. D. Goodwin, H. M. Rcder, and G. C. Straty, Nati. Bur. Stand. Tech Note, No. 684 (1976). W. Pfeiffer, 2. Angew. Pbys., 32, 265 (1971). D. L. Pulfrey, J . Sci. Instrum., Ser. 2 , 2 , 503 (1969). W. Pfeiffer, Thesis, Darmstadt, 1970. R. W. Gallant, “Physical Properties of Hydrocarbons”, Vol. 1, Gulf Publication Co. Houston, 1970. N. Gee and G. R. Freeman, Cbem. Pbys. Lett., 60, 439 (1979). T. Kimura and K. Fueki, J. Chem. Phys., 86, 366 (1977). W. Tauchert, H. Jungblut, and W. F. Schmldt, Can. J. Cbem., 55, 1860 (1977). S. Noda and L. Kevan, J. Cbem. Phys., 61, 2467 (1974). Y. Yamaguchi, T. Nakajima, and M. Nishikawa, J. Cbem. Pbys., 71, 550 (1979). 0. Bakale, W. Tauchert, and W. F. Schmidt, J. Chem. Phys., 83, 4470 (1975). W. F. Schmidt in “Electron-Solvent and Anion-Solvent Interactions”, L. Kevan and B. Webster, Ed., Elsevler Scientific, Amsterdam, 1976, p 247. J. A. Jahnke, L. Meyer, and S. A. Rice, Pbys. Rev. A, 3, 734 (1971). J. M. L. Engels and A. J. M. Kimmenade, Cbem. Pbys. Lett., 48, 451 (1977).
(32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48)
J. P. Dodelet and G. R. Freeman, Can. J. Chem., 55, 2264 (1976). N. E. Cippoiini and A. 0. Alien, J. Cbem. Phys., 67, 131 (1977). J. Lekner, Pbys. Left., 27A, 341 (1968). N. E. Cippoilni, R. A. Holroyd, and M. Nishikawa, J . Chem. Pbys., in press. J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiiey, New York, 1954. “Landolt-Bornstein, Zahlenwerte und Funktionen”, Bd. I, 6. Auflage, Springer-Verlag, Berlin, 1950. P. A. Egelstaff, “An Introduction to the Liquid State”, Academic Press, New York, 1967, p 200. J. Lekner, and A. R. Bishop, Phil. Mag., 27, 297 (1973). W. Shsckley, Bell Syst. Tech. J., 30, 990 (1951). T. L. Cotbell and J. C. Walker, Trans. Fara&ySoc., 81, 1585 (1985). D. L. McCorkle, L. 0. Christophorou, D. V. Maxey, and J. G. Carter, J. Pbys. B , 11, 3067 (1978). 8. Huber, Z . Naturforscb. A , 24, 578 (1969). W. Doldissen, Thesis Free University of Berlin, 1980. L. 0. Christophorou and D. L. McCorkle, Can. J. Cbem., 55, 1876 (1977). J. Bardeen and W. Shockley, Pbys. Rev., 80, 72 (1950). I. Adamczewski, “Ionlzatkn, Conductivity and Breakdown in Dielectric Liquids”, Taylor and Francis, London, 1969. J. P. Dodelet and G. R. Freeman, Can. J. Cbem., 55, 2264 (1977).
Mobilities of Solvated Electrons in Polar Solvents from Scavenging Rate Constants J. A. Delalre,“ M. 0. Delcourt, and J. Belloni Laboratoire de Physico-Cbimie des Rayonnements (associ6 au CNRS), Universit6 de Paris-Sud, Brit 350, 9 1405 Orsay Cedex, France (Received July l7? 1979) Publication costs assisted by Laboratoire de Pbysico-Chlmie des Rayonnements, Orsay
Rate constants k , for the reaction of solvated electrons (e;) with biphenyl have been determined at room temperature by fast spectrophotometric detection after pulse radiolysis. In various solvents where both k, and mobilities of e; (he)are known, it has been checked that the scavenging reaction with biphenyl is diffusion controlled. Then the Smoluchowski equation may be used to determine pe from k , in solventa where conductivity measurements are difficult due to a high intrinsic conductance. Mobilities of e; have been derived in various solvents, including ethers (diethyl ether, 1,2-dimethoxyethane), amines (ethylamine, n-propylamine, ethylenediamine,hydrazine),and amides (hexamethylphosphorictriamide). The values of pe so obtained are compared with those from the literature. For example, there is a significant discrepancy between our values and those for HMPT, n-butylamine,and tert-butylamine determined by pulse conductivity in the microsecond time range, and this discrepancy is discussed. The value of pe in ethylenediamine is larger by a factor of 4 than that of p(Na-). Finally, a rough correlation exists between ps and the energy at the absorption maximum of e; (Emm).
Introduction When low-energy electrons are injected into a liquid, they generally become solvated and can be evidenced by several techniques, mainly by absorption spectra, conductimetry, and scavenging experiments. The properties of solvated electrons (e;) vary greatly with the nature of the solvent, and these studies have received considerable attention in the recent years. Among them, the mobility (p,) seems to be a very interesting property. Its experimental determination carried out mainly in hydrocarbons’ gives information on the nature of the interaction between the solvent and the electron and on the mechanism of electron transport. Furthermore, the value of pe is needed to calculate diffusion-controlled rate constants between e,- and neutral or charged s01utes~--~ or to introduce physical parameters such as diffusion coefficients in models which are developed at present in order to explain primary radiation effeck5p6 Some solvents (NH,, amines, ethers) have the property of dissolving alkali metals and of giving e;. Conductivity measurements can be made in principle by conventional However, due to the formation of ion pairs or anions, the limiting equivalent conductance depends on
the nature of the metal,g10 except for ammonia.’l For most of the liquids, transient pulses of photons or electrons have to be used, and conductivity measurements involve different methods, namely, “time-of-flight” measurement or determination of transient currents.12 Due to the fact that pure solvents of low intrinsic conductivity have to be used, we know many values of pe in hydrocarbons,l and the variations of pe with the length of the carbon chain or with the sphericity of the molecule have been disc~ssed.’~-~~ As for polar solvents, except for ethers,16 there are few determinations of pe in alcohols,17J8amines,18and water.lg Since many difficulties are present in conductivity measurements of pe in polar solvents, we examined whether the determination of diffusion-controlled rate constants can lead to reliable values of pe.
Experimental Section The pulse-radiolysis setup has been described earlier.20 A 600-keV Febetron 706 accelerator with a pulse width of 3 ns was used as the electron source, and it was associated with a spectrophotometric detection system having a whole risetime of 3.7 ns. Most of the rate constants measure-
0022-3654/80/2084-1186$01.0010@ 1980 American Chemical Society
