Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices

Abstract

One of the main reasons for the current interest in colloidal nanocrystals is their propensity to form superlattices, systems in which (different) nanocrystals are in close contact in a well-ordered three-dimensional (3D) geometry resulting in novel material properties. However, the principles underlying the formation of binary nanocrystal superlattices are not well understood. Here, we present a study of the driving forces for the formation of binary nanocrystal superlattices by comparing the formed structures with full free energy calculations. The nature (metallic or semiconducting) and the size-ratio of the two nanocrystals are varied systematically. With semiconductor nanocrystals, self-organization at high temperature leads to superlattices (AlB 2 , NaZn 13 , MgZn 2 ) in accordance with the phase diagrams for binary hard-sphere mixtures; hence entropy increase is the dominant driving force. A slight change of the conditions results in structures that are energetically stabilized. This study provides rules for the rational design of 3D nanostructured binary semiconductors, materials with promises in thermoelectrics and photovoltaics and which cannot be reached by any other technology.KEYWORDS Nanocrystals, self-assembly, superlattices, hard spheres, thermodynamics. C olloidal, monolayer-stabilized nanocrystals (NC) can be synthesized with a nearly spherical shape and with a well-defined diameter that does not vary by more than 5% in the sample. Because of their monodisperse size and shape, such NCs show a strong propensity to assemble into NC superlattices.1 More than a decade ago, the formation of single-component superlattices that consist of CdSe semiconductor NCs was reported.1 This was followed by the demonstration of binary superlattices, consisting of NCs of different diameters and different nature, that is, semiconductor, metallic, or magnetic. [1][2][3][4][5][6][7][8][9][10][11][12][13] In such systems, novel collective properties can arise from the (quantum mechanical) interactions between the different components that are in close contact in a three-dimensional (3D) ordered geometry. Some striking examples have already been reported. 3,4,14,15 For instance, a binary superlattice of two types of insulator nanoparticles is found to become conductive due to interparticle charge transfer.3 Colloidal crystallization is the only method known to date to obtain nanostructured systems with order in three dimensions. However, for further progress in the field of designed nanostructured materials, improved control of nanocolloid crystallization is a key factor.Apart from the viewpoint of emerging nanomaterials, the formation of (binary) NC superlattices is of strong interest in colloidal science. Nanocrystals have a mass that is about a million times smaller than that of the colloidal particles commonly used in crystallization studies; hence, their thermal velocity is about a factor of thousand higher. This agrees with the fact that nanocolloid crystallization is a relatively fast process, still oc...

Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures

“…A variety of forces can be involved in their formation: van der Waals (vdW) attractions between the particles, steric repulsions between the hydrophobic tails of the surfactants (often coating the nanocrystal surface), capillary forces during solvent evaporation, attractive depletion forces, Coulomb forces between surface charges or electric dipoles, and magnetic forces 1,3,5,[7][8][9][10][11][12] . The assembly of many ordered threedimensional (3D) superstructures, for example, simple, binary, or ternary assemblies of spherical nanoparticles [13][14][15][16][17] , and smectic-like multilayers of hexagonally packed nanorods 18 , as well as liquid crystalline phases, is found to be solely driven by entropy [19][20][21] . More elaborate assemblies could be achieved from such simple building blocks by encoding information for the self-assembly in the surface pattern of the nanoparticles, for instance by DNA functionalization to modify the strength and directionality of particle-particle interactions [22][23][24] .…”

Binary colloidal structures assembled through Ising interactions

“…Multi-component colloidal systems [26][27][28][29][30][31][32][33][34][35] (that is, 'colloidal alloys') as well as systems of particles with non-trivial internal structure, such as Janus particles [36][37][38][39] and particles with shape anisotropy [40][41][42] , are currently being explored due to their ability to tailor the particle interactions and enable the assembly of diverse crystalline structures. Current methods for assembling ordered structures with two or three particle types include kinetic techniques based on controlled drying [26][27][28][29][30][31] and thermodynamic techniques [32][33][34][35]43,44 that rely on spontaneous assembly into minimum free-energy configurations.…”

“…Current methods for assembling ordered structures with two or three particle types include kinetic techniques based on controlled drying [26][27][28][29][30][31] and thermodynamic techniques [32][33][34][35]43,44 that rely on spontaneous assembly into minimum free-energy configurations. Kinetic techniques using evaporation of a liquid meniscus have demonstrated a large variety of crystalline colloidal alloy structures [26][27][28] .…”

Phase diagram of hard snowman-shaped particles

“…Comparing the structures we have found to be stable for snowman particles with those found for binary hard-sphere mixtures, [39][40][41][42][43][44][45] we note that only the NaCl crystal structure is predicted to be stable for binary hard-sphere mixtures with size ratios d = 0.3, 45 …”