Lecture 5:
Interactions between
macroscopic bodies I
What did we cover in the last
lecture?
Dispersion interactions
Dispersion interaction
energy
Repulsive interactions and
the Lennard Jones potential


12
6

A C
 
 
U ( x)   12  6  4       
 x 
x
x
x 
   
 repulsive attractive
In this lecture…
1. Interactions between extended and
macroscopic bodies
2. Why do we need to consider macroscopic
bodies? (atomic manipulation, particleparticle interactions and geckos)
3. Interactions between molecules and
surfaces
4. Interactions between particles and surfaces
Recap: Dispersion interactions
between isolated atoms
In the last lecture we saw that dispersion interactions
is short ~0.3nm
Total energy of interaction U
(repulsive + dispersion)


12
6

A C
 
  

U ( x)   12  6  4     
 x 
x
x
x

 





 repulsive attractive
However, they are strong enough to hold
atoms/molecules together and overcome the influence of
thermal (brownian) motion!
Interactions between extended
bodies
What happens when many atoms/molecules come
together?
If central atom/molecule has
N nearest neighbours, then
total interaction energy
Utot~ N U
So energy of interaction increases as more
atoms/molecules are brought together
Explains why dispersion forces are capable of holding
together simple organic liquids and solids (which have
no other interactions)
Dispersion Interactions between
macroscopic bodies…geckos feet
Geckos feet are covered in small
structures called setae
Dispersion interactions allow these
setae to let the gecko walk up
smooth surfaces
Dispersion interactions in
nanoscience
Dispersion interactions are also important in nanoscience
As we will see in later lectures, they are often a significant
component of the forces which are exerted between
nanoparticles and surfaces and in inter-nanoparticle
interactions
Solid
Surface
Dispersion forces in AFM
Dispersion forces also influence the interaction between
an AFM tip and a surface
Position
sensitive
detector
More on this in a future lecture!
Additivity of interactions
The additive nature of short range dispersion interactions
means that interactions between individual atoms/molecules
and macroscopic bodies (solids) can be significant.
Consider…
Atom/molecule
Semi infinite
Solid
What is the force between the atom/molecule
and a semi-infinite solid?
Detailed picture
Firstly we consider dispersion
interactions between the atom/molecule
and a plane within the solid
We start with the form of our potential
between two atoms/molecules and
determine the interaction energy between a
thin ring/annulus in the plane and our
atom/molecule
(See OHP)
C
U ( x)   6
x
Interactions between
macroscopic bodies I
Problem 1: Derive an expression for the dispersion
forces which act between a perfectly flat slab of area S
and a semi-infinite solid if the number density of atoms in
the solid and slab are n1 and n2 respectively.
Summary of key results
Dispersion interactions between
macroscopic bodies occur over longer
ranges than between atoms and simple
molecules
Dispersion interactions can be large
enough to overcome the effects of gravity
Dispersion force between a molecule and
a semi infinite solid scales as
Dispersion force between a slab and a
solid (or two parallel surfaces)
U ( D)  
nC
6D
3
n1n2CS
U ( D)  
12 D 2