Page 184 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN007C-340 July 10, 2001 14:45

Infrared Spectroscopy 795

FIGURE 2 Infrared spectrum of 1-decene in a 0.01-mm NaCl FIGURE 4 Infrared spectrum of n-amyl acetate in a 0.01-mm
cell. NaCl cell.

Another vertical coordinate scale used increasingly is
to restore equilibrium. In the diatomic molecule, there is
the linear absorbance scale, where absorbance A is given only one bond and only one vibration, that which peri-
by the log 10 of the transmittance reciprocal:
odically changes the length of the bond. In the harmonic
A = log (1/T ). (2) oscillator approximation, the restoring force on each mass
10
is assumed to be linearly proportional to the bond length
The advantage of an absorbance scale is that the ab- change from the equilibrium bond length. The proportion-
sorbanceisproportionaltotheproductofsamplethickness ality constant is called the force constant k. The vibrational
and concentration. This is discussed in section V.A. frequency v of the diatomic molecule can be calculated by
the methods of classical mechanics, as in Eq. (3):
C. Diatomic Vibrations 1/2
1 1 1
When molecular vibrations are studied, it is useful to con- ν = k + . (3)
2π m 1 m 2
sider the nucleus of any atom in the molecule as a mass
concentrated at a single point, held in place by chemical Here ν is the vibrational frequency, m 1 and m 2 the two
bonds that act much like massless coil springs. The di- atomic masses, and k the force constant, namely, the
atomic molecule is the simplest molecule type, consisting restoring force on either mass divided by the bond length
of two nuclei connected by a chemical bond formed by change from equilibrium at any time. Note that the fre-
electrons. The electrons in a molecule move much more quency is independent of the vibrational amplitude. The
rapidily than the nuclei, so the electrons can quickly equi- masses move in a manner that keeps the center of mass
librate into new electronic structures as the slowly moving stationary. If a 1 /a 2 is the relative amplitude of the two
nuclei change their spacing. This means that there is a def- masses m 1 and m 2 during the vibration, then
inite potential energy for each nuclear configuration. For a 1 m 2
=− . (4)
the diatomic molecule this is something like the poten- a 2 m 1
tial energy of an ordinary coil spring. There is a certain
Stretching force constants are usually expressed in
equilibrium bond length where the energy is a minimum.
˚
˚
millidynes per angstrom (mdyne/A); 1 mdyne/A equals
If this length is increased or decreased, the potential en-
100 N/m, the equivalent SI unit. Masses are usually ex-
ergy increases and a restoring force is generated, tending
pressedinunifiedatomicmassunits(carbon= 12).Ifthese

FIGURE 3 Infrared spectrum of 2-heptanone in a 0.01-mm NaCl FIGURE 5 Infrared spectrum of n-decyl alcohol in a 0.01-mm
cell. NaCl cell.