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.

Copyright Stuart Lindsay 2008 Amphiphiles Phospholipid Polar head Hydrophobic tail Copyright Stuart Lindsay 2008

Self-assembled amphiphilic structures (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) Copyright Stuart Lindsay 2008

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

Association Kinetics Single-step aggregation Aggregate concentration is divided by N to get monomer equivalent. Association rate Dissociation rate In equilibrium the two rates are equal so the equilibrium constant is:

In units of mole fraction the total mole fraction of solute is: The maximum value of C-X1 is unity Above this critical micelle concentration all added monomer is turned into aggregates

When:

Chemical potential must be lower in aggregate! For: with X1<1 Monomers predominate!

Size-dependent chemical potential The chemical potential depends on the size of the aggregate: Chemical potential for an infinite N aggregate Bond energy (in KT units) p : dimensionality and shape of the aggregate

And so: 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 energy

Critical Micelle Concentration Revisited Since XN can never exceed 1, X1 cannot exceed exp( -) and: for a spherical aggregate For a water/methane interface: γ ≈50mJ·m-2, r≈0.2 nm, T=300K α ≈ 6

For p=1: Above the cmc: And for low 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.

Shape of aggregates Packing effects depend on geometry lc = length of the hydrocarbon chain n = volume occupied by the hydrocarbon chain A0 = area of the head group

Long or double hydrocarbon chains A dimensionless shape factor determining the aggregate geometry Spherical micelles Short hydrocarbon chains Non-spherical micelles Long or double hydrocarbon chains Vesicles or bilayers ‘Inverted cones’

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. Copyright Stuart Lindsay 2008

Lipid bilayer structure – the mitochondrion (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.) Copyright Stuart Lindsay 2008

Self-assembled monolayers 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.

Organothiols on gold surfaces 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.

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

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 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 Vapor deposition of silicon wires Si nanowires from Au/Si eutectic seeded on Au NP. Silicon is incorporated in the gold phase from Si vapors produced by CVD. Copyright Stuart Lindsay 2008