– transitions with Dv > 1 are forbidden.
What additional conclusions can be drawn?
– the higher the vibration frequency, i.e., the larger the vibrational quantum, the
lower the probability of the T-V process;
– the lighter the diatomic species BC or relaxer, the higher the probability of the
process.
The rate constant of vibrational excitation is
k v;v þ 1 ¼ k gk \P v;v þ 1 [
ð5:3:5Þ
The rate constant of vibrational relaxation, V-T, as follows from (3.1.17), is equal to
the rate constant of excitation divided by the exponent exp(−DE v+1,v /kT).
The problem of vibrational excitation or relaxation has been repeatedly considered quantum mechanically, corrections for anharmonicity, etc. have been
introduced. These theories give interesting results; however, if only V-T takes place
in a collision, the conclusions from them are qualitatively the same as those given
above. A significant difference is the fact that when anharmonicity is taken into
account, transitions with Dv > 1 are allowed. The numerical values of the transition
probabilities, as it has been noted above, depend on the parameters introduced very
significantly, i.e., the probability of relaxation is impossible to calculate ab initio.
What are the probabilities of vibrational relaxation of diatomic molecules for
cases that are well described as V-T processes (T = 300 K). They are 9 10
–9 (N 2 )
(approximately the same for CO), 6 10
–8 (O 2 ), 2 10
–5 (Cl 2 ) [6, 7]. The x e values for
these molecules are 2358, 1580, and 557 cm
–1 , respectively [8]. The probability of
vibrational relaxation of CO(X,v) in collisions with helium atoms is approximately
2 orders of magnitude greater than for CO [9].
V-T processes in polyatomic molecules. They have a set of vibrational frequencies, and, at first glance, very complex relaxation kinetics should be expected.
However, due to the presence of repeatedly mentioned intermode exchange
stochastization of vibrational energy occurs. In the relaxation process,
low-frequency vibrational modes, which are ‘fed’ from higher-frequency ones,
should most actively participate. The stochastization time is much shorter than the
relaxation time, and the relaxation probability of the polyatomic
molecule < P M > is related to the probability of relaxation of the low-frequency
vibrational mode < P v > by the relation:
hP M i ¼ hP v i
C
v
1
C
v
M
ð5:3:6Þ
where C
v
M and C
v
1 are the total vibrational heat capacity and low-frequency heat
capacity, respectively [10].
It is empirically established that the probabilities of vibrational relaxation of
molecules (on themselves) containing a hydrogen atom and not containing, differ
160
5 Energy Transfer in Collisions
What additional conclusions can be drawn?
– the higher the vibration frequency, i.e., the larger the vibrational quantum, the
lower the probability of the T-V process;
– the lighter the diatomic species BC or relaxer, the higher the probability of the
process.
The rate constant of vibrational excitation is
k v;v þ 1 ¼ k gk \P v;v þ 1 [
ð5:3:5Þ
The rate constant of vibrational relaxation, V-T, as follows from (3.1.17), is equal to
the rate constant of excitation divided by the exponent exp(−DE v+1,v /kT).
The problem of vibrational excitation or relaxation has been repeatedly considered quantum mechanically, corrections for anharmonicity, etc. have been
introduced. These theories give interesting results; however, if only V-T takes place
in a collision, the conclusions from them are qualitatively the same as those given
above. A significant difference is the fact that when anharmonicity is taken into
account, transitions with Dv > 1 are allowed. The numerical values of the transition
probabilities, as it has been noted above, depend on the parameters introduced very
significantly, i.e., the probability of relaxation is impossible to calculate ab initio.
What are the probabilities of vibrational relaxation of diatomic molecules for
cases that are well described as V-T processes (T = 300 K). They are 9 10
–9 (N 2 )
(approximately the same for CO), 6 10
–8 (O 2 ), 2 10
–5 (Cl 2 ) [6, 7]. The x e values for
these molecules are 2358, 1580, and 557 cm
–1 , respectively [8]. The probability of
vibrational relaxation of CO(X,v) in collisions with helium atoms is approximately
2 orders of magnitude greater than for CO [9].
V-T processes in polyatomic molecules. They have a set of vibrational frequencies, and, at first glance, very complex relaxation kinetics should be expected.
However, due to the presence of repeatedly mentioned intermode exchange
stochastization of vibrational energy occurs. In the relaxation process,
low-frequency vibrational modes, which are ‘fed’ from higher-frequency ones,
should most actively participate. The stochastization time is much shorter than the
relaxation time, and the relaxation probability of the polyatomic
molecule < P M > is related to the probability of relaxation of the low-frequency
vibrational mode < P v > by the relation:
hP M i ¼ hP v i
C
v
1
C
v
M
ð5:3:6Þ
where C
v
M and C
v
1 are the total vibrational heat capacity and low-frequency heat
capacity, respectively [10].
It is empirically established that the probabilities of vibrational relaxation of
molecules (on themselves) containing a hydrogen atom and not containing, differ
160
5 Energy Transfer in Collisions