Fundamentals of ATR-FTIR Spectroscopy and Its Role …
9
the change in the dipole moment corresponding to vibration and it results in the
molecular transition between the ground and excited state vibrational levels. Thus,
the molecule which absorbs the IR radiation or IR active has
dμ
dx
= 0, here dμ is
the change in dipole moment and dx is the change in the bond distance. The IR
absorption intensity (I Abs ) can be given as [1, 2, 22]:
I Abs ∝
dμ
dx
2
(1)
Usually, the IR quantification of the absorbance can be done by Beer-Lambert
law [1, 2, 6, 26, 27]:
A = − log 10
I T (ω I R )
I 0 (ω I R )
= − log 10 (T ) = ε(ω I R )Cd
(2)
Here, A and T are the IR absorbance and transmittance of the sample, ω I R is the
IR wavenumber and I 0 is the intensity of the incident IR radiation while I T is the
intensity of the transmitted IR radiation through the sample; ε is the molar extinction
coefficient, C is the molar concentration of the chemical species present in the sample,
and d is the path length of the IR radiation through the sample. Figure 3 (panel a)
represents a schematic experimental arrangement, which is generally utilized for the
absorbance studies through the detection of IR radiation transmitted from a sample.
Here, we have shown that when an IR beam is made to impinge on a sample, it
undergoes partial reflection due to the cell boundaries, marked by reflection intensity I R , absorption by sample molecules, with absorption intensity I A prior to transmission through the sample with intensity I T . The absorbance from Eq. (2) using
Beer-Lambert law shows the linear dependence on the concentration of the sample
and the optical path length, as shown in Fig. 3 (panel b). Therefore, IR spectroscopy
can be used to identify and quantify the concentration of a substance in a sample.
Fig. 3 a Optical layout of an experimental scheme for absorbance studies; b linear dependency of
absorbance on the sample thickness, d and concentration, C using Beer Lambert’s law
9
the change in the dipole moment corresponding to vibration and it results in the
molecular transition between the ground and excited state vibrational levels. Thus,
the molecule which absorbs the IR radiation or IR active has
dμ
dx
= 0, here dμ is
the change in dipole moment and dx is the change in the bond distance. The IR
absorption intensity (I Abs ) can be given as [1, 2, 22]:
I Abs ∝
dμ
dx
2
(1)
Usually, the IR quantification of the absorbance can be done by Beer-Lambert
law [1, 2, 6, 26, 27]:
A = − log 10
I T (ω I R )
I 0 (ω I R )
= − log 10 (T ) = ε(ω I R )Cd
(2)
Here, A and T are the IR absorbance and transmittance of the sample, ω I R is the
IR wavenumber and I 0 is the intensity of the incident IR radiation while I T is the
intensity of the transmitted IR radiation through the sample; ε is the molar extinction
coefficient, C is the molar concentration of the chemical species present in the sample,
and d is the path length of the IR radiation through the sample. Figure 3 (panel a)
represents a schematic experimental arrangement, which is generally utilized for the
absorbance studies through the detection of IR radiation transmitted from a sample.
Here, we have shown that when an IR beam is made to impinge on a sample, it
undergoes partial reflection due to the cell boundaries, marked by reflection intensity I R , absorption by sample molecules, with absorption intensity I A prior to transmission through the sample with intensity I T . The absorbance from Eq. (2) using
Beer-Lambert law shows the linear dependence on the concentration of the sample
and the optical path length, as shown in Fig. 3 (panel b). Therefore, IR spectroscopy
can be used to identify and quantify the concentration of a substance in a sample.
Fig. 3 a Optical layout of an experimental scheme for absorbance studies; b linear dependency of
absorbance on the sample thickness, d and concentration, C using Beer Lambert’s law