Lecture 3: Polar interactions
What did we cover in the last
lecture?
The force on an object is the gradient in
potential energy
dU
F ( x)  
dx
The range of an interaction is the
distance at which thermal effects start
to dominate
U ( xrange )  kT
Electrostatics can be used to explain the interactions in ionic solids.
The cohesive energy and Born energy of ions/particles can be used to
explain why they are more soluble in water than other solvents
The energies associated with the formation/breaking of strong
covalent, ionic and metallic bonds are
Covalent U ~100-300 kT
Ionic
U ~ kT
Metallic U ~100-300 kT
In this lecture…
• Polar interactions
• What is a dipole?
• E field due to a dipole
• Energy of a dipole in an external field
• Polarisability
P48-69 in ‘Surface
and Intermolecular
Forces’ by J.
Israelachvili
What are polar molecules?
Many molecules are electrically neutral and carry no net
charge
However, they can still possess an electric dipole
moment
Consider the molecule HCl (hydrogen chloride)
More electronegative atoms such as chlorine have a
higher affinity for electrons. In the case of HCl, the
electrons are pulled towards the chlorine atom giving rise
to a permanent dipole
Zwitterions and dipolar ions
In some cases, the polar properties of the molecules
depend upon the local environment (e.g. presence of
solvents). Water soluble polar molecules of this type are
called Zwitterions (Zwitter- German meaning ‘hybrid’ )
Some molecules contain both a net charge and a dipole
moment. These molecules are referred to as dipolar
ions
How do we define an electric
dipole?
Recall from electromagnetism that a dipole consists of two
charges (+q and -q) separated by a distance d
The dipole moment, p, is then defined as
p  qd r̂
~
~
Units of Cm
Electric field due to a dipole
Consider two charges separated by a small distance, d in a
medium of dielectric constant, e
We can calculate the field at the point, x, by summing up
the fields due to the two point charges (see OHP)
When x >> d, this gives
the result that;
qd
1
E
i
3
~
2eeo x ~
Energy of a dipole in an external
electric field
In later lectures we will need to determine the energy of
interaction between dipoles
We will therefore need to calculate the energy of a
dipole in an external electric field (see OHP)
Potential energy of a
dipole in an electric field
U dipole   p . E
~
E
~ ext
~
Polarisation using external fields
Atom and molecules are
polarised by external
electrical fields.
Opposite charges move
in different directions
when an E field is
applied
The dipole moment of an atom or molecule can be related
to the external applied electric field by
p a E
~
~ ext
Units of a = C2m2J-1
Where a is the polarisability of the atom/molecule
Polarisability of atoms and
molecules
We can determine the
polarisability of an
atom/molecule in an
applied external field
(see OHP)
Key result
a  4eo d
Atom or
Molecule
3
d is typically smaller than, but comparable to radius of
atom/molecule R. So a scales with volume of atom/molecule
(V~R3)
Some examples of Polarisabilities
p69 ‘Surface and
Intermolecular
Forces’ by J.
Israelachvili
a(CH4) = 4x a(C-H)
a(H2O) ~ 2x a(O-H)
Summary of key results
Dipole moment
p  qd r̂
~
~
Electric field due to a dipole
1
E
i
3 ~
~
2eeo x
Potential energy of dipole in
an E field
U dipole   p . E
Atoms and molecules can be
polarised by external fields
qd
~
p a E
~
~ ext
~