Influence of Cracks on the Optical Properties of Silver Nanocrystals

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Influence of Cracks on the Optical Properties of Silver Nanocrystals Supracrystal Films Jingjing WEI, Claire Deeb, Jean-Luc Pelouard, and Marie-Paule Pileni ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b07435 • Publication Date (Web): 17 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018

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Influence of Cracks on the Optical Properties of Silver Nanocrystals Supracrystal Films Jingjing Wei1, Claire Deeb2, Jean-Luc Pelouard 2,*, Marie-Paule Pileni 3,*

1

Sorbonne University, Department of Chemistry, 4 Place Jussieu, 75005 Paris

2 MiNaO-Center

for Nanoscience and Nanotechnology C2N, CNRS, Université Paris-Sud,

Université Paris-Saclay, Boulevard Thomas Gobert, 91120, Palaiseau, France 3

CEA/IRAMIS, CEA Saclay, 91191, Gif-sur-Yvette, France

KEYWORDS: supracrystals, silver nanocrystal, localized surface plasmon resonance, cracks, optical properties

ACS Paragon Plus Environment

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ABSTRACT Physical properties of nanocrystals self-assembled into 3D superlattices called supracrystals are highly specific with unexpected behavior. The best example to support such claim was given, through STM/STS experiments at low temperature, of very thick supracrystals (around 1000 layers) where it was possible to image the surpracrystal surface and study their electronic properties. From previous studies, we know the optical properties of Ag nanocrystals selfassembled in hexagonal network (2D) or forming small 3D superlattices (from around 2 to 7 layers) are governed by dipolar interactions. Here, we challenge to study the optical properties of Ag supracrystals film characterized by large thicknesses (from around 27 to 180 Ag nanocrystals layers). In such experimental conditions, according to the classical Beer-Lambert law, the absorption of Ag films is expected to be very large and the film transmission is closed to zero. Very surprisingly, we observe reduced transmission intensity with an increase of the notch linewidth, in the 300-800 nm wavelength range, as the supracrystal film thickness increased. By calculating the transmission through the supracrystal films, we deduced that the films were dominated by the presence of cracks with wetting layers existing at their bottoms. This result was also confirmed by optical micrographs. The cracks widths increased with increasing the film thickness leading to more complex wetting layers. We also demonstrated the formation of small Ag clusters at the nanocrystal surface. These results provide some implications towards the design of plasmonic materials.


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Noble metal nanocrystals had aroused the interest of researchers over the past few decades owing to their particular optical properties. These peculiarities were driven by the Localized Surface Plasmon Resonance (LSPR), which induced a strong optical absorption evolving with several parameters such as the geometry, size, or chemical environment of nanostructures.1-12 Silver (Ag) was identified as the ‘best’ noble metal for its optical properties, it is, however, difficult to characterize mainly due to surface oxidation. Although there has been a recent review on silver parameters, large uncertainties still exist on some parameters.13 Nanocrystals coated with an organic layer and characterized by a narrow size distribution were able to self-assemble into either a two-dimensional (2D) hexagonal compact network or crystallographic orders (3D) called supracrystals, similar to atoms in crystals, with various crystalline structures such as face-centered cubic (fcc), body-centered cubic (bcc), hexagonal closest packed (hcp), etc.14-18 Two growth mechanisms have been identified: i) Heterogeneous growth processes were either controlled by gravitation when the nanoparticles were large enough or by solvent evaporation with formation of layer-by-layer assemblies; and ii) Homogeneous growth mechanism that produced shaped supracrystals.17,19-22 Such suprastructures are expected to become one of the main driving forces in materials research in the next few decades, originated from the collective interactions between nanocrystals. Such materials exhibited specific properties that were neither those of isolated nanocrystals nor those of the corresponding bulk phase. During the last two decades, a rather large variety of collective properties have been investigated, such as collective optical and magnetic properties, due to their dipolar interactions.23-25 In parallel, it has been shown that an intrinsic crystalline growth process takes place by mild annealing of small supracrystals, leading to the formation of triangular single fcc crystals.26 Very surprisingly, intrinsic properties fully analogous to those of atomic nanocrystals were observed with


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supracrystals: Atoms were replaced by (uncompressible) nanocrystals and atomic bonds by coating agents (alkyl chains), which acted as mechanical springs holding the nanocrystals together. This was demonstrated: (i) with thin supracrystals in the range of 4 to 8 layers: One observed coherent breathing of atoms in nanocrystals as well as of nanocrystals in supracrystals.27 Such breathing processes were also observed for supracrystals having a number of layer slightly up to a few tenth layers.27,28 Furthermore, longitudinal acoustic phonons propagated with the speed of sound through coherent movements of self-assembled Co nanocrystals out of their equilibrium positions.29 (ii) with very thick supracrystals of around 1000 layers, the supracrystals morphologies were similar to those of nanocrystals as well as millimeters materials.30 In the same range of thicknesses, by low temperature STM/STS experiments, the supracrystal were imaged and their electronic properties were studied.31 To explain such behavior we had to assume various pathways from the tip to the substrate favored by the breathing mode processes observed previously. Such unexpected properties offer a promising route for discovering intrinsic properties. Supracrystals films grown through heterogeneous processes showed well-defined cracks as those studied since several decades and attributed to a shrinking film restricted by adhesion to a surface. The geometries of different crack patterns were observed over a wide range of scales with specific scaling law.32-38 Cracks in supracrystals films followed a scaling law over three orders of magnitude. This scaling law indicated the universality of crack patterns independently of their dimensions. To observe these scaling laws, it was important to distinguish between different crack generations such as primary and secondary cracks.39-41 The LSPR of Ag nanocrystals self-assembled into a two-dimensional (2D) hexagonal network shifted to lower energies compared to those obtained with nanocrystals dispersed in


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solutions. This energy difference was observed from discrete dipole approximation simulations and experiments and was attributed to interparticle electromagnetic interactions.42-44 On increasing the number of nanocrystals layers forming supracrystals, most of the reported optical properties referred to supracrystals characterized by less than ten layers.22,42,44,46-55 This is due to the fact that the increase of layer numbers induced an increase in the absorption to reach saturation. The optical properties of the thickest Ag supracrystals studied correspond to a number of layers around 30-35.54 In this thickness range, as mentioned, a direct measurement of absorption, reflection, and transmission of the supracrystals is still possible because the number of layers is small enough and the specific behaviors observed were due to collective properties of such assemblies. Note that very few papers investigated the optical properties of supracrystals with Ag compared to with Au nanocrystals as building blocks.22,42,45-53 Shaped Ag nanoparticles selfassembled into supracrystals displayed a frequency selective response in the visible wavelengths giving rise to optical passbands that can be tuned by particle volume fraction.22 Additionally, the optical properties of Ag supracrystals markedly depended on the interparticle distance and exhibited high reflectivity.44 Based on our knowledge, the optical properties of supracrystal films having more than 35 layers have not been investigated. This is due to the fact that, according to the Beer Lambert law, the film is expected to fully absorb. Furthermore, when nanoparticles assembled into three-dimensional supracrytals, due to the stinking of superlattice film and the adhesion of film and substrate, the cracks formed in supracrystals. With the increase of film thickness, the width of cracks also increases. Therefore, the influence of cracks on the optical properties of supracrystals needs further investigation. Here, we challenged to study the optical properties of Ag supracrystals film having a thickness in the range from 200 nm to 1.4 m corresponding to a number of layers varying from


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around 27 to 180 layers. The supracrystal films studied were based on 8.2 nm oleylamine-coated Ag nanocrystals. At the opposite of what could be expected from the Beer-Lambert law, we observed a reduced transmission with an increase in the notch linewidth as we increased the supracrystal film thickness. Calculations showed that cracks dominated the transmission response and a wetting layer at the bottom of the cracks was introduced to have a good agreement with the experimental data.

Figure 1. (a, c, e) TEM image of 3.6 nm (a), 5.5 nm (c) and 7.5 nm (e) Ag nanocrystals deposited on TEM grid. Insert panels are the corresponding histogram of nanocrystals diameter distribution. (b, d, f) the corresponding absorption spectra dispersed in toluene: the best fit between calculated transmission (red line) and experimental transmission (dashed line); calculated transmission considers silver absorption (green line) and (Agn)2+ absorption (blue line).

RESULTS AND DISCUSSION Revisiting Ag NCs colloidal solution


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Here we first revisited the Ag absorption spectra differing by their average diameters, produced by hot injection method, and dispersed in toluene as already described elsewhere.55 By depositing a drop of this colloidal solution on a transmission electron microscope (TEM) grid, Ag nanocrystals self-assembled into 2D superlattices (Figures 1a, c, e). The average diameters and size distribution, deduced from measuring over 500 nanocrystals, were 3.6 nm, 5.0 nm and 7.5 nm and 10 %, 6 % and 7 %, respectively. The LSPR of Ag nanocrystals coated with oleylamine differing by their average diameters and dispersed in toluene ([Ag] = 10-6 M) were characterized by a maximum of absorption at around 430 nm (Figures 1b, d, f). The experimental data did not fit correctly with the calculated spectra by using the real and imaginary part given in literature, indicating that data from literature are too inaccurate to be used.13 Hence, to calculate the optical properties of Ag nanocrystals dispersed in toluene, in the visible range (300-800 nm), we first calculated the optical refractive index of toluene. The real part of toluene optical index is well defined in the literature (Figure 2a).56 By contrast, its imaginary part is reported in the literature only for wavelengths larger than 500 nm.56 To extract the toluene imaginary part from our transmission measurements, we assumed the real part given by Kedendburg et al.57 A good agreement with the Kedenburg’s results, in the 500-800 nm ranges, was obtained at large wavelengths. However, it is observed some discrepancies for the lowest values due to a lack of resolution, (Figure 2b, red line). Note that the absorption increased with decreasing the wavelength from 350 to 300nm with a shoulder around 350nm (Figure 2).


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Figure 2. Optical properties of toluene: (a) real part from references 56 and 57 (b) imaginary part from reference 56 (red line) and from this work after introducing the modifications described in the text (blue line). To determine more accurately the transmission spectra of colloidal solutions we determined the optical permittivity of silver. In the low energy domain, the Ag permittivity was calculated as the sum of a contribution from free electrons given by the Drude Model and a contribution from core electrons described by the constant ∞. The plasma frequency p was known with an excellent accuracy (p/p = 2%), while the carrier relaxation time , and permittivity at infinite frequency

∞ showed important uncertainties (/ = 17% and ∞/∞ = 40%).13 In these calculations, we used the best-known parameters (p and ) from literature and adjusted ∞ to get the best fit with the experimental data (Table 1 and Figure 2).13 We used the Effective Medium Theory (EMT) to calculate the permittivity of colloidal solutions. In its most general form, the effective permittivity of a colloidal solution writes: 𝜀 ― 𝜀ℎ 𝜀 + 2𝜀ℎ

𝑛

𝜀𝑖 ― 𝜀ℎ

= ∑𝑖 = 1𝑓𝑖𝜀𝑖 + 2𝜀ℎ

(1)

where  is the permittivity of the effective medium, h the permittivity of the host material, i the permittivity of the ith type of inclusion and fi its volume filling factor, and n the number of types


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of inclusions.58 Here, n=1, h was the permittivity of toluene, and 1 was the permittivity of silver. The permittivity of silver includes the contribution of the core electrons, the contribution of free electrons, and an additional absorption described by a Lorentz function. Additional information on these simulations can be found in the Supporting Information. Figures 1b, d, and f illustrated the best fits of calculated transmission with the experimental measurements obtained for the parameters listed in Table 1. In addition to f and ∞, four additional free parameters were introduced in this fit: vF the Fermi velocity, Ah the intensity of an additional absorption with λh its resonant wavelength and Γh its full-width at half maximum (FWHM). The resonant absorption in the effective medium was highly dependent on the difference between silver permittivity and host permittivity. A maximum of absorption was obtained when the denominator of the right-hand side term of Equation 1 tended to zero. Resonance wavelength is mainly dependent on the plasma frequency and ∞. Based on literature, the plasma frequency is known with an excellent accuracy (uncertainty of ~2%), thus the fit of the transmission peak leads to an excellent accuracy on ∞ (uncertainty of ~3%).13 The uncertainties over other parameters are reported in the SI. To obtain a good fit between the measured and calculated data, an additional absorption peak in the 350-400 nm wavelength range accounting for the formation of various (Ag)n2+ clusters had to be included. These clusters have been observed experimentally by deposition in Ar matrix Ag atoms produced by bulk phase at high temperature (around 1300°C). The calculated through time-dependent density functional theory and experimental in Ar matrices absorption spectra of these clusters differing by the number of Ag atoms were slightly different from one type of cluster to another, resulting in an absorption peak with larger linewidth.59-61 Interband processes were also taken into account leading to strong absorption for 𝜆 < 320 nm. Here in first approximation we


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can assume that hot injection technique provided clusters differing by the number of atoms and consequently an envelope of the absorption of these various clusters were observed. A good agreement between experiments and calculations were then obtained as shown in Figures 1b, 1d and 1f. Table 1. Fitting parameters of Ag nanocrystal colloidal solutions of toluene for various nanocrystal diameters and from literature.13 In this table f is the filling factor, ω p the plasma frequency,τ the electron relaxation time, ∞ the contribution of electron cores to the permittivity, Ah the intensity of additional absorption, h the additional absorption wavelength, and h the FWHM of additional absorption. d (nm)

f

ωp

(10-7)

(rd/s)

3.6

4.10

13.58×1015

5

4.72

5.0

4.27

13.58×1015

5

7.5

3.25

13.58×1015 13.58×1015

Ref. 13

τ (fs)

ε∞

Ah

λh (nm)

Γh (nm)

2.0

385

45

4.42

2.5

385

35

5

4.34

3.0

385

25

17

4–5

(10-6)

Thick supracrystal films of Ag nanocrystals The colloidal solution (~1 mg/mL) of d=8.2 nm Ag nanocrystals (inset (a) Figure 3) coated with oleylamine with 8% as size distribution and dispersed in toluene was then placed in a beaker containing a glass substrate at its bottom. The solvent slowly evaporated under nitrogen flow, inducing the formation of films onto the substrate. The temperature of this system was set at 35 ºC. At the end of solvent evaporation, a 3D film covering most of the substrate was observed. With the evaporation of solvent, the concentration of nanocrystals increases. Further evaporation induces the shrinkage of this film. Due to the interaction between formed film and glass substrate, it limits the contraction of film, with formation of cracks. The SEM image (Figure 3c) showed


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rather uniform films on a few hundred of nanometers scale with terraces and linear steps having various heights (from one nanocrystal to several nanocrystals thickness). Small-angle X-ray diffraction (SAXD) pattern (Figure 3b) showed well-defined fcc structure of assembled lattices, with the (111) plane of each supracrystal parallel to the substrate. The corresponding Bragg angle 2B and thus the modulus of the diffracted vector q from the Bragg relation converted into dhklspacings permitted to determine the interparticle spacing,  = 2.8 nm. This data clear indicated that 3D fcc superlattices, called supracrystals, were produced with an average distance between nanocrystals of 2.8 nm. Note that at larger scale the SEM pattern showed presence of cracks. (Figure 3a)

Figure 3. (a) SEM image of supracrystals assembled by 8.2 nm Ag nanocrystals and their cracks. (b) Small-angle X-ray diffraction of as-prepared supracrystals. (c) High-resolution SEM image of supracrysals of (a), insets: TEM image of 8.2 nm Ag nanocrystals deposited on TEM grid.


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To study the influence of the supracrystal thickness on the optical properties we produced films with various thicknesses. This was obtained by increasing the amount of colloidal solution. The average thickness of the film was determined by tilting the substrate by 30°. Here four samples differing by their supracrystals film thickness were studied (0.2-0.6 µm, 0.4-1.0 µm, 0.6-1.4 µm, and 0.9-1.6 µm respectively). The SEM images produced after the end of the solvent evaporation showed large surface. Note that the homogeneity of the surface depended on the thickness of the film and is not well controlled. These patterns are highly reproducible. The shrinkage of the film was due to large stresses, which were at the origin of the crack formation (Figure 4). By tilting the samples, we observed formation of thin films within the cracks (insets of Figure 4).

Figure 4. SEM images of supracrystal films with various thicknesses. (a) 0.2-0.6 m, (b) 0.4-1.0 m, (c) 0.6-1.4 m and (d) 0.9-1.6 m respectively. Insets: tilted SEM images.


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To have a deeper understanding of the cracks, we observed the supracrystals films using optical microscopy in transmission mode, bright and dark fields reflection modes. Figure 5 shows the optical micrographs of the 0.4-1 µm supracrystal film: (i) in transmission mode (Figures 5a, 5b), the cracks formed a network of channels (~ 1 µm) separating islands (a few tens of µm) of thick film. Transmitted light coming out of channels was mainly blue, while light from islands was reddish. The cracks in the micrographs are blue suggesting the presence of wetting layers at their bottoms. This conclusion is also valid for films of 1.0-1.4 µm thickness (Figure S1). For the thickest film, cracks are wider and show various colors ranging from blue to green, proposing that the wetting layers consist of different steps (Figure S2). (ii) In reflection mode, bright (Figures 5c, d) and dark (Figures 5e, 5f) field micrographs show dark and bright cracks, respectively, suggesting light scattering at the crack edges.


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Figure 5. Optical micrographs of the 0.4-1.0 µm supracrystal film. (a, b) transmission mode, (c, d) bright field reflection mode, (e, f) dark field reflection mode.

Let us now consider the transmission spectra of homogeneous supracrystals films having various thicknesses without features on their surfaces. The permittivity of supracrystal films is calculated in the same way as for colloidal solutions and using the same parameters (Eq. 1, see Supporting Information). Only the filling factor differs and can be deduced as follows. Ag nanocrystals self-assembled into fcc structured supracrystal films, as was previously observed. For an interparticle distance between nanocrystals (L = 2.8 nm), the fcc supracrystal periodicity was 15.6 nm based on 𝑎 =

2(𝐿 + 𝑑), and the filling factor was 0.3 following 𝑓 =

16𝜋 𝑑 3 3 2𝑎 .

( )

The

air/glass/film/air stack is illuminated under normal incidence with non-polarized light. The transmission and reflection of this optical system are then calculated using the method of S-matrix


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for each zone of constant thickness. Figure 6 shows the calculated transmission of supracrystal films for various thicknesses. Each curve corresponds to the sum of transmission through films with varying number of monolayers deduced from SEM images. The calculated transmission of supracrystal films of constant thicknesses shows non-negligible values only in the red part of the visible spectrum due to a reduced value of the imaginary part of the refractive index in this wavelength range (Figure S3).

Figure 6. Calculated transmission spectra of supracrystals film for various homogeneous films differing by their thicknesses i.e. by the number of 8.2 nm nanocrystals layers.

To explain the disagreement between the calculated transmission spectra of Figure 6 and the experimental data (Figure 7), we introduced the inhomogeneities (cracks, holes, and dislocations) seen on the supracrystal films (Figures 3-5) into our calculations. A wetting layer is first assumed to be present at the bottom of each crack. However, a wetting layer of constant thickness does not allow to fitting the experimental data. We thus assume the formation of steps (several zones of different thicknesses) in the wetting layer. Each zone of constant thickness is correlated with a Fabry-Perot like resonance. The total transmission is then the weighted sum of the transmissions


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of each zone. The weight of each zone is adjusted to get the best fit. The thickness and weight of each zone are the only two free parameters of the fit. Figure 7 reveals the excellent agreement between calculations accounting for the cracks and experiments for films of various thicknesses (0.2-0.6 µm, 0.4-1 µm, 0.6-1.4 µm, and 0.9-1.6 µm). The Fabry-Perot resonances introduce a maximum of transmission when the film permittivity is positive (dielectric material) as well as the film absorptivity is low (green trace at around 660 nm in Figure 7c and Figure S3). In conclusion, the transmission intensity through the supracrystal films decreases with increasing the film thickness, and a wider linewidth is observed. Supracrystal films exhibit Fabry-Perot resonances. When Fabry-Perot resonances are combined with the resonant absorption of LSPR, the transmission spectra of films have peaks corresponding to colored areas in the optical micrographs. For example, the transmission micrographs of the 0.4 - 1.0 µm sample (Figs 5a, 5b) show: -

A dominant blue in the cracks which corresponds to the transmission calculated for films of 5 and 8-12 monolayers. The calculated spectrum also shows a comparable transmission in the red which is not visible on the optical micrographs. This part of the transmission spectrum seems to be preferentially scattered by the edges of cracks (Fig. 5, dark-field).

-

A dominant red in thick islands. It corresponds to the calculated transmission spectrum (Figure 6).

The agreement between calculations and experiments demonstrates that the wetting layers have various thicknesses from one crack domain to another (Figures 5, S1, S2) and are responsible for the optical properties observed with thick films. The thicknesses of the wetting layers sitting on the substrate at the bottom of the cracks are estimated from the fit and summarized in Table 2.


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Figure 7. Calculated (blue solid traces) and experimental (dashed traces) transmission spectra of 8.2-nm Ag NCs supracrystal films with various thicknesses. (a) 0.2-0.6 µm, (b) 0.4-1 µm, (c) 0.61.4 µm, and (d) 0.9-1.6 µm. The calculated spectra account for wetting layers with different thicknesses. Colors correspond to different number of monolayers.


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Table 2. Thickness of the wetting layer at the bottom of the cracks for different film thicknesses. Film thickness

Wetting layer thickness

(monolayer)

(monolayer)

0.2 – 0.6

27 – 78

2 and 3

0.19, 0.12, 0.69

0.4 – 1.0

52 – 129

5 and 8 – 12

0.20, 0.34, 0.47

0.6 – 1.4

78 – 180

9, 13 – 15 and 21 – 23

0.0, 0.38, 0.32, 0.30

0.9 – 1.6

116 – 206

16 – 17 and 22 – 24

0.0, 0.45, 0.55

Film thickness (m)

Respective weights of zones

CONCLUSIONS Ag supracrystal films with thickness ranging from 200 nm to 1.4 m, with a number of layers changing from 27 to 180, had reduced transmission and a wider linewidth as the supracrystal film thickness increased. This unexpected behavior was explained by the presence of wetting layers at the bottom of the cracks produced by shrinking process during the formation of supracrystal films. Wetting layers with different thicknesses exist at the bottom of the cracks and are responsible of the optical response of the films. Wetting layers were incorporated in the calculated spectra and their thicknesses were adjusted to fit the measured data. Note that formation of small (Ag)n2+ clusters at the nanocrystal interface was supported by our calculations. Silver parameters were determined with better precision by combining optical characterization and calculations.

EXPERIMENTAL SECTION Synthesis of Ag nanocrsytals coated with oleylamine


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Ag nanocrystals were synthesized by a one-pot reaction. In a typical synthesis of 8.2-nm Ag nanocrystals, 170 mg AgNO3 dissolved in 20 mL of oleylamine was heated to 160 oC for 1hr under nitrogen flow, resulting a dark-brown solution. After precipitation by adding acetone, the solids were collected by centrifugation (5000 rpm, 5 min). The solids were dispersed in toluene and washed three times with acetone-toluene cycles before the size-selective precipitation process. At the end of synthesis, Ag nanocrystals with narrow size distribution were re-dispersed in toluene. Preparation of three dimensional supracrystalline films The procedure was as follows: Ag nanocrystals solution (~1 mg/mL) was injected into a glass vial where a glass substrate was placed at the bottom. The carrier solvent was evaporated under nitrogen flow. Ag nanocrystal film was deposited onto the upper side of the glass substrate. The bottom side of the glass substrate was cleaned by hexane carefully. The thickness of the film was controlled by adding different amount of the colloidal Ag solution. Apparatus: Conventional transmission electron microscopy was performed using a JEOL 1011 microscope at 100 kV. The UV-visible absorption measurements were performed using a Varian Cary 5000 double monochromator recording spectrophotometer. Optical micrographs have been taken by a camera Zeiss Axiocam 150. ASSOCIATED CONTENT Supporting Information. Extended calculation details and measurement methods. The following files are available free of charge. AUTHOR INFORMATION Corresponding Author


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*to whom correspondence should be addressed: Prof. Marie-Paule Pileni ([email protected]); Prof. Jean-Luc Pelouard ([email protected]) Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT An Advanced Grant of the European Research Council under Grant 267129 has supported the research leading to these results. REFERENCES (1)

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Influence of Cracks on the Optical Properties of Silver Nanocrystals

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