A model is presented for the colloidal synthesis of semiconductor nanocrystals capturing the reactions underlying nucleation and growth processes. The model combines an activation mechanism for precursor conversion to monomers, discrete rate equations for formation of small-sized clusters, and continuous Fokker-Planck equation for growth of large-sized clusters. The model allows us to track the temporal evolution of the entire cluster size distribution and compute several experimental observables including mean size and size distribution. The model predicts five distinct regions: generation of monomers, small cluster formation, size distribution focusing due to precursor depletion, pseudo steady state region, and size distribution broadening, with the latter three explicitly reproducing available experimental data at larger cluster sizes. Furthermore, we identify two nondimensional parameter combinations and discuss how these can be used to guide experiments to yield a more rational approach to synthesis modification. Contrary to the common hypothesis that diffusion is essential for size distribution focusing, the model shows that focusing can be achieved under pure reaction control. In addition, the model yields new insights into the synthesis of small nanocrystals with narrow size distributions either by modulation of temperature over the duration of nanocrystal synthesis or by introduction of small quantities of additives that enhance the rate of precursor conversion to monomers. We show that for a given set of reaction parameters, there is an optimum in the duration of high temperature and additive concentration minimizing polydispersity.

To gain a better understanding of the influence of ligand-surface interactions on nanocrystalline growth, periodic density functional theory calculations were employed in the study of the binding of organic ligands on the relaxed nonpolar (1120) and polar Se terminated (0001) surfaces and the relaxed and vacancy and adatom reconstructed Cd terminated (0001) surface. We examined chemisorption properties of phosphine, amine, phosphine oxide, carboxylic acid, and phosphinic acid model ligands, including preferred binding sites and geometries, vibrational frequencies, and binding energetics, and compared findings to intrinsic growth via addition of CdSe molecules or Cd and Se atoms. Our results indicate that binding of the ligands is preferred in the electron-poor 1-fold sites on all surfaces, with secondary coordination of the acidic ligands through the hydroxyl hydrogen to the electron-rich surface sites. In general ligand adsorption directly obstructs binding sites for growth species on the (1120) surface and only indirectly on the two polar surfaces. The order of binding affinities on the (1120) and (0001) surfaces is PH(3) < OPH(3) approximately HCOOH < NH(3) < OPH(2)OH and that on the (0001) surface is OPH(3) approximately HCOOH < OPH(2)OH < NH(3) < PH(3). Our findings corroborate the experimental observation that incorporation of the nonbulky phosphinic acid-type ligands with high affinity and high selectivity for both the (1120) and (0001) surfaces strongly enhances unidirectional growth on the (0001) surface, while incorporation of either bulky ligands or ligands with moderate affinity does not. Higher affinity of all traditionally used ligands for the (1120) surface compared to the (0001) surface also suggests that new ligands should be engineered to achieve the synthesis of novel shapes that require preferential growth on the (1120) surface.

A systematic study of the chemisorption of both atomic ͑H, O, N, S, C͒, molecular (N 2 , CO, NO), and radical (CH 3 , OH) species on Rh͑111͒ has been performed. Self-consistent, periodic, density functional theory ͑DFT-GGA͒ calculations, using both PW91 and RPBE functionals, have been employed to determine preferred binding sites, detailed chemisorption structures, binding energies, and the effects of surface relaxation for each one of the considered species at a surface coverage of 0.25 ML. The thermochemical results indicate the following order in the binding energies from the least to the most strongly bound: N 2 ϽCH 3 ϽCOϽNOϽHϽOHϽOϽNϽSϽC. A preference for threefold sites for the atomic adsorbates is observed. Molecular adsorbates, in contrast, favor top sites with the exceptions of NO ͑hcp͒ and OH ͑fcc or bridge tilted͒. Surface relaxation leads to insignificant changes in binding energies but to considerable changes in the spacing between surface rhodium atoms, particularly for on-top adsorption where the rhodium atom directly below the adsorbate is lifted above the plane of the surface. RPBE binding energies are found to be in remarkable agreement with the available experimental values. All atomic adsorbates, except for H, have a significant diffusion barrier ͓between 0.4 and 0.6 eV ͑RPBE͔͒ on Rh͑111͒. Atomic H and molecular/radical adsorbates appear to be much more mobile on Rh͑111͒, with an estimated diffusion barrier between 0.1 and 0.2 eV ͑RPBE͒. Finally, the thermochemistry for dissociation of CO, NO, and N 2 on Rh͑111͒ has been examined. In all three cases, decomposition is found to be thermodynamically preferable to desorption.

Colloidal semiconductor quantum dots (QDs) have been used in biological imaging, [1] electroluminescent devices, [2] and lasers [3] due to their size-tunable optical properties and chemical stability. Most of these applications require highly crystalline samples with narrow size distributions, which are often difficult to achieve in a single-step batch process with its often poor control of reaction conditions. Synthesis of QDs in microfluidic devices offers several advantages over conventional macroscale chemical processes, [4] including enhancement of mass and heat transfer, [5] reproducibility, [6] potential for sensor integration for in situ reaction monitoring, [7] rapid screening of parameters, and low reagent consumption during optimization. [8] Previous studies have realized the continuous synthesis of CdSe QDs at atmospheric pressure using single-phase laminar flow microreactor designs. [6,9] One difficulty of these synthetic procedures is the requirement for solvents that can both dissolve the precursors at ambient conditions and also remain liquid over the entire operatingtemperature range (25 8C to 350 8C), significantly limiting the set of solvents, ligands, and precursors that are compatible with continuous flow systems. Furthermore, the solvents that are available are typically very viscous (500 mPa Á s < h < 1500 mPa Á s), leading to slow mixing, broad residence-time distributions (RTD), and as a consequence, broad QD-size distributions (typically >10%). Segmentation of the reacting phase with an immiscible phase [10] can overcome such limitations by narrowing the RTD and improving reactant mixing. [11,12] Application of segmented flow for continuous synthesis of narrowly distributed CdSe QDs has been previously demonstrated for liquid-gas, [13] and liquid-liquid [14] segmented flows.However, even with flow segmentation, limitations on the number of compatible chemistries and the limited number of available high-boiling-point solvents have been major obstacles in the rapid adoption of microreactors as universal platforms for QD synthesis.One way of improving syntheses in microreactors is to perform experiments at high pressure. Indeed, at sufficiently high pressure, virtually any common solvent, precursor, and ligand will either remain liquid or become supercritical (sc) at the temperatures required for QD synthesis. In the supercritical regime, properties of the fluid can be tuned from liquid-like to gas-like, [15] displaying the high miscibility and fast diffusion rates typical of gasses, but with sufficiently high densities for solubilizing a wide range of compounds of low to medium polarity, typical of liquids. The supercritical-fluid technology has been successfully applied to materials processing as an alternative to conventional solvents to achieve the synthesis of both organic [16] and inorganic [17] materials. In microreactors, the low viscosities of supercritical fluids can be used to overcome the inherent limitations of conventional liquid solvents, leading to faster mixing and narr...

Details of the chemical mechanism underlying the growth of colloidal semiconductor nanocrystals remain poorly understood. To provide insight into the subject, we have preformed a comprehensive study of the polar (0001) and (0001) and nonpolar (1120) wurtzite CdSe surfaces that are exposed during crystal growth using first-principles density functional theory (DFT-GGA) calculations. Stabilization of these surfaces by relaxation and reconstruction was considered. Two particular reconstructions of the polar surfaces were examined: vacancy formation on a 2 x 2 unit cell and addition of Se and Cd atoms on the (0001) and (0001) surfaces, respectively. Calculation results indicate that the (1120) is the most stable surface when compared to the two polar surfaces. Furthermore, reconstructions of the (0001) surface are energetically favored when compared to reconstructions of the (0001) facet. Adsorption of Cd and Se atoms and the CdSe molecule on the three relaxed surfaces and two reconstructed (0001) surfaces were also investigated. Several binding sites were considered to determine the most stable binding geometries and energetics. Atomic species preferentially bind in either 2-fold or 3-fold sites, while the CdSe molecule binds parallel to the surface on all of the considered surfaces. Vibrational frequencies of the adspecies were calculated for the most stable binding configurations and were included in the zero point energy correction. Diffusion barriers for the atomic and molecular species were estimated where possible to be between 0.2 and 0.4 eV on the three relaxed surfaces. Thermochemistry of the CdSe molecule binding and dissociation was also investigated. On all considered surfaces, dissociation is preferred to desorption with dissociation only exothermic on the (0001) surface. Comparison of the three relaxed and two reconstructed surfaces indicates that CdSe molecule binding and dissociation is thermodynamically favored on the (0001) surface. This implies that under a reaction-controlled regime, the rate of homoepitaxy would be faster on the (0001) Se terminated surface than on the (0001) and (1120) surfaces, making the (0001) surface of a nanocrystal the primary direction of growth.