J. Phys. Chem. C 2007, 111, 9019-9038
9019
FEATURE ARTICLE Control of the Size and Shape of Inorganic Nanocrystals at Various Scales from Nano to Macrodomains M. P. Pileni Laboratoire LM2N, UniVersite´ Pierre et Marie Curie (Paris VI), BP 52, 4 Place Jussieu, F - 75231 Paris Cedex 05, France ReceiVed: January 25, 2007; In Final Form: March 5, 2007
In this paper, we propose the hypothesis that, in highly pure media, the cluster shape can be retained at various scales. Impurities and/or the additives can control the shape of the developing crystals by adsorption on selective sites. We demonstrate that the shape of clusters is retained at the nanoscale. This is supported by structural studies and both experiment and simulated optical properties of nanocrystal assemblies. We compare the data to those obtained by using a large variety of techniques and observation of crystal growth in nature.
I. Introduction In the past few years, a very large number of reviews concerning growth mechanisms of nanocrystals have been proposed. Most of these reviews were devoted either to clusters grown in vacuum1-5 or specific growth in solution.6-16 Each of these disciplines has brought their own explanations and terminologies. Very few bridges have been proposed between these two approaches with the notable exception of a report on metallic nanocrystals.5a Even though the various mechanisms proposed are encouraging, controllable nanocrystallization is still in its infancy and several important issues remain unresolved. We have proposed the hypothesis that, in highly pure media (i.e., there are no impurities detectable with available analytical techniques), the shape of the clusters of incipient nanocrystals can be retained as they grow to mesoscopic and even macroscopic scales. However, the presence of impurities and/or the deliberate addition of appropriate molecules, free surfactant molecules and/or polymers, ions, even in nanomolar concentration, can control the shape of the developing crystals by adsorption on selective sites. There are many far reaching consequences of this hypothesis. First, it can rationalize the notorious lack of reproducibility of the sizes, size distributions, shapes, and shape distributions of in situ grown nanocrystals. Second, it provides a better understanding of crystal growth from their clusters to bulk materials. Third, it opens the door to theoretical modeling and meaningful experimental verification of size and shape-selected crystal growth. At the atomic level, Kepler described in 1611 the arrangement of hard spheres packed in a face-centered cubic (fcc) arrangement, having the maximum density.17 The densest possible packing of four spheres was a tetrahedron. At the earliest stages of growth of a solid,15 the atoms reorganized into a completely new structure each time an atom was added when a cluster was very small. This cannot go on indefinitely and a preferred symmetry became frozen into the cluster. Further growth took place by adding layers of atoms to this frozen core. Layered growth imposed certain restrictions on the outer symmetry or
morphology of the clusters and explained the magic numbers for a given shape. This was demonstrated for clusters having large binding energies and resisting to the evaporation of atoms. Many symmetric clusters can be constructed from the close packing of hard spheres. For fcc materials,1 the clusters, considered as compact packing of spheres, were cubooctahedra (Figure 1A), decahedra (Figure 1B), and icosahedra (Figure 1C). The surface of a cubooctahedral cluster consisted of 8(111) planes and 6(100) planes with closed atomic shells and represents the most stable form. The defined number of atoms resulted exclusively from the geometric arrangements and cannot be explained by the electronic shell model. The decahedra (Figure 1B) and icosahedra (Figure 1C) were structures with 5-fold symmetry and are called multiple-twinned particles (MTP). In fact, decahedral clusters consisted of five deformed tetrahedral subunits twinned by their {111} planes whereas icosahedral clusters originated from the twinning of 20, (111) faces, deformed tetrahedral subunits. It will be shown that similar shapes are obtained by various methods (see below). The shape of the primary clusters determined the shape of the incipient crystals, specifically: (i) The elongated particles resulted from additional intermediate (110) planes in a regular decahedral cluster with a preferential growth of the {111} facets compared to the growth of {100} facets (Figure 2A) and were attributed to truncated large decahedra with 5-fold symmetry.18 In other words, their formation was induced by the truncation of the 5 subunit edges of the decahedral nuclei. (ii) Nanocubes (Figure 2B) corresponded to cuboctahedral precursors with the specific growth of {111} facets compared to the {100} facets.19-21 (iii) Triangular nanocrystals were, in fact, nanodisks and nanoprisms. Their precursor clusters must contain a unique 3-fold axis, which was expressed in the final shape of the nanocrystal. Only the tetrahedral cluster can be modified simply to give a trigonal lamellar particle. Two regular fcc tetrahedral clusters were truncated on a {111} surface and were stuck together leading to a bitetrahedral cluster with three active sites
10.1021/jp070646e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/07/2007
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Marie-Paule Pileni is a Distinguished Professor and Director of the Mesoscopic and Nanometric Materials Laboratory at the Universite´ Pierre et Marie Curie and chair of Institut Universitaire de France. She studied the development of structure-reactivity relationships in organized molecular systems and, about the physical properties of these new materials, developed the self-organization of the nanocrystals in compact hexagonal networks (2D) and face-centered cubic structures (3D) at the mesoscopic scale. In 1999, she demonstrated the specific collective properties of these assemblies. In addition, she proved the existence of collective intrinsic properties (optical, mechanical, crystal growth) to these assemblies. Between 1999 and 2005, she received the Langmuir award of the American Chemical Society, the lecture award of the Japanese Chemical Society, the Research Award of the Alexander von Humboldt Foundation in Germany and Descartes-Huygens Prize of the Royal Netherlands Academy of Arts and Science, and the Emilia Valeri award from the French Academy of Science. In addition, she was the French citation laureate, the Institute of Scientific Information Award for most-quoted French scientist between 1981 and 1998. She is a member of the Royal Swedish Academy of Engineering Sciences, chair of a scientific committee of the engineering and material sciences division of the European Academy of Science and has a doctorate honoris causa from Chalmers University, Go¨teborg, Sweden. She is a Chevalier dans l’Ordre National de la Le´gion d’Honneur and Officier dans l’Ordre National du Me´rite.
for accelerated growth, maintaining the overall 3-fold symmetry in the final nanocrystal (Figure 2C).16,22-25 Numerous theoretical and computational studies have been performed to calculate the characteristic shape of objects at equilibrium over a range of sizes from a few atoms (clusters) up to 3 nm (nanocrystals).26 The most widely used classical model for shape control of crystals is given by the GibbsCurie-Wulff theorem.27 In the Wulff construction,19 each facet of the crystal was described by its free surface and interfacial energies and the crystal shape results from minimizing these energies for a certain volume. However, the model was valid only at thermal equilibrium, and the resulting shape is therefore the equilibrium shape of the crystal. A proposed pseudo “Wulff construction”28 was based on the fact that the driving factor was not the equilibrium surface but rather the growth rate of each facet as determined by the kinetics. The normal distance from the crystal facets to the center of the crystal was then proportional to the corresponding growth velocity rather than the surface and interfacial energies. This pseudo Wulff construction was far from thermal equilibrium, and the crystal shape was determined by growth kinetics and is not necessarily characterized by the process of minimizing the surface and interfacial energies. Hence, the nucleation stage for the growth of anisotropic shapes play a key role in determining the size/ shape of the resulting nanocrystals. Thermodynamically, all the nanocrystals will grow toward the shape with the lowest energy at equilibrium, which is governed by classical theory. However, the formation dynamics can affect the shape of the resulting
Pileni nanocrystals. In fact, the formation of nanocrystals is found to be a highly kinetics-driven process.28 Most researchers agreed that the nucleation step was the first in producing nanocrystals. Several techniques have been developed in the last two decades to produce nanocrystals with well-defined sizes and shapes. For any technique, a supersaturation regime was needed to produce highly crystalline nanoparticles. The oldest technique used was chemical vapor deposition (CVD),3 which has made a very large contribution to our understanding of cluster formation and crystal growth. Even in the supersaturation regime, it was rather difficult to eliminate perturbations of the cluster surface. When conditions were favorable, it was possible to maintain the shape of the cluster. However, the size range of the obtained nanomaterial changes from one experiment to another.1-4,29-31 On increasing the number of atoms produced, truncated decahedra with a rather small size were the most stable clusters.4 From this it was concluded that CVD can produce clusters in the range of a few nanometers with the same shape as clusters. However, the clusters’ size and shape distribution were still controversial. This is mainly because the major characterization techniques are difficult to perform on the small amounts of crystals produced. Soft chemistry was carried out at room temperature in solution in the presence or absence of various organic molecules, polymers, and/or surfactants. This was now the most widely used technique because it can be scaled to industrial applications.6-15,31-35 Specific adsorptions of polymers,14 surfactants,8,9 molecules,31,32 and ions32-35 on facets of clusters lead to the formation of nanocrystals with distinct shapes such as cubes, polyhedra, nanodisks, rods, prisms, plates, and spherical nanocrystals. Deliberate addition of appropriate molecules, ions, or impurities can result in their selective adsorption on cluster facets, which in turn leads to the growth of differently shaped crystals. In other words, the shape of the incipient larger crystals can be controlled by using soft chemistry. An important benefit of investigating the formation of noble metal nanocrystals was that a wealth of information can be obtained from monitoring their optical behavior during synthesis and growth. Noble metals (gold, silver, and copper, for example) exhibited characteristic surface plasmon resonance peaks that originated in the collective oscillation of the conduction electron cloud relative to the ionic background. Significantly, surface plasmon absorption (and scattering) was highly sensitive to the size and shape (truncation and aspect ratio) of the nanocrystals.36-44,122 This has been well demonstrated via simulations,36-38,42 typically by discrete dipolar approximation (DDA). The combination of structural and optical properties permitted the unambiguous identification of the shapes of nanocrystals even when other techniques indicate the presence of only spheres. In this review, we concentrate on nanocrystallization in colloidal dispersion where reactants are either freely diffuse or confined in a microenvironment. We demonstrate that, the shape of clusters is retained at the nanoscale. This is supported by structural studies and both experiment and simulated optical properties of nanocrystal assemblies. We compare the data to those obtained by using a large variety of techniques as soft chemical reaction, thermal processes in solution, CVD, arc evaporation and observation of crystal growth in nature. Because the cluster shapes are retained at various scales, we conclude that the crystal growth mechanism could be, in some cases, the same from atomic level to mesoscopic scale. Via colloidal syntheses and other techniques described in literature, we demon-
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Figure 1. Various shapes of clusters: cuboctahedronal (A), decahedral (B) and icosahedronal (C). Silver nanocrystal made in reverse micelles at fixed water content (w ) 5) and R (2.4) value with cubooctahedral (D), decahedral (E), and icasohedral (F) shapes. Copper nanocrystals made in reverse micelles with an increase in the size with the water content (from G to K): having cubooctahedral (G,I,L), decahedral (H,J,M) and icasohedral (K) shapes respectively. Copper clusters made by metal vapor deposition12 such as cobooctahedra (0), decahedra (P), and icosohedra (Q).
Figure 2. Schematic of the growth mechanism from clusters to a given shape of nanocrystals (A) truncated decahedral nanocrystals, (B) cubic nanocrystals, and (C) nanodisks.
strate that the addition of small amounts of entities can drastically change the nanocrystal shape. This paper is organized as follows. First, we describe the numerical optical simulation by DDA highly developed by G. Schatz and co-workers36-38,88,90 and the structural characteristics of micelles. Then, we demonstrate that the cluster shapes can be retained at the nanoscale when the colloids are highly pure
and/or specific conditions prevail, whereas additions of reactants, ions, and surfactant molecules markedly influence the shape of the produced nanocrystals. To support such changes in shapes, data obtained via colloidal solution are compared to those obtained in literature by using other diverse techniques such as CVD, arc evaporation, soft chemistry, and nature. We provide a critical analysis of the available data, presented in tabular form,
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Pileni The development of efficient algorithms and the availability of inexpensive computing power together made DDA the method of choice for many scattering problems. For a finite array of point dipoles, the scattering problem may be resolved exactly, so the only approximation in the DDA is the replacement of the continuum target by an array of N-point dipoles. Hence, in DDA method the object studied is represented as a simple cubic lattice of N-polarizable point dipoles localized at ri, i ) 1,2,...N, each one characterized by a polarizability Ri. As already mentioned, there was no restriction on the localization of simple cubic lattice sites so that the DDA represents a particle of arbitrary shape and composition. The dipoles interact with one another via their electric fields. The object was excited by a monochromatic incident plane wave Einc(r,t) ) E0eik.r-iwt, where r, t, w, k ) w/c ) 2π/λ, c, λ were the position vector, the time, the angular frequency, the wavevector, the speed of light, and the wavelength of the incident light, respectively. Each dipole of the system was subjected to an electric field consisting of two main contributions: the incident radiation field Einc,i and the field radiated by all other induced dipoles Edip,i. The local field at each dipole was then given by eq 1
Ei,loc ) Einc,i + Edip,i ) E0eik.ri -
Aij.Pj ∑ i*j
(1)
Pi is the dipole moment of the ith element and Aij with i*j is an interaction matrix with 3 × 3 matrixes as elements described by eq 2
Aij‚Pj )
Figure 3. Surfactant shapes and various self-assemblies in colloidal solution. (A) Shape of surfactant forming water-in-oil colloids; (B) reverse micelles; (C) interconnected cylinders; (D) planar lamellar phase; and (E) supra aggregate.
discuss similar growth rates of the various crystal facets and shape control and compare these properties to crystals grown in nature. We end the paper by describing our ideas of future directions in this area and the problems to overcome to realize the full potential of size and shape-controlled crystallization from nano to macro domains. II. Methods Used To Explore the Change in the Shape of Noble Metal Nanocrystals Two approaches are needed to point out such changes. The first one is numerical optical simulation predicting the change in the optical properties of noble nanocrystals with shape. The second approach is one of the ways to produce nanocrystals. II.1. Numeric Optical Simulations of the Surface Plasmon Calculations of Noble Metals: DDA. Geometry of nanocrystals was a key parameter in understanding the optical properties of noble metal nanocrystals. From our knowledge, the most flexible and powerful technique to compute scatter and absorption of surface plasmon resonance is the DDA method. In fact, the Maxwell’s equations were known only for special geometries as spheres, spheroids, or infinite cylinders, so approximate method as DDA was in general required. Nature provides inspiration for the DDA: the dielectric properties of a substance could be directly related to the polarizabilities of the individual atoms of which it was composed, with particularly simple and exact relationship when the atoms are located on cubic lattice.
{
(1 - ikrij) 2 eikrij 2 k rij × (rij × Pj) + [rij Pj - 3rij(rij‚Pj)] 3 rij rij2
}
(2)
Once we have solved the 3N-coupled complex linear equations given by eq 3 and have determined each dipole moment Pi, we can find the absorption cross sections for a defined target in terms of the dipole moments as in eq 4 where * signifies a complex conjugate.
Pi ) Ri‚Ei,loc
(3)
Note that the metal dielectric constant and that of the surroundings entered into the calculation through a factor []i/ []0, containing the polarizabilities Ri, as shown in ref 47. In our calculation, the wavevector k should be multiplied by ([]0)1/2 because particles were studied in a dilute solution with a refractive index assumed to be around 1.39. The explicit formula for Ri was developed by Draine and Goodman45
Cabs )
4πk |E0|
N
∑ 2 i)1
{
| |}
2 Im[Pi‚(Ri-1) * Pi* ] - k3 Pi 3
2
(4)
where Cabs is the absorption cross section. To solve the complex linear equations in DDA, we used the code adapted by Draine and Flatau.46,47 In actual practice, there were significant advantages associated with performing the sum over dipole fields in eq 1 using fast Fourier transform methods,48 and in substituting eqs 1 and 2 in 3, we obtained a relation in the form A′‚P ) E that we solved with the complex conjugate gradient techniques. A′ (interactions between the overall the dipoles) is a 3N × 3N matrix constructed from A (interaction between two dipoles) and for a system with a total of N elements, and E and P were 3N-dimensional vectors. One of
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TABLE 1: Syntheses of Nanocrystals Retaining the Shape of Nuclei in Various Experimental Conditionsa material
synthesis process
media
Ag
reduction of Ag(AOT) by hydrazine 2< w < 40
reverse mixed micelles Ag(AOT): Na(AOT) R ) 2.4
Ag
inert gas gas phase aggregation source
Cu
reduction mixed Cu(AOT)2 reverse by micelles hydrazine Cu(AOT)2: Na(AOT) 2 < w < 15 R)3 Cu inert gas gas phase aggregation source diamond CH4/H2 CVD Si-substrate
purity of the media
cuboctahedral, Ag(AOT) decahedral (no cosahedral impurities detected) N2H4 >99.% NaAOT: 99% particles cuboctahedral deposited icosahedral on carbon truncated decahedral Cu(AOT)2 decahedral cuboctahedral (no icosahedral impurities truncated detected decahedraland N2H4: 99.9% fcc nanodisks icasohedral cubooctahedral
Au
Au-Ag alloys on AgCl pellets
hydrothermal technique at 300 °C
s > 3.8 nm
transition from 3 icosahedra to fcc clusters change 28 in morphology with the growth conditions (see Table3)
15-20 m
50 m < s < 60 m
1.5 nm < s < 2 nm
icosahedral
s ) 220-40 nm
hexagonal
50 nm
large variety of various shapes 5 m < s < 10 m
icosahedral B60: icasohedral
comments
cuboctahedral, decahedral
cuboctahedral multiple (T ) 800 °C, twinned CH4/H2) 0.9%) particles Icosahedral (T ) 700 °C, CH4/H2) 1%) decahedral (T ) 1025 °C, CH4/H2) 0.6%) decahedral decahedral prismatic grain pseudo-hexagon elongated decahedral selected with other decahedral not identified particles quasi-spheroid particles with polyhedral structures plate-like structures hexagonal decahedral triangular
largest crystals aintaining the shape
icasohedral no other morphologies
20 nm < s < 20 m
very few icosahedra
all the crystals formed are characterized by 5-fold symmetry the larger particles are truncated decahedra
60
77
70
78
80% of hexahedral particles Mars has both water and carbon dioxide ice
86 83
79 size depends on the ressure and on temperature icasohedron is a forbidden morphology
80,81
a Note R ) [N2H4]/[Ag(AOT] or R ) [N2H4]/[Cu(AOT)2], w ) [H2O]/[AOT], TOAB is tetraoctylammonium bromide, PVP is polyvinylpyrrolidone, and CVD is chemical vapor deposition.
the advantages of this technique was that it allowed a certain arbitrariness in the construction of the array of dipole points that represented the studied target in a given geometry. For example, the geometry of the grid where dipoles have to be located was usually chosen to be cubic but it was not uniquely determined. Obviously, the gridding associated with the DDA calculation created distortion of the particle surfaces but, except for the layer closest to the surface, the fields were smooth and well-converged. In a recent publication,49 the question of the number of dipoles needed to mimic the continuum macroscopic particle (to approach a regular particle) with an array of discrete dipoles is treated. The answer seemed to be not straightforward, because the convergence of physical quantities was related to
the number of dipoles.49 Typically, cross sections calculated with the DDA were accurate to a few percent if N g 104 dipoles are used. As has been presented previously, we have a matrix of (3N)2 complex elements that would require a large amount of computational effort. The advantage of the DDA approach, compared to other theoretical approaches50-53 was that each parameter (size, shape, etc.) was determined independently of the others. II.2. Chemical Method. A large variety of chemical methods were developed over this past decade. Because a substantial part of our work has relied on reverse micelles as media for the generation of size and shape-controlled nanoparticles, we present here a brief description of self-associating surfactants. Surfac-
9024 J. Phys. Chem. C, Vol. 111, No. 26, 2007
Pileni
Figure 5. Simulated absorption spectra of copper nanocrystals differing by their shapes 3 nm cuboctahedron (A), 3 nm decahedron (B), 23 nm flat nanodisks (C), and 1.5 nm (red), 3 nm (green), 5 nm (blue), and 6 nm (black), ellipsoidal particles with an aspect ratio of 2 (D).
Figure 4. (A) Electron microscopy patterns of copper metallic particles synthesized in Cu(AOT)2/NaAOT, water, and isooctane reverse micelles at various water contents. [AOT] ) 0.1 M; [Cu(AOT)2] ) 10-2 M. w ) 5, R ) 3. (B) Change in the absorption spectrum with time (from 30 to 300 min) at w ) 5; R ) 3.
tants are molecules with a polar hydrophilic head (attracted by water) and a hydrophobic hydrocarbon chain (attracted by oil). If we dissolved a surfactant in water or in an apolar solvent, the chains tended to self-associate to form various aggregates.54 The shape of the surfactant played an important role in forming the assembly. If 10-3 to 10-1 M of surfactant with the shape of a champagne cork (small polar head and branched hydrocarbon chains, Figure 3A) was dissolved in an apolar solvent, spherical water-in-oil droplets called reverse micelles55 were formed (Figure 3B). The water droplets were displaced randomly, subjected to Brownian motion, and exchange between neighboring reverse micelles took place on the microsecond time-scale. The size of the reverse micelles increased linearly with the amount of water added to the system, typically from a diameter of 4 to 18 nm with no free surfactant present in the apolar solvent. Whatever surfactant was used, it remained at the oilwater interface. However, some differences were observed with mono and divalent surfactants when there was a large amount of water present. With monovalent surfactants, when the total surface area of the surfactant head polar group was too small to cover the hydrophilic molecules, the system collapsed, the solution turned turbid, and surfactant molecules freely diffused in the solution. When two molecules were strongly bound via a divalent metal counterion, known as a functionalized surfactant, by increasing the water content the system adapted to keep the surfactant molecules at the interface. Reverse micelles at surfactant concentration higher than 10-1 M turned into interconnected water channels (Figure 3C). The space was
Figure 6. DDA simulation of the optical properties of spherical particles differing by their diameter, D. (a) D ) 1.5 nm; (b) D ) 3 nm; (c) D ) 6 nm; (D) D ) 12 nm.
divided into two volumes and regularly overlapped so that at any point the surface had the shape of a saddle. These were designated interconnected cylinders and were doubly continuous structures both in water and oil.56,57 Note that the solution was optically clear. Adding more water induced a new phase transition. The system became opalescent and birefringent (the light was not extinguished between two crossed polarizers). At much higher surfactant concentrations, a lamellar phase was formed that upon deposition on a solid substrate produces a planar film (Figure 3D). Alternatively, surfactant-oil-water systems can form a stable emulsion.58 This was a supra aggregate, which contained interconnected cylinders in its external and internal phases. In fact, there was a lamellar phase (the surfactants self-organize like lamella) that was no longer planar but had an onion (or spherulite) shape (Figure 3E). Formation of these structures was explained by geometrical factors related to the shape of the surfactant.58 The different colloidal self-assemblies formed in the three component sodium 2-bis(2-ethylhexyl) sulfosuccinate, Aerosol-OT or Na(AOT) surfactant-water-apolar solvent, system have been well characterized and were, therefore, extensively employed as templates for the syntheses of nanocrystals.6,10,11
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Figure 7. Various materials with different shapes and produced via various techniques. (A), (B), and (C) diamond materials having various shapes such as cubooctahedral (A), decahedral (B), and icasohedral (C) (see ref 28). (D) and (F): Cubooctahedra of CO2 particles produced on Mars (see ref 83) and in nature (see ref 78). (F) and (G) Decahedral particles: gold (see ref 77) and cassiterite (see ref 84). (H-J) icosohedral particles: gold (see ref 78), B4C (see ref 79) and B6O (see refs 80,81).
Figure 8. Schematic representation of the nanodisk geometry simulated with the following three parameters: size (S), snip (TR), and aspect ratio (AR). (A) Top and side view. Schematic representation of the resonance plasmon modes involved in the nanodisks. The dipolar in-plane mode and the dipolar out-of-plane mode are represented on (B) and (C), respectively. The corresponding quadrupolar modes are represented on (D) and (E), respectively.
III. Regular Growth In this section, we describe the formation of differently sized nanocrystals in reverse micelles and under various experimental conditions in which the shape of clusters was retained. III.1. Silver Nanocrystals Made in Reverse Micelles And by Using Ultrahigh Vacuum Inert Gas Evaporation Techniques. The syntheses described below were carried out in mixed reverse micelles formed from an appropriate mixture of Na(AOT) and X(AOT) where X was a reactant counterion (Ag, for example). Typically, hydrazine was used as reducing agent. Two parameters, w (the ratio of water to total surfactant concentration) and R (the ratio of hydrazine to functionalized
surfactant59 concentration), were varied. Silver nanocrystals with 5 nm average diameter were produced from reverse micelles (R ) 2.4, w ) 2), see Table 1. At the end of the synthesis the nanocrystals were coated with dodecanthiol and extracted from the micelles.59 Dodecanthiol formed a well-packed self-assembled monolayer on the surface of the silver nanoparticles, attached by covalent S-Ag bonds.7 The electron diffraction pattern revealed the characteristic distances of an fcc structure. Bright spots, corresponding to various orientations of the nanocrystals, appeared inside the concentric rings showing that the nanoparticles have good crystallinity. The cluster shapes were retained as MTP decahedral nanocrystals viewed along
9026 J. Phys. Chem. C, Vol. 111, No. 26, 2007 the 5-fold axis (Figure 1E), icosahedron viewed along the 3-fold axis (Figure 1F), and cuboctahedron with an fcc structure in the110 orientation (Figure 1D). From this structural investigation, the Ag nanoparticles appeared to be highly crystallized. However, the crystal structure of the silver nanoparticles did not correspond to that of the bulk solid. The shapes of the various clusters (icosahedra, decahedra, and cubooctahedra) were retained. No transformation such as facet truncation or preferential growth of facets occurred during the growth process and exclusively spherical nanocrystals were produced.60 Similar shapes were produced by employing an inert gas aggregate source yielding bimodal distributions of silver clusters including icosahedra in the 1-2 nm size range and both cubooctahedra and icosahedra in the 4-8 nm range,61 (Table 1) whereas decahedra were not formed and were consequently considered to be unstable above 3 nm. This was attributed to the fact that 5-fold symmetry created internal stresses with increasing particle size. Hence, when using techniques highly diverse from each other, such as reverse micelles60 and inert gas evaporation,61 with different types of impurities present during the experiments, the resulting silver nanocrystal shape was similar to the that of the original fcc clusters at the atomic level (Table 1). III.2. Copper Nanocrystals Made in Reverse Micelles. Mainly spherical copper nanocrystals were obtained in mixed reverse micelles [Na(AOT) and Cu(AOT)2] at R ) 3 (Table 1 and Figure 4A).62 However, on closer analysis only 79% of the copper nanocrystals were found to be spheroids comprised of cubooctahedra (Figure 1G,I,L), decahedra (Figure 1H,J,M), icosahedra (Figure 1K) and some polycrystals.20,40,44 The 21% remaining were nanodisks (8%), truncated decahedra (10%) with an aspect ratio close to 2, and cubes (3%) with smooth edges. On increasing the water content, an increase in the size of the cubooctahedra (Figure 1G,I,L) and decahedra (Figure 1H,J,M) was observed whereas very few icosahedra (Figure 1K) were produced. Because reverse micelles are optically clear, it was possible to follow their optical properties during the nanocrystal growth.40,44 Very surprisingly, a plasmon resonance peak appeared around 640 nm, with a residual absorption above 700 nm, 30 min after the start of the copper ion reduction (Figure 4B). The 560 nm resonance band emerged about 1 h later. With time, the spectrum evolved and the 560 nm band became dominant compared to that at 640 nm. Finally, at the end of the synthesis, a well-defined peak at 560 nm characterized the absorption spectrum while a shoulder at around 640 nm remains. The DDA simulated absorption spectrum of (3 nm) cuboctahedra (Figure 5A) was similar to that obtained for spheres with a plasmon resonance centered at 560 nm (Figure 6). On increasing the particle size, the peak position remained unchanged whereas its intensity was increased, as expected from extended Mie theory.63-66 This was mainly related to the increase in the number of dipoles involved in the simulation and was in very good agreement with other simulated methods such as density functional theory-time-dependent local density approximation (DFT-TDLDA) calculations within a model including the absorption and screening properties of both the ionic core background and the surrounding matrix.67-69 The simulated absorption spectrum of (3 nm) decahedra was well defined with a peak centered at 625 nm (Figure 5B). The simulated absorption spectra of tetrahedral nanocrystals, a subunit of these multiple twinned particles, were characterized by an absorption centered at 650 nm and a shoulder at 700 nm. The simulated absorption spectrum of nanodisks was characterized by a peak centered at 650 nm (Figure 5C) whereas that of truncated decahedra optical
Pileni
Figure 9. (A) Simulated extinction spectra of nanodisks with following parameters: AR ) 4 and TR ) 0.33 for different sizes. S: 20 nm (solid line), 44 nm (- - -), 60 nm (---), 86 nm (•••), 128 nm (• • •), 148 nm (-•-•). (B) Simulated extinction spectra of nanodisks with parameters: S ) 105 nm and AR ) 4 for different snips TR ) 0 (solid line), 0.1(---), 0.2(•-•), 0.33(•••). (C) Simulated extinction spectra of nanodisks with parameters: S ) 105 nm and TR ) 0.33 for different aspect ratios AR ) 1.25 (s s), 2.4 (---), 3.33 (•••), 4 (-•-), 5 (- - -), 10 (solid line).
spectrum changed with the aspect ratio (Figure 5D). Hence, the optical properties of copper nanocrystals with the same shape as their clusters markedly differed from one to another.40 From a comparison of experiments and simulations of absorption spectra of particles with similar sizes, it was reasonable to conclude that the 640 nm resonance band observed a few minutes after the chemical reaction started was due to decahedra, nanodisks, and elongated nanocrystals40 and, of course, the 560 nm peak was due to the cubooctahedra and polycrystalline spherical nanoparticles. Because of the high sensitivity of the optical method, even though it was not observed experimentally, the tail of the absorption spectra observed in Figure 4B could be due to the presence of tetrahedral nanocrystals, either truncated or complete. This leads us to conclude that the shapes of copper nanocrystals made in reverse micelles are closely related to those of the corresponding clusters (Table 1). The regular growth of cubooctahedral and decahedral clusters allows the formation of spherical and regular decahedra nanocrystals with very few transformations such as facet truncation or preferential growth of facets occurring during the growth process. Therefore, oil-water interfaces, made of highly pure
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Figure 10. Change in the TEM images and in the optical properties on increasing the amount of hydrazine, R ) [N2H4]/[Cu2+] of copper nanocrystals. Conventional TEM pattern obtained at R ) 3 (A). HRTEM for spheres (B), trigonal prisms (C), and elongated particles (D). The corresponding absorption spectrum of the solution containing the particles with different sizes (E). Conventional TEM pattern obtained at R ) 15 (F). HRTEM for copper nanodisks viewed on [111] (G) and on [110] (H) directions, elongated particles (I) and spheres (J). The corresponding absorption spectrum of the solution containing the copper nanocrystals obtained at R ) 15 (K). Absorption spectra obtained with copper nanocrystals produced at various R values (R ) 3, 5, 10, 15) (L).
surfactant at fixed experimental conditions, produce nanoparticles with a high crystallinity retaining the shape of the clusters with formation of cubooctahedral, decahedral, and icosahedral nanocrystals. Furthermore, reverse micelles permit the controlling of the size of the nanocrystals with nonspherical cluster shapes that produce rather large decahedra (10-15 nm) that were formerly considered unstable above 3 nm.3,70,71 These results imply that the surfactant molecules used to make reverse micelles play a minor role in the relative growth rate of the crystal facets. The regular growth taking place in reverse micelles is probably because the surfactant molecules
stay at the oil-water interface and are not free in the reactive medium This postulate is supported by the Brust-Shiffrin method of producing gold nanocrystals72,73 where the nucleation and growth take place at the water-oil interface74,75 and the nanocrystals formed are extracted from the interface and isolated in the nonpolar phase. In such cases, as in reverse micelles, the nanocrystal growth is protected by the oilwater interface without selective adsorption of any compounds. In both cases, the water structure at the oil interface (bound water) is responsible for preventing any selective adsorption. The only difference between these two techniques
9028 J. Phys. Chem. C, Vol. 111, No. 26, 2007 is that the reverse micelles and optical properties can be recorded to follow the nanocrystal growth, whereas it is more difficult when the chemical reaction takes place at the interface. Furthermore, the size of the reverse micelles controls that of the nanocrystals because of the water structure inside the micelles.11 III.3. Regular Crystal Growth Obtained in Various Experimental Conditions. Cubooctahedral (Figure 1O), decahedral (Figure 1P), and icosahedral (Figure 1Q) copper clusters, as described above, were produced by ultrahigh vacuum techniques28,76 as well as in reverse micelles.20,40 Note that in the first case, the maximum size of the 5-fold symmetry cluster was found to be around 5 nm, whereas it was larger than 10 nm in the last one. By the CVD technique, isolated diamond crystals differing in shape were grown on Si substrates28 with formation of cubooctahedral (Figure 7A), decahedral (Figure 7B) and icosahedral (Figure 7C) crystals. In fact, the morphology of the crystals changed with the experimental conditions (substrate temperature and methane concentration) (Table 1). Hence, a change in the crystal growth conditions leaded to a change in the growth velocities of the various surfaces and therefore cause the crystal to alter its shape. Figure 7F shows the formation of large and unstable Au decahedral crystals77 by using thermal techniques. Very surprisingly, regular crystal growth was also observed in hydrothermal processes in solution,78 arc evaporation,79 CVD,28 as well as by performing chemical reactions under high pressure and temperature.80,81 In all these cases, a rather wide variety of crystals with icosahedral morphologies have been reported for gold (Figure 7H),78 diamond (Figure 7C)28 in the 1-100 nm size range, boron carbide (Figure 7F), B4C79 and boron sub-oxide crystals (Figure 7I), and B6O (Figure 7J),80,81 respectively. Furthermore, truncated icosahedral gold nanoparticles were also produced by biomass processes.82 III.4. Regular Crystal Growth in Nature. At this point one question arises: are these clusters shapes and derivatives found in nature? We have not been able to find a large number of crystals with the same shape as clusters. However, cubooctahedra were found on Mars as solid CO2 crystals (Figure 7D)83 and on the centimeter scale as fluorite crystals on earth (Figure 7E).84 Cassiterite (Figure 7G), characterized by a 5-fold symmetry with a re-entrant facet, has also been observed in nature.84 This was a significant deviation resulting from growth rate enhancement at re-entrant corners providing sites for faster crystal growth, and radicals in the grooves were much more resistant to etching than molecules attached to a planar crystal surface; also, they give rise to enhanced growth rates.85 This was also reported for the growth of flat diamond platelets.14 Similar re-entrant morphology was indicated by molecular dynamics growth simulations for 150-atom silver clusters (2 nm diameter) and was attributed to kinetic trapping during the growth of the decahedral structure.3 III.5. Discussion on Regular Growth Leading to the Retention of Cluster Shape at Various Scales. As described above, a large variety of techniques assist in the production of crystals, in various sizes, which have the same shape as their initially formed clusters. By using chemical techniques, various shapes were produced. Reverse micelles provided three different cluster shapes20,40,60 in the range of 2-10 nm, whereas thermal techniques in an aqueous solution in the presence of polymers gave access to rather large (220 nm) and unique geometrical shapes such as icosahedral gold nanocrystals (Figure 5H).75 In this case, the successful preparation of icosahedral Au
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Figure 11. Comparison of the simulated (full line) and experimental (dotted line) absorption spectra of an assembly of copper nanocrystals produced at R ) 3 (A), R ) 15 (B), and E: 10 (C).
nanocrystals exemplified the exquisite shape control that can be achieved through careful growth-rate regulation along different crystallographic directions. Similarly, 50 nm-hexagonal Au particles were formed using the Burst method at hightemperature (around 180 °C),86 whereas with traces of silver ions Au decahedral particles (2-3 nm) were formed70 (Table 1). Icosahedral B6O crystals (Figure 5J and inset) were formed by chemical reduction of B2O3 with B at high temperatures and pressures (Table 1). The authors indicate that the purity of reactants and the experimental conditions (1777 °C < T < 1880 °C, 5 < P (GPA) < 5.5) controlled the shape of the crystals.80,81 Rather small copper clusters were produced by inert gas aggregate sources in the range of a few nanometers (50%nanodisks 9% cubes Br- > NO3- > I- > ClO4- > SCNNa+ > K+ > Li+> Rb+ > Cs+ The sequence did not depend on the nature of the organic molecules. Figure 15H was obtained with ClO4- corresponding to the right of the series. Similar patterns were obtained with other salts (Figure 15). Note that phosphate ions controlled the form of the nanocrystals with the production of welldefined shapes (Figure 15D). This could be because the interaction of ions with a surface is not related to the size of the ions.99 From this it is concluded that only a particular anion plays a role in the nanocrystal growth with specific adsorption on facets. IV.3. Nanorods. Nanorods have been synthesized by a large number of groups using various methods.18,33,34,100-106 Structural studies showed that highly crystallized nanorods resulted from additional intermediate (110) planes in a regular decahedral cluster with a preferential growth of the {111} facets compared to the growth of {100} facets and was attributed to a truncated large decahedron with 5-fold symmetry.2,107 Studies reported concerning the optical properties of nanorods based on the classical electrostatic approach assumed that the nanorods behave as ellipsoidal particles.108,109 Absorption efficiency was simulated by using the DDA method and takes into account the real shape of the gold nanorods. The dominant surface
9034 J. Phys. Chem. C, Vol. 111, No. 26, 2007
Figure 16. (A) Simulated absorption spectra of nanorods with a width of 15 nm and different lengths: 25 nm (---), 40 nm (s), 50 nm (- -), 60 nm (s s), 75 nm (...), 100 nm (- - -). (B) Simulated absorption spectra of nanorods with a width of 7.5 nm and different lengths: 25 nm (---), 27 nm (- - -), 29 nm (- - -), 40 nm (...), 50 nm (s). (C) Position of the λmax (nm) versus the nanorod length. Simulation results using DDA for a width of 7.5 nm (squares), a width of 15 nm (triangles), a width of 10 nm from El-Sayed et al.101 (circles), and a width of 26 nm from Pe´rez-Juste et al.127 (diamonds).
plasmon band corresponded to the longitudinal resonance mode (LM). At fixed width, the resonance maximum of the LM mode, λmax, of gold nanorods41 was red-shifted on increasing the length (L) value (Figure 16A,B). Furthermore, the position of the LM resonance mode was red-shifted with decreasing nanorod width. Simulation demonstrated a linear dependence of the LM mode maximum with the aspect ratio as λmax ) 96‚AR + 418.41 The transverse and multipolar modes remained unchanged on keeping the width and the length of nanorods constant. The DDA simulations were in good agreement with others resulting from a model using Gans theory, which was an extension of Mie theory with a geometrical factor.109 This theory was first used for elongated particles by Lebedeva et al.,110 and the first experimental evidence supporting Gans theory was obtained by
Pileni Skillman et al.111 for silver ellipsoids embedded in gelatin. van der Zande et al.109 using Lebedeva calculations found linear behavior of the longitudinal mode (LM) resonance mode with AR similar to that described above with the same slope. Moreover, the extreme shift of the longitudinal resonances to longer wavelengths with increasing aspect ratio was clearly observed by Yu et al.121 and was exactly what the electrostatic theory approach108,112 predicted for a similar case of gold prolate nanospheroids. In this case, the trend predicted by classical electrostatic theory was very close to these simulation results. A linear relationship with the nanorod length was observed both in simulations and in experiments (Figure 16C). Taking into account all the experiments101,102,114 and the DDA simulation described above, Figure 17A shows clearly rather large discrepancies (around 100 nm) between the simulated and the experimental data. This was probably due to the high sensitivity of the LM with AR. Let us now consider the Murphy method for nanorod preparation.12 In this method, gold nanorods were prepared by reducing aqueous HAuCl4 solutions in the presence of a rather large amount of cetyltrimethylammonium bromide, CTAB, ascorbic acid, and silver ions (Table 3). The function of silver ions was not rationalized; it could mediate the redox processes.102 Under identical experimental conditions but in absence of CTAB, no nanorod formation was observed (Figure 17B). Increasing the CTAB concentration from 2 × 10-2 to 1.4 × 10-1 M produced better defined Au nanorods (going from Figure 17C to 17G). At a large CTAB concentration (Figure 17H), the nanocrystals self-organized themselves into supramolecular structures with some cubes remaining. However, a careful look at the TEM images clearly showed slight differences in the nanorod shapes. This was supported by optical properties that change with aspect ratio, truncature, and size.41 To demonstrate that these syntheses were not highly reproducible, several experiments were performed in the same experimental conditions. From the TEM images obtained after deposition, the average length, width, and aspect ratio remained in the same order of magnitude (Table 4). The corresponding absorption spectrum of the colloidal solutions shown on Figure 17H markedly differed: the position of the maximum of the absorption spectrum recorded at the end of the synthesis changed by 50 nm from one synthesis to another,113,114 and therefore the major absorption peak of these gold nanorods was due to the in-plane plasmon resonance mode that markedly varies with their length, width, and aspect ratios.41 IV.4. Discussion on the Effect of Specific Adsorption of Various Elements on Crystal Growth. We all agree that selective adsorption on specific facets favors a given shape. We thus have to assume that the so-called seeds,6-15 observed by TEM, are nanocrystals having the same shape as clusters. This agrees with the works of Kepler and Martin5,17 who produced seeds that are hard spheres packed in an fcc arrangement and form stable clusters. The influence of free entities in the reactive medium seems to be a key parameter. We will try to convince the reader of the validity of this claim. In reverse micelles, the copper nanodisk truncation is smooth, indicating regular growth, whereas silver nanodisks are characterized by various truncations and aspect ratios, which increase with the hydrazine concentration.31,32 The major difference between copper and silver nanodisks is related to the synthesis mode: copper nanodisks are synthesized in reverse micelles with no free entities in the reactive medium, whereas with silver nanodisks the required concentration of reducing agent is such that a phase transition takes place and free surfactant molecules appear. Selective
Feature Article adsorption of free surfactant favors various truncations when the surfactant freely moves in the reactive media whereas in reverse micelles the surfactant molecules are located at the water-oil interface. Similar examples can be given where salts such as chloride and bromide ions are added to water-in-oil colloidal solutions.33-35 Changes in the copper nanocrystal shape by adding a relatively low percentage of chloride ions (Table 3) is explained as follows: at low chloride concentrations, selective adsorption of chloride ions on {100} facets in a regular decahedral nucleus favors a preferential growth of the {111} facets compared to the growth of {100} facets (Figure 2A). At higher chloride ion concentrations, adsorption also takes place on {111} facets favoring an increase in the aspect ratio of nanorods and a decrease in their size. On replacing chloride ions with bromide ions (Table 4), the adsorption energies of the latter on {111} and {100} facets on decahedral nuclei are similar, favoring nanorods with a rather low aspect ratio (5). The large number of cubes is explained by selective adsorption on {100} facets of cubooctahedral nuclei favoring the specific growth of {110} facets. Table 4 shows that with a slight increase in the chloride and/or bromide concentration, the change in the percentage of spheres seems to be correlated with the nanodisk formation. This could be due, just like in the case of hydrazine, to a selective adsorption of chloride and/or bromide ions on {111} facets of tetrahedral subunits during the cluster’s formation, limiting the number of spherical nanocrystals. This is supported by the fact that the adsorption of ions markedly depends on the type of ions used.99 Hence Cl- and Br- ions mainly adsorb on {111} facets of tetrahedral clusters preventing the formation of other clusters at the first step of nucleation and favoring that of nanodisks and nanoprims. Gold nanorods are truncated decahedra particles12 implying a decahedron precursor. As is also mentioned, the CTAB surfactant plays a key role in the formation of gold nanorods and in controlling aspect ratios.12,102,113,114 This also explains why, for a given experimental condition with the same procedure, it is impossible to produce exactly the same absorption spectrum of a collection of nanorods (i.e., the same crystallographic structure of nanocrystals) (Figure 16 and Table 3). From the ongoing discussion, it is evident that excess of reactants and/or addition of salt, surfactant, and impurities favor specific adsorption and facets of nuclei leading to various shapes and/or defects at the edges. Perfectly truncated decahedra are quite impossible to produce in the bulk phase. However, in nature cassiterite grown in 5-fold symmetry with a large number of defects (Figure 18E) is found. Cubic crystals are very often observed in nature (from Figure 18H to Figure 18K). Cubic fluorite crystals are found and have different colors, which are attributed to impurities.116 Similarly, very few tetrahedral nanocrystals are produced, whereas tetrahedrite with a welldefined shape (Figure 18F) and its truncated form (Figure 18G), bentonite (Figure 18R) are found in nature.116 From Figure 18, it is clear that it is possible to produce, at various scales from nanometric to mesoscopic, structure truncated decahedra, cubes, and derivatives of tetrahedral crystals. The claim that the growth mechanism for crystals is probably the same at various scales is strongly supported by a number of observations: the presence in nature of cubooctahedra (Figure 7E), cubic fluorite (Figure 18H,I,J), decahedra (Figure 7G), and truncated decahedra (Figure 18E) of cassiterite; the formation of copper nanocrystals with the same shape as that of clusters from 2 to 10 nm (from Figure 1G to Figure 1M) and copper truncated decahedra from
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Figure 17. (A) Position of the λmax (nm) versus the aspect ratio of nanorods. Simulation results using DDA method (black circles) and the corresponding fit (straight line). Experimental data from work of El-Sayed et al.101 (circle) and from Pe´rez-Juste et al.102 (diamonds and squares). Experimental data from our study (crosses). (B-G): Influence of CTAC concentration on the gold nanorods growth produced in the following conditions as described in ref 25: [AuCl42-]/[Au] ) 200; [AA]/[AuCl42-] ) 2, [AuCl42-] ) 2.5 × 10-4 M, [Ag+] ) 5 × 10-5 M, and [CTAC] ) 0 M (B); 2.4 × 10-2 M (C); 4.8 × 10-2 M (D); 1.1 × 10-1 M (E); 1.2 × 10-1 M (F); 1.4 × 10-1 M (G). (H) Absorption spectra of gold nanocrystals produced after various synthesis in the same experimental conditions (and following refs 80, 81): [AuCl42-]/ [Au] ) 320; [AA]/[AuCl42-] ) 1.6; [AuCl42-] ) 4 × 10-4 M; [Ag+] ) 6 × 10-5 M; [CTAC] ) 9.5 × 10-2 M.
10 nm (Figure 18A) to 0.5 µm (Figure 18B) nanocrystals and the occurrence of several micrometer gold nanorods (Figure 18C) and also of diamonds (Figure 18D).
9036 J. Phys. Chem. C, Vol. 111, No. 26, 2007
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Figure 18. Shape of the various crystals at different scales. Truncated decahedra (A,B,C,D,E) obtained from: (A) copper nanocrystals synthesis in reverse micelles,20 (B) in interconnected cylinders in presence of 10-3 M of NaCl,33 (C) gold nanorods produced by soft chemistry,12 (D) diamonds produced by the CVD technique,28 and (E) cassiterite found in nature.116 Cubes (F,G,H,I,J,K) obtained from: (F) copper nanocrystals in reverse micelles,20 (G) in interconnected cylinders in presence of 10-3 M of NaBr,35 (H,I,J) are fluorite found in nature,116 and (K) garnet also in nature. Tetrahedra (L,M,N,O,P,Q) obtained from: (L) copper nanodisk made in reverse micelles,20 (M) silver nanodisks made from reverse micelles,31 (N) silver flat triangle produced from self-assembly of silver nanocrystals,120 (O) and (P) two different types of tetrahedrite observed in nature,116 and (Q) benitoite observed in nature.116
V. Conclusions, Perspectives and Prospectives Evidence has been provided in this paper for regular crystal growth and for retaining and, if desired, controlling the shape of the initially formed clusters in an appropriate medium. The technique employed seems to be crucial for size and shape control. For example, inert vapor deposition yields a preferential cluster shape over the nano range (
