exam info date & time: 21/10 8.30-12.30 m-house form:- questions - what, how, why, - easy...
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Exam infoDate & 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!
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Project infoHand 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 gradeno separate credits for project
Presentation: 14/10 at the lecturemax 2 min max 1 slide - plastic“elevator pitch”
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Self-assembly
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Self-assemblyCharacteristics 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
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4 Characteristics of Soft Matter
i) Length scales:
- Structures of ≈10-1000 nm determine the properties
ii) Time scales: processes from 10-12 - 103 s
- Dynamics processes over a wide time scales 10-12 - 103 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
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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
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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 Mw≈100-1000
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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
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Surfactants and amphiphiles
Amphiphilic molecule: two parts with very different affinities
Ex. hydrophilic head and hydrophobic tail
Hydrophobic tail: CH3(CH2)n-
Hydrophilic head: anioniccationicnon-ionicblock-copolymers
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Surfactants and amphiphiles
Amphiphilic molecule: two parts with very different affinities
Ex. hydrophilic head and hydrophobic tail
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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
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Macro vs. micro phase separation
Simple liquids (water & oil):
free energy when a molecule joins an aggregateN - 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?
€
N = ε∞ + αkBTN1/3
αkBT = 4πγ 3v / 4π( )2 / 3
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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
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Shape of aggregates
Basic shapes:- spheres- cylinders- bilayers- vesicles
Superstructures:- micellar crystals - lamellar phases- bicontinuous networks- …
micelles
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Shape of aggregates
Factors determining the shape
i) Optimum head group are, a0
ii) Critical chain length, lciii) Hydrocarbon volume, v
lc - length of fully extended tail
v - volume of the tail# of tails, side groups, …
v
lc
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Optimum head group area, a0
a0 controlled by
repulsive forces: electrostatic or steric repulsion(can be altered by e.g salt concentration)
attractive forces:protecting the tail
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Shape of aggregates
Spheres - smallest area/volume
Volume: 4r3/3=Nv(N - # of molecules in aggregate)
Surface area:4r2=Na0
-> r=3v/a0
but rmax≤lc
v/lca0 ≤ 1/3 for spherical micells
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Shape of aggregates
Spheres:v/lca0 ≤ 1/3
Cylinders:1/3≤ v/lca0 ≤ 1/2
Bilayer:v/lca0 > 1/2
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Spherical micelles
Spheres formed when:v/lca0 ≤ 1/3
Size of micelles finite ->N has a minimum value at an optimum number M
XN - volume fraction of micelles with N molecules
€
N = εM + Λ N −M( )2
XN = N XMM exp
−MΛ M−N( )2
kBT
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
N /M
N −M 2 = kBT2MΛ
size distribution
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Critical Micelle Concentration
- volume fraction of amphiphile
c - monomers c - micelles of average size M
c exp(-∆/kBT) - CMC
€
XM =M X1 exp ΔεkBT( )[ ]
M Δε = ε1 −εM
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Cylindrical micelles
Spheres formed when:1/3<v/lca0 ≤ 1/2
Size of micelles finite butN has a no minimum - energy of a molecule in the cylinder is independent of the size -> only 2∆Eend
-> forming larger micelles leads to energy gain, but a loss in entropy
€
N = ε∞ + αkBTN , αkBTN = 2ΔEendN
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Cylindrical micelles
If ∆Eend is large -> very long cylinder > µm
Polymer-like system but:
i) Polymer length fixedii) Micelles form and breakiii) Micellar size varies with
external conditionsiv) Change in dynamic
properties
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Bilayers
Bilayers formed when:v/lca0 > 1/2
∆Eedge(A) A1/2 (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
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Bilayers
Cell membranes - phospholipid bilayers
Two tails give a large volume, v
v/lca0 > 1/2
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Bilayers
Bilayers are not flat - highly crumpled
Persistence length:
k - bending modulus of membraneFor r > direction in membrane is lost
Lamellar phases can anyway be obtainedwith very large d -> confinement between two adjacent planes leads to loss in entropy
€
k = aexp 4πkαkBT( )
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Bilayers
Lamellar phase can be distorted by fluctuationsforming complex geometries
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Phase behaviour
Self assembled structures are rich in phases -> response by changing
size and shape and arrangement of micelles
-> dramatic change in properties
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Self-assembly
More complexity from:
- several types of amphiphiles
- mixed solvents
- changing pH, temperature, …
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Self assembly in polymers
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Mixing polymers
Generally polymers don’t mix - why?
Free energy of mixing:(two molecular liquids)
€
FkBT
=φA lnφA +φB lnφB + χφAφB
entropic interaction energy
regular solution model
Interaction parameter :
< 2 always single phase
> 2 phase separation
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Mixing polymers
Generally polymers don’t mix - why?
For two polymer with N monomers
(Flory-Huggins free energy)
N is usually ≈ 103-106 -> even for small we get macro-phase separation
€
F pol
kBT=φA lnφA +φB lnφB +NχφAφB
€
Fmon
kBT= φAN lnφA + φBN lnφB + χφAφB
Interaction parameter :
< 2/N always single phase
> 2/N phase separation
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Block copolymers
Blocks of different polymers covalently linked together
Even if < 2/N the system cannot macro-phase separate(similar to amphiphiles)
A B
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Block copolymers
Symmetric block copolymers -> lamellar structures
Asymmetric structures-> more complex morphology
A B
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Self-assembly
See also chp. 10 Soft Matter in biology
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Friday 14/10 13.00 (Per Jacobsson)
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