The vibrational relaxation of CO₂ isolated in solid argon
For description of the vibrational relaxation of CO₂ molecules embedded in Ar matrix the model based on multiphonon transitions is applied. Rates for the VT and VV processes are determined from a fitting of simulated and experimental data. The calculations confirmed that radiative processes influenc...
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Cenian, A. Grigorian, G. Śliwiński, G. 2018-01-14T13:21:33Z 2018-01-14T13:21:33Z 2003 The vibrational relaxation of CO₂ isolated in solid argon / A. Cenian, G. Grigorian, G. Śliwiński // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1135-1139. — Бібліогр.: 15 назв. — англ. 0132-6414 PACS: 67.40.Fd https://nasplib.isofts.kiev.ua/handle/123456789/128942 For description of the vibrational relaxation of CO₂ molecules embedded in Ar matrix the model based on multiphonon transitions is applied. Rates for the VT and VV processes are determined from a fitting of simulated and experimental data. The calculations confirmed that radiative processes influence significantly the vibrational energy relaxation of CO₂ embedded in solid Ar, e.g., the determined rate for energy transfer between n₃ and n₂. mode is significantly lower than that predicted under assumption of the nonradiative relaxation. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Spectroscopy in Cryocrystals and Matrices The vibrational relaxation of CO₂ isolated in solid argon Article published earlier |
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The vibrational relaxation of CO₂ isolated in solid argon |
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The vibrational relaxation of CO₂ isolated in solid argon Cenian, A. Grigorian, G. Śliwiński, G. Spectroscopy in Cryocrystals and Matrices |
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The vibrational relaxation of CO₂ isolated in solid argon |
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The vibrational relaxation of CO₂ isolated in solid argon |
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The vibrational relaxation of CO₂ isolated in solid argon |
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The vibrational relaxation of CO₂ isolated in solid argon |
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vibrational relaxation of co₂ isolated in solid argon |
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Cenian, A. Grigorian, G. Śliwiński, G. |
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Cenian, A. Grigorian, G. Śliwiński, G. |
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Spectroscopy in Cryocrystals and Matrices |
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Spectroscopy in Cryocrystals and Matrices |
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2003 |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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For description of the vibrational relaxation of CO₂ molecules embedded in Ar matrix the model based on multiphonon transitions is applied. Rates for the VT and VV processes are determined from a fitting of simulated and experimental data. The calculations confirmed that radiative processes influence significantly the vibrational energy relaxation of CO₂ embedded in solid Ar, e.g., the determined rate for energy transfer between n₃ and n₂. mode is significantly lower than that predicted under assumption of the nonradiative relaxation.
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The vibrational relaxation of CO₂ isolated in solid argon / A. Cenian, G. Grigorian, G. Śliwiński // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1135-1139. — Бібліогр.: 15 назв. — англ. |
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2025-11-26T01:42:50Z |
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Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1135–1139
The vibrational relaxation of CO2 isolated in solid argon
A. Cenian1, G. Grigorian2, and G. Œliwiñski1
1Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdansk 80-952, Poland
E-mail: cenian@imp.gda.pl
2Institute of Physics, St. Petersburg State University, St. Petersburg 198504, Russia
For description of the vibrational relaxation of CO2 molecules embedded in Ar matrix the
model based on multiphonon transitions is applied. Rates for the VT and VV processes are deter-
mined from a fitting of simulated and experimental data. The calculations confirmed that radiative
processes influence significantly the vibrational energy relaxation of CO2 embedded in solid Ar,
e.g., the determined rate for energy transfer between �3 and �2 mode is significantly lower than
that predicted under assumption of the nonradiative relaxation.
PACS: 67.40.Fd
Introduction
A large number of physical and chemical processes
in the solid-state involve the vibrational energy relax-
ation (VER) of molecules. A study of this process for
molecules isolated in noble-gas matrices has attracted
considerable attention over past years. Among the
studied systems a spectacular class constitute the CO,
NO, O3, CO2 or XeF* in solid Ar [1–4]. The vibra-
tional energy transfer in 13C16O2 isolated in solid Ar
has been investigated by laser induced fluorescence
method [2]. The intense radiation observed in
the 16-�m region after strong excitation of the state
(00°1) was ascribed to the vibrational stimula-
ted emission. Also, for processes of the type
(1110(2)��1,2�2) and (0001� �1 + �2, 3�2) the relax-
ation times �VT and �V3V
were estimated from decay
times of stimulated emission basing on the assumption
that nonradiative relaxation prevails.
In this work we aim at clarifying the influence of
different relaxation channels on populations of vibra-
tional levels using the theory of multiphonon relax-
ation proposed by Nitzan et al. [5]. Also results of esti-
mation of the VER rate constants for the CO2/Ar
system by comparing the experimental and calculated
temporal pulse-shape of radiation are discussed.
In particular, we refer to the experimental results
for the 13CO2 vibrational-energy relaxation in solid
argon under conditions of matrix-to-reagent molecular
ratio M/R = 2000 [2]. The laser excitation of the
�3 (v = 1) level of carbon dioxide molecules was found
to induce strong emissions (�1 + �2, 3�2) � (�1, 2�2)
and (�1, 2�2) � �2 in the spectral region around
16 �m. Their sharp threshold as a function of laser ex-
citation density was interpreted as a signature of vi-
brational stimulated emission. It is known that the
CO2 molecules are trapped in solid argon in two dis-
tinct sites: single substitutional, which is stable, and
© A. Cenian, G. Grigorian, and G. Œliwiñski, 2003
0001
1110(1)
033 0
1110(2)
VT
1000(1)
0220
1000(2)
0110
000 0
= 0 1 2 3
V3V
15.8 16.7
16.2 �
� �
m
m m
VVT
Fig. 1. Diagram of the CO2 vibrational levels with energy
lower than 3000 K; solid arrows denote the transitions of
vibrationally stimulated emission observed in Ar matrices,
dashed arrows represent the exemplary nonradiative transi-
tions of the type VT, V3V and VVT.
double substitutional, which appears to be an unstable
site [2]. The first one due to the limited free-space is
characterized by a stronger vibration-phonon coupling
and shorter relaxation times (one order of magni-
tude). The lasers used in experiments [2], allowed for
a good time resolution and a site selective excitation.
Both sites were found to be luminescent. The reported
emission spectrum due to stable site consisted of three
lines (see Fig. 1). The relaxation times �VT and �V3V
for processes of the type (1110(2) � �1,2�2) and
(0001� �1 + �2, 3�2) were estimated in [2] from decay
times of the stimulated emission on the assumption
that the radiative relaxation may be neglected. In the
case of stable site the respective decay times were
� 700 and �100 ns.
During final stage of paper preparation, we became
aware of the interesting work of Chabbi et al. [6], re-
porting the rate constants for the VER processes of
isolated CO2, determined by radiation-pulse fitting-
procedure using 6 independent constants, i.e., not re-
lated by any scaling law.
Model description
The vibrational energy relaxation following strong
pulsed excitation is studied by solving the kinetic
equations describing the time evolution of populations
of different vibrational levels of CO2 molecules
dn dt R R R R Rv
v v v v v/ � � � � �VT VVT V V sp ind3
, (1)
where nv denotes the population of vibrational level v
and the Rv terms describe population changes due to
the VT, VVT and V3V intramolecular processes of
nonradiative relaxation as well as to spontaneous and
induced radiative transitions (the notations are the
same as those of Ref. 2). The intermolecular VV pro-
cesses are neglected because of low concentration of
CO2 in Ar matrix. The Boltzmann-type initial vibra-
tional-distribution is assumed. Excitation is taken
into account by a sudden increase of initial vibra-
tional population (N001) of the 0001 state up to the
arbitrary level (fitting parameter).
The equations describing evolution of the photon
number has the form:
dN
i
/dt = R R Ri i i
sp ind loss� � , (2)
where Ni is the number of photons of the ith transi-
tion (see Fig. 1), Ri corresponds to photon gain (both
through spontaneous and induced processes) and loss
processes. The main loss channel is related to the pho-
ton leaving the excited region as described in Ref. 2.
For spontaneous emission the Einstein coefficients
are applied [7]:
A
v,v–1 =
64
3
4
1
3
� �
v v
hc
,
��v���v–1>�2n
n2 2
2
3
�
�
�
�
�
�
�
� ,
where �v,v–1 is the frequency of the v� v–1 vibra-
tional transition, �<v���v–1>� is the respective ma-
trix element of the dipole moment and n is the refrac-
tive index. The last term describes generally the
effects of solid environment.
The stimulated emission cross-section are derived
from expression [8]
�
v,v–1 = c2A
v,v–1/8��2
v,v–1n
2� ,
where � is the FWHM of the spectral line associated
with the v � v–1 transition of assumed Gaussian pro-
file and estimated to be equal to 0.15 cm–1 [2].
For discussion of the nonradiative vibrational-re-
laxation of a guest molecule in a dense medium several
approaches have been proposed [5,9–11]. Here, the re-
laxation rates are described by the multiphonon relax-
ation model proposed by Nitzan et al. [5]. This model
has proven to provide a satisfactory description of the
relaxation for the case of matrix isolated diatomic
[12–14]. Accordingly, the rate constant of the v�v–1
transition is given by [5]
K
v,v–1(T) = K
v,v–1(0)F(T), (3)
where F(T) = (1 + ~n)Ne2S~n is the temperature coeffi-
cient, S is the average vibration-phonon coupling
strength (assumed here to be 1), N = �Ev,v–1/h�ph is
the number of matrix phonons involved in dissipation
of the vibrational energy gap �Ev,v–1 in the nonradi-
ative relaxation process, �ph is the average phonon
frequency (h�ph = 64 K was assumed for Ar matrix),
~n = [exp (h�ph/kT) –1]–1 is the phonon occupation
number. For low temperatures (T � 5 K) ~n � 0,
F(T) � 1, and Kv,v–1(T) � Kv,v–1(0). The expression
K Av
S
N Ev v
S N
v v
,
,
( )
!
�1
1
0
1e
�
(4)
corresponds to the relaxation rate at T = 0 K, where A
is a constant related to the value of average phonon
frequency and the variation of the interaction poten-
tial between CO2 molecules and the surrounding ma-
trix atoms.
Three types of processes are taken into account, and
the notation corresponds to that of Ref. 2:
VT: CO2(�1 + �2, 3�2) + Ar � CO2(�1, 2�2) + Ar,
(5)
VVT: CO2(�1, 2�2) + Ar � CO2(�1, 2�2
�) + Ar ,
(6)
V3V: CO2(00
01) + Ar � CO2(�1 + �2, 3�2) + Ar ,
(7)
1136 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
A. Cenian, G. Grigorian, and G. Œliwiñski
where CO2(�1, 2�2) and CO2(�1, 2�2 �) denote differ-
ent vibrational states of the (�1, 2�2) multiplet at
Fermi resonance – see, e.g., [15].
Due to the strong dependence of the rates (3) upon
N, only VT processes of ��� = 1 contribute signifi-
cantly to energy relaxation. The other processes (V3V
and VVT) also proceed with the minimum vibrational
energy gap. The VT and V3V reverse processes respon-
sible for energy transfer from translation to vibration
are neglected. However, in the case of VVT processes
some rates obtained from the principle of detailed
equilibrium are not negligibly small.
Results and discussion
For the stable site emission the time evolution of
photon numbers related to radiative profiles is studied
in order to get best agreement with experimental data
reported in [2]. Accordingly, three fitting parameters
AVT, AVVT and AV3V
, related to the constant A in ex-
pression (4) for the rates of nonradiative processes,
which correspond to transitions of the VT, VVT and
V3V type (Eqs. (5)–(7)) are determined. As a result,
all rates for vibrational energy exchange can be calcu-
lated. So, this procedure replaces the determination of
the seven independent rate constants as proposed in
Ref. 6. In both cases, the initial excitation N001 is an
additional fitting parameter.
The sets of equations (1) and (2) are solved using
the GEAR code for numerical integration. Equations
describe populations of all the nine vibrational states,
which become populated during relaxation process at
temperature T = 5 K, and photon numbers of the three
active radiative-transitions (�1 + �2, 3�2 � �1, 2�2)
and (�1, 2�2 � �2) – see Fig. 1. The terms related to
radiation gain and losses were determined from Ein-
stein coefficients, the stimulated emission cross-sec-
tions and populations of respective levels. The
nonradiative terms were determined by rates (4)
scaled by the constants AVT, AVVT and AV3V
.
It should be stressed again that in [2] the following
rates for the processes
VT: CO2(11
10(2)) + Ar � CO2(10
00(1)) + Ar ,
KVT_exp = 1.4·106 s–1 (�VT = 700 ns), ( �5 )
V3V: CO2(00
01) + Ar � CO2(11
00(1)) + Ar ,
KV3V_exp = 107 s–1 (�V3V
= 100 ns) ( �6 )
were proposed, basing on assumption of nonradiative
relaxation. The saturation condition (N001 = 0.5) for
initial excitation was assumed, also.
Results of calculations are presented in Fig. 2–7.
Figure 2 demonstrates the evolution of radiation in-
tensity determined by rates scaled (by changing AVT
and AV3V
) to the values as proposed in [2] (see dotted
line). The assumed value of excitation is evidently too
high – as was also confirmed in later considerations on
energy conservation [6]. It was found here that the best
fit is obtained for N001_b = 0.07, KVT_b = KVT_exp and
KV3V_b = 0.3KV V3 _exp (see solid line in Fig. 2). A si-
milar value 4·106 s–1 for the rate KV3V
was proposed
in [6]. The signal profile is not very sensitive to the
The vibrational relaxation of CO2 isolated in solid argon
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 1137
N = 0.5
N = 0.07
N = 0.07
001
001
001
1.0
0.8
0.6
0.4
0.2
0 1.0 1.50.5 2.0
In
te
n
si
ty
, r
e
l.
u
n
its
K
K
K 0.3 K
K
K
K K
V V_exp
V V_exp
V V V V_exp
VT_exp
VT_exp
VT VT_exp
3
3
3
3 3=
=
Time, s�
Fig. 2. Time resolved pulse of vibrational stimulated emis-
sion from CO2 located in a stable site of Ar matrix; sym-
bols ♦ correspond to the measurements, lines represent si-
mulations: solid line – for the best fit parameters, dotted
line – for the rates determined in [2] and saturation condi-
tion (N001 = 0.5), dashed line – for the rates determined
in [2] and N001 = 0.07.
N = 0.09
0.05
0.07
001
1.0
0.8
0.6
0.4
0.2
0 0.5 1.0 1.5 2.0
Time, s�
In
te
n
si
ty
, r
e
l.
u
n
its
Fig. 3. Time evolution of the stimulated emission pulse
from CO2 located in a stable site of Ar matrix; symbols ♦
correspond to the measurements, lines represent simula-
tions: solid line – for the best fit parameters, dotted line –
for optimal rates and N001 = 0.09, dashed line — for opti-
mal rates and N001 = 0.05.
rates of quasiresonant processes of the type (7) as long
as they exceed the value of KV3V
. The optimal value
of the rate for the process VVT
CO2(10
00(1)) + Ar � CO2(02
20) + Ar , ( �7 )
KVVT_b � 109 s–1 was found and it was assumed for
all curves in Fig. 2. Figure 3 presents sensitivity of
the profile on the parameter of initial excitation.
The signal profile depends strongly on the rate
KV3V
(see Fig. 4). Both the position of maximum and
the slope change with the rate variation. The value
KV3V_b is smaller by a factor of about 1/3 if com-
pared to KV3V_exp — this should be related to radia-
tive effects neglected in [2]. It is evident that the radi-
ative processes influence the kinetic seriously, e.g.,
they determine the temporal scale of the pulse profile.
This agrees well with the data reported in [6], and it
stays in sharp contrast to the previous assumptions
[2]. If we decrease further the rate for the V3V pro-
cess, an additional maximum on the temporal pulse-
shape appears; clear evidence of the independent radi-
ation from all 3 transitions.
The changes of KVT rate influence the investigated
profile much less significantly (see Fig. 5). The rate
increase shifts the maximum to smaller value and
1138 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
A. Cenian, G. Grigorian, and G. Œliwiñski
1.0
0.8
0.6
0.4
0.2
0 1.0 1.50.5 2.0
In
te
n
si
ty
, r
e
l.
u
n
its
1.2 K
K
0.8 K
V V_b
V V_b
V V_b
3
3
3
Time, s�
Fig. 4. Same as Fig. 3; solid line — for the best fit pa-
rameters, dotted line — for the best fit parameters except
KV3V
= 1.2 KV3V_b , dashed line – for the best fit parame-
ters except KV3V
= 0.8 KV3V_b .
1.0
0.8
0.6
0.4
0.2
0 1.0 1.50.5 2.0
Time, s�
In
te
n
si
ty
, r
e
l.
u
n
its
1.2 K
0.8 K
KVT_b
VT_b
VT_b
Fig. 5. Same as Fig. 3; solid line — for the best fit pa-
rameters, dotted line — for the best fit parameters except
KVT = 1.2 KVT_b , dashed line — for the best fit parame-
ters except KVT = 0.8 KVT_b .
1.0
0.8
0.6
0.4
0.2
0 1.0 1.50.5 2.0
Time, s�
In
te
n
si
ty
, r
e
l.
u
n
its
10 K
0.1 K
KVVT_b
VVT_b
VVT_b
Fig. 6. Same as Fig. 3; solid line — for the best fit pa-
rameters, dotted line — for the best fit parameters except
KVVT = 10 KVVT_b , dashed line — for the best fit param-
eters except KVVT = 0.1 KVVT_b .
1�s
0.2 �s
2 �s 00011110(2)100 0(2)
0110
1000(1)
1110(1)
0220
0330
10
10
10
10
10
0 1000 2000 3000
– 1
– 3
– 5
– 7
– 9
V
E
D
, r
e
l.
u
n
its
Energy, K
Fig. 7. The Treanor—Likal’ter type of distribution for the
best fit parameters and its time evolution; dotted line —
0.2 �s, dashed line — 1 �s, solid line — 2 �s after excita-
tion.
smoothes all structures. In contrast, the KVT decrease
leads to more pronounce structures. The profile is even
less sensitive to the changes of rates for near resonant
transitions (7) — in Fig. 6 we compare the results for
KVVT differing two orders of magnitude. Again, the
decrease of the KVVT rate leads to structure enforce-
ment, besides it widens also the profile maximum —
compare broken and solid lines.
Figure 7 presents the time evolution of vibrational
distribution function. The characteristic saw-tooth
distribution of Treanor—Likal’ter type, as described
previously in detail [15], can be observed. The grad-
ual saturation of the all laser-active transitions
(�1 + �2, 3�2 � �1, 2�2) and (�1, 2�2 � �2) is evident.
Conclusion
It was shown that the vibrational relaxation of
CO2 molecules embedded in solid Ar matrix could be
well described by the theory of multiphonon transi-
tions. The performed simulations confirmed that radi-
ative processes influence significantly the vibrational
energy relaxation of CO2 embedded in solid Ar, e.g.,
the determined KV3V
rate is significantly lower than
that predicted under assumption of the nonradiative
relaxation.
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Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 1139
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