On the Thermodynamic Stability of Binary Superlattices of Polystyrene-Functionalized Nanocrystals

Abstract

Assembly of two types of functionalized nanocrystals by tuning the solvent quality always leads to phase-separated single-component superlattices, while if directed by solvent evaporation, it may result in cocrystallization into binary superlattices, thus raising the following obvious question of: What phase is the thermodynamic equilibrium? We address this fundamental problem by evaluating the free energies of single-component and binary superlattices of nanocrystals functionalized with polystyrene. We show that most binary superlattices reported in the literature are metastable against phase separation. We also characterize the structure of the different superlattices and show that they are accurately described by the orbifold topological model (OTM). We discuss the implications of the results for ongoing experiments and for the general assembly of nanostructures.

Thermodynamic Equilibrium of Binary Nanocrystal Superlattices

“…Still, we did find several instances for AlB 2 , CaB 6 , NaCl, MgZn 2 , bccAB 6 , NaZn 13 , and CaCu 5 where the BNSL are stable. This is in contrast with recent calculations with long polystyrene capping ligands, which are dominated by phase separation. We did not find any instance where the following BNSLs were stable: Li 3 Bi, AuCu 3 , Fe 4 C, or cubAB 13 .…”

Shape-Directed Co-Assembly of Lead Halide Perovskite Nanocubes with Dielectric Nanodisks into Binary Nanocrystal Superlattices

“…NC self-assembly into SLs is driven by both energetic interactions and entropic contributions. − The former include dipole–dipole, Coulombic, magnetic, and van der Waals forces between inorganic cores and capping ligands, whereas relevant entropic factors comprise free volume entropy gain, depletion attraction interactions, and entropy associated with ligand configurations . In the case of entropy-driven crystallization of binary mixtures of spheres, the binary SLs of NaCl-, AlB 2 -, and NaZn 13 -type are known for hard-sphere systems of micrometer-sized colloidal beads characterized by only a steep steric repulsion term in their interparticle potential, , as they maximize the packing fraction (η) at a given size ratio (γ = d B / d A ≤ 1), exceeding that of single-component densest lattices of spheres (face-centered cubic or hexagonal closed packed; fcc and hcp ).…”

Nanocomposite tectons as unifying systems for nanoparticle assembly

“…23,24 We will achieve these goals by examining NCTs as intermediate systems that bridge the supramolecular DNA and SE strategies. Specifically, a binary NCT system with passivated hydrogen bonding, all Thy (or DAP) for example, is basically just a NP core functionalized with polystyrene, which has already been demonstrated, both from experiment 10 and theory [25][26][27][28] to assemble by SE into the rich diverse phases as reported with short hydrocarbon chains.…”

“…A convenient way to illustrate the role of these four parameters is to describe solvent quality (parameterized by the Flory-Huggins parameter w) along the x-axis, for example polystyrene, (w ¼ 1 2 being the y-point). The y-axis parameterizes the hydrogen bond strength between end moietes (e.g., Thy-DAP) nanoparticles are stable, while w ) 1 2 is akin to solvent evaporation, which in the absence of the hydrogen bonding, has been shown to lead to BNSLs 10 (although questions regarding their overall thermodynamic stability are still under some debate 28 ). Moving upwards in this parameter space, for good or y conditions, sufficiently strong hydrogen bonding leads to the stability of the phases reported in DNA assembly, 6 with the addition of the Th 3 P 4 phase depending on the persistence length of the ligands, as shown in Fig.…”