Many Body Effects and Icosahedral Order in Superlattice Self-Assembly

Abstract

We elucidate how nanocrystals "bond" to form ordered structures. For that purpose we consider nanocrystal configurations consisting of regular polygons and polyhedra, which are the motifs that constitute single component and binary nanocrystal superlattices, and simulate them using united atom models. We compute the free energy and quantify many body effects, i.e., those that cannot be accounted for by pair potential (two-body) interactions, further showing that they arise from coalescing vortices of capping ligands. We find that such vortex textures exist for configurations with local coordination number ≤6. For higher coordination numbers, vortices are expelled and nanocrystals arrange in configurations with tetrahedral or icosahedral order. We provide explicit formulas for the optimal separations between nanocrystals, which correspond to the minima of the free energies. Our results quantitatively explain the structure of superlattice nanocrystals as reported in experiments and reveal how packing arguments, extended to include soft components, predict ordered nanocrystal aggregation.

Assembly by solvent evaporation: equilibrium structures and relaxation times

“…9c), that converges to the dry equilibrium separation reported in Ref. 39. Rather interestingly, as shown in Fig.…”

“…Following our previous simulations [37][38][39] we kept the temperature at T = 387 K, where according to ref. 34, the toluene coexistence between liquid and gas occurs at a pressure P c (387 K) = 1.097 atm, saturated densities ρ l = 777.9 kg m −3 and ρ g = 3.3 kg m −3 , and isothermal compressibility κ T = 1.866 × 10 -4 atm −1 .…”

The entropic bond in colloidal crystals

“…Nevertheless, we found that the, ostensibly, nonbonded platelet systems we studied exhibit a form of bonding that could be extracted from considering effective interactions arising between platelets. We consider the form of bonding discussed here different not only from chemical bonds but also from nonbonded interactions considered in, e.g., proteins and clusters (37,(45)(46)(47)(48)(49)(50)(51). There, supramolecular objects reconfigure among different conformations via transition states that can also be described with disconnectivity graphs.…”

Topological order in densely packed anisotropic colloids

“…To leverage this topological order in experiment we note that though our order parameters are based on contact types that nominally arise at infinite pressure, we showed that topological order persists at finite pressure. This finding is potentially useful in constructing plasmonic materials that have robust response in the presence of thermal fluctuations, changes in particle shape [26] or the behavior of stabilizing ligands [27,28]. It is known that the plasmonic response of systems of anisotropic nanoparticles depends strongly on the type of contacts between nanoparticles [29].…”