2

Infrared Radiation

2.1 Absorption

2.1.1 General Aspects

The infrared portion of the electromagnetic spectrum is commonly divided into the near-, mid-, and far-infrared (IR) regions, named for their relation to the visible part of the spectrum (see Table 2.1).

Table 2.1 Regions of infrared radiation.

As regards organic molecules, IR photon energies correspond in the case of small molecules to rotational motions, and in the case of large molecules to collective intramolecular and intermolecular vibrational modes (far-IR), fundamental vibrations (mid-IR), and to overtone and combination vibrations (near-IR). The molecules rotate and the atoms of the molecules vibrate at frequencies corresponding to discrete energy levels that are determined by the shape of molecular potential energy surfaces, the mass of the atoms, and by associated vibronic coupling. Necessary conditions for the absorption or emission of IR of frequency ν are: (i) the photon energy hν must correspond to the difference ΔE v of discrete energy levels; and (ii) the transition between the two energy states must cause a change in the charge distribution in the molecule, that is, a change in the electric dipole moment of the molecule. In terms of quantum mechanics, the absorption of a photon occurs when the transition moment M has a nonzero value. Since M is a vector composed of three components (M = Mx, My, Mz), at least one component must have a nonzero value. There need be no permanent dipole moment. Vibrations fulfilling the requirements are termed IR-active, and whether or not a vibration is IR-active depends on the symmetry properties of the molecule. In totally asymmetric molecules all vibrations are associated with a change in the dipole moment, and therefore these are IR-active. In molecules possessing symmetry elements, certain vibrations are not associated with a change in the dipole moment, and these therefore are IR-inactive.

To obtain an insight into the interaction of IR radiation with molecules it is helpful to consider a simple case, namely a diatomic oscillator undergoing harmonic oscillations. The respective potential energy function is depicted in Figure 2.1.

Figure 2.1 Potential energy versus interatomic distance for a diatomic molecule undergoing harmonic or anharmonic oscillations.

For a diatomic molecule, modeled as a harmonic oscillator, quantum mechanics reveals that the vibronic molecular energy levels are restricted to discrete values given by Equation 2.1

(2.1)

where v is the vibration frequency and n v is the vibration quantum number taking only the integer values 0, 1, 2, 3, and so on. Hence, the zero point energy (n v = 0) corresponds to E v = 0.5 hν. When the molecules interact with IR radiation, transitions to higher energy levels are induced. Raising n v from 0 to 1, a highly probable (allowed) process, corresponds to the fundamental (normal) transition, while raising n v to higher levels, a (forbidden) process of low probability, results in overtone transitions. It should be noted that, in an IR absorption spectrum, the frequencies of overtone bands are multiples of those of fundamental mid-IR absorption bands. Therefore, frequencies of the first and second overtones can be estimated by multiplying the frequency of the fundamental by a factor two or three, respectively. The amplitudes of overtone bands are approximately one to two orders of magnitude smaller than the amplitudes of the corresponding fundamental absorption bands.

A more realistic approach towards atomic vibrations is the anharmonic oscillator (see Figure 2.1). Here, the vibronic molecular energy levels are given by Equation 2.2.

(2.2)

where xe is the anharmonicity constant. In this case, the difference between vibronic levels decreases with increasing potential energy up to D e, the dissociation energy corresponding to bond breakage. For a single vibronic stretch, the dependence of the potential energy on the interatomic distance r is fairly well described by the empirical Morse function (see Equation 2.3):

(2.3)

where r e is the equilibrium distance and β is a parameter governing the width of the function.

In contrast to diatomic molecules vibrating in a single mode only, polyatomic molecules can vibrate in many modes. A molecule containing N atoms has 3N − 6 vibrational degrees of freedom (linear molecules 3N − 5), which correspond to the number of possible fundamental vibrations (normal modes). As an example, Figure 2.2 shows the various vibration modes feasible for a 3-atomic side group. Here, N > 3 due to the polymer rest (not shown).

Figure 2.2 Vibration modes for an AX2 side group (e.g., CH2, NH2).

It has been mentioned briefly before that, apart from fundamental vibrations, atoms in molecules also can undergo overtone vibrations. Moreover, combination vibrations (coupled vibrations) are possible. When two fundamental vibrations, corresponding to frequencies ν 1 and ν 2, are excited, transitions occur to combined levels corresponding to the sum of the frequencies ν 1 + ν 2, or to the difference ν 1 − ν 2 [1]. This can be seen from the energy level diagram in Figure 2.3, which also shows IR radiation-induced transitions commencing at the ground state. Obviously, transitions related to overtone and combination vibrations corresponding to the addition of frequencies are more energetic than fundamental transitions. Hence, the absorption bands are located in the near-infrared (NIR) region. Recently, NIR spectroscopy has gained importance with respect to the polymer field (see Section 2.2.3) [2,3]. The so-called “hot band” transition between higher energetic levels shown in Figure 2.3 is named for its increased occurrence probability at higher temperatures.

Figure 2.3 Vibrational energy levels and typical transitions regarding two vibrating modes with frequencies ν 1 and ν 2. n v: vibrational quantum number, FT: fundamental transition, HB: hot band transition, 1st OT: first overtone transition, 2nd OT: second overtone transition.

Difficulties in the assignment of IR bands of organic polymers in the region between 1500 and 650 cm−1 often arise because vibrations can become coupled. Coupling may involve part of the carbon backbone atoms, plus atoms of any adjacent groups, such that the energy levels mix and bands can no longer be assigned to one bond. This very common phenomenon occurs when adjacent bonds vibrate with closely similar frequencies [4].

The model developed for diatomic molecules serves as the basis to understand absorption and emission processes in polyatomic molecules. As pointed out before, linear N -atomic molecules can undergo 3N − 5 vibrations [5,6], and hence a polyethylene chain containing, for example, 104 CH2 groups can vibrate in 9 × 104 modes. In fact, the IR absorption spectra of polyethylene and other polymers do not exhibit such a large number of lines. This is due not only to the similarity of force fields of the equivalent chemical groups in the macromolecules, with the consequence that many atoms vibrate with the same frequency, but also to the fact that the interaction of remote repeating units is almost negligible. The mutual interaction of atoms is restricted to those atoms being in close proximity, and IR absorption by polymers is characteristic of certain chemical groups. Hence, the interpretation and assignment of the IR spectra of polymers relies on the concept of group frequencies, which is based on theoretical concepts and computations on small molecules. As a typical example, Figure 2.4 presents the mid-IR absorption spectra of double-stranded nucleic acids with framed spectral domains associated with characteristic groups.

Figure 2.4 Mid-IR spectra of nucleic acids recorded in (a) H2O and (b) in D2O solution. Framed spectral domains: (I) in-plane base double-bond vibrations; (II) base-sugar bending motions; (III) phosphate group vibrations; (IV) phosphate-sugar backbone vibrations. Adapted with permission from Ref. [7]; © 1996, John Wiley & Sons.

Generally, resonant vibration frequencies are associated with particular bond types and particular chemical groups. The correlations between various specific chemical bonds and groups contained in organic polymers and mid-IR absorption bands are listed in Table 2.2, while overtone and combination bands associated with stretching and bending vibrations of hydrogenic functional groups contained in organic polymers are listed in Table 2.3.

Table 2.2 Mid-IR absorption bands of typical chemical groups contained in organic polymers.

Table 2.3 Near-IR absorption bands of hydrogenic functional groups contained in organic polymers.