Lecture 9: Surface Energy,
Surface tension and Adhesion
energy
In the last lecture…
Optical tweezers
F
The wave nature of light
Optical trapping
A point dipole in a field
revisited
Using lasers to trap particles
Applications of optical trapping
F
F
2 dI
i
~
co n dx
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.
Bulk
atom
If each interaction with the
central atom/molecule has
an energy, -u, the total
interaction energy becomes
UBulk = -NBulku
neighbours
Cohesive Energy near a surface
When 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
DU = Usurf -UBulk = (NBulk - Nsurf ) u
associated with each surface atom/molecule
Surface Energy
Surface energy is the excess energy required per unit area
to create a surface in vacuum (or air)
Area,
S
The energy required to create two new surfaces in a
material, each having area S is
where  is the surface
energy of the material in
Jm-2
W  2S
Interfacial Energy
Interfacial energy is the excess energy per unit area
required to create an interface between two different
materials.
Area,
S
The interfacial energy between materials 1 and 2 is
represented by 12
Surface and Interfacial Tensions
Surface/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…
Surface
Barrier
F
L
F
  Nm 1
L
Barrier
Nm-1 = Jm-2
dx
See notes
The same reasoning applies to interfacial tension and
interfacial energy
Typical values
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)
P315 Intermolecular and Surface Forces,
J. N. 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
LV  4N A 



8 N A  3M 
2
3
=density (kgm-3)
NA=Avogadro’s number (mol-1)
M=molar mass (kgmol-1)
Calculating surface energies from
dispersion potentials
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
Surface
AS
Area, S
U 
Do
Surface energy is half this
energy (there are two
surfaces) per unit area
U
A


2 S 24Do2
12D02
A= Hamaker
constant (J)
Do these simplistic approaches
work?
Material
Liquid
Helium
Measured
 (mJm-2)
2
L  4N A  3
 V 

8 N A  3M 
(mJm-2)
A/(24Do2)
(mJm-2)
A (x10-20J )
(Do=0.165nm)
0.12-0.35
-
0.28
0.057
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
-
-
13
14
-
-
Polystyrene
Liquid
Argon
Problem
A 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
13
12
23
W   13   23 



creation of new
surfaces

12
breakingof
initialbonds
Wetting interactions
Surface and interfacial energies determine the shape of
macroscopic liquid droplets when they are placed on a
surface
Partially wetting films
Wetting film (q=0)
Contact Angles
The 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
 13   12   23 cos q
Material 3
Mat. 2
Material 1
Huang et al.,
Science , 650
(2007)
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
Summary of key concepts
• 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
LV  4N A 


8 N A  3M 
A

24Do2
2
3