Self-Assembly

• Bottom-up assembly generally means making complex nanostructures starting from the random collisions of molecular components in solution.

• Entropy plays a large role in the formation of self-assembled structures put together with weak bonds.

• Binding enthalpies generally results from the sum of weak interactions.

Self-assembly of complex nanostructures requires achieving the right balance between entropy at a given temperature and binding enthalpies.

Amphiphiles

Copyright Stuart Lindsay 2008

Hydrophobic tailHydrophobic tail

Polar headPolar headPhospholipidPhospholipid

Self-assembled amphiphilic structuresSelf-assembled amphiphilic structures

Copyright Stuart Lindsay 2008(From Molecular Cell Biology, 4th ed. By H. Lodish, A. Berk, S.L. Zipursky, P. Matsudara, D. Baltimore, J. Darnell. © 2000, W.H. Freeman and Company. Used with permission)

MD Simulation of vesicle formationMD Simulation of vesicle formation

(Reprinted with permission from Molecular dynamics simulation of the spontaneous formation of a small DPPC vesicle in water in atomistic detail, A.H de Vries et al. , A.E. Mark, and S.J. Marrink, J. Am. Chem. Soc. 2004 126: 4488. Published 2006 by American Chemical Society)

1017 DPPC (dipalmitoylphosphatidylcholine) molecules randomly distributed in a box of 106,563 water molecules. MD simulation was run for 90ns.

Association KineticsAssociation Kinetics

NA Xkv 11

Single-step aggregation

N/Xkv ND 2

Aggregate concentration is divided by N to get monomer equivalent.

NN

NX

X

k

kK

12

1

In equilibrium the two rates are equal so the equilibrium constant is:

N

XNX N1

Association rate Dissociation rate

In units of mole fraction the total mole fraction of solute is:

N

NK

XCX

1

11

)(

N

NKX

1

1

1

The maximum value of C-X1 is unity

Above this Above this critical micelle concentration critical micelle concentration all added monomer all added monomer is turned into aggregatesis turned into aggregates

NN NKXXXXC 111

N

NKcmc

1

1

110

1 XlnRT)X()X(

N

XlnRT

N

X

N

X NNN 0

)X(NN

XKlnRTG N

1000

)X(NN

XN

N 00

When: NN XN

X1 00 G1K

Tk

)X(Nexp

Tk)X(N

exp

K

B

N

B

1

)X()X(Tk

Nexp N

B

01

0

N

B

NN Tk

)X()X(expXNX

01

0

1

Chemical potential must be lower in aggregate!Chemical potential must be lower in aggregate!

For:

NN NXX 1

with X1<1

)X()X( N0

10

Monomers predominate!

Size-dependent chemical potentialSize-dependent chemical potential

pB

N N

Tk 00

The chemical potential depends on the size of the aggregate:

0 Chemical potential for an infinite N aggregate

Tk

)X()X(

B

N0

10

Bond energy (in KT units)

pp : dimensionality and shape of the aggregate

NNpN XNNXNX exp)/11(exp 11

3

10

3

2

00

N

Tk

N

Nttancons B

N

For a spherical aggregate, the total number of molecules in the sphere is proportional to r3, while those on the surface are proportional to r2. Thus, the chemical potential per particle:

γ = monomer/solvent interfacial energyTk

r

B

24

And so:

Critical Micelle Concentration RevisitedCritical Micelle Concentration Revisited

NNpN XNNXNX exp)/11(exp 11

Since XN can never exceed 1, X1 cannot exceed exp( -) and:

Tk

rX

Bcrit

2

1

4exp for a spherical aggregate

For a water/methane interface: γ ≈50mJ·m-2, r≈0.2 nm, T=300K

J.r 202 10524 α ≈ 6 0025.01 cmcX

For p=1:

)exp(exp)/11(exp 11 NNN XNNXNX

Above the cmc: 1exp1 X

And for low N: NX N

The concentration of aggregates grows linearly with N (p=1).For N→∞, XN→0.For p<1 the aggregate size grows infinitely large above the cmc.

The distribution of aggregate size is sensitive to the geometry of the aggregates.

Packing effects depend on geometryPacking effects depend on geometry

c

v

a0

lc = length of the hydrocarbon chain

= volume occupied by the hydrocarbon chainA0 = area of the head group

Shape of aggregatesShape of aggregates

3

1

0

ca

v

2

1

3

1

0

ca

v

12

1

0

ca

v

10

ca

v

Spherical micellesSpherical micelles

Non-spherical micellesNon-spherical micelles

Vesicles or bilayersVesicles or bilayers

‘‘Inverted cones’Inverted cones’

ca

v

0

A dimensionless shape factor determining the aggregate geometry

Short hydrocarbon chains

Long or double hydrocarbon chains

Copyright Stuart Lindsay 2008

The final folding of a planar bilayer into a spherical vessel is determined by a balance between the excess surface energy associated with the edges of a bilayer and the elastic energy required to fold a planar layer into a sphere.

Lipid bilayer structure – the mitochondrionLipid bilayer structure – the mitochondrion

Copyright Stuart Lindsay 2008

(EM image is reproduced with permission from Chapter 4 of The genetic basis of human disease by G. Wallis published by the Biochemical Society 1999. Copyrighted by the Biochemical Society. http://www.biochemj.org.)

Chemisorption of long-chain amphiphilic molecules (both hydrophobic and hydrophilic functionalities) at surfaces.

→ creation of long-range order

• active head group for chemisorption

• activated surfaces

• modification of the hydrophobic/hydrophilic character of the surface.

Self-assembled monolayersSelf-assembled monolayers

• long-chain alkanethiolates (SH end group)

STM image of a dodecanthiol SAM on Au(111) (40nm·40nm)

• I step: attachment of the sulfur atom to the gold surface driving force: Au-S interaction (≈40 kcal·mol-1)

X(CH2)nSH + Au0 → X(CH2)nS- + Au+ + ½H2

• Sulfur atoms for long chain alkanethiolates (n>11) formed a hexagonally packed arrangement on the Au(111) surface.

Separation of individual molecules on the surface is ≈5Å (van der Waals radius is around 4.6Å).

Chains tend to tilt at an angle of 30° to fill the available space.

Kinetic studies on SAM formation show that the adsorption process is consistent with a first-order Langmuir isotherm: the growth rate is proportional to the number of unoccupied gold sites.

The methylene groups tilt at an angle of 30° degrees from the surface normal to maximize the favorable Van der Waals interactions between adjacent chains.

Bulky or polar groups terminating the alkyl chain may reduce the packing density and overall order of the SAM.

Long-lasting self-healing dynamics

• II step: lateral organization of the alkyl chains to form a densely packed monolayer. driving force: Van der Waals lateral interactions

A series of STM images of a single octanedithiol molecule inserted into an octanethiol monolayer.

Sulfur with the gold atom attached to it moves over the surface in almost liquid-like manner.

The consequence of the mobility of the sulfur-gold bond is a substantial restructuring of the gold surface resulting in the formation of pits on the surface that are one gold atom in depth.

Nanoparticles kinetically trappedNanoparticles kinetically trapped

CdSe quantum dots from two phase synthesis with Ostwald ripening (diameter: 8 nm).

(TEM Image)

Ostwald ripening: heating/cooling cycles. Small crystallites (less stable) dissolve and recrystalize onto more stable existing crystallites to produce a much more uniform size distribution of crystallites.

Copyright Stuart Lindsay 2008

Si nanowires from Au/Si eutectic seeded on Au NP.

Silicon is incorporated in the gold phase from Si vapors produced by CVD.

Vapor deposition of silicon wires