Optical Properties of Materials – OSE 5312, Summer 2002
Wednesday, May 29, 2002
Interaction of radiation with dipole active rotational modes in
condensed matter
Rotational modes of molecules do not lend themselves to classical treatment,
particularly in gases. This is because there is no classical resonance
frequency associated with rotational motion like there is with vibrations.
Hence the discrete absorption lines observed in the far infrared in gases only
have an explanation in quantum mechanics, and we shall look at these
quantum results presently. But in condensed matter, e.g. liquids, where
intermolecular collisions occur at such a rapid rate that they occur more than
once per rotational period. – “Hindered” rotational modes.
Let c = mean time between collisions. Hence c N-1 where N is the
molecular density. If r is the rotational frequency, (r = 2/r, where r is
the rotational period) then the rotational modes are said to be hindered if rc
< 1.
Or, rc = Nc/N, where Nc is the molecular density at which rc = 1.
For Nc << N, we have the dilute medium limit, where we see discrete
rotational spectra. (Lines spaced by r, as we shall describe later.)
Consider the effect of an electric field on a dipole-active molecule (i.e. one
with a permanent dipole.)
cos
Potentialn Interactio
0
EpV
t
in
For now, we assume that E is a DC field, although the above definition for
Vint does not depend on this assumption.
E+
p0
