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Electrostatic Self-Assembly of Binary Nanoparticle Crystals with a Diamond-Like Lattice

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Science  21 Apr 2006:
Vol. 312, Issue 5772, pp. 420-424
DOI: 10.1126/science.1125124

Abstract

Self-assembly of charged, equally sized metal nanoparticles of two types (gold and silver) leads to the formation of large, sphalerite (diamond-like) crystals, in which each nanoparticle has four oppositely charged neighbors. Formation of these non–close-packed structures is a consequence of electrostatic effects specific to the nanoscale, where the thickness of the screening layer is commensurate with the dimensions of the assembling objects. Because of electrostatic stabilization of larger crystallizing particles by smaller ones, better-quality crystals can be obtained from more polydisperse nanoparticle solutions.

Crystalline aggregates composed of one or more types of metallic and/or semiconductor nanoparticles (NPs) are of great interest for the development of new materials with potential applications in areas such as optoelectronics (1), high-density data storage (2), catalysis (3), and biological sensing (4). To date, methods for the crystallization of two-dimensional (2D) and 3D NP superlattices have relied on the differences in the sizes of component particles and on attractive van der Waals or hard-sphere interactions between them. This strategy has been successful in preparing several types of lattices [such as AB (5), AB2 (6), AB5 (7), and AB13 (6)], but the all-attractive nature of the interparticle potentials limits its applicability to relatively few and usually (8) close-packed structures.

To overcome this limitation, we and others (8, 9) have focused on systems of NPs interacting via electrostatic forces; such forces provide a basis for ionic, colloidal (9), or even macroscopic (10) crystals, but, despite promising attempts (8, 11), have not been successfully exploited for controllable or predictable long-range organization of matter at the nanoscale. Here, we report electrostatic self-assembly (10) (ESA) of oppositely charged, nearly equally sized metallic NPs of different types into large 3D crystals characterized by sphalerite (diamond-like) (12) internal packing, and of overall morphologies identical to those of macroscopic diamond or sphalerite crystals (Figs. 1, 2, 3, 4). Formation of these non–close-packed structures results from the change in electrostatic interactions in the nanoscopic regime, where the thickness of the screening layer becomes commensurate with the dimensions of the assembling particles, and is facilitated by the presence of smaller, charged NPs in the crystallizing solutions that stabilize larger NPs by what can be termed a nanoscopic counterpart of Debye screening.

Fig. 1.

(A) Scheme and average dimensions (in nm) of AuMUA and AgTMA nanoparticles used as the model system. Particle compositions estimated using the method from (39) are Au4100L380 (where L is MUA) and Ag3400L340 (where L is TMA); the ratio of the particles' charges Q(AgTMA)/Q(AuMUA) = –0.90. (B) Experimental, normalized size distributions of metallic cores of Ag and Au NPs; statistics are based on high-resolution TEM images of at least 500 NPs of each type. (C) Typical UV-Vis spectra for the titration of AuMUA solution (here, 2 mM, 0.4 ml) with small aliquots (40 μl = 0.1 equiv.) of AgTMA solution (2 mM; concentrations are given in moles of metal atoms). The legend gives numbers of AgTMA equivalents added. Initially, absorption of the SPR band of gold (λmax,Au = 520 nm) rises and that of the SPR band of silver (λmax,Ag = 424 nm) is extinguished. Precipitation begins at ∼ 0.7 equiv. AgTMA and is complete when [AgTMA]/[AuMUA] ∼ 0.9. The precipitation point corresponds to the formation of charge-compensated (electroneutral) complex and is consistent with an estimate derived from particle compositions: ([AgTMA]/[AuMUA])neutral = (NAg/NAu)|QAuMUA/QAgTMA| = (3400/4100)/0.9 = 0.92, where NAg and NAu are the numbers of Ag and Au atoms in one AgTMA and one AuMUA particle, respectively). Further addition of silver NPs solubilizes the precipitate, as evidenced by the increasing intensities of SPR bands of both types of NPs (and also by visual examination of the sample). (D) (Solid curve) Progress of the titration represented by absorption coefficient ϵ(λmax,Au) defined in (15). The initial increase in ϵ is the result of close proximity of oppositely charged particles within soluble aggregates (15). Aggregation is confirmed by the red shift of the Au plasmon band maximum, λmax,Au, from 520 to ∼558 nm (dashed curve). For χ ≳ 0.5, precipitate redissolves, and λmax,Au decreases. (E) Large-area SEM image of binary crystals obtained from AuMUA/AgTMA precipitates.

Fig. 2.

Structure of AuMUA-AgTMA binary crystals. (A) Small-angle powder XRD spectrum of the crystals. Bragg reflections on planes specified by Miller indices shown are characteristic of a diamond-like structure. (Inset) Comparison between experimental (de) and theoretical (dt) spacing between crystal planes with Miller indices {hkl}. Values of dt were calculated based on the lattice constant a = 19.08 nm. The center-to-center distance between nanoparticles on the (100) face, calculated as Embedded Image, is D = 13.49 ± 0.37 nm; interparticle distance along body-diagonal axis calculated from XRD data is 8.27 ± 0.26 nm. (B) An SEM image of a {100}SL square face taken from a twinned-octahedron crystal (inset); estimated lattice constant a = 18.5 nm. (C) An SEM image of a {111}SL plane of a triangular face of an octahedron (inset) with estimated interparticle distance of 8.5 nm. (D) Scheme of an AB unit cell and the projections of {100}SL, {110}SL, {111}SL planes. NPs of one type are positioned in the nodes of a face-centered cubic lattice, whereas the others occupy half of the tetrahedral voids. The crystals are isostructural with sphalerite ZnS (SG 216) or, for crystals made of only one type of metal cores (compare Fig. 5B), with the diamond lattice (SG 227).

Fig. 3.

Compositional analysis of the NP crystal faces. The left panel shows a typical scanning TEM (STEM) image of a hexagonal {111} face recorded on Hitachi HF2000 instrument. The EDS analysis was performed in the STEM mode with small aperture and 2-nm electron probe size. The aperture settings (#3) were chosen such as to minimize scattering from neighboring/underlying particles while retaining sufficient image contrast. Drift correction area is delineated by the red box. Graphs in (A) and (B) give typical EDS data collected along directions indicated in the STEM image at 60° with respect to one another (compare Fig. 2D). Because a measurement at each nanoparticle took 30 s and the residual drift of the instrument (inherent and due to sample heating) was ∼1 nm/min, it was possible to collect reliable data over up to four successive NPs and two scans. EDS data were obtained from the x-ray emission lines of AgLα (2.98 keV, blue line) and of AuLα (9.71 keV, magenta line). The graph in (A) corresponds to the Au-Ag-Ag-Au sequence of NPs and that in (B), to Ag-Au-Au-Ag that can be expected at these relative locations. The counts are relatively high because the beam penetrates into the crystal beyond the top layer of NPs. Although x-ray emission is thus collected from several layers, signal undulation is due to the top layer—when the aperture is increased (to #1 or #2) and signal is collected from an even larger volume/depth, the counts for Ag and Au equalize, giving the ∼1:1 bulk composition of the crystal (15).

Fig. 4.

Different morphologies of the AuMUA-AgTMA crystals (left column) and their macroscopic sphalerite (SL) (A to D) and diamond (E) counterparts (right column). (A) Octahedron; insets show {111}SL and {100}SL faces. (B) Cut tetrahedron; insets show {111}SL and {100}SL faces from cut top and from cut edge, respectively. (C) Octahedron with two triangular faces cut; inset shows the {111}SL face. (D) Twinned octahedron; insets magnify {111}SL faces at the location of twinning and the {100}SL face of a broken neighboring crystal. (E) Truncated tetrahedron; inset shows top view of the {111}SL face.

We used Ag and Au NPs coated with ω-functionalized alkane thiols (13): HS(CH2)10COOH (MUA) and HS(CH2)11NMe3+Cl (TMA) (Fig. 1A). These NPs were prepared according to a modified procedure (14) [see Supporting Online Material (15)] and had average diameters of 5.1 nm (with dispersity σ = 20%) for Au and 4.8 nm (σ = 30%) for Ag (Fig. 1B). We chose this pair as a model system, because the average sizes of Au NPs passivated with MUA [self-assembled monolayer (SAM) thickness = 1.63 nm (16)] and Ag NPs covered with TMA (SAM thickness ∼ 1.9 nm) were very similar overall (∼8.36 nm versus ∼8.60 nm).

Both types of NPs were stable and unaggregated when kept in separate aqueous solutions. At the concentration used (2 mM), the pH of AuMUA solution was 9.7, so the NPs presented deprotonated carboxylate groups, and the ratio of NP charges was Q(AgTMA)/Q(AuMUA) = –0.90 (compare Fig. 1A). When the solutions were mixed, the positively charged AgTMAs interacted with the negatively charged AuMUAs. As suggested by the absence of the silver plasmon band centered at Embedded Image and concomitant growth of the gold band at Embedded Image (Fig. 1C), the interaction involved close proximity of particles of the two types within small, soluble aggregates (15). These aggregates precipitated rapidly when the molar ratio of the NPs was near unity and the overall charge of the NPs was neutralized (Fig. 1D).

Crystals were obtained from the NP precipitate, from which the excess of ammonium salt hindering the crystallization process was removed by washing with water. Subsequently, the precipitate was dissolved in a 1:4 v/v mixture of water and dimethyl sulfoxide (DMSO), and crystals were grown by slow (∼12 hours) evaporation of water at 70°C (17). This procedure yielded large numbers of regularly faceted crystals, each composed of several million NPs and with dimensions up to 3 μm in each direction (Figs. 1 and 4). When the crystals were partly dissolved in water, the ultraviolet-visible (UV-Vis) spectra showed no blue-shift of the surface plasmon resonance (SPR) of Au and an extinguished SPR band of Ag. These data suggest that (i) Ag and Au NPs in the crystals were in close proximity and (ii) that they did not amalgamate (18) during crystallization. Amalgamation was also ruled out by performing successful crystallization without heating.

The crystal structure was solved by small-angle, powder x-ray diffraction (XRD) (15). The XRD spectrum in Fig. 2A shows three peaks located at 2θ = 0.801°, 1.308°, and 1.539°. This diffraction pattern characterizes the sphalerite [or diamond (15)] structure with the lattice constant a = 19.08 ± 0.53 nm and with peak positions corresponding to Bragg reflections on planes specified by Miller indices (111), (220), and (311), respectively. The lattice constant agrees with the value of a ≈ 18.5 nm based on scanning electron microscopy (SEM) measurements (Fig. 2B). Also, the interparticle distance along the body-diagonal axis calculated from XRD data is 8.27 ± 0.26 nm, near the value of ∼8.48 nm estimated from hard-sphere radii of individual NPs (compare Fig. 1A) and 8.5 nm from the SEM image (Fig. 2C). Finally, both the bulk composition of the crystals as well as the identities of NPs on crystalline faces were examined via energy dispersive spectroscopy (EDS) in SEM and in transmission electron microscopy (TEM); it was found that the bulk contents of Ag and Au were approximately equal [compare (15)] and that the arrangement of surface particles was congruent with the XRD analysis (Fig. 3).

All of these experiments indicate that NPs are arranged on a diamond lattice with each NP surrounded by four oppositely charged neighbors at the vertices of a tetrahedron (Fig. 2D). This structure is closely related to that of ZnS, except that the NP “ions” have nearly identical radii. Not surprisingly, the overall crystal morphologies—including octahedral, truncated tetrahedral, truncated and twinned octahedral, and triangular—are identical to those observed for their macroscopic diamond or sphalerite (ZnS) counterparts (Fig. 4).

Crystallization of NPs into a diamond-like structure is mediated by screened electrostatic interactions. Screening occurs because (i) the NP cores are metallic and (ii) each charged NP is surrounded by a layer of counterions. As a result, the particles interact by short-range electrostatic potentials. To show why such interactions do not lead to more closely packed NaCl or CsCl structures that might have been expected on the basis of NP charges alone, we first note that the screening length, Embedded Image, for the crystallized NPs is ∼2.7 nm (19, 20). This short distance relative to the interparticle distance means that the electrostatic energy of the crystals is well approximated by accounting only for the interactions between nearest oppositely and like-charged NPs.

With this simplification, crystal energies (per NP) of structures, in which each NP has n oppositely and m like-charged neighbors [e.g., n = 4, m = 12 for diamond; 6 and 12 for NaCl; 8 and 6 for CsCl (21)], can be written as a sum of favorable, nEop, and unfavorable, mElike(d), contributions. Here, Eop and Elike denote, respectively, the energy of two oppositely charged NPs brought into contact, and two nearest like-charged NPs. The value of Elike depends on the separation, d(m), between the surfaces of like-charged NPs. If d > 2κ–1, the electrostatic interaction is screened and Elike ≈ 0; for smaller separations, Elike increases rapidly with decreasing d (20, 22). In particular, for diamond structure (Fig. 4A, left), 2κ–1dd = 5.3 nm, and only Eop contributes effectively to the crystal energy, which is thus favorable (i.e., negative). In contrast, for NaCl and CsCl lattices (Fig. 5A, right), the values of d(m) are considerably smaller (3.5 and 1.3 nm, respectively), and the like-charge repulsions offset the energetic gain compared to that of the diamond lattice (2Eop for NaCl and 4Eop for CsCl). Overall, the diamond structure has the lowest energy.

Fig. 5.

(A) Qualitative schemes of NP arrangements and counterion “atmospheres” in lattice structures considered [more realistic drawings of the lattices and the discussion of the m and n values defined in the main text can be found in (20)]. For diamond, the separation between the like-charged particles, d, is larger than the sum of screening lengths, Embedded Image, and the energy of repulsive electrostatic interactions is negligible. For NaCl and CsCl lattices Embedded Image, and the repulsions between like-charged NPs offset the energetic gain of oppositely charged interactions. (B) Effect of NP polydispersity on the quality of crystals. Graphs (i) to (iii) give normalized size distributions of the metallic cores of oppositely charged NPs used in crystallization experiments; typical outcomes of these experiments are illustrated by SEM or TEM images shown in the bottom row (scale bars correspond to 200 nm). In all cases, experimental conditions were the same, and crystallization was attempted at least five times. (i) Cocrystallization of similarly sized AuTMA and AuMUA gave mostly amorphous aggregates. Sparse, poor-quality crystals (100 to 800 nm) were observed in only one out of five experiments. (ii) Crystals grown from narrowly distributed AuMUA (σ = 20%) and polydisperse AgTMA (σ = 45%, bimodal distribution with a large fraction of smaller particles of sizes 1 to 3 nm) were large (up to 3 μm) and regularly shaped. (iii) Broadly distributed AuMUAs (σ = 30%) and AgTMAs (σ = 45%) did not aggregate or crystallize at all. (C) Effect of small particles on the stability of the dispersed, large NPs. In the absence of small particles (phase “1”), large NPs of opposite charges interact by relatively strong electrostatic forces, and the dispersed phase has a high chemical potential, μ1. In this case, the NPs instantly flocculate to form amorphous aggregates (A). If small NPs of one type are present (phase “2”), they surround large NPs of the opposite charge and effectively screen electrostatic interactions between them. Phase “2” is characterized by a chemical potential, μ2, much lower than that of phase “1”—as a result, large NPs nucleate and aggregate into ordered crystal structures. If small NPs of both types are present in the suspension (phase “3”), all large NPs are screened and interact very weakly. Thus, phase “3” has chemical potential lower than phases A and C, and NPs remain stable in solution.

We emphasize that this effect does not scale with the size of the assembling objects. For example, with larger particles such as those recently described in (9) and (23), the characteristic separation distance between like-charged particles is much larger than the screening length, and close-packed lattices are favored. We also note that theoretical models without screening but accounting for either entropic effects (24) and/or van der Waals interactions (2528) cannot justify the formation of a diamond lattice.

Progress of the crystallization process depends on the degree of monodispersity of the nanoparticles used. Surprisingly, polydispersity skewed toward smaller particles facilitated crystallization and gave rise to crystals of better quality. To understand this effect, we performed a series of experiments under identical experimental conditions (solvent and temperature) but with NPs characterized by various size distributions (Fig. 5B). When Au particles taken from the same, narrow distribution (σ = 20%) but functionalized with either MUA or TMA were cocrystallized, the quality of crystals was poor, and a large proportion of NPs formed amorphous aggregates (Fig. 5B, left). In contrast, when one of the distributions was broader (e.g., AgTMA with σ = 45%) than the other (as with the AuMUAs that we used in the model system; σ = 20%), large numbers of high-quality crystals were obtained (Fig. 5B, middle). Finally, when both distributions were broad (e.g., AgTMA with σ = 45% and AuMUA with σ = 30%), particles stayed in solution and did not crystallize at all (Fig. 5B, right). That is, some polydispersity—but not too much—aided crystallization.

These observations can be explained qualitatively on the basis of screening of electrostatic forces acting between large NPs by smaller particles present in solution. The electrostatic interaction between two large NPs can be approximated by a screened potential (29), in which the effective screening length decreases with increasing concentration of screening charge carriers (here, small NPs) and determines the stability of dispersed nanoparticles. When large NPs are surrounded by smaller, oppositely charged ones, the effective screening length is small, and the NPs interact weakly and do not aggregate (30, 31). In contrast, when no small particles are present, the screening length is large, long-range attractive electrostatic forces are strong, and flocculation (32) ensues.

Thermodynamically, the presence of small NPs shifts the equilibria between dispersed (D), amorphous-aggregate (A), and crystalline (C) phases (Fig. 5C). In the absence of small particles, the chemical potential of the dispersed phase, μ1, is—due to the electrostatic interactions—very high compared to both μA and μC. In this case, the NPs either condense via flocculation or nucleate to the crystalline phase. Because the nucleation processes are less likely to occur, the condensed phase consists mostly of amorphous aggregates. Addition of small particles weakens the electrostatic interactions substantially and lowers the potential of the dispersed phase to μ2, which is only slightly higher than the potentials of condensed phases A and C. Here, the effective attractive forces are sufficient to overcome the energetic barrier accompanying aggregation, but are weak enough to allow the aggregates to anneal into low-energy crystals (9, 33). The formation of the crystalline phase occurs via the nucleation/aggregation processes (34), in which a stable nucleus is formed if its radius, R, is large enough and if the gain in the bulk energy, ΔEbulk ∝ Δμ2CR3, dominates over the surface energy ΔEsurf ∝ σR2, where Δμ2C and σ denote, respectively, the difference in chemical potentials and the surface energy between dispersed and crystalline phases. The critical size, Rcrit, of the nucleus that remains in suspension and serves as a seed for further crystallization is determined by the condition that the sum ΔEbulk + ΔEsurf—inversely proportional |Δμ|—reaches its maximum value (34). Because |Δμ|2C « |Δμ|1C, crystals obtained from suspension “2” were much larger than those formed from phase “1.” Finally, if large numbers of small particles of both types are present, the chemical potential of the dispersed phase is lower than both μA and μC, and no aggregation or crystallization is observed.

Several comments are in order. We emphasize that the experimental trends cannot be explained by entropic “depletion” forces (35). In such cases, the presence of small particles would destabilize the free-floating, large particles and would lead to phase separation. The electrostatic stabilization of large NPs by small ones is analogous to the Debye screening affected by high–ionic strength solutions (36, 37); in this respect, small, charged nanoparticles behave like ions. However, if the sizes and charges of the crystallizing particles were increased, one would need proportionally more small particles to provide efficient electrostatic stabilization (30). We have seen this effect in collections of 6- and 12-nm NPs that we tried to cocrystallize, where the particles kept in solution could not be stabilized even by broad distributions of small NPs. Although the screening can, in principle, be modulated by increasing the ionic strength of the crystallization medium by adding salts, these salts stabilize isolated particles and also crystallize themselves—as we verified experimentally, both of these effects hinder the formation of NP crystals.

Finally, from a practical standpoint, extension of the ESA approach to other types and combinations of NPs (e.g., magnetic or photoluminescent) may open new avenues to nanostructured materials of composite properties deriving from the unique properties of the diamond lattice (38).

Supporting Online Material

www.sciencemag.org/cgi/content/full/1125124/DC1

Materials and Methods

Figs. S1 and S2

References and Notes

References and Notes

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