442
R. M. MTNDAY, L. D. SCHMIDT, AND H. T.DAVIC,
Mobility of Excess Electrons in Liquid Hydrocarbon Mixtures1 by R. M. Minday,* L, D. Schmidt, and H. T. Davis Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 66466 (Received July 81, 1971) Publication costs assisted by the Petroleum Research Fund
I n an effort to further elucidate the mechanism of excess electron transport in nonpolar hydrocarbons, electron mobilities are studied in mixtures of n-hexane and neopentane in both liquid and vapor and in liquid toluene, a molecule with a permanent dipole moment. Mobility measurements in the liquid mixtures as functions of mole fraction and temperature show that the mobility varies as exp[--zhE/RT] where 2 h is the mole fraction of hexane and E is a constant. The mobility in liquid toluene is almost the same as in benaene, showing that the permanent dipole moment of toluene does not significantly alter the transport process. From these results it is concluded that, while the mechanism of electron transport in liquid hydrocarbons appears to involve short lived traps in the fluid as suggested previously, these traps must be a collective property of the fluid rather than being associated with individual molecules,
Introduction Stable excess electronic-charge carriers have recently been observed in carefully purified hydrocarbon liquids,2 but their properties are considerably more complex than in the rare gas liquid^.^^* I n the alkanes the room temperature mobilities vary by as much as three orders of magnitude between isomers: from 0.07 in pentane to 70 cm2/(V sec) in neopentane. Electronic carriers have also been observed in liquid olefins and aromatics, with mobilities of 3.6 in 2-methylbutene-2 and 0.6 cm2/(V sec) in benzene.' Electron mobilities in all the hydrocarbons examined to date appear to show an Arrhenius dependence on temperature p = poe-EIRT
(1)
and possess larger activation energies in those liquids with lower mobilities. The purpose of this paper is to describe additional experiments which give further insight into the mechanism of electron transport in hydrocarbon liquids. A preliminary report of these results has been published.6 Room temperature electron mobilities have been measured as a function of mole fraction in mixtures of nhexane and neopentane; the temperature dependence of the mobilities in the mixtures has also been measured to determine activation energies. Free electrons have also been produced in liquid toluene, a molecule which possesses a permanent dipole moment; these results are compared with those in benzene, a molecule structurally similar to toluene but with no permanent dipole moment. Electron drift velocities were also measured in vapors of n-hexane and neopentane as a function of pressure and field to determine electron mobilities in these systems a t low densities. Experimental Section The hydrocarbon liquids were purified in an ultrahigh vacuum system by contact with zeolite molecular The Journal of Physical Chemistry, Vol. 76, No. 5 , 1978
sieves and evaporated barium films.2n Mobilities in the liquids were determined from the time of flight of photoinjected electrons across a drift space in a uniform electric field. The time of flight was measured by periodically interrupting the electron flow by either chopping the ultraviolet light source to the photocathode (single shutter method) or by electron shuttering within the mobility cell through use of a system of grids between the cathode and collector (double shutter method). Earlier publications2* give complete descriptions of the purification procedures and the two techniques of mobility measurement ; however, the procedures followed in the hexane-neopentane mixing experiment involve techniques which require discussion in some detail. The mixing experiment was performed in a system that contained two chambers connected to each other and to the pumps by three high-vacuum metal valves. One valve isolated from the pumps a manifold that connected the valves leading to the two sample chambers. Each chamber contained barium film getters, a cell for mobility measurements, and a cell calibrated for volume measurements. Hexane and neopentane samples of -50 cm3, >99 mol% initial purity (Phillips Petroleum Go.), were separately purified until electronic charge carriers were observed in each. Before any mixing, the mobility for each pure liquid was determined in
* Address correspondence to this author at the Esso Research and Development Laboratory, Linden, N. J. (1) Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society-Petroleum Research Fund Fellows. (2) (a) R. M. Minday, L. D. Schmidt, and H. T.Davis, J . Chem. Phys., 50, 1473 (1969); 54, 3112 (1971); (b) W.F. Schmidt and A. 0. Allen, J . Chem. Phys., 50, 5037 (1969); 52, 4788 (1970). (3) L. S. Miller, S. Howe, and W. E. Spear, Phys. Rev., 166, 871 (1968). (4) J. A. Sahnke, L. Meyer, and S. A. Rice, ibid., A , 3 , 734 (1970). (5) R. M. Minday, L. D. Schmidt, and H. T. Davis, Phys. Rev. Lett., 26,360 (1971).
443
MOBILITY OF EXCESS ELECTRONS
L
ebclrons in liquid argon
o~
eieciron8 in liquid nsopenlane
4Pc-t
t io
0
' ,
KP
ib
E(
-
I
I
..I
io.
V h )
Figure 1. Plot of electron drift velocity in liquid neopentane us. electric field. Drift velocities were measured using the electronic double shutter method. The solid line indicates measured drift velocities in liquid argon.s The variation of ffd with E shows that electrons in the polyatomic neopentane remain a t thermal energy even a t high fields.
the double shutter cell and the initial number of moles of each was determined from volume measurements and the densities. Inaccuracies of the double shutter method associated with measurement of grid spacings and with distortion of the electric field are estimated to be less than &lo%, but the precision obtainable with this method is =k2%in a given cell. Portions of one liquid were cryogenically pumped from one sample chamber to another through the manifold, after which the valves were closed and the liquids allowed to warm to room temperature. The mole fraction of the mixture was determined from the volume of liquid transferred. Mobility measurements were made over time periods of several hours to ensure that the liquids were thoroughly mixed and at thermal equilibrium. Activation energies of the mixtures were determined by measuring the mobility as a function of temperature in the double shutter cell immersed in various baths in the temperature range from 180 to 300°K. The mixing experiment was performed twice: in one experiment successive amounts of n-hexane were added to neopentane, in another neopentane was added to nhexane. It was often desirable to obtain other mole fractions after the liquids were mixed. This could be accomplished by slow distillation from one sample chamber to another since the volatility of neopentane is more than seven times that of hexane. Assumption of Raoult's law and ideal differential distillation allowed determi-
le 0
0.2 0.4 0.6 0.4 LO Mole Fraction Hexane in Neopentane
Figure 2. Plot of mobility vs. mole fraction of n-hexane in neopentane-hexane mixtures a t 300°K.
nation of the mole fractions in the residue and distillate from volume measurements. Vapor phase mobility measurements in hexane and neopentane were performed in an identical double shutter cell. The mobility was measured as a function of &/p, the electric field divided by the pressure in the cell. Different pressures were obtained by maintaining the vapor-filled cell at 300°K in contact with a chamber containing the liquid thermostated at a known lower temperature. The pressure in the vapor cell was then calculated from the vapor pressure of the liquid a t the thermostat temperature corrected for transpiration.
Results Hexane-Neopentane Mixtures. Room Temperature Mobilities. Prior to the mixture experiment, mobilities in the pure components were determined by double shutter measurements. The mobility in n-hexane was found to be 0.076 cm2/(V sec), very close to the values reported previously.2 Figure 1shows the drift velocity in neopentane as a function of field. The mobility of 70 cm2/(V sec) is somewhat above the value previously reportedYzb and is found to remain independent of field between 19 and 950 V/cm. Figure 2 shows a plot of the logarithm of the mobility vs. the mole fraction of hexane in hexane-neopentane mixtures. The data lie on a straight line indicating that the mobility in the mixture can be expressed very well by an equation of the form The J O U Tof~Physical ~ Chemistry, Vol. 78, No. 3,107S
R. M. MINDAY,L. D. SCHMIDT, AND H. T. DAVIS
444 pmix
pnpeAxh
(2)
where pnp = 70 cm2/(V sec) is the mobility in pure neopentane, A = -6.8 is the slope of the line in Figure 2, and Z h is the mole fraction of hexane. I n Figure 1we also show the electron drift velocity in liquid argon3 a t its normal boiling point. It is evident that 2)d in argon (and in the other rate gas liquids) dcviates from a linear dependence on & for 2)d > 105 cm/ (sec) while 2)d in liquid neopentane remains precisely proportional t o field up to a t least 106 cm/sec. Even more striking are the measurements in liquid tetramethylsilane2b for which the drift velocity is constant up t o z)d = 106 cm/sec. Deviations from linearity are due to excess kinetic energy of the electrons at high field~.~,BAbove lo5 cm/sec the data in the rare gases dependence predicted by can be fit quite well by the the Schottky theory of hot electron^.^ The absence of these deviations in the polyatomic fluids indicates that electrons remain at thermal energy even at very high fields and drift velocities. This is undoubtedly associated with the greater efficiency of energy transfer beT CK)
4
1.0
2.0 I/T
3.0
4.0
5.0
P K - l x IO')
Figure 3. Arrhenius plots of the mobilities in various liquid hydrocarbons. All curves lie on straight lines which extrapolate to 'v 150 cm2 (V sec) a t 1/T = 0. The Journal
of
Physical chemistry, Vol. 76,No. 9,1978
tween electrons and the polyatomic molecules of the fluid either due to inelastic collisions or trapping. Temperature Dependence. The temperature dependences of the mobilities are shown in Figure 3 for neopentane, 2-methylbutene-2, hexane, and two hexaneneopentane mixtures. Curves of log p vs. 1/T are shown in compressed form to allow comparison on a single graph and extrapolation to 1/T = 0; the actual determination of activation energies mas performed on graphs with expanded scales. It is seen that data for all systems can be described quite well by an Arrhenius expression. The activation energies in kcal mol-' for the pure liquids were 0.5 f 0.1 in neopentane, 2.6 f 0.3 in 2-methylbutene-2, and 4.3 f 0.3 in hexane, while in the hexane-neopentane mixtures they were 1.6 f 0.1 for x h = 0.35 and 2.9 f 0.15 for = 0.66. It is uncertain whether the mobility in pure neopentane is truly given by an Arrhenius expression because the temperature range over which neopentane is liquid is small and the mobility varies only slightly with temperature. The possibility exists for some other temperature dependence for neopentane. For the other liquids the temperature dependences could only be fit assuming an Arrhenius dependence. Figure 4 shows that the activation energy in mixtures of hexane and neopentane varies almost linearly with the mole fraction of hexane. I n fact all data except that for neopentane can be fit by a straight line passing
Mole Fraction Hexane in Neopentane
Figure 4. Variation of the mobility activation energy with xh in hexane-neopentane rnixhres. (6) M. Cohen and
J. Lekner, Phys. Rev., 158, 305 (1967).
MOBILITY OF EXCESS ELECTRQNS
445
through the origin; this suggests that the activation energy in neopentane may be zero and that the observed temperature dependence may have other causes. The experimental results for electron mobilities in liquid n-hexane and neopentane mixtures may be summarized by the expression p = pnpe-dWRT
/
(3)
with Eo = 3.7-4.3 kcal/mol. Toluene. Single shutter measurements of the drift velocity in toluene at fields between 1.6 and 3.3 kV/cm gave a mobility of 0.54 f 0.1 cmz//V sec). This mobility is only slightly below the value of 0.6 i 0.1 cm2/ (V sec) measured in benzene.2a Purification of toluene, as well as benzene,2awas considerably more difficult than for the alkanes; many cycles of barium contact and vacuum pumping were required before electronic charge ca,rriers were observed. At best, the current due to electrons was no more than 20% of the total current measured in the mobility cell. The remaining 80% of the current was ionic and probably resulted from electron scavenging impurities which could not be removed. All currents were shown to originate a t the cathode, however, because reversing the voltage polarity caused reduction of currents by several orders of magnitude. Because electron currents were so low in toluene and benzene, accuracy of the mobility measurements was not as great as in the other liquids studied, and it was not possible to determine the temperature dependences of the mobilities. Electron Mobilities in Gaseous Hydrocarbons. To determine whether the large difference in the mobilities between alkane isomers is only observed a t the high densities of the liquids rather than being associated with radically different scattering cross sections for the molecules, electron drift velocities were also measured in n-hexane and neopentane vapors using the double shutter method. Extensive mobility studies have been carried out for simple gases.7 Cottrell and Walkers have measured mobilities in polyatomic gases such as CH4, CzHs, and CzH4, but to our knowledge no low-field measurements have been reported in the larger alkanes. Room temperature drift velocities in pure n-hexane and neopentane vapors vs. & / p are shown in Figure 5. All data points for both systems lie on straight lines passing through the origin. I n mixtures of n-hexane and neopentane vapors the drift velocity varied linearly with mole fraction as expected for single molecule scattering. The temperature dependence of the drift velocity in n-hexane was also measured between 250 and 320°K. At constant E / p the drift velocity increased slightly with increasing temperature : a T+’’’% dependence fit the data fairly well over this range. If the electron molecule scattering cross section were determined entirely by the polarization potential, a T+’dependence would be observed. The observed dependence implies
Figure 5 . Drift velocity versus & / p for electrons in gaseous n-hexane (upper curve) and neopentane (lower curve) at 300°K.
that the scattering potential is a little “softer” than the polarization potential. From the gas data it is clear that none of the anomalies in the electron mobilities found in these liquids are observed a t low densities: the mobilities are almost the same for different isomers, the mobility in mixtures varies linearly with mole fraction, and the temperature dependence shows no activation energy. It is also interesting to extrapolate the gaseous drift velocities up to the liquid densities to determine what the mobilities in liquids would be if electron scattering a t high density were from isolated molecules. The data shown in Figure 5 give “liquid” mobilities of 30 and 15 cm2/(V sec) for n-hexane and neopentane, respectively. It should also be noted that in contrast to the liquids the mobility in hexane is slightly higher than in neopentane; this is as expected because the angle averaged cross section for the linear molecule should be slightly smaller than for the almost spherical neopentane molecule.
Discussion Although no quantitative theory presently exists which explains the behavior of excess electrons in hydrocarbons, the fact that the mobilities obey an Arrhenius temperature dependence argues strongly that electron transport involves trapping or localized states. The temperature and composition dependences ob(7) H. S. 147. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena.” Oxford University Press, London, 1952. (8) T. L. Cottrell and I. C . Walker, Trans. Faraday SOC., 61, 1585 (1965). The Journal of Physical Chemistry, Vol. 7 6 , N o . 5, 197.8
A. R. MONAHAN, J. A. BRADO, AND A. F. DELUCA
446 served in liquid n-hexane arid neopentane mixtures (and summarized by eq 3) allow one to conclude that the trapping process giving rise to the activation energy of the mobility is a collective effect. If this were not true, Le., if the activation process were a single molecule process (e.g., short-lived negative ion state, rotational resonance, etc., of a single molecule), then the activation energy a t low neopentane concentration should be approximately equal to the n-hexane activation energy in contradiction to our observation that the activation energy is proportional to the mole fraction of nhexane. I n fact, eq 3 requires that the activation energy E* of the mixture be of the form
E*
= EhXh
-k
EnpXnp
(4)
where Eh and E,, are the activation energies of pure hexane and neopentane, respectively. Thus, as in water, ammonia and amines, the electron trap in hydrocarbons involves many molecules acting collectively. However, unlike the polar liquids, the long-range Landau potential, of the form (5)
nearly equal for the hydrocarbons studied here. The traps must be due to local configurations of groups of molecules whose group-electron potential energy is favorable for trapping the electron. We have previously suggested the following mechanism of electron transport in hydrocarbons.2* The electron moves as a quasi-free particle ( i e . , in the conduction band) until it is trapped by a group of molecules in a configuration favorable for trapping. The electron then remains in the relatively immobile trap until thermally promoted back to the conduction band. The activation energy of the mobility then arises from the thermal promotion step. Another possible transport mechanism is electron tunnelling from trap to trap. In this picture the electron remains trapped until a thermal fluctuation (the activation step) provides a neighboring trap into which the electron may move by tunnelling. Theoretical investigation of these and other possible mechanisms suggested by recent work on amorphous solids will be the subject of a future pub1ication.O (9) NOTEADDEDIN PROOF.I n a note to appear in Chem. Phys.
Lett., the authors have shown that a polyatomic version, the Cohen-
is not important in forming the trap since D,and Do,, the static and optical dielectric constants, are very
Lekner quasi-free electron theory, accounts for the preexponential factor in eq 1 and for the observed field independence of electron mobilities in hydrocarbons.a
The Dimerization of a Copper (11)-Phthalocyanine Dye in Carbon Tetrachloride and Benzene by Alan R. Monahan,* James A. Brado, and Allen F. DeLuca Xerox Rochester Research Center, Rochester, New York Publication costs assisted by Xerox Corporation
14603
(Received .July 19, 1971)
Analyses of the absorption spectra of 4,4',4",4'''-tetraoctadecylsulfo~~amidophthalocyaninecopper(II) in carbon tetrachloride and benzene solutions demonstrate the existence of monomer-dimer equilibria in the 10-6-10-4 M concentration range. The dimerization constants, K,, = Cd/Cmz,are (2.97 f 0.02) X lo6M-I and (1.58 f 0.09) x lo* M-1 at 22 f 2' in carbon tetrachloride and benzene, respectively. The absorption spectra of the pure monomer and pure dimer were calculated and found to be nearly identical in both solvent systems. A close correspondence was found to exist between the spectra of the resolved solution dimer and the solid state absorption spectrum of the phthalocyanine dye. The nature of the intermolecular interactions between phthalocyanine dye molecules in solution and the solid state is discussed.
The electronic spectroscopy of phthalocyanines and porphyrins has received a great deal of attention due to the similarity in structure between these molecules and chlorophyll and In addition' the semiconduction and photoconduction properties Of The Journal of Physical Chemistry, Vol. 76, N o . 3, 1979
phthalocyanines as well as their importance as cyans in colored reprographic systems has added to the intensity of research on this class of compounds.l (1) F. H.Maser and A. L. Thomas, "Phthalocyanine Compound&" Reinhold, New York, N. Y., 1963.
