Methane chemistry in the hot supersonic nozzle

Article abstract of DOI:10.1021/jp010366d

The combination of pyrolysis and expansion to a supersonic molecular beam was shown to be very effective in conversion of pure CH₄ to heavier hydrocarbons. Pure CH₄ conversion reached 70% when it reacted in a hot (1000°-1150°C) supersonic nozzle made of quartz with 100 μ dia orifice. Hydrogen, acetylene, benzene, methyl, and propargyl radicals were the major products in the distribution. CH₄ conversion rate was not improved with the addition of O₂, NO, or CO₂ as O₂ reacted primarily with surface carbon formed by CH₄ decomposition. No oxygen containing hydrocarbon derivatives were observed. The lifetime of the nozzle was longer than pure CH₄ as a reactant resulting from surface carbon removal by oxygen. The mechanism involved pyrolytic rather than catalytic surface generation of free hydrocarbon radicals with subsequent coupling to heavier hydrocarbon products prior to desorption to the gas phase and expansion to the supersonic beam.

Full text of DOI:10.1021/jp010366d

J. Phys. Chem. A 2001, 105, 7025-7030
7025
Methane Chemistry in the Hot Supersonic Nozzle
L. Romm,† Y. H. Kim,‡ and G. A. Somorjai*,†,§
Lawrence Berkeley Lab, Department of Materials Science, Berkeley, California, Catalysis Center for Molecular
Engineering, Korea Research Institute of Chemical Technology(KRICT), Yusong, Taejon, Korea, and
Department of Chemistry, UniVersity of California, Berkeley, Calfornia
ReceiVed: January 29, 2001
Combination of pyrolysis and expansion to a supersonic molecular beam is shown to be very effective in
conversion of pure methane to heavier hydrocarbons. The conversion reaches ∼70% in the supersonic nozzle
made of quartz with the diameter of orifice equal 100 µ. The major products are acetylene, benzene and its
homologues. Free radicals are also detected in the product distribution. The mechanism consists of the surface
generation of the radicals, C-C bond formation, desorption to the gas phase, and expansion to the supersonic
beam. It is suggested that relatively short gas-surface contact time (about 50 ms at Tnozzle ) 1000 °C) enables
simultaneous kinetic and thermodynamic control.
1. Introduction
withdrawal of the molecules to vacuum to enable their detection
and analysis. D. Herschbach and co-workers7,8 recently utilized
Great industrial interest in methane as a potential dominant
future source for the synthetic replacement of petroleum-derived
hydrocarbons has long been a driving force for the research
and development of methane-coupling techniques to form the
higher hydrocarbon products. There are two major methods of
the direct conversion of methane to heavier hydrocarbon
products: catalytic oxidative coupling and high-temperature
pyrolysis. The oxidative condensation involves heterogeneous
catalysis over a variety of metal oxides1-3 at optimal temperature
range 550-850 °C. The process is characterized by above 50%
CH4 conversion and yields a considerable amount of C2
hydrocarbons. However, the selectivity to ethane and ethylene
decreases with the increase of the methane conversion rate. Of
course, the simultaneous formation of CO, CO2, and water is
unavoidable.
Thermal steady state pyrolytic dehydrogenation of methane
is favorable only at temperatures above 1200 °C.2,4 The
dominant product of this process is acetylene due to the decrease
of its free energy of formation at higher temperatures. However,
acetylene is less stable than its constituents at this temperature
and readily decomposes to carbon deposited on the surface and
hydrogen in the gas phase. Thus, the stabilization of acetylene,
and possibly longer chain hydrocarbons that may form from
acetylene, requires a very short contact time of methane with
the reactor walls for the rapid desorption and cooling of the
products. Thus, kinetic rather than thermodynamic control over
the high-temperature self-coupling of methane must be estab-
lished.
this approach to demonstrate facile formation of higher hydro-
carbons from ethane in the heated supersonic nozzle beam.
Flowing through 1000 °C nickel nozzle, ∼60% of the reactant
ethane was converted to C3 ÷ C12 unsaturated hydrocarbons
within 10 ms contact time. However, no conversion of methane
was observed under similar conditions.8 Work in our laboratory
has shown that ethane conversion can be increased to almost
100%.9 We were also able to detect higher hydrocarbons formed
from methane in the hot (1150 °C) nozzle made of quartz with
the orifice diameter of about 200 µ.9 The product distribution
from methane resembled that from ethane. The direct nonoxi-
dative conversion of methane was estimated to be equal to 20%
within 10 ms.
In this paper, we report much larger (up to 70%) conversion
of methane to longer chain hydrocarbons in the hot quartz nozzle
with the orifice diameter of 100 µ. No self-coupling of methane
to the heavier products was detected in the metal nozzles (Ni,
Mo, Fe) e1000 °C, whereas at higher temperatures, the metal
nozzles rapidly clogged with soot and, possibly, metal carbides.
The product distribution from methane presents a variety of
higher hydrocarbon molecules with number of carbon atoms in
the range of 2 to 12. The intensity of the peaks with even number
of carbon atoms is somewhat higher,7-9 than the peaks with
odd number.
The mechanism of the chemical process is discussed in terms
of the formation of precursor free radicals from methane, which
are generated and react on the surface followed by the desorption
to the gas phase and supersonic expansion. We detected methyl
(CH3) and propargyl (C3H3)7,8 free radicals in the supersonic
beam. An attempt was made to form products other than
hydrocarbons. For this purpose, we added either oxygen or NO
or CO2 to the reactant methane. However, no hydrocarbon
derivatives could be detected among the hot nozzle reaction
products.
Expansion of a gas through a hot nozzle orifice to form a
supersonic molecular beam is thought to be an appropriate
experimental technique to overcome the thermodynamic limita-
tions of the steady-state equilibrium conditions. During pyroly-
sis, very fast transition of a compressed gas to free-molecular
flow during the supersonic expansion provides sufficient cooling
of the internal molecular degrees of freedom5,6 along with a
A time-of-flight (TOF) technique was employed to determine
the nozzle temperature because it is not possible to measure,
without sizable error, high temperatures of the quartz nozzles
using a standard thermocouple method. The TOF technique
† Lawrence Berkeley Lab, Department of Materials Science.
‡ Catalysis Center for Molecular Engineering, Korea Research Institute
of Chemical Technology(KRICT).
§ Department of Chemistry, University of California.
10.1021/jp010366d CCC: $20.00 © 2001 American Chemical Society
Published on Web 06/28/2001

7026 J. Phys. Chem. A, Vol. 105, No. 29, 2001
Romm et al.
provides a reliable estimation of the nozzle orifice temperature
based on the measurement of velocity distribution of a super-
sonic beam constituents.6,10
2. Experimental Section
Detailed description of our experimental setup has been given
elsewhere.9 Briefly, a CW supersonic molecular beam is
generated in the source chamber, propagates to the 1st differ-
entially pumped chamber through a skimmer and enters the 2nd
detection chamber through an additional collimating aperture
that is placed between the detection and the 1st differentially
pumped chamber. The quadrupole mass spectrometer (QMS)
detector was placed in the detection chamber in the line-of-
sight of the beam. Base pressure in the detection chamber was
maintained at less than 1 × 10-9 Torr.
We used nozzles fabricated from quartz with the orifice
diameter of 100 ( 10 µ throughout the entire set of experiments
reported here. We tried two different shapes of nozzles: bird
beak-like and that similar to the metal nozzles used previously.9
We did not find a significant difference within uncertainties of
our experimental setup. The manufacturing of quartz nozzles
is fast, easy, and inexpensive, whereas the orifice diameters can
be readily reproduced within the control limits of 10 µ.
We employed TOF method to measure the nozzle tempera-
ture. Helium was flowed through the nozzle prior to and after
the experiments with CH4 or gas mixtures at the same conditions
of the nozzle heating. We monitored the temperature stability
of the outer nozzle wall in the heating zone using K-type
thermocouple. Normally, the thermocouple reading was stable
within 2 degrees, when methane (or a gas mixture) was switched
to helium and conversely. A tiny synchronous gyro-motor
(Condor Pacific Ltd., Israel) carrying a chopper wheel was
placed in the 1st differentially pumped chamber. Solid 0.5 mm
thick stainless steel wheel has two 0.5 mm wide slits cut opposite
each other. The motor was attached to the linear transfer
mechanism to enable the insertion of the wheel into the beam
of molecules emerging from the source chamber. Typical
rotation rate was 320 Hz, as was measured by an optocoupler
with very fast rise time. The optocoupler also served as a trigger
for the detection of the time of arrival at the QMS.
A Digital oscilloscope was used to record the time of arrival
signal directly from the secondary electron multiplier of the
QMS via a homemade fast (2 µs rise time) preamplifier. The
spectra were stored on the floppy disk and analyzed afterward
to determine the nozzle temperature. After the ion time-of-flight
inside the QMS filter was subtracted from the raw data, the
time of arrival spectra were converted to velocity distribution
spectra using Jacobian10 dV/dt ) |L/t2|, where L is a distance
between chopper wheel and QMS ionizer; L ) 72.1 cm.
Experimental distributions of the velocity of the helium beam
F(V) were then fit by the modified Maxwellian function for a
supersonic beam,10,11 as follows
Figure 1. Typical low resolution mass spectrum of the products from
the pure methane at Tnoz ) 1066 °C, Pupstream ) 215 Torr. The nozzle
was made of quartz and has a 100 µ orifice. Some peaks are marked
by the number of carbon atoms. Inset presents detailed product
distribution of the masses above 55 amu.
5
where γHe ) CP(He)/CV(He) ) /3. The accuracy of the TOF
nozzle temperature measurement was estimated to be ( 50
degrees at Tnoz ) 1000 °C.
All gases used in the present work (CH4, He, O2, NO, CO2)
were of nominally high (99.99%) and ultrahigh purity, and no
impurities were observed by QMS within our experimental
detection limits. All of the mass spectra were refined by
subtraction of the corresponding background gas signal from
the raw mass spectra. Background gas mass spectra were taken
when the beam was on and cut from the QMS by a shutter.
The nozzles were cleaned up in situ by flowing oxygen at
Tnoz > 700 °C. We used the same technique to burn surface
carbon and unclog the nozzle when necessary.
3. Results
3.1. Methane Conversion. A discernible signal in the C2
region of the mass spectrum appeared when the nozzle tem-
perature reached ∼950 °C ÷ 1000 °C. The Cm (m g 2)
hydrocarbon signals became stronger with the temperature up
to ∼1100 °C and leveled off in the range 1100 ÷ 1150 °C.
Above 1150 °C, the rate of surface carbon deposition (probably
soot) exceeded the rate of methane coupling, and the nozzle
clogged. A typical low resolution mass spectrum of the products
of nozzle methane conversion is shown in Figure 1. The product
distribution essentially resembles qualitatively that from pure
ethane,7-9 indicating the same mechanism of conversion.
High-resolution mass spectrum of the 1-35 amu region, taken
under the same conditions as that in Figure 1, is presented in
Figure 2. Major contribution to the intensity of the C2 signal
comes from acetylene, the formation of which is thermodynami-
cally favorable.2,12 Weak peaks at 27 and 28 amu are also seen,
indicating the presence of small amount of ethylene, the
formation of which during methane pyrolysis is thermodynami-
cally favorable13 under 1000 °C. Note an unusually high ratio
of the intensities of peaks 15 and 16 amu.
He(ν-ν0)2/2kT|
F(ν) ν3‚e -m
(1)
where V0 is the terminal velocity of the beam, T| describes
velocity spread relative to V0 along the beamline. Then, the mean
square velocity V2 was calculated using the fit parameters, and
the nozzle temperature was established through the expression
26
Conversion of methane to higher hydrocarbons changes at
1066 °C from about 60% at Pupstream ) 50 Torr to almost 70%
at Pupstream ) 215 Torr. At higher pressures the rate of methane
decomposition CH4 f C(s) +2H2(g) is apparently higher than
the rate of formation of acetylene and other products due to
longer contact time, and the nozzle rapidly clogs with carbon.
Pressure dependence of the yields of various products is shown
γHe -1 mHe ν2
Tnozzle
)
‚
(2)
γHe
2k

Methane Chemistry in the Hot Supersonic Nozzle
J. Phys. Chem. A, Vol. 105, No. 29, 2001 7027
Figure 2. High-resolution mass spectrum of 0 to 35 amu region for
the same reaction conditions as in Figure 1. Bargraph shows a reference
spectrum of acetylene. Discernible peaks at 27 and 28 amu may be
identified as originated from ethylene.
Figure 4. Yield trends of the products of pure methane conversion at
Tnoz ) 1000 °C and Pupstream ) 63 Torr. The products are marked as in
Figure 3.
Figure 5. High-resolution mass spectra of C1 region, taken at different
temperatures of the nozzle, through which pure methane was flowed
at Pupstream ) 90 Torr.
Figure 3. Yields of some products of methane beam reaction in the
quartz supersonic nozzle at Tnozzle ) 1066 °C as a function of the
stagnation pressure. 9 denote C1 products, b - C2, 2 - C3, 1 - C4,
[ - C5, and + - C6.
much longer. Figure 4 shows the yield trends for various
products of the methane conversion at Tnoz ≈ 1000 °C and
Pupstream ) 63 Torr. Integral intensity of the products (not shown)
was measured to be half as much after about 3.5 h of the
continuos run.
in Figure 3. Although the yield of C2 - C5 products practically
does not change with the stagnation pressure, the C6 (benzene7-9
)
yield rises from 20% at Pupstream ) 50 Torr to 28% at Pupstream
) 215 Torr. Selectivity to benzene increases from 33% to 41%
within this pressure range, whereas that for the C2 products
(apparently acetylene and ethylene) drops from 32% to 26%.
Because it is not possible to separate fragmentation patterns of
some of the products from the parent peaks of others in the
same region of the mass spectrum, the calculations of the yields
and selectivities are semiquantitative and serve as an estimation
of the reaction kinetics. These calculations are based on the
area-under-peak measurements and carbon atom balance. No
coke formation in the nozzle is allowed for. Because of our
lack of ability to resolve certain mass signals, no additional
special calibration of the QMS sensitivities has been done.
The deactivation of the nozzle strongly depends on the
temperature and stagnation pressure. Usually, higher Tnoz and
Pupstream values lead to rapid nozzle degradation and clogging
with carbon. Unlike metal nozzles, we were able to recover the
chemical activity of the quartz nozzle by flowing oxygen.
Gaseous CO and CO2 were formed and evacuated from the
nozzle into the vacuum system. At moderate temperatures and
lower Pupstream (shorter contact time), the nozzle lifetime was
3.2. Formation of C1 Radicals. As it was mentioned, the
experimentally observed signal in the C1 mass region comprises
possibly the contributions from methane and other C1 products.
In pure CH4, the mass spectrum fragmentation pattern at mass
15 (CH3+) is only 83% of the 16 amu parent peak intensity
(UTI 100 QMS, Electron impact energy is -70 eV). This is
illustrated in Figure 5 by the lowest curve obtained for a methane
nozzle beam at room temperature. As the Tnoz was increased,
the intensities of masses 12 through 15 gradually increased
relative to mass 16. Figure 5 demonstrates this experimental
observation. All spectra were normalized to mass 16 peak.
An enhancement of the signals from masses 12 to 15 is likely
due to formation of methyl radicals in the hot nozzle.14-16
Relative intensities of these radicals in the beam were obtained
by subtraction of the pure methane signal (obtained at Tnoz
)
25 °C, Figure 5) from every measured raw spectrum. The
corresponding curves are shown in Figure 6. We argue that
peaks in Figure 6 belong to methyl radicals and their cracking
patterns rather than derive from fragmentation patterns of

7028 J. Phys. Chem. A, Vol. 105, No. 29, 2001
Romm et al.
Figure 6. High-resolution mass spectra of methyl radicals, produced
from methane in the heated supersonic nozzle at Pupstream ) 90 Torr.
The curves were obtained by subtraction of pure methane mass
spectrum, taken at Tnoz ) 25 °C (lowest curve in Figure 5), from the
spectra, taken at higher nozzle temperatures. The subtraction followed
the normalization to the mass 16 intensity.
Figure 8. Yield of different products from CH4/O2 mixture with 20%
vol. of oxygen as a function of the nozzle temperature at Pupstream
)
102 Torr. The products are marked as follows: 9, - C1, b - C2, 1-
C3, 2- C4, [- C5, + - C6, × - CO, * - CO2. Open symbols belong
to the products of pure methane conversion. The shapes of these
symbols correspond to the filled ones.
3.3. Reactivity of CH4/O2, CH4/NO, and CH4/CO2 Mix-
tures. As we were able to observe the direct nonoxidative
reactivity of pure methane in the hot supersonic nozzle, we made
an attempt to probe oxidative methane coupling. For this
purpose, we used different mixtures of methane with oxidizers
O2, NO, and CO2. To our surprise, methane chemistry, when
in the mixture essentially reproduced that of the pure methane
under similar reaction conditions. We were not able to synthesize
hydrocarbon derivatives, nor could we improve the yields and
selectivities to the longer chain hydrocarbons. Figure 8 presents
the temperature dependence of the yield of various products
from the mixture of CH4 and O2 in proportion approximately 4
to 1. The data on the yield of higher hydrocarbons from pure
methane is given for the comparison.
Mass spectra of the products from pure methane and from
the gas mixtures feed looked similar at the same nozzle
conditions, except the presence of H2O, CO, and CO2 peaks
for the mixtures. Oxygen reacts predominantly with hydrogen
and surface carbon, which are the products of the decomposition
of methane. Formation of water indicates release of hydrogen
during the oligomerization of methane in the quartz nozzle.
Quantitative analysis of the rate of hydrogen formation during
the course of reaction in the nozzle is not possible due to the
poor performance of our mass spectrometer in the H2 mass
region. Selective interaction of oxygen with surface carbon can
account for our ability to run reactions of mixtures at higher
nozzle temperatures for longer times as compared with pure
methane as a reactant. In fact, the mixture of methane with
oxygen in proportion ∼4:1 (ratio by volume) taken as a feed
gas exhibits essentially the same reactivity under similar nozzle
conditions as pure methane relative to the formation of higher
oxygen-free hydrocarbons. However, the great advantage of
using oxygen was the ability to carry out the reaction continu-
ously for about 3-4 h at Tnoz above 1100 °C, whereas for pure
methane, nozzle clogging occurs within minutes under the same
conditions. The disadvantage of using oxygen-methane mixtures
is the formation of considerable amount of water, CO and CO2.
CO signal was twice as high as that of acetylene at Tnoz > 1100
°C, the signal from water has roughly the same intensity as that
from acetylene. The rate of formation of CO2 was measured
qualitatively to be much lower than that of CO and comparable
Figure 7. Yield of the methyl radical production as a function of the
nozzle temperature. The yield values are calculated relative to methane,
no higher hydrocarbons were taken into account.
methane. The intensities of the signals from CH and CH2
radicals were below our detection limit, as was verified by the
variation of the electron impact energy15 from -25 to -100
eV.
It is unlikely that the fragmentation upon electron impact in
the ionizer is coupled with the vibrational excitation of methane
molecules in the supersonic beam, emerging from the heated
nozzle. An effect of the translational energy activation may also
be ruled out as a possible source for the changing cracking
patterns of methane in the mass spectrum. The CH4 molecule
spends even less time in the ionizer when emerges from the
heated nozzle in contrast to the room-temperature nozzle. Thus,
extra cracking by electron impact in the QMS ionizer is
unfavorable and unlikely.
The yield of the methyl radicals is shown in Figure 7, as a
function of the nozzle temperature. The relative concentration
of the free radicals in the supersonic molecular beam increases
linearly with nozzle temperature and reaches values above 20%
relative to unreacted methane. Note that the signal from methyl
radicals is noticeable even at low Tnoz, when no higher
hydrocarbons are formed. This observation may be rationalized
by CH3/CH4 equilibrium thermodynamics considerations.2,17

Methane Chemistry in the Hot Supersonic Nozzle
J. Phys. Chem. A, Vol. 105, No. 29, 2001 7029
with that of benzene (no carbon atom balance was taken into
account).
were not able to detect in the beam composition. The rate of
formation of these radicals increases with the nozzle temperature
such, that adequate amount can be produced within the contact
time of methane. Thermodynamically, this enables the formation
of the more stable acetylene, benzene and its higher homologues.
The rate of their decomposition is apparently slower than the
rate of desorption and expansion to the supersonic beam. Thus,
interplay between thermodynamic and kinetic regimes makes
possible the production of higher hydrocarbons from methane
with considerable rates in the hot supersonic nozzle. Under-
standing the details of such the interplay will help to explore
the ways to establish control over the selectivities to certain
products. Pyrolysis coupled with the supersonic flow is a
relatively poorly studied area of reaction chemistry, and we are
unable at this point to discuss specific elementary chemical
processes involved in the overall reaction mechanism. Probably,
modification and optimization of the nozzle design may lower
a concentration of unreacted CH3 radicals and, consequently,
drive the reaction toward the formation of more C2 or C6
hydrocarbons.
4. Discussion
We propose that the formation of higher hydrocarbons from
pure methane occurs essentially by the same mechanism as that
from ethane.7-9 This includes (1) a generation of free radicals
on the hot surface of the nozzle14 via hydrogen atom(s)
abstraction,16 (2) desorption to the gas phase or C-C bond
formation by oligomerization and desorption to the gas phase.
Desorption is thought to be caused by both the thermal activation
of the desorbing species and the intensive flow inside the
nozzle.7,8 We believe we were able to observe the hot nozzle
reactivity of methane in contrast to previous studies7,8 due to
application of quartz as a nozzle material and decreasing the
nozzle orifice diameter. Quartz, unlike metals, is relatively inert
to surface carbide formation at high temperatures. This process,
along with the deposition of carbon, leads to the rapid
degradation and clogging of metal nozzles. The smaller nozzle
orifice lengthens contact time within the hot reaction zone. We
calculated the contact times following Shebaro18 and obtained
values in the range of 30 to 100 ms for different stagnation
pressures and Tnoz ) 1000 °C. These contact times are
sufficiently long to produce thermodynamically unfavorable (as
compared with C and H2) heavier hydrocarbons as reaction
intermediates, that desorb and expand in the supersonic beam
and exit in a vacuum where they are detected by mass
spectrometry. These contact times are too short for methane,
however, to decompose completely to carbon and hydrogen
inside the nozzle. At the nozzle temperatures used in the current
study, acetylene and benzene are the most stable hydrocarbons.17
Moreover, their Gibbs free energy of formation decreases with
increasing temperature. This may account for the experimental
observation that their intensities are strongest among the
products (see Figures 1, 3, 4, 8).
Free radical mechanism of the formation of higher hydro-
carbons from methane is clearly illustrated by the experimental
observation of methyl radicals as supersonic beam constituents.
Short contact time within the nozzle and small number of
collisions between the reactive molecules6 makes the survival
of the methyl radicals possible prior to the expansion to the
supersonic beam, as detected by the QMS. The number of
collisions rises with the nozzle temperature. However, the rate
of reaction of the nascent products (e.g., ethane) also increases.8
Our findings, that the addition of oxygen or other oxygen
containing gases to methane neither boosts the conversion rate
nor leads to the formation of hydrocarbon derivatives, are
supported by theoretical studies of equilibrium methane py-
rolysis.19 Catalytic rather than pyrolytic approaches should be
used in order to achieve discernible rates of the formation of
oxygen containing hydrocarbon products. Quartz is apparently
a poor catalyst and should be substituted with metal oxides.2,20
Selective interaction of oxygen with surface carbon when
added to methane, stresses the surface mediated mechanism of
the nozzle beam reaction. Previously, in our experiments with
ethane, we seeded C2H6 in Ar in proportion 1 to 10. The rate
of the formation of benzene was measured to be even slightly
higher than that for pure ethane as a reactant under the same
nozzle conditions. The C6H6 signals were compared after
normalization to the intensity of acetylene signal. This experi-
mental observation indicates that the process of oligomerization
occurs predominantly on the surface of the hot nozzle.
5. Summary
Conversion of pure methane reached 70%, when it reacted
in a hot (1000-1150 °C) supersonic nozzle made of quartz with
the orifice diameter of 100 µ. Major products in the distribution
were hydrogen, acetylene, benzene, methyl, and propargyl
radicals, but other hydrocarbons were also detected. Addition
of O2, NO or CO2 did not enhance methane conversion rate as
oxygen reacts primarily with surface carbon formed by methane
decomposition. No oxygen containing hydrocarbon derivatives
were detected. The lifetime of the nozzle was longer compared
with pure methane as a reactant as a result of surface carbon
removal by oxygen.
The mechanism has apparently involved pyrolytic rather than
catalytic surface generation of free hydrocarbon radicals with
subsequent coupling to heavier hydrocarbon products prior to
desorption to the gas phase and expansion to the supersonic
beam. This predominantly surface mediated mechanism is
probably dictated by the delicate interplay between kinetic and
thermodynamic regimes of the formation of higher hydrocar-
bons.
Acknowledgment. We would like to thank Prof. M. Asscher
for providing us with the chopper motor, and Dr. Y. Gotkis,
Dr. L. Baranov, Dr. Y. Borodko, and especially Dr. S. H. Kim
for very helpful and stimulating discussions. This work was
supported by the Director, Office of Energy research, Office of
Science, Division of Materials Sciences, of the U.S. Department
of Energy under Contract No. DE-AC03-76SF00098.
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