1. Exam info Date & time: 21/10 8.30-12.30 M-house Form:- questions - what, how, why, - easy calculations - order of magnitude estimation - know central equations & discuss - discuss & explain phenomena Allowed material:Physics Handbook (or equivalent) Pocket calculator Dictionary Don’t forget to register!

2. Project info Hand in: 14/10 at the lecture Form:3-5 pages (longer is ok) references (especially figures) Grading:passed/not passed (not passed=correct & hand in again) good report can help total course grade no separate credits for project Presentation:14/10 at the lecture max 2 min max 1 slide - plastic “elevator pitch”

3. Self-assembly

4. Characteristics of self-assembly - what, how, why Self assembly with surfactants & amphiphiles - what/types - energies - aggregation geometries & phase behaviour Self assembly with polymers - phase separation - structures

5. 4 Characteristics of Soft Matter i)Length scales: - Structures of ≈10-1000 nm determine the properties ii) Time scales: processes from 10 -12 - 10 3 s - Dynamics processes over a wide time scales 10 -12 - 10 3 s - Very slow processes in non-equilibrium configurations iii) Weak interactions - Interactions between molecules and molecular structures ≈ kT iv) Self assembly - Hierarchical arrangement of structures - Competition between interaction energy and entropy

6. Self-assembly i)Hierarchical arrangement of structures ii)Competition between interaction energy and entropy iii)Structures of ≈10 to >1000 nm formed and determine the properties of the material

7. Surfactants and amphiphiles Amphiphilic molecule: two parts with very different affinities Surfactant: an amphiphilic molecule with a tendency to adsorb onto free surfaces and interfaces Small molecules M w ≈100-1000

8. Surfactants and amphiphiles Amphiphilic molecule: two parts with very different affinities Ex. hydrophilic head and hydrophobic tail a single molecule is never really comfortable in a solvent ->aggregation to minimize the interfacial energy -> micro-phase separation, thermodynamically stable aggregates - micelles

9. Surfactants and amphiphiles Amphiphilic molecule: two parts with very different affinities Ex. hydrophilic head and hydrophobic tail Hydrophobic tail: CH 3 (CH 2 ) n - Hydrophilic head:anionic cationic non-ionic block-copolymers

10. Surfactants and amphiphiles Amphiphilic molecule: two parts with very different affinities Ex. hydrophilic head and hydrophobic tail

11. Surfactants and amphiphiles Ex. hydrophilic head and hydrophobic tail Self-assembly of molecules in order to minimise free energy ->minimising the contact between water (solvent) and hydrophobic tail while keeping the hydrophilic head in contact with water

12. Macro vs. micro phase separation Simple liquids (water & oil): free energy when a molecule joins an aggregate N - number of molecules in the aggregate  - interfacial energy, v - molecular volume  N - monotonic decreasing function of N -> infinite aggregates - macroscopic phase separation Amphiphiles: -> finite size of aggregates - microscopic phase separation Why?

13. Macro vs. micro phase separation Amphiphiles: -> micro-phase separation -> finite size of aggregates -> entropic considerations more important Why?Balance between protecting the hydrophobic tail and keeping the head in contact with the water associating tails vs. repulsion of head groups

14. Shape of aggregates Basic shapes: - spheres - cylinders - bilayers - vesicles Superstructures: - micellar crystals - lamellar phases - bicontinuous networks - … micelles

15. Shape of aggregates Factors determining the shape i)Optimum head group are, a 0 ii)Critical chain length, l c iii)Hydrocarbon volume, v l c - length of fully extended tail v - volume of the tail # of tails, side groups, … v lclc

16. Optimum head group area, a 0 a 0 controlled by repulsive forces: electrostatic or steric repulsion (can be altered by e.g salt concentration) attractive forces: protecting the tail

17. Shape of aggregates Spheres - smallest area/volume Volume: 4  r 3 /3=Nv (N - # of molecules in aggregate) Surface area: 4  r 2 =Na 0 -> r=3v/a 0 but r max ≤l c v/l c a 0 ≤ 1/3 for spherical micells

18. Shape of aggregates Spheres: v/l c a 0 ≤ 1/3 Cylinders: 1/3≤ v/l c a 0 ≤ 1/2 Bilayer: v/l c a 0 > 1/2

19. Spherical micelles Spheres formed when: v/l c a 0 ≤ 1/3 Size of micelles finite ->  N has a minimum value at an optimum number M X N - volume fraction of micelles with N molecules size distribution

20. Critical Micelle Concentration  - volume fraction of amphiphile  c - monomers  c - micelles of average size M  c  exp(-∆  /k B T) - CMC

21. Cylindrical micelles Spheres formed when: 1/3<v/l c a 0 ≤ 1/2 Size of micelles finite but  N has a no minimum - energy of a molecule in the cylinder is independent of the size -> only 2∆E end -> forming larger micelles leads to energy gain, but a loss in entropy

22. Cylindrical micelles If ∆E end is large -> very long cylinder > µm Polymer-like system but: i)Polymer length fixed ii)Micelles form and break iii)Micellar size varies with external conditions iv)Change in dynamic properties

23. Bilayers Bilayers formed when: v/l c a 0 > 1/2 ∆E edge (A)  A 1/2 (A - area of a layer) dependent on the size of the bilayer -> formation of infinite layers Vesicles - closed surface by a bilayer -> model for cell membranes -> drug delivery systems -> colloidal behaviour

24. Bilayers Cell membranes - phospholipid bilayers Two tails give a large volume, v v/l c a 0 > 1/2

25. Bilayers Bilayers are not flat - highly crumpled Persistence length: k - bending modulus of membrane For r >  direction in membrane is lost Lamellar phases can anyway be obtained with very large d -> confinement between two adjacent planes leads to loss in entropy

26. Bilayers Lamellar phase can be distorted by fluctuations forming complex geometries

27. Phase behaviour Self assembled structures are rich in phases ->response by changing size and shape and arrangement of micelles -> dramatic change in properties

28. Self-assembly More complexity from: - several types of amphiphiles - mixed solvents - changing pH, temperature, …

29. Self assembly in polymers

30. Mixing polymers Generally polymers don’t mix - why? Free energy of mixing: (two molecular liquids) entropicinteraction energy regular solution model Interaction parameter  :  < 2 always single phase  > 2 phase separation

31. Mixing polymers Generally polymers don’t mix - why? For two polymer with N monomers (Flory-Huggins free energy) N is usually ≈ 10 3 -10 6 -> even for small  we get macro-phase separation Interaction parameter  :  < 2/N always single phase  > 2/N phase separation

32. Block copolymers Blocks of different polymers covalently linked together Even if  < 2/N the system cannot macro-phase separate (similar to amphiphiles) A B

33. Block copolymers Symmetric block copolymers -> lamellar structures Asymmetric structures -> more complex morphology AB

34. Self-assembly See also chp. 10 Soft Matter in biology

35. Next lecture Friday 14/10 13.00 (Per Jacobsson) - Summary, time for questions… - Project presentations - Feedback