Lecture 9: Surface Energy, Surface tension and Adhesion energy

In the last lecture…

Optical tweezers

The wave nature of light

Optical trapping

A point dipole in a field revisited

Using lasers to trap particles

Applications of optical trapping

~

2i

dx

dI

ncF

o

F

F

In this lecture…

Surface energy and interfacial energy

Surface tension

Calculating Surface energy of materials

Adhesion energy of simple materials

Wetting interactions

Contact angles

Further reading P201-206 and p312-325 in

Cohesive Energy of bulk materials

In the bulk of a material, atoms and molecules are surrounded by NBulk nearest neighbours.

If each interaction with the central atom/molecule has an energy, -u, the total interaction energy becomes

UBulk = -NBulku

Bulk atom

neighbours

Cohesive Energy near a surfaceWhen we create a surface in material and expose it to vacuum each surface atom/molecule has fewer nearest neighbours

Nsurf < NBulk

The interaction energy per atom/molecule is then

Usurf = -Nsurfu

There is therefore an excess amount of energy

U = Usurf -UBulk = (NBulk - Nsurf ) u

associated with each surface atom/molecule

Surface EnergySurface energy is the excess energy required per unit area to create a surface in vacuum (or air)

The energy required to create two new surfaces in a material, each having area S is

SW 2 where is the surface energy of the material in Jm-2

Area, S

Interfacial Energy

Interfacial energy is the excess energy per unit area required to create an interface between two different materials.

The interfacial energy between materials 1 and 2 is

represented by 12

Area, S

Surface and Interfacial TensionsSurface/interfacial tension is the force required per unit length to extend a surface/interface (measured in Nm-1)

The surface energy and surface tension are identical. They act to prevent a surface from increasing in area. Consider…

The same reasoning applies to interfacial tension and interfacial energy

Barrier

Surface

dx

Barrier

FL

1 NmL

F

Nm-1 = Jm-2

See notes

Typical values

P315 Intermolecular and Surface Forces, J. N. Israelachvili

Many materials have surface energies of ~10-50 mJm-2

Metals typically have higher surface energies of 1-3 Jm-2 (see page 205, Israelachvili)

Interfacial energies are of the same order of magnitude as surface energies

Calculating the surface energy of materials

The surface energy of a material can be described in terms of unsatisfied bonds or missing interactions at the surface.

Each atom/molecule at the surface can be thought of as having approximately half as many neighbours as one in the bulk material.

Excess surface energy Energy required to break half the bonds around an

individual atom/molecule (See OHP)

Calculations based upon latent heat of vapourisation

The energy required to break all the bonds in a mole of material and separate all the atoms and molecules is equal to the Latent heat of vapourisation Lv

The surface energy should be equal to half the energy required to break all the bonds around an atom/molecule.

This gives the result that

3

2

3

4

8

M

N

N

L A

A

V =density (kgm-3)

NA=Avogadro’s number (mol-1)

M=molar mass (kgmol-1)

Calculating surface energies from dispersion potentials

2012 D

ASU

The surface energy is the energy required to separate two surfaces from their inter-atomic/molecular distance and remove them to infinity

Recall from lectures 5 and 6 that inter-surface potential energy, U is

2242 oD

A

S

U

Surface energy is half this energy (there are two surfaces) per unit area

Do

Surface Area, S

A= Hamaker constant (J)

Do these simplistic approaches work?

Material Measured (mJm-2)

(mJm-2)

A/(24Do2)

(mJm-2) (Do=0.165nm)

A (x10-20J )

Liquid Helium

0.12-0.35 - 0.28 0.057

Polystyrene 33 - 32.1 6.6

Benzene 28.8 110 24.4 5

Ethanol 22.8 - 20.5 4.2

Mercury 600 630 - -

Nitrogen 10.5 11 - -

Liquid Argon

13 14 - -

3

2

3

4

8

M

N

N

L A

A

V

ProblemA conical AFM tip with a half angle of =26.56o and height , l, is placed at a flat interface between two immiscible liquids (liquids 1 and 2) such that the tip protrudes a distance, D, into liquid 1.

If the interfacial energies between the tip material and the liquids are 1 and 2 respectively and 12 is the interfacial energy between the two liquids;

a) Derive an expression for the total surface energy of the tip as a function of the distance D

b) Hence derive an expression for the force on the tip

c) If 1=0.99 Jm-2 , 2=1Jm-2 and 12=50mJm-2 calculate the magnitude and direction of the force on the tip if it protrudes 10nm into liquid 1

Work of Adhesion

The energy required per unit area to separate two surfaces of materials 1 and 2 in a third medium (medium 3) is called the work of adhesion (W)

It is the energy required to break the interface between two materials and form two new interfaces

2313

12

bondsinitialofbreaking

surfacesnewofcreation

W 122313

Wetting interactions

Surface and interfacial energies determine the shape of macroscopic liquid droplets when they are placed on a surface

Wetting film (=0)

Partially wetting films

Contact AnglesThe contact angle made between a droplet and a surface is determined by a subtle balance of the interfacial energies/tensions.

We can derive the expression for the contact angle by considering the balance of forces/interfacial tensions at the 3 phase contact line. Resolving horizontally we have

Huang et al., Science , 650 (2007)

cos231213

Material 1

Material 3

Mat. 2

Unbalanced vertical components

The assumption of a planar surface results in unresolved vertical forces due to interfacial tension of the droplet.

Clearly this can not happen otherwise the droplet would accelerate upwards!

The flat interface must deform to compensate for these unresolved components

• Surface/Interfacial Energy is the energy per unit area associated with the creation of a surface/interface (Jm-2)

• Surface tension (Nm-1) = Surface energy (Jm-

2)

• Surface energies can be calculated using the latent heat of vapourisation of a material or from the inter-atomic/molecular potentials

• A subtle balance of interfacial energies determines the adhesive properties of simple materials and the shape of droplets on surfaces

Summary of key concepts

224 oD

A

3

2

3

4

8

M

N

N

L A

A

V