Experiment 3, page 1
Version of September 4, 2009
Experiment 446.3
DIPOLE MOMENTS
Theory
A molecule has an electric dipole moment if it has a net separation of centers of positive
and negative charge.
If the separation of charge is characteristic of the molecule without the
application of an electric field, it is said to have a
permanent electric dipole moment
.
Molecules
with no net separation of charge outside a field may also have, through interaction with the field,
an
induced electric dipole moment
that exists only when the molecule is in the field.
Permanent dipole moments are fixed relative to molecular axes.
A permanent electric
dipole may be modeled as two charges, -Q and +Q, of equal magnitude and opposite sign,
separated by a distance given by the vector
r
.
If the vector
r
points from the negative to the
positive charge, the electric dipole is
r
d
Q
.
(3.1)
In real molecules, charges are distributed (as shown for electrons by a plot of the square of the
electronic wave function.), and the dipole moment results from the fact that the distributions of
positive and negative charge are not commensurate.
The dipole moment of such a molecule is
determined by integration over the charge distributions.
In the SI system of units, the appropriate unit of dipole moment is the coulomb-m.
This
is much too large a unit to be useful, so one typically finds molecular dipole moments reported in
debyes
.
1
[1 D = 1
10
-18
statcoulomb-cm]
2
In SI units, the debye is 3.33564 x 10
-30
coulomb-
meter.
In what follows, I shall use the centimeter-gram-second (cgs) set of units, where the unit
of charge is the statcoulomb.
When an electric field is applied, a dipole has an energy of interaction,
U
, with the
electric field,
E
, that depends on the orientation,
,
of the dipole relative to the electric field.
cos
E
d
E
d
U
.
(3.2)
For
N
molecules, each of which has a permanent dipole,
d
, exposed to an electric field, at
equilibrium there is a tendency for the dipoles, on average, to be oriented along the field.
This
situation is described by the
molar
electric polarization
,
P
, the total electric dipole moment per
mole.
If
L
is Avogadro’s number, the total equilibrium polarization is
d
P
L
(3.3)
where
d
is the average molecular dipole moment.
1
The naming of this unit honors the great Dutch scientist, Peter J. W. Debye, who did pioneering work on the
electrical properties of solutions, among his many contributions to science.
2
The statcoulomb is the unit of charge in the cgs system of units.
1 statcoulomb = 3.3356 x 10
-10
coulomb.