60
P. Panwaria and A. Das
orifice of ~0.5–1 mm diameter (Fig. 3). A supersonic molecular beam is produced
while the orifice diameter (D) is greater than the mean free path (λ) of the sample
molecules at the orifice (D λ). Under the condition of the supersonic molecular
beam, enormous collisions between the sample molecules and carrier gas at the orifice
cools down the internal degrees of freedom of the molecules of interest. Generally,
the translational temperature of the molecular beam goes down to ~1 K, while the
rotational and vibrational temperatures reach to 3–5 K and 30–50 K, respectively.
The density of the molecules, i.e., the number of collisions, is maximum near the
orifice and decreases with the distance x from the orifice. Thus the cooling depends
on the (x/D) ratio, where D is the orifice diameter [103–109]. The extent of cooling
in the supersonic beam is expressed in terms of Mach number, (M), which is the
ratio of the velocity of molecules in the supersonic beam to speed of the sound. In
the supersonic beam, M is greater than 1, and thus, the name supersonic originates
from there. The following equation gives the relationship between M and (x/D):
M = A(x/D)
γ−1 , where γ is the ratio of the heat capacity (C p /C v ) and A is a constant
that depends on γ [104]. It is important to note that the molecules in the supersonic
beam remain in the gas phase even the temperature is far lower than the freezing
point of the sample. This is because the number density of the sample molecules in
the supersonic beam rapidly decreases after a minimal distance from the orifice, and
condensation cannot happen due to the lack of any significant three-body collision
there [103, 104].
Supersonic expansion is isentropic under reversible adiabatic conditions, i.e., in
the absence of any shock wave, shear force, heat source or sink, etc. Thus, the
following isentropic equation of the ideal gas can be used to find out the temperature,
pressure, and density of the expanding gas in the supersonic jet,
T
T 0
=
P
P 0
(γ −1)/γ
=
ρ
ρ 0
γ −1
=
1
1 +
1
2 (γ − 1)M 2
where T 0 , P 0, and ρ 0 are temperature, pressure, and density of the gas in the
high-pressure reservoir, respectively, while T, P, and ρ are the same quantities of the
expanded gas after supersonic expansion [104].
2.2 Vaporization of Samples for the Gas-Phase Experiment
Samples, which are studied using gas-phase laser spectroscopy, are generally solid
or liquid. There are two methods for the vaporization of the sample molecules.
One of those is thermal heating, and another one is laser desorption. However, the
volatile liquid samples, which have significant vapor pressure at room temperature
are required to cool at low temperature to control the sample vapor pressure used in
the experiment.
P. Panwaria and A. Das
orifice of ~0.5–1 mm diameter (Fig. 3). A supersonic molecular beam is produced
while the orifice diameter (D) is greater than the mean free path (λ) of the sample
molecules at the orifice (D λ). Under the condition of the supersonic molecular
beam, enormous collisions between the sample molecules and carrier gas at the orifice
cools down the internal degrees of freedom of the molecules of interest. Generally,
the translational temperature of the molecular beam goes down to ~1 K, while the
rotational and vibrational temperatures reach to 3–5 K and 30–50 K, respectively.
The density of the molecules, i.e., the number of collisions, is maximum near the
orifice and decreases with the distance x from the orifice. Thus the cooling depends
on the (x/D) ratio, where D is the orifice diameter [103–109]. The extent of cooling
in the supersonic beam is expressed in terms of Mach number, (M), which is the
ratio of the velocity of molecules in the supersonic beam to speed of the sound. In
the supersonic beam, M is greater than 1, and thus, the name supersonic originates
from there. The following equation gives the relationship between M and (x/D):
M = A(x/D)
γ−1 , where γ is the ratio of the heat capacity (C p /C v ) and A is a constant
that depends on γ [104]. It is important to note that the molecules in the supersonic
beam remain in the gas phase even the temperature is far lower than the freezing
point of the sample. This is because the number density of the sample molecules in
the supersonic beam rapidly decreases after a minimal distance from the orifice, and
condensation cannot happen due to the lack of any significant three-body collision
there [103, 104].
Supersonic expansion is isentropic under reversible adiabatic conditions, i.e., in
the absence of any shock wave, shear force, heat source or sink, etc. Thus, the
following isentropic equation of the ideal gas can be used to find out the temperature,
pressure, and density of the expanding gas in the supersonic jet,
T
T 0
=
P
P 0
(γ −1)/γ
=
ρ
ρ 0
γ −1
=
1
1 +
1
2 (γ − 1)M 2
where T 0 , P 0, and ρ 0 are temperature, pressure, and density of the gas in the
high-pressure reservoir, respectively, while T, P, and ρ are the same quantities of the
expanded gas after supersonic expansion [104].
2.2 Vaporization of Samples for the Gas-Phase Experiment
Samples, which are studied using gas-phase laser spectroscopy, are generally solid
or liquid. There are two methods for the vaporization of the sample molecules.
One of those is thermal heating, and another one is laser desorption. However, the
volatile liquid samples, which have significant vapor pressure at room temperature
are required to cool at low temperature to control the sample vapor pressure used in
the experiment.