+
Measurement of the H3 Destruction
Rate Due to Ambipolar Diffusion in an
AC Positive Column Discharge
C. Michael Lindsay, Edmund T. White, and Takeshi Oka
Department of Chemistry, Department of Astronomy and Astrophysics, and
the Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637,
USA
Abstract: It has been assumed from an order of magnitude
calculation that ambipolar diffusion to the wall and then
recombination with electrons at the wall has the rate of 105 106 s-1 and is the dominant destruction path for molecular
ions in positive column discharges. We have developed a
method to observe such destruction rates experimentally
based on the competition between the ambipolar diffusion
rate and the destruction rate by added impurities. The
decrease of a velocity modulated H3+ absorption signal was
studied when small amounts of CH4, N2, and CO were added
to a pure hydrogen AC positive column discharge. The
+
destruction rate constant of H3 due to ambipolar diffusion
was then obtained using a steady state model and previously
reported ion-neutral reaction rate constants. The ambipolar
diffusion destruction rate constant for H3+ in a 1.2 cm
diameter bore discharge tube was measured to be (8.7 ± 1.8)
Introduction
Hollow cathode and positive column glow discharges have been
used for decades by spectroscopists to create molecular ions in the
abundance necessary for direct absorption studies. AC positive
columns are particularly important in this work because of the high
degree of sensitivity and discrimination possible by the velocity
modulation technique. [1] Kinetic models of these systems help
predict discharge conditions (i.e. current, pressure, mixing ratios of
starting gases) that should increase the steady state concentration of
a species of interest. These models can also help identify the carrier
of an absorption spectrum especially when it is unassignable, such as
the recent case of the infrared spectrum of CH5+. [2]
Kinetic models are constructed by considering the formation and
destruction mechanisms. The production rate of molecular ions in
the glow discharge depends on the charge density and ion-neutral
reaction cross sections. Most ion-neutral reaction rate constants have
been measured by various techniques, [3] and the charge density can
be estimated from the electric current through the plasma. Ions are
destroyed by either recombination with electrons or reaction with a
neutral molecule. In hollow cathode discharges with a large diameter
and low electron temperature the destruction rate is approximated by
the dissociative recombination reaction rate in the bulk, which is
easily obtained if the recombination rate constant is known. This is
not, however, the quickest destruction process in the positive column
where fast ambipolar diffusion occurs.
Ambipolar Diffusion
!
Molecules are primarily ionized in the center of the discharge
tube and diffuse outward at the ambipolar drift velocity.
!
Ambipolar motion can be described as an equilibration of the
velocity of electrons and cations--the massive cations tend to be
accelerated by the quick electrons and the latter, in turn, slowed.
Models for this motion exist for simple systems and depend on
the charge density, cation mobility, and electron temperature.
!
Once cations reach the wall, they are destroyed very efficiently
with electrons in the wall. This destruction rate can be very fast
particularly when the tube diameter is small and the electron
temperature is high as is generally the case in the positive
column. Crude estimates of this process predict the average ion
lifetime to be on the order of 10-5 ~ 10-6 sec.
!
Due to the complexity of the partially ionized molecular plasma,
a direct measurement of the ambipolar velocity has not been
made. Consequently we are left only with an estimate of the
destruction rate based upon an idealized model of a dissimilar
system. We need some method to estimate the destruction rate
more reliably.
A direct approach...
Study the primary destruction rate by supplying a
secondary destruction machanism of the same order of
magnitude
Formation of H3+
-
H2+ e
k1
H2+ H2+
+
H2 + 2e
k2
-
H3+ + H
Destruction of H3+
+
H3 + X
H 3+ + e -
k3
XH + + H 2
k4
slow in the
positive column
H2 + H, or H2 + H
kAD
+
H3 + wall
H + H + H, or H2 + H
k
Reaction
Mean a (cm3s-1)
k1
k2
k4
k3
H2 + eH2+ + H2
H3+ + eH3+ + CH4
H3+ + N2
H3+ + CO
(0.4 - 8) × 10-11 b
2.04 × 10-9
10-7 - 10-11 c
2.33 × 10-9
1.86 × 10-9
2.02 × 10-9
a
Uncertainty a (cm3s-1)
± 0.10 × 10-9
± 0.26 × 10-9
± 0.24 × 10-9
± 0.28 × 10-9
Unless otherwise noted, values are averages of the rates published in Reference [3] with uncertainties reported at the
95% confidence interval.
b
Calculated from ionization cross section published in Reference [4]. Range is due to uncertainty in the electron
temperature of our plasma (we assume Te ~ 2-3 eV). Since k1 drops out of the final expression, this large uncertainty
does not affect the results.
c
The dissociative recombination rate constant has been part of a controversy in recent years, [5-8] taking on a wide
range of values. Even if we assume the fastest rate, the destruction by dissociative recombination is still two orders of
magnitude smaller than the estimated destruction rate of H3+ by ambipolar diffusion.
d[H2+]
+
=
k
[e
][H
]
k
[H
]
[H
2 ] = 0
1
2
2
2
dt
1
d[H3+]
+
+
+
k
k
X
k
=
[H
][H
][
][H
]
[H
2
2
2
3
3
AD
3 ] = 0
dt
2
From
2
+
k2[H2][H2 ]
(k3[X] + kAD)
1
Rearrange and insert
k1[H2][e-]
(k3[X] + kAD)
Ratio [H3+] with and without impurity
=
k 3 [X ] + 1
kAD
For weak absorptions, the concentration is proportional to
the velocity modulation absorption signal, I(H3+), therefore:
k3
= k [X] + 1
AD
Example of Raw Data
4
2
0
-2
-4
0
5
10
15
20
Impurity Pressure (mTorr)
25
This is an example of the raw H3+ signal plotted versus
N2 pressure @ 200 mA. The dashed line is the function
a
b + x , added to emphasize the agreement with the
expression derived in the experimental model. The first
derivative lineshape is a result of the velocity
modulation technique.
Destruction Rate Plots
3.5
3.0
k4 /kAD = (2.13 ± 0.03) × 10 -15 cm3
2.5
2.0
1.5
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Number Density of N2at 200 mA (in 1015 cm-3 )
3.5
3.0
k4 /kAD = (2.30 ± 0.05) × 10 -15cm 3
2.5
2.0
1.5
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Number Density of CH 4 at 150 mA (in 1015 cm -3 )
Here are two examples of the H3+ relative intensity
versus number density of impurity. Each cluster of data
contains 5 measurements. The slope of the least squares
fit is equal to kk as shown in the experimental model.
3
AD
Measured Destruction Rate Constants
X
Current
kAD (×105 s-1) Uncertainty a (×105 s-1)
CH4
150
10.1
± 1.38
CH4
175
10.0
± 1.38
CH4
200
9.96
± 1.38
N2
150
5.96
± 0.91
N2
175
6.06
± 0.92
N2
200
6.74
± 1.02
CO
150
10.0
± 1.67
CO
175
9.48
± 1.58
CO
200
9.48
± 1.60
Mean:
8.66
± 1.83
a
Uncertainties reported at 95% confidence interval.
Conclusion
These results provide the first experimental evidence
demonstrating that the initial order of magnitude
estimate of the H3+ destruction due to ambipolar
diffusion is correct and that this destruction mechanism
is indeed very fast in the partially ionized positive
column. Since the uncertainty in kAD presented here is
not much worse than the error of most published ionneutral reaction rate constants, we can now model these
plasma chemical systems without having to make any
crude estimates. Furthermore, this technique is
generally applicable in measuring destruction rates in
any type of discharge cell as long as it is hydrogen
dominated.
References
[1] C. S. Gudeman, M. H. Begemann, J. Pfaff, and R. J. Saykally, Phys. Rev. Lett. 50, 727 (1983).
[2] E. T. White, J. Tang, and T. Oka, Science 284, 135 (1999).
[3] V. G. Anicich and W. T. Huntress, Astophys. J. Suppl. 62, 553 (1986).
[4] D. Rapp and P. Englander-Golden, J. Chem. Phys. 43, 1464 (1965).
[5] M. T. Leu, M. A. Biondi and R. Johnsen, Phys Rev. A8, 413 (1973).
[6] N. G. Adams, and D. Smith, IAU Symposium 120, Astochemistry, M. S. Vardya and S. P. Tarafdan, eds.
(Reidel Publ. Co., Dordrecht 1987).
[7] T. Amano, Ap. J 329, L121 (1988).
[8] T. Oka, in Dissociative Recombination: Theory, Experiment and Application IV, edited by M. Larsson, J. B. A.
Mitchell, and I. Schneider (World Scientific, Singapore, 2000).