Submitted to Chemical Physics
1
Pressure Studies of Subthreshold Photoionization: CH3I, C2H5I and
C6H6 Perturbed by Ar and SF6
C. M. Evans,a,b,c E. Morikawab and G. L. Findleyc,*
b
a
Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA
Center for Advanced Microstructures and Devices (CAMD), Louisiana State University, Baton Rouge, LA 70803, USA
c
Department of Chemistry, University of Louisiana at Monroe, Monroe, LA 71209, USA
Submitted 3 October 2000, Revised 3 December 2000
Abstract
Subthreshold photoionization spectra of CH3I doped into Ar and SF6, and C2H5I and C6H6 doped into SF6, are reported for variations in both the
dopant number density DD and perturber number density DP. The DD and DP dependence of the subthreshold structure is discussed in terms of the excited
state processes of electron attachment and associative ionization. The variation in the subthreshold photocurrent as a function of DD and DP leads to
the determination of the effective rate constants for these processes. These constants are then analyzed with respect to the properties of the excited
dopant Rydberg state. For CH3I, the variations in the effective rate constants are discussed in terms of ground-state dopant and perturber properties.
1. Introduction
Photoionization spectroscopy of a dopant (D)
molecule in the environment of a perturber (P) serves as
a sensitive probe of dopant/perturber electronic
interactions. In many D/P systems, photoionization
structure has been observed to occur at energies lower
than the unperturbed dopant ionization threshold [1-12].
This subthreshold photoionization structure, which tracks
the photoabsorption of discrete dopant Rydberg states in
the same energy region, has been interpreted as arising
from electron attachment and associative ionization
mechanisms involving both D and P species [1-4,10-12].
Previous studies of these mechanisms have explored the
effect on the subthreshold photoionization structure of
varying separately either the dopant number density DD [14,10] or the perturber number density DP [10-12]. In the
present paper, we report subthreshold photoionization
*Corresponding author: E-mail: chfindley@ulm.edu
results for variations in both DD and DP for the dopants D
= CH3I, C2H5I, C6H6 and the perturbers P = Ar, SF6. As
described below, we are thereby able to determine
effective rate constants for electron attachment and
associative ionization in these systems.
Subthreshold photoionization spectra of pure CH3I
[10], of CH3I doped into Ar, N2, CO2 [11] and SF6 [10],
and of C2H5I and C6H6 doped into Ar and SF6 [12] have
been reported. Based upon measurements in which only
the number density of the perturber was varied, we
proposed two possible pathways for generating
subthreshold structure [10-12]. The first pathway requires
direct D/P interactions leading both to charge transfer and
to heteromolecular dimer ion formation:
(1)
(2)
where D* is a Rydberg state of the dopant molecule.
Since the first process (i.e., Eq. (1)) of this pathway
invokes electron attachment to the perturber, this
Submitted to Chemical Physics
mechanism should be enhanced in perturbers exhibiting a
large electron-attachment cross-section (e.g., SF6). The
second process (i.e., Eq. (2)) constitutes associative
ionization, which should lead to a perturber-dependent
onset energy as a result of D/P dimerization.
The second pathway, namely†
(3)
electron attachment in the two pathways (i.e., Eqs. (1) and
(3)).
Pathways 1 and 2 differ with regard to the associative
ionization contribution to the subthreshold photocurrent,
however. If one again assumes that DD* % DD in the linear
absorption regime, the associative ionization contribution
from pathway 1 is given by
(8)
(4)
(5)
differs significantly with regard to D/P interactions. In
the first process (i.e., Eq. (3)), electron attachment is now
to the dopant rather than to the perturber. Therefore, if
the dopant itself has a large electron attachment crosssection, subthreshold structure should be observed even
when the perturber has a low electron attachment crosssection (e.g., Ar, N2 and CO2). The second process (i.e.,
Eq. (4)) invokes associative ionization that is independent
of the perturber, while the third process (i.e., Eq. (5))
constitutes associative ionization that is only stabilized by
the perturber [13]. Therefore, the onset energy should
remain constant even if the perturber is varied. Finally,
for the case of a pure dopant that exhibits subthreshold
photoionization structure (e.g., CH3I [1-4,10]), pathway
2 reduces to Eqs. (3) and (4).
For either of the above pathways, the subthreshold
photocurrent is given by a sum of two contributions,
namely
(6)
where iea is the photocurrent contribution resulting from
electron attachment, and iai is the photocurrent resulting
from associative ionization. If one now assumes that the
electron attachment is saturated (i.e., dependent only
upon DD*), and if one further assumes that DD* % DD in the
linear absorption regime, the electron attachment
contribution to the photocurrent for both pathways 1 and
2 reduces to
(7)
where kea(1,2) is the effective rate constant for saturated
†
Pathway 2 was originally introduced to analyze
subthreshold photoionization for systems in which the dopant number
density was constant and small, and in [11,12] only Eqs. (3) and (5)
were employed. The expansion of this pathway to include Eq. (4),
therefore, has necessitated a change in notation for the rate constants
presented below, in comparison to the notation used in [12].
2
while the same contribution from pathway 2 is given by
(9)
where the associative ionization effective rate constants
(2)
(2)
! refer to Eqs. (2), (4) and (5), respectively.
k(1)
ai , kai and kai
The total subthreshold photocurrent is given by
(10)
for pathway 1, and
(11)
for pathway 2. Clearly, when a D/P system exhibits
subthreshold photoionization, both pathways 1 and 2 may
be operative simultaneously. However, in a system where
both pathways are available, pathway 1 should dominate
when DP o DD. Therefore, if the perturber has a large
electron attachment cross-section and DP o DD, one should
expect that the subthreshold photocurrent will be modeled
by Eq. (10), with little contribution from pathway 2. This
has indeed been found to be the case for a small constant
DCH I doped into varying DSF [10].
3
6
If the perturber has a small electron attachment crosssection, one should expect that the subthreshold
photocurrent will be modeled by Eq. (11), with little
contribution from pathway 1. In fact, Eq. (11) has been
found to be sufficient to explain the subthreshold
photocurrent for pure CH3I [10] and for a constant
number density of CH3I doped into varying number
densities of Ar, N2 and CO2 [11]. However, the
accessibility of pathway 2 depends upon the nature of D/D
interactions. If electron attachment to the dopant and
homomolecular dopant dimerization are not favored,
subthreshold photocurrent generated via pathway 2 is
unlikely.
This has been shown to be the case
experimentally for pure C2H5I and pure C6H6 [12], and for
a constant number density of C2H5I and C6H6 doped into
varying number densities of Ar [12].
As discussed above, subthreshold photoionization
structure has been observed in CH3I [10], C2H5I [12] and
C6H6 [12] perturbed by SF6, which is linearly dependent
Submitted to Chemical Physics
upon DSF . This subthreshold structure was explained
6
within the confines of pathway 1, since SF6 has a large
electron attachment cross-section. However, in the case
of pure CH3I, the existence of subthreshold structure
which is quadratically dependent upon DCH I [1-4,10]
3
implies that subthreshold photoionization can proceed
through pathway 2. Therefore, if DCH I is no longer much
3
smaller than DSF , contributions from pathway 2 should be
6
considered when modeling CH3I/SF6. On the other hand,
the lack of subthreshold photoionization structure in pure
C2H5I and pure C6H6 [12], as well as a lack of
subthreshold photocurrent in C2H5I and C6H6 doped into
Ar [12], indicates that C2H5I and C6H6 perturbed by SF6
should always be modeled within pathway 1. Additional
measurements involving variations in both DD and DP are
needed in order to distinguish the pathways leading to
subthreshold photoionization in these systems, however.
In the present paper, we present a systematic number
density study of the subthreshold photoionization
structure of CH3I perturbed by Ar and SF6, and of C2H5I
and C6H6 perturbed by SF6. The perturber Ar was
selected because of its small electron affinity, which
makes this perturber a prime candidate for investigating
pathway 2. The perturber SF6, on the other hand, was
selected because of its large electron affinity, which
makes this perturber ideal for investigating pathway 1. As
reported below, C2H5I/SF6 and C6H6/SF6 can be modeled
within pathway 1, while CH3I/SF6 requires both pathways
1 and 2 in order to explain sufficiently the dopant and
perturber density dependence. CH3I/Ar, however, can be
modeled solely within the confines of pathway 2. By
varying DD and DP separately, we were able to determine
the effective rate constants for electron attachment and
associative ionization. Finally, we discuss the effect of
electron affinity (of D or P) on kea(1,2), and the effect of
(2)
ground-state polarizability (of D or P) on k(1,2)
! .
ai and kai
2. Experiment
Photoionization spectra were measured with
monochromatic synchrotron radiation (with a resolution
of 0.09 nm, or - 8 meV in the spectral region of interest)
[14], which entered a copper experimental cell [15,16]
equipped with entrance and exit MgF2 windows. This
cell, which is capable of withstanding pressures of up to
100 bar, possesses two parallel plate electrodes (stainless
steel, 3 mm spacing) aligned perpendicular to the
windows. The light path within the cell is 1.0 cm. The
applied voltage was 100 V, and all photoionization
3
spectra were current saturated (which was verified by
measuring selected spectra at different applied voltages).
Photocurrents within the cell were of the order of 10-10 A.
All photoionization spectra were measured at room
temperature. The intensity of the synchrotron radiation
exiting the monochromator was monitored by measuring
the current across a Ni mesh intercepting the beam prior
to the experimental cell. All photoionization spectra are
normalized to this current. Furthermore, all C2H5I spectra
are intensity normalized to unity at the same spectral
feature above the X̃1 2E1/2 [17,18] ionization threshold; all
C6H6 spectra are intensity normalized to unity at the same
spectral feature above the 2E1g [19] ionization threshold;
and all CH3I spectra are intensity normalized to unity at
the same spectral feature above the 2E3/2 [20] ionization
threshold. Spectral peak areas were obtained by
integrating a gaussian deconvolution of the subthreshold
peaks.
CH3I (Aldrich, 99.5%), C2H5I (Sigma, 99%), C6H6
(Aldrich, 99.9+%), Ar (Matheson Gas Products,
99.9999%) and SF6 (Matheson Gas Products, 99.996%)
were used without further purification. Both the gas
handling system and the procedures employed to ensure
homogeneous mixing of the dopant and perturber have
been described previously [16,21].
3. Results
In what follows, we report subthreshold
photoionization results for C2H5I/SF6, C6H6/SF6, CH3I/Ar
and CH3I/SF6 for variations in both DD and DP. For the
sake of brevity, however, only representative subthreshold
photoionization spectra are presented for each D/P system
for a chosen DP (varying DD) and then a chosen DD (varying
DP). (Data omitted here will be found in [22].) From the
density dependence of the subthreshold structure as a
function of DD and DP, a determination is made as to which
pathway best models the observed subthreshold
photocurrent. The density-dependent variation of the
subthreshold structure is then used, in Section 4, to
determine the effective rate constants for electron
attachment and associative ionization in these systems.
Figs. 1a and 1a! present subthreshold photoionization
spectra of C2H5I/SF6 at constant DSF and at constant DC H I,
6
2 5
respectively, and the peak areas obtained from these
spectra are plotted versus DC H I and DSF in Figs. 1b and
2 5
6
1b!, respectively.
(An example of a gaussian
deconvolution used to obtain the peak areas is shown in
Fig. 1a.) Similarly, the subthreshold spectra of C6H6/SF6
Submitted to Chemical Physics
4
Fig. 1. Subthreshold photoionization spectra of C2H5I/SF6: (a)
photoionization of varying C2H5I number densities DC H I (1019 cm-3), as
2 5
indicated on the spectra, perturbed by 0.63 × 1019 cm-3 SF6. In the first
spectrum, the dotted lines are an example of a gaussian deconvolution
used to obtain peak areas. (a!) Photoionization of 0.00024 × 1019 cm-3
C2H5I perturbed by varying SF6 number densities DSF (1019cm-3), as
6
indicated on the spectra. (b) Peak areas (by gaussian fits to the
photoionization spectra) for the subthreshold structure shown in (a)
plotted vs. DC H I. (b!) Peak areas (by gaussian fits to the photoionization
2 5
spectra) for the subthreshold structure shown in (a!) plotted vs. DSF . In
6
(a) and (a!): each spectrum is intensity normalized to unity at the same
spectral feature above the X̃1 2E1/2 ionization threshold. In (b) and (b!):
(!) 10d, (") 11d, (•) 12d, (–) 13d, and (—) 14d. The solid lines
represent linear least-square fits to Eq. (10).
Fig. 2. Subthreshold photoionization spectra of C6H6/SF6: (a)
photoionization of varying C6H6 number densities DC H (1019 cm-3), as
6 6
indicated on the spectra, perturbed by 0.63 × 1019 cm-3 SF6. (a!)
19
-3
Photoionization of 0.012 × 10 cm C6H6 perturbed by varying SF6
number densities DSF (1019cm-3), as indicated on the spectra. (b) Peak
6
areas (by gaussian fits to the photoionization spectra) for the
subthreshold structure shown in (a) plotted vs. DC H . (b!) Peak areas
6 6
(by gaussian fits to the photoionization spectra) for the subthreshold
structure shown in (a!) plotted vs. DSF . In (a) and (a!): each spectrum
6
is intensity normalized to unity at the same spectral feature above the
2
E1g ionization threshold. In (b) and (b!): (!) 8R', (") 9R', (•) 10R',
(–) 11R', and (—) 12R'. The solid lines represent linear least-square
fits to Eq. (10).
are given in Fig. 2. The linearity of the subthreshold
photoionization intensity as a function of DD (D = C2H5I,
C6H6) and DP (P = SF6) in both of these systems indicates
that the subthreshold photocurrent can be modeled
exclusively by Eq. (10). Thus, these measurements fully
confirm our previous supposition [12] that the
subthreshold photocurrent observed in C2H5I/SF6 and
C6H6/SF6 arises from pathway 1 with no contribution from
pathway 2.
Unlike the cases of C2H5I and C6H6 [12], pure CH3I
is known to exhibit subthreshold photoionization that is
quadratically dependent upon DCH I [1-4,10]. This
3
subthreshold structure, which is shown in Fig. 3a, can be
modeled through pathway 2 (in the absence of P). The
peak areas from this structure, which are plotted versus
DCH I in Fig. 3b, can be analyzed with least-square second3
order polynomial regressions on Eq. (11). These
nonlinear regressions lead directly to the electron
attachment rate constant kea(2) and the associative ionization
rate constant k(2)
ai for each discrete CH3I Rydberg state
observed (n = 10 - 14), and the values for these rate
constants are given in Table 1.
Submitted to Chemical Physics
5
Fig. 3.
Subthreshold
photoionization spectra of CH3I:
(a) photoionization spectra of
varying CH3I number densities
DCH I (1019cm-3), as indicated on
3
the spectra. Each spectrum is
intensity normalized to unity at
the same spectral feature above
the 2E3/2 ionization threshold.
(b) Peak areas (obtained from
gaussian fits to the
photoionization spectra) for the
subthreshold photoionization
structure in (a) plotted vs. DCH I.
3
(!) 10d, (") 11d, (•) 12d, (–)
13d, and (—) 14d. The solid
lines represent least-square
second-order polynomial fits to
Eq. (11) (cf. Table 1). See text
for discussion.
The subthreshold photoionization spectra of CH3I/Ar
at constant DAr, along with the peak areas of this structure
plotted versus DCH I, are presented in Figs. 4a and 4b.
3
Analogous data are shown for CH3I/Ar at constant DCH I in
3
Figs. 4a! and 4b!. The quadratic dependence of the
subthreshold photocurrent on DCH I (cf. Fig. 4b), coupled
3
with the linear dependence of this photocurrent on DAr (cf.
Fig. 4b!) fully substantiates our original conclusion [11]
that the CH3I/Ar subthreshold photocurrent arises via
pathway 2.
Fig. 4. Subthreshold photoionization spectra of CH3I/Ar: (a)
photoionization spectra of varying CH3I number densities DCH I (1019cm3
3
), as indicated on the spectra, perturbed by 0.63 × 1019 cm-3 Ar. (a!)
Photoionization spectra of 0.061 × 1019 cm-3 CH3I perturbed by varying
Ar number densities DAr (1019cm-3), as indicated on the spectra. (b)
Peak areas (obtained from gaussian fits to the photoionization spectra)
for the subthreshold photoionization structure in (a) plotted vs. DCH I.
3
(b!) Peak areas (obtained from gaussian fits to the photoionization
spectra) for the subthreshold photoionization structure in (a!) plotted vs.
DAr. In (a) and (a!): each spectrum is intensity normalized to unity at
the same spectral feature above the 2E3/2 ionization threshold. In (b)
and (b!): (!) 10d, (") 11d, (•) 12d, (–) 13d, and (—) 14d. The
solid lines represent linear least-square fits to Eq. (11). See text for
discussion.
Table 1.
Effective rate constants* determined from subthreshold photoionization peak areas for CH3I (cf. Fig. 3b).
(2)
kea
k(2)
ai
10d
11d
12d
13d
14d
0.15 ± 0.08
1.2 ± 0.1
0.57 ± 0.09
3.7 ± 0.2
0.94 ± 0.10
7.7 ± 0.3
1.3 ± 0.2
14 ± 0.4
1.7 ± 0.3
25 ± 0.5
*
The effective rate constants were determined by least-square second-order polynomial fits of the peak areas [22] to Eq. (11) (DP = 0),
as shown in Fig. 3b. (The quoted errors result from assuming a variance of ± 1 standard deviation both in the fitting of the
subthreshold peaks and in the regression analysis used to obtain these rate constants [22].)
Submitted to Chemical Physics
Subthreshold photoionization spectra of CH3I
perturbed by SF6 for constant DSF and constant DCH I are
6
3
shown in Figs. 5a and 5a!, respectively, and the peak areas
obtained from these spectra are plotted versus DSF and
6
DCH I in Figs. 5b and 5b!, respectively . As in the case of
3
CH3I/Ar, the quadratic dependence of this subthreshold
structure on DCH I, and the linear dependence upon DSF ,
3
6
indicate that the subthreshold photocurrent follows
pathway 2. However, previous studies of CH3I/SF6 [10]
have shown that when DCH I n DSF the subthreshold
3
6
structure can be modeled via pathway 1. (The
6
accessibility of pathway 1 in CH3I/SF6 is further
substantiated by the lower onset energy (50 meV)
observed for this system in comparison to pure CH3I, or
to CH3I/Ar when DCH I is small.) Therefore, over the
3
complete density range, the CH3I/SF6 subthreshold
photocurrent should be given by the sum of Eqs. (10) and
(11), or
(12)
4. Discussion
The determination of the effective rate constants for
electron attachment and associative ionization requires a
variation in both DD and DP. We begin the evaluation of
these constants by studying the density dependence of the
subthreshold photocurrent when DP is varied at different
constant values of DD. For constant DD, the total
subthreshold photocurrent for pathway 1 (i.e., Eq. (10)),
pathway 2 (i.e., Eq. (11)) and the sum of the two pathways
(i.e., Eq. (12)) reduces to the same form, namely
(13)
The DD dependence of the regression coefficients b0 and
b1 differs significantly for each pathway, however.
Since pathway 1 was invoked to explain the
subthreshold photoionization structure observed in
C2H5I/SF6 (cf. Fig. 1) and C6H6/SF6 (cf. Fig. 2), the
coefficients b0 and b1 are, in this case,
(14)
Fig. 5. Subthreshold photoionization spectra of CH3I/SF6: (a)
photoionization spectra of varying CH3I number densities DCH I (1019cm3
3
), as indicated on the spectra, perturbed by 0.63 × 1019 cm-3 SF6. (a!)
Photoionization spectra of 0.061 × 1019 cm-3 CH3I perturbed by varying
SF6 number densities DSF (1019cm-3), as indicated on the spectra. (b)
6
Peak areas (obtained from gaussian fits to the photoionization spectra)
for the subthreshold photoionization structure in (a) plotted vs. DCH I.
3
(b!) Peak areas (obtained from gaussian fits to the photoionization
spectra) for the subthreshold photoionization structure in (a!) plotted vs.
DSF . In (a) and (a!): each spectrum is intensity normalized to unity at
6
the same spectral feature above the 2E3/2 ionization threshold. In (b)
and (b!): (!) 10d, (") 11d, (•) 12d, (–) 13d, and (—) 14d. The
solid lines represent least-square second-order polynomial fits to Eq.
(12). See text for discussion.
Therefore, if b0 and b1 are obtained for various values of
DD (D = C2H5I, C6H6), and if b0 and b1 are linear functions
of DD, then pathway 1 has been substantiated and the
effective rate constants kea(1) and k(1)
ai can be obtained from
Eq. (14). The values for b0 and b1, obtained as described
above, are plotted as functions of DC H I in Fig. 6a and 6b,
2 5
respectively. Similar plots of b0 and b1 as functions of
DC H are shown in Fig. 6a! and 6b!, respectively. Clearly,
6 6
b0 and b1 are linearly dependent upon DD (D = C2H5I,
C6H6) and, therefore, Eq. (14) can be employed. The
effective rate constants kea(1) and k(1)
ai , obtained from leastsquare linear regressions of b0 and b1 [22], are given in
Table 2a (C2H5I/SF6) and Table 2b (C6H6/SF6).
Since kea(1) is proportional to the (saturated) electron
attachment cross-section which, in turn, scales as the
Submitted to Chemical Physics
7
principal quantum number n of the dopant Rydberg state
[23], kea(1) should vary linearly with n. k(1)
ai , on the other
hand, is determined by molecular interactions which are
dependent upon the excited state polarizability of the
dopant [24]. Since Rydberg state polarizability scales as
7
n7 [23], k(1)
ai should scale as n . That this is indeed the case
is shown in Figs. 7a and 7b (C2H5I/SF6) and Figs. 7a! and
7b! (C6H6/SF6). The n dependence of these rate constants,
when coupled with the analysis presented above, allows
one to conclude that pathway 1 is sufficient to explain the
behavior of the subthreshold photocurrent in both
C2H5I/SF6 and C6H6/SF6.
On the basis of the observed density dependence of
the CH3I/Ar subthreshold photocurrent described in
Section 3 (cf. Fig. 4) and in [11], we chose to evaluate this
structure using pathway 2. In this case, the coefficients b0
and b1 are given by
(15)
Fig. 6. (a) Constant and (b) linear regression coefficients for the
subthreshold density dependence of C2H5I/SF6 plotted vs. DC H I. (!)
2 5
10d, (") 11d, (•) 12d, (–) 13d, and (—) 14d. (a!) Constant and (b!)
linear regression coefficients for the subthreshold density dependence
of C6H6/SF6 plotted vs. DC H . (!) 8R!, (") 9R!, (•) 10R!, (–) 11R!,
6 6
and (—) 12R!. The solid lines represent linear least-square fits to Eq.
(14). See text for discussion.
Unlike pathway 1, b0 and b1 for pathway 2 are
quadratically dependent upon the dopant number density.
The values of b0 and b1 obtained from the CH3I/Ar data
are plotted as functions of DCH I in Figs. 8a and 8b,
3
respectively. Nonlinear regressions on the data of Figs.
8a and 8b [22] show that b0 and b1 are quadratically
dependent upon DCH I. Evaluating b0 and b1 using Eq. (15)
3
then leads to a determination of the effective rate
Table 2.
Effective rate constants* determined from b0 and b1 for (a) C2H5I/SF6 (cf. Figs. 6a and 6b) and (b) C6H6/SF6 (cf. Figs. 6a! and 6b!).
a. C2H5I/SF6
10d
k(1)
ea
k(1)ai
1.0 ± 0.1
1.2 ± 0.1
11d
12d
13d
14d
3.1 ± 0.2
3.9 ± 0.3
5.1 ± 0.3
7.6 ± 0.4
7.3 ± 0.4
15 ± 0.4
9.4 ± 0.6
25 ± 0.6
9R!
10R!
11R!
12R!
4.3 ± 0.4
1.9 ± 0.4
6.2 ± 0.5
4.1 ± 0.5
8.1 ± 0.5
7.8 ± 0.6
b. C6H6/SF6
8R!
k(1)
ea
k(1)ai
*
0.50 ± 0.08
0.038 ± 0.010
2.4 ± 0.2
0.67 ± 0.1
The effective rate constants were determined by least-square second-order polynomial fits of b0 and b1 [22] to Eq. (14), as shown in Fig. 6. (The
quoted errors result from assuming a variance of ± 1 standard deviation both in the fitting of the subthreshold peaks and in the regression analysis used
to obtain these rate constants [22].)
Submitted to Chemical Physics
C2H5I/SF6
10
8
C6H6/SF6
a
a!
8
kea (arbitrary units)
6
6
4
(1)
4
(1)
kea (arbitrary units)
8
2
0
10
11
12
13
2
0
14
8
9
25
b
kai (arbitrary units)
10
(1)
kai(1) (arbitrary units)
15
5
2
4
6
7
11
12
b!
8
20
0
10
n
n
8
-7
n (x 10 )
10
6
4
2
0
0
1
2
n7 (x 10-7)
3
Fig. 7. Effective rate constant k(1)
ea for the electron attachment
mechanism (i.e., Eq. (1)) in (a) C2H5I/SF6 and (a!) C6H6/SF6 plotted vs.
the excited-state principal quantum number n of C2H5I and C6H6,
respectively. Effective rate constant k(1)ai for the associative ionization
mechanism (i.e., Eq. (2)) in (b) C2H5I/SF6 and (b!) C6H6/SF6 plotted vs.
n7 of C2H5I and C6H6, respectively. The solid lines are linear least(1)
square fits to the data. The error bars for kea
and k(1)ai result from the
assumption of a variance of ± 1 standard deviation both in the fitting
of the subthreshold peaks and in the regression analysis used to obtain
these rate constants. See text for discussion.
(2)
constants kea(2), k(2)
! , which are given in Table 3a.
ai and kai
The electron attachment rate constant kea(2) should be
equivalent to that determined directly from the analysis of
the pure CH3I spectra (cf. Fig. 3 and Table 1). Similarly,
the value of the associative ionization constant k(2)
ai
determined from CH3I/Ar should be equivalent to k(2)
ai
obtained from pure CH3I (cf. Fig. 3 and Table 1). In both
cases, these rate constants agree remarkably well with one
another.
As discussed in Section 3, an explanation of the
density dependence of the CH3I/SF6 subthreshold
photoionization structure should require both pathways 1
Fig. 8. (a) Constant and (b) linear regression coefficients for the
subthreshold density dependence of CH3I/Ar plotted vs. DCH I. (a!)
3
Constant and (b!) linear regression coefficients for the subthreshold
density dependence of CH3I/SF6 plotted vs. DCH I. (!) 10d, (") 11d,
3
(•) 12d, (–) 13d, and (—) 14d. The solid lines represent least-square
second-order polynomial fits to Eq. (15) for CH3I/Ar and to Eq. (16) for
CH3I/SF6. See text for discussion.
and 2. In this case, the coefficients b0 and b1 become
(16)
which differ significantly from the form of these
coefficients for C2H5I/SF6 and C6H6/SF6, and for CH3I/Ar.
In Fig. 8a! and 8b!, respectively, b0 and b1 are plotted as
functions of DCH I for the CH3I/SF6 system, and the
3
(2)
effective rate constants kea(1), k(1)
! obtained from
ai , and kai
least-square second-order polynomial fits of b0 and b1 [22]
to Eq. (16) are given in Table 3b. (We must point out
that, from our regression analysis of b0, only k(2)
ai and the
Submitted to Chemical Physics
9
Table 3.
Effective rate constants* determined from b0 and b1 for (a) CH3I/Ar (cf. Figs. 8a and 8b) and (b) CH3I/SF6 (cf. Figs. 8a! and 8b!).
a. CH3I/Ar
k(2)
ea
k(2)ai
(2)
kai!
10d
11d
12d
13d
14d
0.15 ± 0.07
1.2 ± 0.1
2.3 ± 0.1
0.57 ± 0.09
3.7 ± 0.2
2.4 ± 0.2
0.94 ± 0.11
7.6 ± 0.3
2.6 ± 0.3
1.3 ± 0.2
14 ± 0.4
2.8 ± 0.4
1.7 ± 0.3
25 ± 0.5
3.0 ± 0.5
10d
11d
12d
13d
14d
0.77 ± 0.11
0.95 ± 0.11
1.1 ± 0.1
8.2 ± 0.1
2.9 ± 0.2
3.1 ± 0.2
3.8 ± 0.2
8.3 ± 0.2
4.7 ± 0.3
6.1 ± 0.3
7.5 ± 0.4
8.9 ± 0.3
6.6 ± 0.5
12 ± 0.5
14 ± 0.5
9.6 ± 0.4
8.7 ± 0.5
20 ± 0.7
24 ± 0.6
11 ± 0.5
b. CH3I/SF6
k(1)
ea
k(1)ai
k(2)ai
kai(2)
!
*
In (a), the effective rate constants were determined by least-square second-order polynomial fits of b0 and b1 [22] to Eq. (15), as shown in Figs. 8a
and 8b. In (b), the effective rate constants k(1)ai, k(2)ai and kai(2)
! were determined by least-square second order polynomial fits of b0 and b1 [22] to Eq. (16),
(2)
as shown in Figs. 8a! and 8b!. The rate constant k(1)
ea results from subtracting the value for kea obtained from pure CH3I (cf. Table 1) from the first-order
regression coefficient of the least-square fit of b0 (see text for discussion). (The quoted errors result from assuming a variance of ± 1 standard deviation
both in the fitting of the subthreshold peaks and in the regression analysis used to obtain these rate constants [22].)
sum of the electron attachment rate constants kea(2) + kea(1) are
obtained. However, since k(2)
ai obtained from this analysis
agrees, to within experimental error, with k(2)
ai as
determined from pure CH3I (cf. Table 1) and CH3I/Ar (cf.
Table 3a), we have used the kea(2) value determined from
pure CH3I in order to obtain the kea(1) values reported here.)
The n dependence of the effective rate constants for
CH3I/P (P = Ar, SF6) can be used to substantiate further
the above choice of pathways. Moreover, variations in
the rate constants for different perturbers can also be
investigated for the CH3I data presented here. In Fig. 9a,
kea(1) for CH3I/SF6 and kea(2) from CH3I are plotted versus n.
As was the case for C2H5I/SF6 (cf. Figs. 7a and 7b) and
C6H6/SF6 (cf. Figs. 7a! and 7b!), kea(1,2) has a linear n
dependence. In Figs. 9b and 9c, the associative ionization
rate constants k(1,2)
ai and the perturber-stabilized associative
ionization constants kai!(2), respectively, are plotted as
functions of n7 for CH3I/P (P = Ar, SF6). Again the
linearity is striking. Since the effective rate constants kea(1,2),
(2)
k(1,2)
! determined for pure CH3I and CH3I/P (P = Ar,
ai and kai
SF6) show the correct n dependence, one can conclude
that electron attachment (i.e., Eqs. (1) and (3)) and
associative ionization (i.e., Eqs. (2), (4) and (5)) are
sufficient to explain the density dependence of the
subthreshold photocurrent observed in CH3I, CH3I/Ar and
CH3I/SF6.
Additionally, Fig. 9a also shows that kea(2) < kea(1),
implying that electron attachment to SF6 is more efficient
than electron attachment to CH3I. If the electron
attachment rate constant increases linearly with increasing
stability of the molecular anion, then normalization of kea(1,2)
to the electron affinity of the neutral species involved in
anion formation should result in a single linear correlation
of the electron attachment rate constant. In Fig. 10a, we
present kea(1,2) normalized in this way to electron affinity and
plotted as a function of n, which shows, to within
experimental error, that one correlation line does indeed
result. (In Fig. 10a, kea(1) and kea(2) are normalized to the
electron affinities of SF6 and CH3I, respectively. The
electron affinities used are 1.05 eV [25] for SF6 and 0.20
eV [26] for CH3I.)
(1)
From Fig. 9b, k(2)
ai > kai , thus indicating that
homomolecular CH3I dimerization (i.e., Eq. (4)) is more
favorable than heteromolecular CH3I/SF6 dimerization
(i.e., Eq. (2)). The associative ionization rate must
depend upon the polarizability of the ground-state
molecule in the dimer pair, albeit in ways that depend
sensitively upon the nature of the potentials chosen to
model these interactions [24]. Therefore, if one assumes
ionization rate constant upon the polarizability of the for
Submitted to Chemical Physics
Fig. 9. (a) Effective rate constants k(1,2)
ea for electron attachment to SF6
(i.e., Eq. (1) and Table 3b) and CH3I (i.e., Eq. (3) and Table 1) plotted
vs. the excited-state principal quantum number n of CH3I. (") SF6 and
(!) CH3I. (b) Effective rate constants k(1,2)
ai for associative ionization of
CH3I with SF6 (i.e., Eq. (2) and Table 3b) and k(2)ai for associative
ionization of CH3I with itself (i.e., Eq. (4) and Table 1) plotted vs. n7.
(") SF6 and (!) CH3I. (c) Effective rate constants kai(2)
! for the perturberstabilized associative ionization of CH3I (i.e., Eq. (5)) plotted vs. n7.
(!) Ar (cf. Table 3a) and (") SF6 (cf. Table 3b). The solid lines are
linear least-square fits to the data. The error bars for the effective rate
constants result from the assumption of a variance of ± 1 standard
deviation both in fitting the subthreshold peaks and in the regression
analysis used to obtain these rate constants. See text for discussion.
simplicity a linear dependence of the associative groundstate molecule involved in dimerization, normalization by
this polarizability should collapse k(1,2)
to a single
ai
correlation line. Fig. 10b shows that this does in fact hold
for pure CH3I and CH3I/SF6 (where we have normalized
to the following values of the polarizability (10-24 cm3):
CH3I, 7.97 [27] and SF6, 6.54 [28]). If one further
assumes a linear dependence of the rate constant for
perturber-stabilized associative ionization on the groundstate polarizability of the perturber, kai!(2) should collapse to
a single linear correlation for all perturbers. That this is
10
Fig. 10. (a) Effective rate constants k(1,2)
ea for SF6 (") and CH3I (!)
normalized to the electron affinity of SF6 and CH3I, respectively. (b)
Effective rate constants k(1)ai for SF6 (") and k(2)ai for CH3I (!) normalized
to the ground-state polarizability of SF6 and CH3I, respectively. (c)
Effective rate constants kai(2)
! for Ar (!) and SF6 (") normalized to the
ground-state polarizability of Ar and SF6, respectively. The error bars
shown for the effective rate constants are the maximum errors from the
data presented in Table 3. See text for the values of the electron
affinities and ground-state polarizabilities used.
the case for CH3I/Ar and CH3I/SF6 is shown in Fig. 10c
(where we have normalized kai!(2) to the following values of
the polarizability (10-24 cm-3): Ar, 1.6411 [29,30] and SF6,
6.54 [28]).
5. Conclusions
We have presented subthreshold photoionization
spectra of CH3I, CH3I/P (P = Ar, SF6), C2H5I/SF6, and
C6H6/SF6 for variations in DD and DP. The analysis
presented here validates the earlier preliminary results
[12] that pathway 1 (i.e., Eqs. (1), (2) and (10)), which
depends upon direct D/P interactions, is sufficient to
explain the origin and behavior of subthreshold
Submitted to Chemical Physics
photoionization in both C2H5I/SF6 and C6H6/SF6. The
present analysis also confirms an earlier study [11] which
concluded that the CH3I/Ar subthreshold photocurrent can
be modeled solely within the confines of pathway 2 (i.e.,
Eqs. (3) - (5) and (11)). However, the more complete
density analysis presented here shows that CH3I/SF6
subthreshold photoionization proceeds through both
pathways simultaneously (i.e., Eqs. (1) - (5) and (12)).
This observation, therefore, represents an extension of
previous work [10], where DCH I n DSF and where the
3
6
subthreshold structure was modeled within the confines of
pathway 1.
By systematically varying both DD and DP, the
effective rate constants for the various processes leading
to subthreshold photoionization have been determined.
We have also shown that the effective rate constant for
electron attachment to CH3I (i.e., kea(2)) obtained for
CH3I/Ar agrees well with that obtained for pure CH3I.
Moreover, the CH3I homomolecular dimerization
effective rate constant (i.e., k(2)
ai ) obtained for pure CH3I
agrees with the same constant determined for both
CH3I/Ar and CH3I/SF6, thus demonstrating the
consistency of these analyses.
(2)
We have also demonstrated that kea(1,2), k(1,2)
! scale
ai and kai
in a simple fashion with respect to the principal quantum
number n of the dopant Rydberg state. One can conclude,
therefore, that the mechanisms of (saturated) electron
attachment and associative ionization are sufficient to
explain the behavior of the subthreshold photocurrent for
all of the D/P systems studied. Furthermore, for the
dopant CH3I, the variation in the effective rate constants
for electron attachment to CH3I (i.e., kea(2)) and to SF6 (i.e.,
kea(1)) has been shown to scale in a simple manner with
electron affinity. The variation in the associative
ionization rate constant k(1,2)
ai has been shown to be directly
proportional to the polarizability of the ground-state
molecule in the CH3I…X dimer pair
(X = CH3I, SF6). Finally, the perturber-stabilized
associative ionization rate constant kai!(2) for CH3I/Ar and
CH3I/SF6 has been shown to be linearly dependent upon
the ground-state polarizability of the perturber.
Additional measurements of subthreshold
photoionization for variable DD and DP in different D/P
systems will provide further tests of the wider
applicability of pathways 1 and 2. If CH3I is chosen as
the dopant, one may continue to probe the dependence of
the effective rate constants upon perturber properties.
Such measurements have recently been made for the
perturbers CF4 and c-C4F8 [31], for example.
11
Acknowledgments
This work was conducted at the University of
Wisconsin Synchrotron Radiation Center (NSF DMR9531009) and was supported by a grant from the Louisiana
Board of Regents Support Fund (LEQSF (1997-00)-RDA-14).
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