Ligand displacement exposes binding site heterogeneity on CdSe nanocrystal surfaces

Nanocrystal ligand interactions and ligand exchange processes are usually described by a uniform distribution of equal binding sites. Here, we analyze this assumption by a quantitative study of the displacement of Z-type cadmium oleate ligands from CdSe nanocrystals by addition of L-type ligands. First, we determined the stoichiometry of the displacement reaction by analyzing the equilibrium upon dilution using solution nuclear magnetic resonance spectroscopy. We found that 1 equiv of tetramethylethylene-I,2-diamine (TMEDA) or 2 equiv of n-butylamine or benzylamine bind to the displaced cadmium oleate. We only reached a comprehensive description of the displacement isotherm by including two types of binding sites with a different equilibrium constant. We corroborated this finding by density functional theory calculations on a CdSe model nanocrystal, which show that even single facets contain a broad variety of binding sites. Finally, we analyzed the thermodynamics of the displacement equilibrium for the weaker binding sites by constructing van't Hoff plots for the different displacers. Whereas displacement with TMEDA appears to be enthalpically neutral, it is entropically favorable. In contrast, displacement with the primary amines is entropically unfavorable but is associated with a negative change in enthalpy. Since the distribution of binding energy emanates from the large fraction of edge and vertex sites on a nanocrystal facet, these findings are most likely inherent to nanocrystals in general and should be considered when analyzing surface reactions on such materials

Etude matricielle des machines synchrones autopilotées à commutation naturelle de courant

RESUMÉDes travaux récents ont montré que l’utilisation d'une écriture matricielle simplifiait nettement le calcul numérique des constantes d’amortissement d'une machine synchrone ainsi que celui de l'intensité des courants. Il était donc normal de cherher à profiter des mêmes avantages pour l’étude des machines autopilotées. Dans le présent article, nous considérons le cas d’une machine triphasée classique

Chemically triggered formation of two-dimensional epitaxial quantum dot superlattices

Two dimensional superlattices of epitaxially connected quantum dots enable size-quantization effects to be combined with high charge carrier mobilities, an essential prerequisite for highly performing QD devices based on charge transport. Here, we demonstrate that surface active additives known to restore nanocrystal stoichiometry can trigger the formation of epitaxial superlattices of PbSe and PbS quantum dots. More specifically, we show that both chalcogen-adding (sodium sulfide) and lead oleate displacing (amines) additives induce small area epitaxial superlattices of PbSe quantum dots. In the latter case, the amine basicity is a sensitive handle to tune the superlattice symmetry, with strong and weak bases yielding pseudohexagonal or quasi-square lattices, respectively. Through density functional theory calculations and in situ titrations monitored by nuclear magnetic resonance spectroscopy, we link this observation to the concomitantly different coordination enthalpy and ligand displacement potency of the amine. Next to that, an initial similar to 10% reduction of the initial ligand density prior to monolayer formation and addition of a mild, lead oleate displacing chemical trigger such as aniline proved key to induce square superlattices with long-range, square micrometer order; an effect that is the more pronounced the larger the quantum dots. Because the approach applies to PbS quantum dots as well, we conclude that it offers a reproducible and rational method for the formation of highly ordered epitaxial quantum dot superlattices

On the Yang-Lee and Langer singularities in the O(n) loop model

We use the method of `coupling to 2d QG' to study the analytic properties of the universal specific free energy of the O(n) loop model in complex magnetic field. We compute the specific free energy on a dynamical lattice using the correspondence with a matrix model. The free energy has a pair of Yang-Lee edges on the high-temperature sheet and a Langer type branch cut on the low-temperature sheet. Our result confirms a conjecture by A. and Al. Zamolodchikov about the decay rate of the metastable vacuum in presence of Liouville gravity and gives strong evidence about the existence of a weakly metastable state and a Langer branch cut in the O(n) loop model on a flat lattice. Our results are compatible with the Fonseca-Zamolodchikov conjecture that the Yang-Lee edge appears as the nearest singularity under the Langer cut.Comment: 38 pages, 16 figure

Probing solvent-ligand interactions in colloidal nanocrystals by the NMR line broadening

Although solvent-ligand interactions play a major role in nanocrystal synthesis, dispersion formulation, and assembly, there is currently no direct method to study this. Here we examine the broadening of H-1 NMR resonances associated with bound ligands and turn this poorly understood descriptor into a tool to assess solvent-ligand interactions. We show that the line broadening has both a homogeneous and a heterogeneous component. The former is nanocrystal-size dependent, and the latter results from solvent-ligand interactions. Our model is supported by experimental and theoretical evidence that correlates broad NMR lines with poor ligand solvation. This correlation is found across a wide range of solvents, extending from water to hexane, for both hydrophobic and hydrophilic ligand types, and for a multitude of oxide, sulfide, and selenide nanocrystals. Our findings thus put forward NMR line-shape analysis as an indispensable tool to form, investigate, and manipulate nanocolloids