Lecture 3: Polar interactions

What did we cover in the last lecture?The force on an object is the gradient in potential energy

The range of an interaction is the distance at which thermal effects start to dominate

dx

dUxF )(

kTxU range )(

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 kTIonic 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 momentConsider 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

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

Units of Cm

How do we define an electric dipole?

~~r̂qdp

Consider two charges separated by a small distance, d in a medium of dielectric constant,

We can calculate the field at the point, x, by summing up the fields due to the two point charges (see OHP)

Electric field due to a dipole

When x >> d, this gives the result that;

~3~

1

2i

x

qdE

o

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)

extE~

~~.EpU dipole

Potential energy of a dipole in an electric field

The dipole moment of an atom or molecule can be related to the external applied electric field by

Units of = C2m2J-1

Polarisation using external fieldsAtom and molecules are polarised by external electrical fields.

Opposite charges move in different directions when an E field is applied

extEp~~

Where is the polarisability of the atom/molecule

Polarisability of atoms and molecules

Key result

d is typically smaller than, but comparable to radius of atom/molecule R. So scales with volume of atom/molecule (V~R3)

34 do

Atom or Molecule

We can determine the polarisability of an atom/molecule in an applied external field(see OHP)

Some examples of Polarisabilities

p69 ‘Surface and Intermolecular

Forces’ by J. Israelachvili

(CH4) = 4x (C-H)

(H2O) ~ 2x (O-H)

Summary of key results

~3~

1

2i

x

qdE

o

~~.EpU dipole

~~r̂qdp Dipole moment

Electric field due to a dipole

Potential energy of dipole in an E field

extEp~~

Atoms and molecules can be polarised by external fields