{690202}

[690295]

[690400]

(690547)

(699050)

[700140]

[700243]

(710064

[710642]

[719062]

{719091}

[719353]

[720034]

[720153]

[720242]

transport in solid and liquid Ar, Kr, and Xe,
PHYS. REV. 166(3): 871~78 (1968).

Spear, W.E.; Le Comber, P.G., A possible
explanation of the observed electron drift
velocity saturation in solid Ar, Kr, and Xe,
PHYS. REV. 178(3): 1454-56 (1969).

Schmidt, K.H.; Ander, S.M., Formation and
recombination of H,O* and hydroxide in
irradiated water, J. PHYS. CHEM. 73(9): 2846-
52 (1969).

Taub, L.A.; Gillis, H.A., Optical detection of
transient solvated electrons in pulseirradiated
viscous squalane, J. AMER. CHEM. SOC.
91(23): 6507-8 (1969).

Beck, G., Elektrische Leitfachigkeitsmessungen
zum Nachweis geladener Zwischenprodukte der

Pulsradiolyse, INT. J. RADIAT. PHYS.
CHEM. 1: 361-71 (1969).
Miyakawa, T.; Dexter, D.L., Stability of

electronic bubbles in liquid neon and hydrogen,
PHYS. REV. 184(1): 166-72 (1969).

Schmidt, W.F.; Allen, A.O., Mobility of
electrons in dielectric liquids, J. CHEM. PHYS.
52(9): 4788-94 (1970).

Barker, G.C.; Fowles, F.; Sammon, D.C.;
Stringer, B., Pulse radiolytic induced transient
electrical conductance in liquid solutions. Part
1. Technique and the radiolysis of water,
TRANS. FARADAY SOC. 66(6): 1498-508
(1970).

Fowles, P., Pulse radiolytic induced transient
electrical conductance in liquid solutions. Part
4, The radiolysis of methanol, ethanol, 1-propanol
and 2-propanol, TRANS. FARADAY SOC. 67(2):
428-39 (1971).

Baxendale, J.H.; Bell, C.; Wardman, P., Pulse
radiolysis observations of solvated electrons in
liquid hydrocarbons, CHEM. PHYS. LETT.
122): 347-8 (1971).

Minday, R.M.; Schmidt, L.D.; Davis, H.T.,
Excess electrons in liquid hydrocarbons, J.
CHEM. PHYS. 54(7): 3112-25 (1971).

Holroyd, R.A.; Allen, M., Energy of excess
electrons in nonpolar liquids by photoelectric
work function measurements, J. CHEM. PHYS.
54(12): 5014-21 (1971).

Jahnke, J.A.; Meyer, L.; Rice, S.A., Zero-field
mobility of an excess electron in fluid argon,
PHYS. REV. PT, A 3(2): 734-52 (197).

Fuochi, P.G.; Freeman, G.R., Molecular
structure effects on the free-ion yields and
reaction kinetics in the radiolysis of the
methyl-substituted propanes and liquid argon:
Electron and ion mobilities, J. CHEM. PHYS.
56(5): 2333-41 (1972).

Vannikov, A.V.; Mal'tzev, E.1.; Zolotarevskii,
V.L; Rudnev, A.V., Transient charged
radiolysis products of organic liquids studied by
electrical and optical methods, INT. J.
RADIAT. PHYS. CHEM. 42): 135~48 (1972).

Schiller, R., Localization probability and
mobility of electrons in liquid hydrocarbons, J.
CHEM. PHYS. 57(5): 2222-3 (1972),

16

[720269]

(720404)

[720439]

[720574]

1720839}

[720840]

1727460)

[728005]

[728065]

[729022]

[729075]

[729251]

(730316]

{730414}

[731035]

[731030]

Dodelet, J.-P.; Freeman, G.R., Mobilities and
ranges of electrons in liquids: Effect of
molecular structure in C,—Cyy alkanes, CAN. J.
CHEM. 50(16): 2667-79 (1972).

Schmidt, K.H., Electrical conductivity
techniques for studying the kinetics of
radiation-induced chemical reactions —_ in

aqueous solutions, INT. J. RADIAT. PHYS.
CHEM. 4(4): 439-68 (1972).

Holroyd, R.A.; Dietrich, B.K.; Schwarz, H.A.,
Ranges of photoinjected electrons in dielectric
liquids, J. PHYS. CHEM. 76(25): 3794-800
(972).

Rudnev, A.V.; Vannikov, A.V.; Bakh, N.A.,
Optical absorption spectra and mobility of
solvated electrons in aliphatic alcohols, HIGH
ENERGY CHEM. 6(): 416-7 (1972), Transl.
from Khim, Vys. Energ. 6(5): 473-5 (1972).

Loveland, R.J.; Le Comber, P.G.; Spear, W.E.,
Experimental evidence for electronic bubble
states in liquid Ne, PHYS. LETT. A 39(3):
225-6 (1972).

Loveland, R.J.; Le Comber, P.G.; Spear, W.E.,
Charge transport in the diatomic molecular
solids and liquids: N,, O,, and CO, PHYS.
REV. B 6(8): 3121-7 (1972).

Nakato, Y.; Ozaki, M.; Tsubomura, HL,
Photoionization and Rydberg states of
tetraaminoethylenes in organic solutions, J.
PHYS. CHEM. 76(15): 2105-12 (1972).

Jahnke, J.A.; Holzwarth, N.A.W., Rice, S.A.,
Comments on the theory of electron mobility in
simple fluids, PHYS. REV. PT. A 5(1): 463-7
(1972).

Fueki, K., On the mobility of quasifree electrons
in liquid methane, CAN. J. CHEM. 50(20):
3379-80 (1972).

Minday, R.M.; Schmidt, L.D.; Davis, H.T.,
Mobility of excess electrons in liquid
hydrocarbon mixtures, J. PHYS. CHEM. 76(3):
442-6 (1972).

Bruschi, L.; Mazzi, G.; Santini, M., Localized
electrons in liquid neon, PHYS. REV. LETT.
28(23): 1504-6 (1972).

Schwarz, K.W., Charge~carrier mobilities in
liquid helium at the vapor pressure, PHYS.
REV. A 6(2): 837-44 (1972).

Schoepe, W.; Rayfield, G.W., Tunneling from
electronic bubble states in liquid helium
through the liquid-vapor interface, PHYS.
REY. A 7(6): 2111-21 (1973).

Schiller, R.; Vass, S.; Mandics, J., Energy of
the quasi-free electrons and the probability of
electron localization in liquid hydrocarbons,
INT. J. RADIAT. PHYS. CHEM. 5(6): 491-503
(1973).

Dodelet, J.-P.; Shinsaka, K.; Freeman, G.R.,
Electron mobilities in liquid olefins: Structure
effects, J. CHEM. PHYS. 59(3): 1293-7 (1973).

Bakale, G.; Schmidt, W.F., Excess electrons
and positive charge carriers in liquid methane,
L, Z. NATURFORSCH. TEIL A 28(3-4): 511-8
(1973).



TABLE 2. Zero-field mobility in liquid hydrocarbons — Continued

Name Even. Method* Reference
kcal/mole

n—Pentane 0.16 296 — H 700140
0.08 300 — ds 719062

0.15 293 — pe 731035

0.14 296 — H 741036

2~Methylbutene-2 3.6 300 2.6 ds 719062
Neopentane 68 296 0.32 ds 729022
70 295 — ny 739187

70 258-296 0 pe 741111

Tetramethylsilane 90 296 — H 700140
100 223-292 0 H 750003

Cyclopentane 1 296 — H 700140
n-Hexane 0.076 300 4.35 ds 729022
0.09 296 5.5 ate 700140

0.082 296 — H 741036

0.069 294 = H 750003

2,2-Dimethylbutane 10. 296 14 H 700140
12. 295, _ ad ‘739187

2,3-Dimethylbutene—2 5.8 293 — pe 731035,
Cyclohexane 0.35 296 — H 700140
0.45 294 29 pe 720269

0.24 296 H 741036

0.22 294 — H 750003

Cyclohexene 1.0 293 3.6 pe 731035,
Methyleyclohexane 0.068 296 47 H 741036
2,2,4-Trimethylpentane 1. 296 — H 700140
5.3 293 1.16 H 750003

2,2,3,3-Tetramethylpentane 5.2 295 15 pe 720269
2,2,4,4-Tetramethylpentane 24. 295 14 pe 720269
2,2,5,5~Tetramethylhexane 12 293 Ll pe 720269
Benzene 0.6 300 — ds 719062
0.11 293 14 pe 741110

Toluene 0.54 300 — ds 129022
0.063 293 3.4 pe 741110

o-Xylene 0.018 292 44 pe 741110
m-Xylene 0.057 292 45 pe 741110
p-Xylene 0.062 293 — pe 741110
1,2,3-Trimethylbenzene 0.022 293 48 pe 741110
1,2,4-Trimethylbenzene 0.035, 292 4.3 pe 741110
1,3,5-Trimethylbenzene 0.16 293 3.2 pe 741110
1,2,3,4-Tetramethylbenzene 0.040 323 5. pe 741110

“Abbreviations: ds, double shutter; H, Hudson; pc, pulse conductivity; tl, thick layer.

The most striking feature of this work is the variation in the mobilities observed in the alkanes,
which range over a factor of 1000 in a group of compounds whose other properties are very similar.
There is a general correlation of mobility with other electronic properties — free—ion yields and V, values
— but not with dielectric constants or other commonly listed properties. The most important factor in
fixing _ seems to be the symmetry of the molecules. Those of nearly spherical shape — methane,
neopentane, TMS — have the highest mobilities, and Bakale and Schmidt [731036, 739187] have shown
that the apparent electron mobility in these compounds decreases with increasing field, as in liquid
argon. The difference in electron mobilities between liquid ethane and methane is striking, and the field
effects are actually opposite, with the apparent mobility at 200 K increasing in ethane at fields above 70
kV/cm [740317]. Propane behaves similarly to ethane, with the apparent mobility increasing above 100
kV/cm. In other hydrocarbons, the velocity remains proportional to the field up to the highest field
studied. In all cases except methane and TMS, the observed mobilities as a function of temperature

10


Drift Mobilities and Conduction Band Energies of
Excess Electrons in Dielectric Liquids *

A. O. Allen

Department of Chemistry
Brookhaven National Laboratory
Upton, N.Y. 11973

The properties of electrons in liquids which are covered in this review include drift
mobilities and the energy level (V,) at the base of the conduction band. Tables are given
of zero-field electron mobilities for several liquefied diatomic and inert gases, a number of
aliphatic and aromatic hydrocarcarbons, and polar solvents. V, values are given for liquid
helium and argon, a number of hydrocarbons, tetramethylsilane and tetramethyltin.
Theories attempting to explain these results are described in a qualitative way.

Keywords: Conduction band; drift mobility; energy levels; excess electrons; hydrocarbons;
ion mobility; liquids; mobility; quasifree electrons; solvated electrons.

1. Introduction

Modern views on the nature of matter arose from experiments on electrical conduction in gases,
which led to the discovery of the electron as a constituent particle of all substances. Application of the
electron concepts to electrical conduction in solids then led to such advances that the majority of all
physicists now devote themselves to solid state studies. Though such great results have followed from
studies of electrons in gases and solids, little work on electrons in liquids has been done until very
recent years. Experiments at the University of Chicago on electrons in liquid helium and argon, and
their remarkably successful theoretical interpretation, have in the last seven or eight years stimulated
work at other laboratories on a variety of other liquids. Much of this work has been motivated by desire
to obtain better basic understanding of effects of radiation on materials and biological organisms.

The most significant, readily measurable properties of the electron in a medium are its drift
mobility, and the energy level of the conduction electrons. This publication summarizes data on these
topics.

2. Definitions
An electron or ion, accelerated in a fluid medium by an electric field E, quickly attains a terminal

velocity v (when the frictional force balances the electrical force) which is proportional to the field, if the
field is not too large:

v=yE e)
The mobility 1 is always given in cm/s per volt/cm, or cm?V-!s~!. Values of jz are characteristic of the

charged species and the medium. The mobility of an electron or singly—charged ion is related to the
diffusion coefficient D by the Nernst equation

yw = DelkT @

a data review prepared for, and in cooperation with, the Radiation Chemistry Data Center of the Radiation Laboratory, University of Notre Dame, Notre Dame,
12 46556. The Laboratory is operated under contract with the Energy Research and Development Administration. The work of the Center is supported in part by the
National Bureau of Standards, Office of Standard Reference Data



1738029]

739187]

[740079]

(740192]

(740317)

[740346]

(741012]

[741036]

(741110)

Kestner, N.R., Jortner, J., Conjecture on
electron mobility in liquid hydrocarbons, J.
CHEM. PHYS. 59(1): 26~30 (1973):

Bakale, G.; Schmidt, W.F., On excess electron
transport in hydrocarbons, CHEM.
PHYS. LETT. 22(1): 164-6 (1973).

Holroyd, R.A.; Tauchert, W., On the relation of
electron mobility to the conducting state energy
in nonpolar liquids, I. CHEM. PHYS. 609):
3715 (1974).

Noda, S.; Kevan, L., Conduction state energy of
electrons in liquid methane and ethane, J.
CHEM. PHYS. 61(6): 2467-8 (1974).

Schmidt, W.F.; Bakale, G.; Sowada, U., Excess
electrons and positive charge carriers in liquid
ethane, J. CHEM. PHYS. 61(12): 5275-8 (1974).

Bakale, C.; Sowada, U.; Schmidt, W.F., 1974
‘Ann. Rept. of the Conf. on Electrical Insulation

and Dielectric Phenomena, U.S. National Acad. «

Sci., 1975.
Robinson; M.G.;
mobilities. and ranges in liquid C,.~C,
hydrocarbons and in xenon: Effects of
temperature and field strength, CAN. J.
CHEM. 52(3): 440-6 (1974).

Allen, A.O.; Holroyd, R.A., Chemical reaction
rates of quasi free electrons in nonpolar liquids,
J. PHYS. CHEM. 78(8): 796-803 (1974).
Shinsaka, K.; G.R.. Epithermal

Freeman, G.R., Electron

Freeman,

17

(7411)

(741134)

[747297]

[749281]

[750003]
[750009]

[750045]

electron ranges and thermal electron mobilities

in liquid aromatic hydrocarbons, CAN. J.

CHEM. 52(20): 3495-506 (1974).
i K; Freeman, G.R., Electron

3 and ranges in solid neopentane:
Effect of liquid-solid phase change, CAN. J.
CHEM. 52(20): 3556-9 (1974).

Kimura, T.; Freeman, G.R., Band-nonband
mohility transition for extra electrons in liquid
xenon, CAN. J. PHYS. 52: 2220-22 (1974).
Holroyd, R.A.; Russell, R.L., Solvent and
temperature effects in the photoionization of
tetramethyl-p-phenylenediamine, J. PHYS.
CHEM. 78(21): 2128-35 (1974).

Tauchert, W.; Schmidt, W.F., Energy of the
excess electron state in liquid methane, Z.
NATURFORSCH. TEIL A 29(10): 1526 (1974).

Allen, A.O.; Gangwer, T.E.; Holroyd, R.A.
Chemical reaction rates of quasifree electrons
in nonpolar liquids. U., J. PHYS. CHEM.
79(1):25-31 (1975).

Holroyd, R.A.; Tames, S.; Kennedy, A., Effect
of temperature on conduction band energies of
electrons in nonpolar liquids, J. PHYS. CHEM.
79(26): 2857-60 (1975).

Sowada, U.; Hakale, G.; Yoshino, K.; Schmidt,
W.F., Electric field effect on electron capture
by SF, in liquid argon and xenon, CHEM.
PHYS. LETT. 34(3): 466-9 (1975).



Vo lev)

-o.6! ee oe ee

a
200 240 280 320 360

T(K)

Ficure 9. Temperature effects on Vo values, from [750009]
Triangles (point down), n-hexane. Circles with cross,
n-pentane, Squares, 2,2,5-trimethylhexane. Triangles

(point up), 2,2,4-trimethylpentanc. Diamonds, 2,2-di-
methylbutane. Circles, 2,2,4,4-tetramethylpentane.
Diamonds with cross, tetramethylsilane.

obtained by work function measurements. The method of photoionization of solutions gives only relative
V, values for different solutes at any one temperature; the results for room temperature in [747297] and
[727460] were assigned absolute numbers by comparing the results for a few. liquids to the V, values
previously determined for the same liquids by the work function method. Temperature effects on V, are
not accurately determined by the photoionization method since the ionization efficiency at any
wavelength may vary with temperature in an unknown manner. Consequently the V, values quoted in
the above references for temperatures other than that of the room are not given here. Determinations by
the work function method made on different days with different preparations reproduce to no better than
+0.05 eV. Determinations made on the same day reproduce to about +0.02 eV.

Considerable effort has been expended on theoretical estimation of V,. Lekner [670446] in the
course of calculating the potential distribution in liquid argon for estimation of the mobility, obtained a
value of —0.46 eV for V,, compared with the experimental value of —0.33 eV. Springett, Jortner and
Cohen [688042] developed a more general approximate expression, which in the case of argon gave a
value of -0.63 eV. Miyakawa and Dexter [699050] provide an alternative approximate expression, which
leads to similar results. Both methods use the gas—phase scattering length as a basic datum; and this
may not be very accurately established experimentally. They also assume isotropic molecules, so the
theories provide only a very rough guide for polyatomics. K. Fueki [728065] estimated by these methods
V, for methane to be —0.74 eV,.in poor agreement with later measured values 0.0; but he used an
estimated value for the gas-phase scattering length; one hopes that use of an experimental value for this
parameter would result in a better number for V.. In these theories, V, is regarded as the sum of a
negative polarization energy term and a positive kinetic energy term which results from the electron
being restricted to the free volume. For liquid argon, these terms are respectively —2.50 and 1.87 eV, so
that the sum, V,, is the difference between two larger numbers and is accordingly inaccurate in absolute
value.

The relation between V, and , for aliphatic hydrocarbons has been much discussed. Comparison
between the data of tables 2 and 4 shows a close correlation, especially for the linear and branched
alkanes. N. R. Kestner and J. Jortner [738029] suggested an explanation in terms of a “percolation
theory”, in which V, is assumed to be linearly related to an “average electron energy” in the liquid,
which in turn is related to the volume fraction of the liquid in which the electrons are in the quasifree

14


repulsive terms lead to a highly positive V,; but in the liquid, the atoms are free to move away from the
electron and form the low—mobility “bubble”. The bubble will be stable when V, is larger than the sum
of energy terms required to form the bubble (pressure, surface tension and electrostatic forces). Before
the mobility measurements were made, Miyakawa and Dexter [699050] calculated V, for neon by two
methods, and concluded that the electron in a bubble should be only slightly more stable than in the
conduction band. If this is true, application of a few hundred atmospheres pressure should collapse the
bubble and cause a dramatic increase in the mobility; but this experiment-has not been tried.

The electron mobility in liquid argon has been examined in great detail both experimentally and
theoretically (figs. 2-4). Lekner [670446] calculated the drift velocity of electrons in liquid argon for a
temperature near the melting point (84 K) using methods developed for explaining the conductivity of
semiconductors, but calculating the potentials within the liquid from the atomic polarizability and
electron scattering data for dilute argon gas. The final result gave the zero-field mobility of the liquid to
within 5% of the experimental value, and also agrees extraordinarily well with the high-field electron
velocity data, much of it obtained after the calculation was done (fig. 3). The levelling off of the velocity
at the very highest fields studied was explained in a theory of Spear and Le Comber [690202]. Moreover,
the decrease in mobility between 84 and 110 K follows the expected 7-** law. Thus it may be said that
the electron mobility in liquid argon up to 110 K is basically understood at least as well as any property
of the liquid. At higher temperatures the mobility rises to a high maximum, with a sharp fall appearing
just below the critical temperature (151 K) (fig. 2). The cause probably lies in changes of the electron’s
environment caused by microscopic density fluctuations that appear in the liquid as the critical

1000 -- °
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& FIGURE 2. Comparison of apparent electron mobilities at —100
1 V/em on a 50-atm isobar in liquid argon. Data from
ra a the isothermal experiments were obtained by taking
y2I f 1 1 1 1 1 sli
10 the value at 50 atm from plots of apparent mobility
05 10 eet 29. 2S 30 Versus pressure at constant temperature. Refer to
TUK [660394] for data obtained using a Po? alpha-ray
Ficure 1. Mobility of electrons in liquid helium at pressures source. The figure shows the agreement between data
below 1 atm, plotted against recriprocal absolute using ‘different sources and between data obtained
temperature: open circles {729251 closed circles through different thermodynamic routes. Figure
{6000073}; open triangles (620159). from {719353}


Amsotropy of the molecular polarizability and the presence of permanent dipoles in the liquid create
stronger irregularities which break up the electron wave and cause the electrons to become localized at
the points of lowest potential. In a solid crystal or glass, these electrons are said to be trapped, and do
not contribute to the conductivity. In a liquid, the electrons are said to be solvated, and the whole
complex of electron and trapping molecules can move in an electric field and exhibit conductivity; but
its mobility is orders of magnitude less that that of a quasifree electron, and is similar to that of ordinary
molecular ions. The mobility of the quasifree electron normally decreases with increasing temperature,
because of increased phonon scattering; but the mobility of a solvated electron like that of a molecular
ion depends largely on the fluidity of the medium and increases with increasing temperature.

The energy level of a quasifree electron in a liquid, relative to a free electron in the vacuum, is
called V,, and is always given in electron volts. For a given liquid, V, increases with density and
therefore decreases with rising temperature. The exchange forces tend to repel the electron from the
molecules of the liquid, but the electron also induces dipoles in the molecules by polarization, which
tend to attract the electron. The greater the attraction compared to the repulsion, the more negative is
V,. In liquid helium, the polarizability is low and V, is distinctly positive. An electron formed by
ionization in this liquid repels the atoms of the liquid and forces about itself a region of reduced density,
the behavior of which can be closely approximated by assuming the electron to be enclosed by a bubble
with a sharp boundary, containing no helium. The mobility of such a “bubble” is very close to that of a
molecular ion, like that of a solvated electron; but the nature of these three negatively charged entities’
is thought to be entirely different.

Liquid hydrocarbons exhibit a wide range of electron mobilities lying between those of quasifree and
solvated electrons. It is thought that the traps in these liquids hold electrons less firmly than those in
polar liquids, so that diffusion of electrons from trap to trap is possible. Two mechanisms are proposed
for this passage. In one model, the electrons are in shallow traps having energies not far below the
conduction band, so that a thermodynamic equilibrium exists between solvated and quasifree states. On
this model, the observed mobility is given by the quasifree mobility, multiplied by the quasifree
equilbrium fraction, which increases with temperature. For the other model, we note that quantum
mechanics allows an electron, retained in a certain energy state by a potential barrier, to leak through
the barrier, provided a state of matching energy exists for the electron on the other side of the barrier.
In general, a potential trap in a liquid, adjacent to a solvated or trapped electron, is not likely to be of
the right size to provide the energy match that will make leakage possible; but thermal agitation
continually alters the shape of the traps, so that the higher the temperature the more frequently the
energy match will occur. This model is called phonon—assisted—hopping, or simply hopping.

The bubble model, hopping model and passage through the conduction band lead to similar
phenomenological predictions. Perhaps the future will provide a more comprehensive theory for cases in
which the electron is neither firmly solvated nor entirely “quasifree”.

3. Methods of Measurement

3.1. Electron Mobilities in Non—Polar Liquids

Measurements of drift times in work reported here have involved electron lifetimes of at least
several microseconds. Extremely high purity of the liquid is then required with respect to electron—
attaching impurities. If the rate constant for the electron—impurity reaction is 10° M-'s"! (not unusually
high) and a mean electron lifetime of 10-°s is required for the measurement, the concentration of
reactive impurity should be kept below 10°M.

Given sufficient purity, the double—shutter method is the most direct and accurate [660394].!
Electrons formed at a cathode, usually by ionization, drift to a collecting anode, while retarding
potentials are periodically applied: to a pair of double grids, acting as gates, located in the drift space.
The current reaches a maximum when the time to drift between the grids is a multiple of the period
between openings of the gates. By this method, electron mobilities in liquid argon have been measured
with an accuracy of +1.5% [719353].

Numbers in brackets indicate the references at the end of this paper.


where e is the electronic charge, k Boltzmann's constant and T the absolute temperature.

Under steady-state conditions with a constant applied field, the amount of positive charge reaching
the cathode per unit time must equal the amount of negative charge reaching the anode. Then the total
current density in unit field (in units of ions per second per cm”) is

IE = Ecqabte + ECpZplty @)

where the subscripts refer to negative and positive charge carriers, c is concentration in ions per cm*, z
is the number of electron charges on each ion (unity in all cases considered here) and the two sums are
equal. The current density J in amperes per cm?is related to i by i = IN/F = I + 6.24 x 10" where N is
Avogadro’s number and F is the Faraday constant. The ratio I/E is the conductivity o; if E is in
volts/em, o is given in ohmTM'cmTM

However, under different conditions, the physical systems governed by this equation may be quite
different. In electrolyte solutions, the applied field is always relatively small, and the concentration of
ions so large (c > 10") that a small fractional excess of ions of one sign would lead to an internal field
large compared to the applied field, so this excess charge would neutralize itself by diffusion. Hence in
the physical chemistry of electrolyte solutions, the maintenance of electrical neutrality in all
macroscopic volumes is assumed. The conductivity of the solution per g—equivalent of total electrolyte
per cm! (extrapolated to zero concentration) is called A,:

— o@N/Sez — FilEXcz @)

where %cz is the total number of unit charges of either sign per cm*. A, is the sum of equivalent
conductances of each individual ion present, weighted by their respective relative concentrations:

A, = TAgea/Ecz + Edpep/Ecz (5)
Comparing eqs (4) and (5) with eq (3), we see that
A=F 1=96500 ps (6)

if as usual A is given in cm?ohmTM'g—equivTM and yz in cm?V~'s"'. This equation is used in determining
the mobility of solvated electrons.

In an ionization chamber, as used to determine the dose rate from ambient y— or X-rays, the
situation is quite different. Here the field is kept high so that ions are swept out of the chamber as fast
as formed. The positive and negative ions have concentration gradients in opposite directions, and the
mean concentration of each ion varies inversely with its mobility; so with parallel plates electrical
neutrality exists only at one plane in the chamber. It is still true under constant irradiation, that at the
steady state half the current is carried by positive charges and half by negative; but the time required to
attain this state after any change in conditions is the time for the slowest ion to traverse the entire width
of the chamber. Drift time determinations for highly mobile electrons are made under conditiuns
resembling those of the ion chamber.

The states available to an electron in a liquid resemble those in a solid, and fall into two classes:
localized and delocalized. The delocalized state is that of a conduction electron in a metal or
semiconductor, or an electron moving through a dilute gas; such electrons are often called quasifree.
Only an electron in a vacuum is really free; the motion of the quasifree electron is limited by scattering
from gas molecules, or (in crystals) from lattice imperfections or irregularities due to thermal motions
(phonon scattering). That existence of delocalized states in condensed matter does not depend on long—
range crystalline order is proved by the simple fact that liquid mercury is a good conductor. In most
non-metallic liquids, electrons introduced by ionization (or by photodetachment from immersed metal
surfaces) enter the delocalized conduction state and will remain there if the electrical potential field
within the liquid is reasonably regular. Monatomic liquids (argon) and those polyatomics having
molecules of nearly spherical symmetry (neopentane) provide the most regularly varying potentials.

2


condition. R. Schiller [730414] has developed a theory of the electron in a hydrocarbon based on the
bubble model, assuming that the solvated state can be treated as an electron in a bubble of fluctuating
size. The two theories lead to somewhat different relations between V, and log yu,. For a simple test of
these theories, Holroyd and Tauchert [740079] measured V, for a series of mixtures of n—hexane and
neopentane, since it had been found (Minday et al., [729022}) that log 2, varied linearly with mole
fraction in these mixtures. It was found that V, was also linear with mole fraction, and hence with log
Me, while the theories give a quite different prediction (fig. 7). A similar result was found in mixtures of
hexane and tetramethylsilane. The linear relation found experimentally was unexpected, since many
different factors have been thought to affect the values of V, and yu. Further insights are needed.

Figures 2 and 4 are reproduced by permission
of the American Institute of Physics from Physical

Acknowledgements

Review, Part A, Volume 3, 1971, pp.734-52.

Figures 3 and 5 are reproduced by permission
of the American Institute of Physics from Physical
Review, Volume 166, 1968, pp.871-8 and Volume

150, 1966, pp.122—-45, respectively.

{219001}

[460003]

[539005)

[539006]

{599008}

{600073}

{609010}

[620159]

[638002]

{658008}

Figure 6 is reproduced by permission of the
National Research Council of Canada from the
Canadian Journal of Physics, Volume 52, 1974,
pp-2220-2222.

Figure 7 is reproduced by permission of the
American Institute of Physics from the Journal of
Chemical Physics, Volume 60, 1974, p.3715.

References

Kraus, C.A., Solutions of metals in non—metallic

solvents. VI. The conductance of the alkali
metals in liquid ammonia, J. AMER. CHEM.
SOC. 43: 749-70 (1921).

Hudson, D.E., Method of measuring the drift
velocity of electrons in gases, MDDC-524,
1946, 23p.

Saxton, R.L.; Drickamer, H.G, Diffusion in
liquid sulfur, J. CHEM. PHYS. 21(8): 1362-3
(1953).

Cova, D.R.; Drickamer, H.G., The effect of
pressure on diffusion in liquid sulfur, J. CHEM.
PHYS. 21(8): 1364-5 (1953).

Evers, E.C.; Frank, P.W.,Jr., Solutions of
metals in amine solvents. II. A conductance
function for dilute solutions of sodium in liquid
ammonia, J. CHEM. PHYS. 30(1): 61~4 (1959).

Reif, F.; Meyer, L., Study of superfluidity in
liquid He by ion motion, PHYS. REV. 119%(4):
1164-73 (1960).

Dye, J.L; Sankuer, R.F.; Smith, G.E., Ion
transport in sodium-ammonia solutions, J.
AMER. CHEM. SOC. 82: 4797-4803 (1960).

Meyer, L.; Davis, H.T.; Rice, S.A.; Donnelly,
R.J., Mobility of ions in liquid He‘I and He’ as
a function of pressure and temperature, PHYS.
REV. 126(6): 1927-34 (1962).

Zessoules, N.; Brinkerhoff, J.; Thomas, A.,
Recombination and mobility of nuclear radiation
induced ionization in liquid hydrogen, J. APPL.
PHYS. 347): 2010-4 (1963).

Jortner, J.; Kestner, N.R.; Rice, S.A.; Cohen,
M.HL, Study of the properties of an excess~
electron in liquid helium, I. The nature of the
electron-helium interactions, J. CHEM. PHYS.
43(8): 2614-25 (1965).

{658009}

[659054]

[660394]

[660590]

{670195}

[670446]

[680854]

(687280]

(688042)

[688043]

{689006}

15

Hiroike, K.; Kestner, N.R.; Rice, S.A.; Jortner,

J., Study of the properties of an excess electron
in liquid helium. If. A refined description of
configuration changes in the liquid, J. CHEM.
PHYS. 43(8): 2625-32 (1965).

Woolf, M.A.; Rayfield, G.W., Energy of negative
ions in liquid helium by photoelectric injection,
PHYS. REV. LETT. 15(6): 235-7 (1965).

Schnyders, H.: Rice. S.A.: Meyer. L.. Electron
drift velocities in liquefied argon and krypton at
low electric field strengths, PHYS. REV.
150(1): 127-45 (1966).

Gibbons, D.J.; Spear, W-E., Electron hopping
transport and trapping phenomena in
orthorhombic sulphur crystals, J. PHYS.
CHEM. SOLIDS 27: 1917-25 (1966).

Halpern, B.; Lekner, J.; Rice, S.A.; Gomer, R.,
Drift velocity and energy of electrons in liquid
argon, PHYS. REV. 156(2): 351-2 (1967).

Lekner, J., Motion of electrons in liquid argon,
PHYS. REV. 158(1): 130-7 (1967).

Schwarz, K.W.; Stark, R.W., Phonon-limited
drift of the electron bubble in superfluid
helium, PHYS. REV. LETT. 21(14): 967-9
(1968).

Ghosh, P.K.; Spear, W.E., Electronic transport
in liquid and solid sulphur, J. PHYS. C. Ser. 2,
1: 1347-58 (1968).

Springett, B.E.; Jortner, J.; Cohen, M.H.,
Stability criterion for the localization of an
excess electron in a nonpolar fluid, J. CHEM.
PHYS. 48(6): 2720-31 (1968).

Lekner, J., Scattering of waves by an ensemble
of fluctuating potentials, PHIL. MAG. 18:
1281-6 (1968).

Miller, L.S.; Howe, S.; Spear, W.E., Charge



and the vacuum measurement repeated to make sure no change has occurred in the metal surface to
affect the work function; clean hydrocarbons do not affect the surface.

Relative values of V, for different liquids are also obtained by determining photoionization
thresholds in different liquids, using solutions of a readily ionized solute such as TMPD
(tetramethylphenylenediamine). Photoionization shifts from one liquid to another were found to be equal
to photoelectric work—function differences between the same liquids [747297]. These determinations are
not sensitive to the presence of electron—attaching impurities, even at concentrations as high as 10°M.

4. Data on Electron Mobi

ities
4.1. Elements and Diatomic Gases

Electron or negative ion mobilities z_ in some liquefied monatomic and diatomic gases, and in
liquid sulfur are shown in table 1. All these data were obtained by some version of the double— or
single—shutter methods. Some data on solids are included to show the behavior of jz_ on melting.

The bubble model for the electron in liquid helium [658008, 658009] is now generally accepted (see
for example (730316). Above the \ point (2.2 K) the mobility varies approximately inversely with the
viscosity; but at lower temperatures, though the viscosity vanishes there is no discontinuity in the
mobility; it rises (fig. 1) from 0.033 at 2.2 K to 220 at 0.5 K, and at lower temperatures is proportional to
T7; .T3 = 27.64 K? em? V7! 5"! (T < 0.5 K), according to [729251] which presumably supersedes an
earlier publication [680854] by the same author. These results have led to some new insights on
superfluid behavior.

In liquid neon, as in helium, the electron mobility is close to that of the positive ion. In solid neon,
however, the electron mobility is many orders of magnitude larger, and is close to that of solid argon;
but in argon, krypton and xenon the mobility falls only by a factor of 2 on melting. The difference is that
electrons injected into the solid are expected to remain in the conduction band, even though the

Tapte 1. Zero-field mobility of electrons (or negative ions) in condensed.
phases of elements and diatomic gases

Substance State Me TK Temp. effect, Temp. range, _ Reference
em?V's? equation
He lig. 0.020 4.2 See fig. 1 0.274-5.18 620159,
600073,
729251
Ne 600. 25. — — 720839
0.0016 25.5 p= 3.0x 107 + 0.0070 26-31 720839
0.0008 25.5 lu(z_T) — 2.03 — (151/7) 25.5-43 729075,
Ar 1000 82 = — 689006
415 85 — — 689006
410 90.1 See fig. 2 90-160 660394,
719353
Kr 3700 113 — _— 689006
1800 uz — — 689006
1300 120 See fig. 5 120-180 660394
Xe 4500 157 —_— — 689006,
2200 163 _— — 689006
1080 167 See fig. 6 167-315 741134
N,* 0.0017 63 — — 720840
0.00065 63 p= 3.57 x 10°°7-0.00160 63-77 720840
0," 0.00045 62 = 3.70 x 10°°7-0.00185 62-89 720840
co* 0.003 68 —_ —_ 720840
0.00087 69 p_= 4.78 x 10°7-0.00242 69-78 720840
H,* 0.0086 21 — — 638002
Sulfur* 0.000100 393 E xeire, = 0-15 + 0.02 €V 393-433 687280

“Interpretation of these data as electronic rather than ionic mobilities is quite doubtful; see text.

5


Drift Mobilities and Conduction
Band Energies of Excess Electrons
in Dielectric Liquids

A. O. Allen

Department of Chemistry
Brookhaven National Laboratory
Upton, N.Y. 11973

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary
James A. Baker, Ill, Under Secretary
Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology
NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued May 1976


T TT T T T T T
2400- 4

Liquid Krypton

| E*-t00 vem 4

2300- —s 2502060Im

4 150202a1m
2200-0 320¢15atm 4

= 2100- \

fy
8
8
3
T

s ‘

> 1900- i 4
1800-- \ 4

3 ‘

H

8 1700- u 4

= ‘

3 ry

§ 1600) 1 +

=

* 1500} 4
1400} 4
B00), eazam$ |

1 4 _L 1 1 1 Lb L
20070 130 140 150 160 170 180 190 200 20
TUK)

Ficune 5. Apparent electron mobility in liquid krypton as a
function of temperature. All points are measured at
a constant electric field strength of ~100 V/cm.
Figure from [660394],

pelem?/Vs)

160 200 7240 280
T(K)

320

FicuRE 6. Apparent mobility of electrons in liquid xenon as a
function of temperature. The pressure on the sample
was the vapor pressure. Applied field strength=16
Viem. Triple point, t.p.=161.3 K; critical tempera-
ture T-=289.7 K. Figure from [741134]

‘| NEOPENTANE-n-HEXANE

-0.2
vev)

0.3

‘ 0.2 04
NEOPENTANE

MOLE FRACTION

0.6 0.8 to
HEXANE

Ficure 7. Vo in electron volts vs. mole fraction hexane for

neopentane-n-hexane mixtures;

open points are

from work function shifts of Zn; filled points are

from TMPD photoionization threshold shifts;
bubble model prediction, [720242];

<=, ef:

fective medium prediction, [738029]. Figure from

[740079).


Halpern et al.
‘Swan
36 360

10

#70 a1m
365,
60

a)
—  (Vvem")

+50

Ficure 3. The field dependence of the electron drift velocity

in liquid Ar at 85 K. Curve S, calculated from Shock- F
ley theory; curve C, theory of Cohen and Lekner; a? os
curve B is corrected for multiple scattering and also in 4
indicates the linear field dependence. Curve A: typical Se Saee 4
results from a speciment with short electron lifetime Leer rritp pp tepyp yyy
(= 200 ns). The sound velocity in the liquid is de- TBS OU eS a 1s Ue 1 19 20
noted by u;, Figure from [689006]. Number Density (102A)

$8

Ficure 4. Zero-field electron mobilities as a function of number
density in fluid argon. Figure from 719353}.

temperature is approached. The treatment which was so successful at lower temperatures assumed the
potential to be isotropic about the average position of each atom, which predicts that mobility should
depend only on the liquid density. Figure 4, which summarizes the extensive and precise data of Jahnke,
Meyer and Rice, shows that this is indeed true at the higher densities, but that at the higher
temperatures the mobility for a given density is higher, the higher the pressure (and therefore the higher
the temperature). Thus thermal fluctuations of the density lead to an increase in mobility, though it is
not obvious that this should be so. Lekner [688043] pointed out that his calculated scattering length or
square root of the scattering cross section for the electron in the liquid is positive, corresponding to
scattering from repulsive centers, while in argon gas the scattering length is negative. At some
intermediate density then the mean scattering length should be zero, and the mobility should fail to
become infinite only because of fluctuations in the scattering process. It was to test the theory derived
from this model that Jahnke carried out his extensive measurements. The results agreed with the theory
in that the maxima at different pressures always occurred at temperatures such that the density was the
same (0.0120 atoms/A®*), and predicted the right shape for the mobility rise from the high-density side,
but failed to explain other features of the data. Later, Jahnke, Holzwarth and Rice [728005] reported that
no theoretical calculation of the scattering length could predict a zcro at densities above the critical
liquid density (0.0080 atoms/A*). Thus at present there is no good theory for the maximum in mobility
below the critical temperature.

The mobility maximum also occurs in liquid krypton (fig. 5) and xenon (fig. 6). It is not known
whether it exists in any of the many polyatomic liquids which have been studied, since measurements in
these liquids have not been made sufficiently close to their critical temperatures.

Electron mobility increases with increasing density and polarizability in the series argon, krypton,
xenon. The field dependence of the mobility sets in at lower fields in the higher atomic weight liquids,
and the extrapolation to zero field is somewhat uncertain for xenon. In fact, Robinson and Freeman
[741012] who looked at electron velocities in xenon by the maximum pulse current method, found that
the velocity was proportional to the square root of the field, so extrapolation of yz to zero field would be
impossible. However, their velocity figure was obtained by dividing the maximum conductivity by the
free—ion yield, the value of which is perhaps somewhat dubious and is also field~dependent. More
recently, Kimura and Freeman [741134] have published numbers obtained at fields of only 16 V/em.
Neither theory nor experiment has been applied as thoroughly to krypton and xenon as to argon. Since
the theory of these cases, in which self—trapping is essentially absent, is basic to the understanding of

7


Alternatively a single grid near the cathode can be pulsed; or, if the electrons are generated by
illuminating the cathode with ultraviolet light, the period is obtained by winking the light on and off with
a shutter (single shutter method) [729022].

A simpler method (thin layer method), used for tetramethylsilane [700140] is simply to turn on
X-rays, which pass through the solution only in the vicinity of the cathodes, and note the time required
for the current to reach its maximum, which is the drift time across the cell. In the “thick layer
method” [731036] the entire cell is irradiated with a very short pulse of X-rays. As the ions are pulled
out by the field, the current decreases linearly with time, reaching zero at the drift time.

The Hudson method [460003] has proved useful for measuring electron mobilities in hydrocarbons
[700140]. When X-rays are turned on, irradiating uniformly the entire volume between cathode and
anode, the current rises parabolically with time to a maximum value, the time to maximum being the
drift time of electrons across the cell. The rise of the electron current is followed by the much slower
rise of the positive ion current. Impurities distort the electron rise curve and tend to give too high
mobility values; a method of correcting for the impurities has been devised [741036].

All the above methods require the use of extremely small electron currents in order to avoid space
charge effects, with corresponding care to avoid spurious readings in the electrical measurements.

Judging by consistency of the results when applied to hydrocarbons, the thin layer, thick layer and
Hudson methods are subject to errors of about +10%. However, the shutter methods do not seem to
have given much better results with hexane, and the difficulties in obtaining higher accuracy with
hydrocarbons may lie more in impurity effects than in the physical methods used.

A less direct method, which entails less strict purity requirements, is used at laboratories which
have pulse radiolysis setups with nanosecond resolution times. Conductivity is measured after a known
pulse of radiation, much more intense than used in the drift time methods, and the decay of the current
is usually largely due to ion recombination. In liquids such as hydrocarbons, where the electron mobility
is hundreds of times greater than that of the positive ions, the current is fixed essentially by the product
of the electron concentration and mobility; if the electron yield is known by other measurements, and
the absolute dose has been accurately determined, extrapolation of the current back in time to the end
of the radiation pulse allows the mobility to be calculated. Uncertainties as great as 30% in the value of
the free-ion yields make this method less accurate as a measure of mobility than the drift—time
determinations.

3.2. Mobilities of Solvated Electrons

The pulse conductivity method has been used to determine the mobility of solvated electrons in
water. The concentration of the electron is determined optically, simultaneously with the conductivity.
As the electron disappears, it is replaced in the solution by the OH~ ion; the change in conductivity
measures the difference in mobility of e~ and OH~, which turns out to be surprisingly small. Similar
methods have heen used for other polar liquids [720153]; but the mobility of other ions in these solvents
is less well known than in water, so these results are presumably less accurate.

Ammonia dissolves alkali metals such as Na to form stable solutions. The extrapolated conductivity
A, = Me) + A(Na*), and a transference number experiment has given the mobility of e~ in this solvent.
The stability of the electron thus allows the mobility to be determined by purely 19th—century methods.

3.3. Conduction Band Energies

Conduction band energies are measured by noting the difference in work function of a metal in
vacuum and immersed in the liquid. The logarithm of the photoelectric current emitted from a metal
illuminated at different wavelengths in the ultraviolet and visible is plotted against the quantum energy
of the light, showing a curve (Fowler function) which rises rapidly when the energy exceeds a certain
value, the work function, characteristic of the metal. Liquid is distilled onto the metal, and the
experiment repeated; the same shape curve is found, but is shifted along the energy scale to give a
different value of the work function. The electrons initially go into the conduction band of the liquid, so
the change in the work function is equal to V,. After the liquid measurement, the liquid is distilled out

4


Preface

This repcrt is one of a series of data publications on radiation chemistry; the aim of the series
is to compile, evaluate, and present the numerical results on processes occurring in systems which
have been subjected to ionizing radiation. Various kinds of data are important in radiation chem-
istry. The quantities which were measured first were the observed radiation yields or G values (mole-
cules formed or destroyed per 100 eV). Various indirect methods based on G values have been used to
determine yields of transient species and relative rates of reactions. The spectral properties (optical,
electron spin resonance) of transients have provided a direct method for their identification, and rates
of the very fast reactions of transients which occur in irradiated systems have been measured directly
by spectroscopic methods. Conductivity and luminescence methods have also provided a means of
measuring properties of transients and their kinetics. Some reactions which occur in irradiated systems
have also been studied by other methods, such as photochemistry, electric discharge, ultrasonics, chem-
ical initiation, electron impact, etc. The emphasis in these publications is on the data of radiation
chemistry, but where other pertinent data exist, they are included.

The data of radiation chemistry are voluminous; thousands of systems have been investigated.
As a result there are certain collections, e.g. rate constants of particular types of reactions or certain
properties of transients, for which tabulations of the data are considered essential, but for which
critical assessment of each value is impossible. On the other hand, certain systems and properties
have been studied so extensively that critical examination of these data is desirable and timely.
Authors of this series of data publications have been asked to evaluate the extent to which the data
can be critically assessed, to describe their criteria for evaluation, and to designate preferred values
whenever possible.

Iv


2 rr
re 4
L 4
mo loth 4
» oF 1
Tt
> L 4
a
E propane ethane
2 |
> L
=
= 4
8 tL 4
€ 5 4
0 J i 1 i 2
3.4 5 6 T 8 9 10
103 peat
T {k']—

FicuRe 8. Temperature dependence of the electron low field
mobility of ethane and propane. Ethane curve:
circles, data from [740317 squares, data from
[741012]. Propane curve: triangles, data from {740346};
squares, data from (741012].

ppear to fit an Arrhenius expression, with the activation energies in general being lower the higher the
room—temperature mobilities.

It is thought that molecular shape influences the mobility through the anisotropy of the polarizability
in unsymmetrical molecules. Orientations of acyclic hydrocarbon molecules in a liquid are mainly
random. If a group of neighboring molecules happens to have their directions of high polarizability
oriented towards a central point, an electron coming to that point would be at a lower potential than at
other points, and would tend to be localized there; the less symmetrical the polarizability, the deeper the
traps. Electrons localized in such traps are solvated, and have the broad absorption spectrum in the
infrared typical of solvated electrons in polar liquids (see, for example, [690400] and [710642]. It is
reasonable to suppose that the only difference between the electrons in hydrocarbons and the
permanently solvated, low conductivity electrons in polar solvents such as ammonia is that the traps in
the latter are so much deeper that the equilibrium fraction of electrons in the conduction band ‘is

ag



5. Conduction Band Energies

Values of V, for various liquids at selected temperatures are shown in table 4. Temperature effects
on V, are shown in figure 9 for those liquids for which values at more than one temperature were

TABLE 4. Conduction band energies Vo in various liquids

Liquid References
Helium 659054
Argon 670195
750045,
Xenon 750045
Methane 740192
749281
Ethane 740192
Propane 747297
n-Butane 747297
cis~Butene-2 750009
n~Pentane 747297
295, 720439
205 ‘T9001
295 750009
727460
Neopentane 295, 719091
2905 720439
295, 741297
Cyclopentane 295 720439
295, 741297
n-Hexane 295 719091
295 720439
295 "747297
295 730414
202 750009
2-Methylpentane 295 720439
295 741297
295 730414
2-Methylpentane. 205, 720439
295, 741297
295 730414
2,3-Dimethylbutane 295 730414
205, 750009
2,2-Dimethylbutane 295 730414
295, 741297
2,3—Dimethylbutene-2 295 727297
Cyclohexane 295 721291
Methylcyclohexane 295 727297
n-Octane 295, 727297
2,3,4-Trimethylpentane 295 721297
2,2,4~Trimethylpentane 295 719091
295, 741297
2,2,5~Trimethylhexane 295 747297
2,2,4,4-Tetramethylpentane 295 747297
n—Decane 205, 741297
1,3-Dimethyladamantane 295 741297
n-Tetradecane 295 747297
Benzene 295 730414
727460
Toluene 295 730414
Tetramethylsilane 295, 719091
295 720439
295 747297
293 750009
Tetramethyltin 293 750009

18


Foreword

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Ernest AMBLER, Acting Director


Library of Congress Cataloging in Publication Data

Allen, Augustine 0.
Drift mobilities and conduction band energies of excess clec-
trons in dielectric liquids.

(Nat, stand. ref. data ser.; NSRDS-NBS 58)

“CODEN: NSRDAP.”

“Prepared for, and in cooperation with, the Radiation Chem-
istry Data Center of the Radiation Laboratory, University of
Notre Dame.”

Supt. of Docs. No.: C13.48:58

1. Dielectrics. 2, Liquids—Electric properties. 3. Excess elec-
trons. 4. Drift mobility. 5. Conduction band, I. Notre Dame, Ind.
University. Radiation Yohomietry Data Center. II, Title. II]. Se-
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QC100.U573 No. 58 [QC585] 6021s [537.2'4] 75-44460

NSRDS-NBS 58

Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U.S.), 58,23 pages (May 1976)
CODEN: NSRDAP

© 1976 by the Secretary of Commerce on Behalf of the United States Government

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electrons in polyatomic liquids, in which widespread interest is now being shown, additional study of
krypton and xenon would be desirable.

The other substances in table 1 all show much lower mobilities. Hydrogen was predicted by
Miyakawa and Dexter [699050] to form “bubbles” about electrons, and the measured mobility, which lies
between those of helium and neon, is consistent with this prediction. Oxygen gas (but not N, or CO) at
reasonably high pressures reacts with electrons to form the ion Oz, and the negative species in liquid
oxygen would be expected to exist in this form.

Mobile positive and negative species were seen in solid N, and CO, with » 1-3 x 10% em? V"'s
and in the low-temperature form of solid O, (36-44 K) but not in the high-temperature form (44— 54 8.
In liquid N, and CO, p_ increased from about 0.8 x 10 to 1.3 x 10°* cm? V~' s“' in the range from the
melting point to 10° above it, in parallel with 4, and with the decrease in viscosity of the liquids. In
sulfur similar phenomena were found, with _ falling by a factor of 25 to 1 x 10 on melting, then
increasing at higher temperatures. At 160° C sulfur suddenly begins to polymerize and the viscosity
increases by more than two orders of magnitude over a range of 4°; but in this range the mobilities y_
and p, showed no significant change. The experimenters, in the belief that ionic mobilities (but not
electronic) should vary inversely with viscosity, ascribed the mobilities in sulfur to electron hopping, but
in N,, CO and O, to ionic drift (presumably of impurity negative ions in N, and CO). However,
Drickamer and coworkers (539005, 539006] showed that the rate of self—diffusion in liquid sulfur changes
little over the range where viscosity increases, and the effect of pressure on self—diffusion showed the
activation volume to be only 1 to 6 atomic volumes. Apparently diffusion of small molecules may occur
with little hindrance within the network of polymer molecules, while viscous flow requires motion of the
macromolecules. Ionic drift should be more closely related to self—diffusion than to viscosity, so it
seems possible that in all these liquid elements the mechanism of charge transfer is ionic. However, this
can hardly be true for the solid crystals, where electron hopping would seem to be the only plausible
mechanism; and the fairly small change of mobility and its temperature coefficient on melting argues in
favor of the same mechanism holding in both phases. The data on mobility of negative charge carriers in
these liquids is therefore included in table 1, with the notation that interpretation of these numbers as
electron mobilities is doubtful.

4.2. Hydrocarbons

Electron mobilities in hydrocarbons and tetramethylsilane (TMS) are shown in table 2. The aliphatic
hydrocarbons, saturated and unsaturated, are listed first, in the order of carbon number, followed by the
aromatic liquids.

Taste 2. Zero-field mobility in liquid hydrocarbons

Name TK Eveivs Method* —_—_—Reference
kcal/mole

Methane 400 ul Negative, small a 731036
430 140 Negative, small pe 741012
Ethane 08 200 Sce fig. 8 a ‘739187
740317
0.97 200 3 pe 741012
Ethylene 0.0030 170 — pe 741012
Propane 0.55 238 3 pe 741012
0.12 200 See fig. 8 tl 740346
Propylene 0.008 234 4 pe 741012
Cyclopropane 0.0043, 234 4 pe 741012
n—Butane 0.073 250 4 pe 741012
0.4 296 — H 700140
Butene-1 0.064 293 — pe 731035,
cis~Butene-2 2.2 293 37 pe 731035
trans—Butene—2 0.029 293 54 pe 731035
Isobutane 5. 294 — pe 720034
Isobutene 14 293 — pe 731035

9


negligibly small. These qualitative considerations await confirmation by an actual calculation of the
potentials in liquid hydrocarbons. Such a calculation, even for ethane, would be far more complex and
difficult than for liquid argon.

The effect of the double bond in ethylene and propylene is to decrease the mobility by a large
factor; but in larger molecules this effect is not seen. The remarkable difference in the electron mobility
in the cis and trans forms of butene~2 emphasizes the dependence of this property on the molecular
geometry.

Comparison of the results of different laboratories shows that the absolute accuracy is not always as
good as the experimenters believed. The worst discrepancies appear with benzene and toluene; however,
the experimenters who measured drift time reported that only 20% of the current appeared to be carried
by the fast negative carriers, the rest being ascribed to impurity ions; the conductivity method would
then be expected to give lower values. Somewhat discrepant values also appear for cyclohexane and
normal pentane. In the case of neopentane, a number of lower reported values have been excluded from
the table because they have been superseded by more recent values from the same laboratories.

4.3. Polar Solvents

Mobilities of solvated electrons in polar liquids are given in table 3. These measurements are all
made by determining that part of the conductivity due to the electron, as outlined above. The results in
water and ammonia are based on rigorous treatment of accurate data on conductivities and transference
numbers, and should be good to a few percent; but the results on the other compounds are based on
small deviations in conductivity decay curves brought about by small additions of anthracene or other
electron acceptors, which are analyzed on the assumption that the mobilities of the acceptor negative ion
and the positive ion are equal. The results are of interest chiefly in showing that the mobilities of
solvated electrons in all these solvents are of comparable magnitude.

Taste 3. Mobilities of solvated electrons in polar solvents

Solvent a T.K E, References
kcal/mole
Ammonia 0.0092 239 — 609010 for transference
number;

599008, for conductance,
recaled. from

219001

Water 0.00197 298 — 690295,
0.00197 295 — 690547

0.00187 298 48 700243

0.00162 292 42 720404

Methyl ethyl ketone* 0.0015 293 _— 720153
Hexamethylphosphoramide 0.00055 293 = 720153
Butylamine 0.0027 293 — 720153
Tributylamine 0.002 293 — 720153
Methyl alcohol 0.00059 293 — 710064
Ethyl alcohol 0.00025 293 — 710064
Isopropyl alcohol 0.00051 293 — 720574
Isobutyl alcohol 0.00068 293 — 720574
n-Butyl alcohol 0.00075 293 — 720153
0.00073 293 — 720574

Isopentyl alechol 0.00095 293 — 720153
0.00097 293 = 720574

n—Hexyl alcohol 0.00043 293 — 720574
Ethylene glycol 0.00028 293 — 720574

“May be a molecular anion rather than a solvated electron.

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