814 Charged Particle and Photon Interactions with Matter
The association reaction, C
2
H
3
+ H
2
→ C
2
H
5
, may be one of the candidates for the formation
of ethane. However, it has been widely accepted that this reaction is slow (Knyazev and Slagle,
1996; Knyazev et al., 1996), for example, the rate constant of the reaction is of the order of
10
−16
cm
3
molecule
−1
s
−1
even at ∼600K. This is mainly due to the large energy barrier for the reaction
(>33kJmol
−1
) (Knyazev and Slagle, 1996; Knyazev et al., 1996). The contribution of this reaction
may be minor for the formation of ethane.
In order to examine the reactivity of the H atom with C
2
H
6
, the reaction of D atoms with a C
2
H
6
lm was investigated. If reaction D + C
2
H
6
→ C
2
H
5
+ HD takes place, C
2
H
5
D will be formed as a
primary product. When a 10ML thick C
2
H
6
lm was sprayed by D atoms for 1h at 10K, 0.2% of
the reactant C
2
H
6
was converted to C
2
H
5
D. This indicates the occurrence of abstraction reaction,
D + C
2
H
6
→ C
2
H
5
+ HD, but the yield of C
2
H
5
D (0.2%) is much lower than the ethane yields from
the reactions of D with C
2
H
4
(33%) or C
2
H
2
(4%) at 10K for 1h D-atom spray. At temperatures above
20K, no C
2
H
5
D could be detected. The extremely low yield of C
2
H
5
D indicates the much smaller
rate
constant for D + C
2
H
6
than those for D + C
2
H
4
/C
2
H
2
at 10 K.
The negative temperature dependences for the rates of reactions H/D + C
2
H
4
/C
2
H
2
in Figure 29.3
may be reasonably explained either by the increase of the sticking probability of H/D atoms on solid
lms or by the slower rate of the H/D atom diffusion on and in the solid lm at lower temperatures.
It is highly probable that the temperature dependence of the sticking probability and the diffusion
rateof H atoms reect the yields in Figure 29.3. During the H-atom spray over the solid lm, the
number of H atoms sprayed over the lm surface per unit time (d[H]/dt) is equal to the sum of the rates
of the H-atom annihilation due to recombination reaction, H + H → H
2
, the reaction of H with the
reactant, and the H-atom desorption from the surface. That is, the following relationship should hold:
d H /d constant H H reactant H
d
[ ] [ ] [ ][ ] [ ]t k k k= = + +
1
2
2
(29.1)
where k
1
, k
2
, and k
d
are the rate constant for reaction H + H → H
2
, that for the reaction of H withthe
reactant, and that for the desorption of H from the surface, respectively. The experimental fact that
the rates of the tunneling reactions increase with decrease of temperature (Figure 29.3) means that
the value of k
2
[H][reactant] in Equation 29.1 increases with decrease of temperature. That is, k
2
and/or [H] increase with decrease of temperature. In Equation 29.1, k
d
must be highly temperature
dependent, that is, k
d
= A exp(−E
d
/RT) (A, pre-exponential factor; E
d
, activation energy for the
desorption of the H atoms from the surface). At high temperature, the larger k
d
keeps the steady-
state concentration of H ([H]) on the solid surface extremely low. With decrease of temperature, k
d
decreases exponentially, and concomitantly [H] on the sample surface increases. Besides, the slower
diffusion rate of H atoms on and in the lm at lower temperatures results in the smaller value of k
1
in Equation 29.1. This also leads to the increase of the H-atom concentration at lower temperatures.
In Figure 29.3, the yield of C
2
H
6
from reaction H + C
2
H
2
is of the same order as that from H +
C
2
H
4
at 10K. In case k
2
for H + C
2
H
4
is much larger than k
2
for H + C
2
H
2
, as predicted by Bennett and
Mile (1973), [H] on the C
2
H
2
lm must be much larger than [H] on the C
2
H
4
lm at ∼10K. In order to
examine this possibility, the reactions of H atoms with a few ML thick C
2
H
2
or C
2
H
4
deposited on the
C
3
H
6
were studied (Hiraoka and Sato, 2001).
If the sticking probability of H atoms on the C
2
H
2
is much higher than that on the C
2
H
4
lm, the
conversion of C
3
H
6
to C
3
H
8
for the lm C
2
H
2
/C
3
H
6
would become much larger than that for C
2
H
4
/
C
3
H
6
. The yields of C
3
H
8
were 22% and 28% for the C
2
H
2
(3ML)/C
3
H
6
(10ML) and C
2
H
4
(3ML)/C
3
H
6
(10ML) lms, respectively. This suggests that the steady-state concentrations [H] on the C
2
H
2
and
C
2
H
4
lms are of the same order. Thus, the steep increase of the yield of C
2
H
6
from reaction H + C
2
H
2
could possibly be due to the negative temperature-dependent rate constant k
2
for H + C
2
H
2
. A nega-
tive temperature dependence of the rate constants for the low-temperature tunneling reactions has
been predicted theoretically by Takayanagi and Sato (1990). They performed the bending-corrected
rotating-linear-model calculations of the rate constants for the H + H
2
reaction and its isotopic vari-
ants at low temperatures and examined the effect of the van der Waals well. They found that van der