Fundamentals of ATR-FTIR Spectroscopy and Its Role …
15
Fig. 7 a Evanescent field penetrated the water medium and b variation in the penetration depth
with the incident angle; a comparative study at Ge/Water and ZnSe/Water interfaces
interface in comparison to the Ge/water interface, which seems more suitable for the
characterization of molecules present at the surface comparatively.
Till now, we have observed that for an angle of incidence greater than the
critical angle, a non-absorbing IR beam will undergo total internal reflection,
and an absorbing IR radiation will follow attenuated total reflectance at the ATR
crystal/sample interface. Now, in the calculation of penetration depths in the TIR
mode, n 1 and n 2 will be the real refractive indices of the ATR crystal and the sample
respectively (Eq. 16). Whereas in the case of ATR mode, it has been suggested that
we can evaluate the penetration depth values either by taking n 2 as the real values of
the sample refractive index or a modulus value of penetration depth can be calculated
with n 2 as a complex number.
The ATR approach can be employed experimentally in two different modes: (i)
single reflection mode and (ii) multiple reflection mode (Fig. 2). The effective path
length (L e f f ) of the input IR radiation within the sample depends on the product of
the total number of internal reflections (N R ) that take place in the ATR crystal at the
interface in contact with the sample and penetration depth which is given as [27]:
L e f f = N R × d p
(17)
In the case of multiple reflection mode of ATR, the number of reflection (N R ) can
be estimated by the length of the crystal (l AT R ), the thickness of the crystal (t AT R )
and effective angle of incidence of IR radiation beam (θ ) as [27]:
N R =
l AT R
2 × t AT R × tan θ
(18)
The light-matter interaction process occurs during the IR radiation absorbed by
the molecules and it induces the dipole moment (μ ind ), which is given as [27]:
μ ind = α
E
(19)
15
Fig. 7 a Evanescent field penetrated the water medium and b variation in the penetration depth
with the incident angle; a comparative study at Ge/Water and ZnSe/Water interfaces
interface in comparison to the Ge/water interface, which seems more suitable for the
characterization of molecules present at the surface comparatively.
Till now, we have observed that for an angle of incidence greater than the
critical angle, a non-absorbing IR beam will undergo total internal reflection,
and an absorbing IR radiation will follow attenuated total reflectance at the ATR
crystal/sample interface. Now, in the calculation of penetration depths in the TIR
mode, n 1 and n 2 will be the real refractive indices of the ATR crystal and the sample
respectively (Eq. 16). Whereas in the case of ATR mode, it has been suggested that
we can evaluate the penetration depth values either by taking n 2 as the real values of
the sample refractive index or a modulus value of penetration depth can be calculated
with n 2 as a complex number.
The ATR approach can be employed experimentally in two different modes: (i)
single reflection mode and (ii) multiple reflection mode (Fig. 2). The effective path
length (L e f f ) of the input IR radiation within the sample depends on the product of
the total number of internal reflections (N R ) that take place in the ATR crystal at the
interface in contact with the sample and penetration depth which is given as [27]:
L e f f = N R × d p
(17)
In the case of multiple reflection mode of ATR, the number of reflection (N R ) can
be estimated by the length of the crystal (l AT R ), the thickness of the crystal (t AT R )
and effective angle of incidence of IR radiation beam (θ ) as [27]:
N R =
l AT R
2 × t AT R × tan θ
(18)
The light-matter interaction process occurs during the IR radiation absorbed by
the molecules and it induces the dipole moment (μ ind ), which is given as [27]:
μ ind = α
E
(19)