Lecture 16:
Self Assembly of Amphiphiles
What did we cover in the last
lecture?
Aggregates will form when the free
energy per molecule/particle inside an
aggregate becomes less than that of a
free molecule/particle
The form of the free energy per
molecule (chemical potential) depends
2
upon the shape of the aggregate and
 3  3 1
the aggregation number
   bulk  4  
1
 4 
3
N
A critical cluster size sometimes has to
form before growth can occur because
of the excess surface energy of the
aggregate.
 4 

N c  
 bulk 
3
 3 


 4 
2
In this lecture…
1) Amphiphilic molecules
2) Critical Micelle Concentration
3) Aggregation of amphiphilic molecules
4) Geometric packing considerations
5) Spherical micelles
6) Cylindrical micelles
7) Bi-layers
Further Reading
Intermolecular and surface forces,
J. Israelachvili, Chapters 16 and 17
Soft Condensed Matter, R.A.L. Jones, Oxford University
Press 2002, Chapter 9
Amphiphilic molecules
Amphiphiles are molecules
which have a water soluble
head group and a
hydrophobic tail group
~1 nm
The head group can be
anionic, cationic or
uncharged
The tail group is
made up of a
hydrocarbon chain
Hydrophilic
head groups
Hydrophobic
tail groups
The critical micelle concentration
When amphiphilic molecules are
added to water initially they will
disperse and some will migrate to
the surface to reduce the
unfavourable contact between the
hydrocarbon tails and the water.
The molecules exist as monomers
At a concentration called the
critical micelle concentration
aggregates (or micelles) start to
form in such a way that the
hydrophobic tails become
shielded from the aqueous
environment
The structure of a micelle
The free energy per molecule of amphiphiles in a micelle
has a minimum at a specific aggregation number.
It is easy to see why this might be the case
Optimum size
hydrocarbon tails pack in
interior and are shielded
from water by headgroups
Too small
Gaps between
headgroups allow
water to contact
hydrophobic tails
Too big
Unfavourable
interactions between
headgroups and tail
groups between
molecules in micelle
Factors influencing micelle
shape
Amphiphiles are capable of
forming many different shaped
micelles including spheres,
cylinders and bi-layers
The fluid like nature of these
molecules means that we can
determine the shape of micelles
by considering how the
amphiphiles pack together
To do this we require 3 parameters
The hydrocarbon volume, v
The critical chain length, lc
The optimum head group area, ao
The hydrocarbon volume and
critical chain length
The hydrocarbon volume ,
v, is defined as the volume
that is occupied by the
hydrocarbon tails of the
molecules
The critical chain length, lc ,
is the length of the
hydrocarbon chain when it
is fully extended
v is the effective
volume occupied
by the
hydrocarbon tail
Optimum headgroup area
There are two contributions to the optimum headgroup area
Electrostatic or steric effects
Hydrophobic interactions
Repulsion between the head
groups acts to force
neighbouring molecules
apart
If the head groups are
separated too much then
hydrocarbon tails are
exposed to water
A balance between
these interactions
determines the
optimum area that is
occupied by each
headgroup
How do these parameters
determine the shape of a micelle?
The critical chain length determines the size and shape of
a micelle as it sets the maximum length to which an
individual amphiphile molecule can be stretched
Clearly the radius of any micelle that forms has to be less
than or equal to this chain length.
R ≤ lc
Spherical micelles
The volume and surface area of a spherical micelle can be
related to the aggregation number, N, the hydrocarbon
volume, v, and the optimum head group area, ao
4R 3
Volume 
 N
3
Area  4R 2  Nao
3v
Radius  R 
ao
R
Number of
molecules, N
If the radius of the micelle is less than the critical chain
length, lc for spheres to form we require that (see OHP)
v
1

l c ao 3
Cylindrical Micelles
Similarly for cylindrical micelles
l
Volume  R l  N
2
Area  2Rl  Nao
R
2v
Radius  R 
ao
Number of molecules, N
If the radius of the micelle is less than the critical chain
length, lc for cylinders to form we require that (see OHP)
1
v
1


3 l c ao 2
Bi-layers
Volume  A(2 R)  N
Area  2 A  Nao
v
Radius  R 
ao
Area, A
2R
Number of molecules, N
If the radius of the micelle is less than the critical chain
length, lc for bilayers to form we require that
1
v

1
2 lc ao
Problem
The volume of a linear hydrocarbon chain containing 10
carbon atoms is v= 0.296 nm3 and its critical chain length
is lc=1.419 nm
If this chain is incorporated into an amphiphilic molecule
with an optimum headgroup area of ao=0.65 nm2
a) Determine what shape micelles are formed by this
amphiphile
b) Calculate the average size (radius) and aggregation
number of the micelles formed
Summary of key concepts
Amphiphilic molecules contain a
hydrophobic head group and
hydrophobic tail group.
When added to water in they form
micelles above a critical concentration.
Their shape is determined by the
volume and length of the tail and the
optimum area of the molecular
1
v
1


headgroups.
3 l c ao 2
A geometric packing parameter can be
used to identify whether spherical,
cylindrical or bilayer structures will
form.
Hydrophilic
head groups
Hydrophobic
tail groups
v
1

l c ao 3
1
v

1
2 lc ao