PARTICLES AS MOLECULES
C. M. S ORENSEN
3.6 SUPERLATTICES
The hard sphere interaction causes a liquid to solid transition at a solution volume fraction of 0.545, as described above with reference to Figure 3.4. The resulting solid has an fcc lattice. This is slightly, about 0.001 kT, more stable than its close packed counterpart at 0.74, the hcp lattice. Binary hard sphere systems can form five different lattices of different stoichiometry depending on the size ratio.
Addition of the van der Waals interaction can cause formation of condensed phases at much lower volume fractions than 0.545. If strong relative to the thermal energy kT, the phases are ramified aggregates, usually fractal, and these can lead to gels. Variation of the relative strength of the interaction can yield more compact structures like
“fat fractals” and lattices, illustrated in Figure 3.9 (59). Ohara et al. (60) showed that since the van der Waals interaction is size dependent, bigger nanoparticles will nucleate to superlattices first when the solution is destabilized and size segregation can occur. Korgel and Fitzmaurice (61) showed that van der Waals interaction with a substrate when the solution is dried can compete with the nanoparticle-nanoparticle interaction. Then depending on the relative strength of the two interactions, the morphology of the resulting dried layers can be controlled.
Inclusion of screened Coulomb electrostatic interaction along with the van der Waals and hard sphere interactions can engender the entire description of Figure 3.4. This has been realized in many ways in protein solutions, but not yet for nanoparticle solutions.
Superlattices are now very common, and it is not my intent to provide a comprehen-sive review of all the work. From a historical perspective I note that Bentzon et al. (63) first observed superlattices of iron oxide nanoparticles. It was description of CdSe superlattices by Murray, Kagan, and Bawendi (25), however, that effectively estab-lished this new paradigm of molecular solids. The superlattices of Murray et al., were formed of CdSe nanoparticles with sizes ranging from 1.5 to 10 nm. Any given lattice used a size in this range narrowed to +4%. The CdSe particles were ligated with trioctylphosphine oxide or selenide. Faceted superlattice crystals up to 50 mm in size could be grown by gentle evaporation of the solvents. Control of the spacing between nanoparticles was achieved by exchanging the octyl ligands for butyl or hexadecyl ligands (64). Spectrographic evidence was given for interparticle coupling.
Many examples now exist in the literature for both 2d and 3d nanoparticle superlattices, including gold (65–67), silver (68), palladium and platinum (69, 70), and magnetic materials like iron, cobalt, FePt, CoFe2O4 (71, 72); see also References 1–4. Examples are given in Figures 3.10 and 3.11. The lattice spacing is typically much less than the combined length of the ligands to imply significant interdigitation, as sketched in Figure 3.7(a). Systematic variation of the chain length has shown that the gap between particles increases by 0.12 nm per carbon atom on the ligand chain (73). This agrees well with the increase of the linear length of an
Figure 3.10 A large, 2d superlattice of 5.5-nm gold nanoparticles ligated with dodecanethiol on a silicon nitride surface. Note hexatic, close-packed structure (like pennies on a table top) and the spacing between the nanoparticles, which is filled with the alkane chains of the ligands, which keeps the gold particles from touching, which would lead to irreversible aggregation.
PARTICLES AS MOLECULES 56
alkane chain of 0.126 nm per carbon atom given the bond length of 0.154 nm and the bond angle of 109.47 degrees and the assumption of complete interdigitation.
Multilayers have been shown to form by addition of particles to either the threefold sites on the hexatic lattice, as expected, or a more unusual addition at twofold sites, as shown in Figure 3.12 (29, 74). Lin and coworkers (75, 76) demonstrated a kineti-cally driven 2d superlattice formation at the interface between an evaporating solvent and the air above. Essentially the liquid evaporated faster than the nanoparticles could move via diffusion out of the way of the falling interface and once the interface hit them, they were stuck by surface forces. Lin et al. (77) have also created 2d free-standing superlattices with structural integrity that show elastic properties.
Most 3d nanoparticle superlattices have a close-packed twofold coordination.
Nature forms crystal lattices of lower coordinations in a great variety of ionic crystals.
Recently Kalsin et al. (78) assembled an ionic lattice of oppositely charged nano-particles. The nanoparticles were gold ligated with mercaptoundecanoic acid and silver ligated with N,N,N-trimethyl(11-mercaptoundecyl) ammonium chloride salt.
The nanoparticles were essentially the same size, each about 5 nm in diameter.
Figure 3.11 TEM micrographs of nanoparticle superlattices of Au nanoparticles prepared by the inverse micelle method: (a) and (b) low-magnification images; (c) – (f) regularly shaped nanoparticle superlattices; (g) magnified image of a superlattice edge (note the perfect arrange-ment of the Au nanoparticles).
3.6 SUPERLATTICES 57
A diamond-like (four nearest neighbors) sphalerite lattice was achieved despite the presence of only spherically symmetric dispersion and electrostatic interactions.
This was explained as due to a screened Coulomb potential with screening length greater than the four oppositely charged nearest neighbors but less than the 12 same charged second nearest neighbors. This delicate combination of different relative scales of the interactions made the sphalerite lattice more energetically favorable than the usual close-packed lattices.
Systems of two different particle types and sizes have led to a wealth of possible superlattices with stoichiometry dependent on the particle size ratio (79–84). Murray and coworkers (81–84) showed that in addition to size ratio a key experimental component is to charge tune the nanoparticles with either oleic acid or trioctyl-phosphine to yield superlattice stoichiometries of AB, AB2, AB3, AB4, AB5, AB6, and AB13, a greater diversity than found in nature for micron-sized particles (see Fig. 3.13). This charge tuning is successful because at the nanoscale (not the micro-scale) all the interactions above can contribute with comparable weight. These, combined with substrate interactions and the inherent nonequilibrium nature of the evaporative process to create the superlattices, yields the diversity.
Molecular dynamics simulations have been used to study the structure and dynamics of superlattices (31, 85, 86). Ligand alkyl chain bundling is found as a func-tion of temperature. For example, for a gold nanoparticle with 1289 atoms (diameter ca. 3.5 nm) ligated with decane thiol there was chain bundling below 300 K, and par-tial bundling up to 375 K, where an effective chain melting occurs at roughly the bulk melting point of the alkane. These changes were reversible. Infrared spectrographic Figure 3.12 Au colloid digestively ripened with C12H25NH2. (a) and (b) are pictures taken from different samples. The different types of ordering observed are highlighted. 2d superlat-tices show second layers adding at either the threefold sites or the twofold sites of the lattice below.
PARTICLES AS MOLECULES 58
studies of alkane thiols bound to gold NPs for chain lengths from 3 to 24 have shown liquid-like disorder of the shorter chains and crystalline packing for longer chains (87).
The molecular dynamics studies also showed structural change with temperature from bcc orthorhombic to bcc. Relative ligand length also affected the superlattice structure such that the structure was fcc for L/R , 0.6, bcc for 0.60 , L/R , 0.66 and bct for L/R . 0.66. The van der Waals forces between the ligands were important. Very similar results were seen experimentally for superlattices of approximately 4-nm silver nanoparticle capped with octyl and dodecylthiol (88), but theoretical analysis implicated core-core attractive forces were important as well as ligand-ligand forces.
3.6.1 Superlattice Melting
There appear only a few discussions of superlattice melting in the literature (89–91).
Such melting is expected to involve both the melting of the lattice and the possible order to disorder transition of the chains of the attached ligand molecules. Pradeep et al. (89, 90) studied 3d superlattices of 4.0-nm silver nanoparticles ligated with either octyl or octyldecylthiol. These superlattices showed reversible melting with x-ray diffraction and DSC measurements at about 400 K with the C8SH slightly lower in temperature. For the C18SH superlattice the DSC showed transitions at 340 and 399 K, which were ascribed to ligand melting and superlattice melting, respectively. Respective enthalpies were on the order of 130 and 10 J/g. Melting and subsequent recrystallization seemed to change the system and reproducibility Figure 3.13 Example of a binary superlattice with AB13 stoichiometry composed of 5.8-nm PbSe and 3.0-nm Pd nanoparticles.
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was hard to gain. Some of this was ascribed to changes in ligand conformations via interdigitation. A liquid system of nanoparticles, 2.0-nm Pt ligated with a very large ligand, N,N-dioctyl-N-(3-mercaptoptopyl)-N-methylammonium sulfonate, was shown to freeze at 2208C and remelt at 308C with DSC scans (92). It is reason-able to speculate that this lower temperature melting was a result of the small NP size compared to the large ligand and the concomitant small van der Waals force between NPs.