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 upon the shape of the aggregate and the aggregation number A critical cluster size sometimes has to form before growth can occur because of the excess surface energy of the aggregate.

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 The head group can be anionic, cationic or uncharged Hydrophilic head groups Hydrophobic tail groups ~1 nm The tail group is made up of a hydrocarbon chain

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, l c The optimum head group area, a o

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, l c, 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 Repulsion between the head groups acts to force neighbouring molecules apart Hydrophobic interactions 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 ≤ l c

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, a o If the radius of the micelle is less than the critical chain length, l c for spheres to form we require that (see OHP) R Number of molecules, N

Cylindrical Micelles Similarly for cylindrical micelles If the radius of the micelle is less than the critical chain length, l c for cylinders to form we require that (see OHP) R Number of molecules, N l

Bi-layers If the radius of the micelle is less than the critical chain length, l c for bilayers to form we require that 2R Number of molecules, N Area, A

Problem The volume of a linear hydrocarbon chain containing 10 carbon atoms is v= nm 3 and its critical chain length is l c =1.419 nm If this chain is incorporated into an amphiphilic molecule with an optimum headgroup area of a o =0.65 nm 2 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 headgroups. A geometric packing parameter can be used to identify whether spherical, cylindrical or bilayer structures will form. Hydrophilic head groups Hydrophobic tail groups