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Self-Assembly of CdTe Nanocrystals into Free-Floating Sheets

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Science  13 Oct 2006:
Vol. 314, Issue 5797, pp. 274-278
DOI: 10.1126/science.1128045

Abstract

In their physical dimensions, surface chemistry, and degree of anisotropic interactions in solution, CdTe nanoparticles are similar to proteins. We experimentally observed their spontaneous, template-free organization into free-floating particulate sheets, which resemble the assembly of surface layer (S-layer) proteins. Computer simulation and concurrent experiments demonstrated that the dipole moment, small positive charge, and directional hydrophobic attraction are the driving forces for the self-organization process. The data presented here highlight the analogy of the solution behavior of the two vastly different classes of chemical structures.

Understanding the ability of nanoparticles (NPs) to self-assemble will influence both the fundamental picture of the properties of matter on the nanoscale and the practical realization of bottom-up fabrication technologies (13). Self-organization processes in solution have been well established for proteins and other biomacromolecules (46), which have physical dimensions of several nanometers, i.e., the same scale as that of many inorganic nanocolloids. Recent studies demonstrate nanoparticle self-organization into one-dimensional (1D) structures driven by anisotropic dipolar interparticle forces (79). Highly uniform nanocolloids, with presumably isotropic interactions, can form 3D arrays or crystals (1014). Two-dimensional arrays of NPs produced at two-phase interfaces—such as gas-solid (10), liquid-solid (15), gasliquid (16), or liquid-liquid (17)—where the interfaces act as a template, are well known. We report that the combination of the electrostatic interaction and anisotropic hydrophobic attraction between NPs with tetrahedral shape result in the spontaneous formation of 2D free-floating sheets. The sheets display considerable mechanical robustness and retain size-quantized properties of the semiconductor NP with characteristic luminescence. Notably, they do not require any interface that may give dimension-restrictive cues and form entirely due to specific NP-NP interactions, which changes the paradigm of self-organization processes for NPs.

2-(Dimethylamino)ethanethiol (DMAET)–stabilized CdTe NPs with positive charges were synthesized by the Rogach-Weller method (18, 19). Transmission electron microscopy (TEM) (Fig. 1A) and tapping-mode atomic force microscopy (AFM) images (Fig. 1B) indicate the formation of objects that can be characterized as free-floating sheets formed by a 2D network of assembled NPs (Fig. 1C). In both TEM and AFM images, these sheets appear as flat, semifolded, and even wrinkled platelets. The semifolded structures demonstrate that the 2D NP sheets form in solution rather than on the substrate during drying. Using TEM, we estimate that more than 99% of the NPs assembled into sheets. We found similar sheets for CdSe NPs when we used the same stabilizer, which indicates the potential generality of the phenomenon (fig. S3).

The sheets possess some physical integrity, and some pieces as large as 50 μm by 30 μm (Fig. 1A) remain after gentle stirring and drying. The average AFM thickness of the NP sheets is 3.4 ± 0.2 nm (50 measurements). Because our DMAET-stabilized CdTe nanocrystals are 3.4 nm in diameter as determined by TEM, we conclude that the sheets are monolayers. A total height of 6.8 nm is found for smaller pieces spread atop larger ones and corresponds to the height of NP bilayers (Fig. 1B).

The NP sheets in solution have easily detectable photoluminescence (PL) with a quantum yield of 2.1%, which is considerably lower than the 30% quantum yield of the unassembled CdTe. The assembly also caused the PL peak to be red-shifted from 557 to 564 nm, i.e., by 27 meV (Fig. 2A). These observations are consistent with PL quenching due to excitation transfer in the closely spaced NP system also resulting in the preferential emission from larger NPs (20, 21). Nevertheless, the optical activity is sufficiently high to obtain confocal microscopy images under ambient conditions (Fig. 2, C and D). The confocal images correlate well with the TEM and AFM micrographs. The green-yellow emission of the films is the same over the entire sheet regardless of size, and the corresponding PL image matches the optical image (Fig. 2, B and C), which reflects the equal degree of quantization of the NPs that form the free-floating film. In this size regime, the emission color of CdTe is extremely sensitive to changes in particle diameter. Thus, the particles retain the individuality of their semiconducting cores. The same conclusion can be reached with CdTe NPs of different diameters (from 2.4 to 5.0 nm) and with different PL wavelengths (Fig. 2D). Confocal images also indicate that the interparticle forces driving sheet formation do not involve recrystallization of the CdTe atomic structure as observed in the self-assembly of CdTe nanowires (7); otherwise, color variations would have been observed. Some intensity variations along the sheet surface reflect the presence of films with double thicknesses due to additional pieces picked up from the solution (Fig. 1, A and B).

What is the mechanism underlying the formation of free-floating NP sheets rather than traditional 3D agglomeration and precipitation? One hypothesis, that sheets form on the vessel walls, has been excluded after multiple blank experiments based on a variety of techniques (see supporting online material). The results of confocal optical microscopy (fig. S1), light-scattering data (fig. S2, A to E), and TEM of the intermediate state (fig. S2F) are consistent with this conclusion. Semiconductor nanocolloids with zinc blend atomic packing (Fig. 1C) were experimentally determined by several groups to have a dipole moment (2224) contributing to the self-assembly of these particles into 1D chains and nanowires (7, 2426). Additionally, DMAET molecules confer some positive charge to the NPs, which we estimate to be 1 to 3e as in (27). There is also a strong hydrophobic attraction between the NPs, because DMAET has two hydrophobic methyl groups (28). We did not deplete the stabilizer layer by precipitating it with methanol (antisolvent), as our group had done previously with thioglycolic acid (7). This method maintains the individuality of the NP cores seen in the TEM images (Fig. 1, A and C).

On the basis of these observations and considering the relatively short length of the stabilizers (0.55 nm compared with the NP size of 2 to 5 nm), we conjecture that anisotropic electrostatic interactions arising from both a dipole moment and a small positive charge, combined with directional hydrophobic attraction, are responsible for the formation of the 2D free-floating films. Molecular simulations based on a coarse-grained model with proper parameters determined by semi-empirical quantum mechanics calculations were performed to validate the proposed hypothesis. The origin of the dipole moment in zinc-blend structured NPs is attributed to the truncation of the tetrahedrons (22, 24, 29). The high-energy apices of the tetrahedron are likely to be replaced with less energetic crystal planes in NPs (1, 30). Some of the four apices may be truncated, and some of them may remain. For the molecular simulations, we start from a model NP with three truncated apices. For a NP of 2.53-nm width and 2.95-nm height (Fig. 3A), semi-empirical PM3 quantum mechanical calculations indicate that the CdTe NP has a dipole moment of 107.74 D when the truncated corners are coated with H2O and 56.75 D when the truncated corners are coated with sulfhydryl (SH). These values are consistent with reported values of 50 to 100 D (22).

A coarse-grained “patchy particle” model proposed previously by Zhang and Glotzer is used to study the self-assembly of NPs with complex shape and anisotropic interactions, here by Monte Carlo (MC) simulations (31). Sixty-two beads were rigidly linked together into the shape of a truncated tetrahedron (Fig. 3B). The beads interact with a hard core repulsive interaction to model the excluded volume effect between the NPs. The diameter of each bead is σ = 0.5 nm. The corresponding NP size is h = 2.86 nm and w = 2.50 nm, which is close to the size used in the quantum calculation in Fig. 3A. As mentioned previous-ly, the stabilizer length is much smaller than the NP size; therefore, the hydrophobic attraction only exists between the pair faces and is short-ranged and directional. This is modeled by a square-well potential modulated by an angular term (Fig. 3C) (32) $Math$(1) where uhssw is the regular hard sphere square-well potential $Math$(2) Here ξ is the depth of the square-well potential related to the strength of the hydrophobic attraction, rij is the distance between the centers of mass of NP i and j, l is the distance from the mass center of the NP to the tetrahedron face, and λ is the interaction range. The function f(Qi, Qj) = 1 only if NPs i and j are oriented so that the angle between the vector joining their mass centers and the normal vector of the crystal face is less than δ; otherwise, f(Qi, Qj) = 0. The angle δ and interaction range λ in combination determine the directionality of the attraction between the faces of two NPs, which can be estimated by the length ratio of the stabilizer and NP. For example, the stabilizer length is ∼0.55 nm and δ is ∼18° (Fig. 3A). Thus, we chose λ = 0.55 nm and δ = 18° in the MC simulations (Fig. 3C). The electrostatic potential between two NPs Uij is modeled by $Math$(3) $Math$ $Math$ $Math$ which was proposed by Phillies for polyelectrolyte colloids and proteins in dilute solution (33).

In the above equation, $Math$ and $Math$(4) Here qi and qj are the net charge carried by NP i and NP j; μi and μj are dipole moments; rij is the distance between two NPs; θi and θj are angles of the dipole vector with respect to the vector connecting the centers of the NPs, where 0 < θ < π; φi and φj are dihedral angles describing the relative rotation of dipoles, where 0 < φ < 2π; 1/k is the Debye screening length, which is set to be 2.5 nm; ϵ0 is the permittivity of vacuum; ϵ is the effective permittivity of the solvent (water); and $Math$ is the radius of a NP. The dipole moment is set to be 100 D, as suggested by our quantum calculations. The net charge q is set to be +3e as determined by experimental measurements (27).

MC simulations in the canonical ensemble (constant number of NPs, volume, temperature) are performed in a cubic box with periodic boundary conditions implemented in all three Cartesian directions. A MC step is defined as N (number of NPs) attempts at moving the particles by either translation or rotation. The simulations begin from a disordered state that is obtained by running 3 to 5 million MC steps with attractive energy ξ = 0.0 and temperature T = 25°C. ξ is then gradually increased from a low value (disordered state) to a high value at which ordered films are formed. We investigated three different systems: N = 20 at volume fraction ϕ = 0.13, N = 30 at ϕ = 0.12, and N = 60 at ϕ = 0.13. Twenty independent runs were performed for the first two systems and four independent runs were performed for the third system. All of them demonstrate that CdTe NPs self-assemble into 2D monolayer films in solution (Fig. 3, D and E). We did not observe sheet formation in simulation in the absence of either the dipole moment, the net positive charge, or the hydrophobic attraction. This point was also exhaustively confirmed experimentally by varying the surface charge, ionic strength, stabilizer length, and the NP material (figs. S3 to S9). For instance, Au NPs with a very small dipole moment do not form the sheets, whereas similar CdSe NPs do. Simulated structures for these cases also match the experimental observations well (figs. S5, S7, and S11).

The simulation results further reveal that the basic units in each 2D monolayer are rings composed of six NPs, in which every bottom-upward NP is adjacent to three corner-upward NPs, and vice versa (Fig. 3E). The ring structures can also be seen in high-resolution TEM images of CdTe NP sheets (Fig. 1C, inset). The large-scale ordering in this system is difficult to discern (Fig. 1C). This is due to variations of NP diameter, geometry, truncations, and stabilizer distribution, which are inevitable for NPs produced in aqueous solutions with a relatively short stabilizer.

It is convenient to introduce the order parameter $Math$ in which S is the orientational tensor defined by S = 〉uu 〈–1e, where u is the unit vector of the dipole moment and e is the unit tensor, to describe the organization of the NP system, as used for liquid crystals. Ordering in the system should depend on the strength of the specific interactions. Indeed, there is a transition in the order parameter S at ξ = 58 to 59.5 kJ/mol as the attraction increases (Fig. 3F), which is similar for different systems (fig. S10). Simulations of larger systems confirmed the stability of the sheets (see supporting online material).

We also evaluate the potential energy between two NPs as a function of relative orientation to elucidate how the locally anisotropic interactions conspire to produce a global symmetry-broken 2D structure. The truncated tetrahedral shape of the NP causes the hydrophobic attraction between them to be anisotropic, i.e., the bottom-bottom, bottom-side, and side-side alignments are favored. The energy of attraction remains the same (square-well interaction) in all of these orientations, whereas the energy of electrostatic interactions does not (Table 1). The combined lowest energy state is the side-side orientation with opposite dipole directions (Δφ = 180°), which we indeed find in the simulations. The energy difference between the lowest energy state (side-side, Δφ = 180°) and the next lowest energy state (side-side, Δφ = 120°) is 2.52 kJ/mol, which is comparable with the energy of thermal noise. Table 1 also demonstrates the necessity of a small positive charge in addition to the dipole moment to form sheets. Without net charge the lowest energy state is the bottom-side orientation, preventing the formation of 2D monolayers (fig. S11).

Table 1.

Electrostatic energy of two NPs as a function of relative orientation (separation r = 0.55 nm). Uqq: charge-charge interaction; Uqμ: charge-dipole interaction; Uμμ: dipole-dipole interaction; Ut: total electrostatic interaction. All energy is in units of kJ/mol. Δφ is the dihedral angle between the dipole directions of neighboring NPs.

Relative orientationBottom-bottomBottom-sideSide-side
Δφ = 0°Δφ = 60°Δφ = 120°Δφ = 180°
Uqq 53.47 53.47 53.47 53.47 53.47 53.47
U qμ 45.63 15.21 -15.21 -15.21 -15.21 -15.21
U μμ 12.40 -4.13 5.91 3.64 -0.89 -3.15
U t 111.50 64.55 44.17 41.90 37.37 34.85

Using the same modeling strategy, one can consider NPs with different numbers of corners truncated. NPs with zero or one truncated corners cannot form 2D monolayers due to the steric constraints between the untruncated corners of adjacent NPs. NPs with two truncated corners form chains instead of monolayers (fig. S12). Although 2D self-assembly was observed only for NPs with three truncated corners, we do not exclude the existence of NPs with other number of truncated corners in the experimentally obtained sheets, including those with four truncated corners, because the net dipole moment inside those NPs can be induced by other adjacent NPs (24). The inclusions will show up as defects within the sheet (Fig. 1C). Nevertheless, the arrangement of NPs with three adjacent NPs in a 2D film is the most energetically favorable.

The interactions between NPs in general are complex and diverse, which offers tremendous opportunities for the design of NP assemblies with varying shapes, structures, and functions (31, 34). This study of 2D self-assembly of NPs demonstrates (i) the importance of anisotropy of interparticle interactions at the nanoscale and (ii) methods for the manipulation and prediction of spontaneous NP assemblies. These data also show a surprising resemblance of NPs to self-ordering biological systems, such as S-layer–forming proteins (46). This is particularly important for establishing correlations between protein superstructures and inorganic nanostructures on the basis of their similar sizes.

Supporting Online Material

Materials and Methods

Figs. S1 to S12

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