Langmuir 2000, 16, 3803-3812
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Self-Assemblies of Silver Sulfide Nanocrystals on Various Substrates L. Motte,† E. Lacaze,§ M. Maillard,† and M. P. Pileni*,† Laboratoire SRSI, URACNRS 1662, Universite´ Parie et Marie Curie (Paris VI), B.P. 52, 4 Place Jussieu, 75231 Paris Cedex 05, France, and Groupe de Physique des Solides, URA 17, Universite´ P6-P7, 4 Place Jussieu, Tour 23, 75251 Paris Cedex 05, France Received June 24, 1999. In Final Form: January 16, 2000 The influence of the substrate on the morphology of 2D and 3D superlattices made of 5.8 nm silver sulfide nanocrystals coated with dodecanethiol is reported. The two substrates used are highly oriented pyrolytic graphite (HOPG) and molybdenum disulfide (MoS2). The self-assemblies of nanocrystals were characterized with scanning electron microscopy and atomic force microscopy techniques, and it was found that the self-organization in 2D and 3D superlattices markedly differs with the substrate used. These changes in behavior are explained in terms of particle-particle and particle-substrate van der Waals interactions and capillary forces.
I. Introduction Self-assembled nanocrystals and their specific properties represent an area between macroscopic and microscopic physics that has progressed rapidly over the last 5 years. The self-assembled 2D and 3D superlattices were first observed with Ag2S and CdSe.1-4 A proliferation of publications followed. A large number of groups have now succeeded in forming various self-organized nanocrystals of silver,5-10 gold,11-14 cobalt,15,16 and cobalt oxide.17 When the experimental conditions for deposition are changed, various states of self-organization have been observed. At low particle concentrations in an initial bulk suspension of oil, very large rings were obtained with silver, gold, and CdS nanoparticles.10,18 These rings separate areas covered with monolayers from the bare surface. These patterns have been explained in terms of wetting properties. † §
Universite´ Parie et Marie Curie. Universite´ P6-P7.
(1) Motte, L.; Billoudet, F.; Pileni, M. P. J. Phys. Chem. 1995, 99, 16425. (2) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Science 1995, 270, 1335. (3) Motte, L.; Billoudet, F.; Lacaze, E.; Pileni, M. P. Adv. Mater. 1996, 8, 1018. (4) Motte, L.; Billoudet, F.; Lacaze, E.; Douin, J.; Pileni, M. P. J. Phys. Chem. B 1997, 101, 138. (5) Taleb, A.; Petit, C.; Pileni, M. P. Chem. Mater. 1997, 9, 950. (6) Taleb, A.; Petit, C.; Pileni, M. P. J. Phys. Chem. B 1998, 102, 2215. (7) Harfenist, S. A.; Wang, Z. L.; Whetten, R. L.; Vezmar, I.; Alvarez, M. M. Adv. Mater. 1997, 9, 817. (8) Chung, S. W.; Markovich, G.; Heath, J. R. J. Phys. Chem. B 1998, 102, 6685. (9) Korgel, B. A.; Fitzmaurice, D. Adv. Mater. 1998, 10, 661. (10) Ohara, P. C.; Heath, J. R.; Gelbart, W. M. Angew. Chem., Int. Ed. Engl. 1997, 36, 1078. (11) Hostetler, M. J.; Stokes, J. J.; Murray, R. W. Langmuir 1996, 12, 3604. (12) Badia, A.; Cuccia, L.; Demers, L.; Morin, F.; Lennox, R. B. J. Am. Chem. Soc. 1997, 119, 2682. (13) Kiely, C. J.; Fink, J.; Brust, M.; Bethell, D.; Schiffrin, D. J. Nature 1998, 396, 444. (14) Brown, L. O.; Hutchison, J. E. J. Am. Chem. Soc. 1999, 121, 882. (15) Petit, C.; Taleb, A.; Pileni, M. P. J. Phys. Chem. B 1999, 103, 1805. (16) Petit, C.; Taleb, A.; Pileni, M. P. Adv. Mater. 1998, 10, 259. (17) Yin, J. S.; Wang, Z. L. J. Phys. Chem. B 1997, 101, 8979. (18) Maenosono, S.; Dushkin, C. D.; Saita, S.; Yamaguchi, Y. Langmuir 1999, 15, 957.
It has been observed that self-organization changes with the length of the alkyl chains19 that coat the particles. It was shown that the 3D superlattices, which are here called “aggregates”, are usually self-organized in a crystalline phase in a face-centered cubic (FCC) structure.1-6 Recently it was demonstrated that the physical properties of silver6,20,21 and cobalt15,16 nanocrystals organized in 2D and/or 3D superlattices differ from those of isolated nanoparticles. Collective properties are observed. Similarly cobalt nanocrystals organized in 2D superlattices reach saturation at very low applied fields compared to isolated particles.15,16 In this paper, we report on the influence of the substrate on formation of 2D and 3D quantum dot superlattices made of 5.8 nm silver sulfide nanocrystals coated with dodecanethiol. The substrates used were highly oriented pyrolytic graphic (HOPG) and MoS2. II. Experimental Section II-1. Chemicals. Sodium bis(2-ethylhexyl) sulfosuccinate [Na(AOT)] was from Sigma. Isooctane was from Fluka, and sodium sulfide (Na2S) from Janssen. Heptane and 1-dodecanethiol (C12H25SH) were from Merck. Silver bis(2-ethylhexyl)sulfosuccinate [Ag(AOT)] was prepared as described previously.1 II-2. Apparatus. II-2.1. Scanning Electron Microscopy SEM. A JSM 840A Instrument was used. By tilting the substrates at angles R (in degrees) for the scan, the height (H) of the aggregates was determined from H ) h/sin R where h is the height measured from the image by taking into account the scale bar. II-2.3. Atomic Force Microscopy (AFM). The measurements were made in tapping mode (TMAFM), with a Nanoscope III (Digital Instrument) using a silicon tip in ambient atmosphere, with a maximum scanning size of 10 × 10 µm. II.3. Synthesis of 5.8 nm Ag2S Nanocrystals Coated with Dodecanethiol. Synthesis of Ag2S nanosized particles in reverse micelles and control of the size and size distribution were described previously.1 Ag2S nanocrystals were obtained by a coprecipitation reaction between silver and sulfide ions in water(19) Motte, L.; Pileni, M. P. J. Phys. Chem. B 1998, 102, 4104. (20) Taleb, A.; Russier, V.; Courty, A.; Pileni, M. P. Phys. Rev. B 1999, 59, 13350. (21) Russier, V.; Pileni, M. P. Surf. Sci. 1999, 425, 331.
10.1021/la9908283 CCC: $19.00 © 2000 American Chemical Society Published on Web 03/14/2000
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Figure 1. TEM pattern on amorphous carbon (A) and AFM pattern on HOPG pattern (B) obtained with 5.8 nm coated silver sulfide particles. in-oil droplets that had an average diameter of 6 nm. Silver sulfide (Ag2S) nanocrystals were formed with an average diameter of 4.6 nm and 20% size distribution. A size-selective precipitation was induced by addition of dodecanethiol to the reverse micellar solution containing Ag2S nanoparticles. The nanocrystallites coated with dodecanethiol were then dispersed in heptane, giving an optically clear solution. The size distribution was reduced to 14% with an average particle diameter of 5.8 nm. The particle concentration for film formation on substrates was adjusted to either 10-6 or 10-5 mol L-1. II-4. Sample Preparations. The same procedure was employed to deposit the particles on the two substrates used, HOPG and MoS2: The cleaved substrates (MoS2 and HOPG) were immersed horizontally in the solution containing 5.8 nm silver sulfide coated particles (10-6 mol L-1). The solution was removed by pumping, leaving a film containing particles on the substrate. Then, because
of the fast evaporation of solvent, the substrates were dried in air at room temperature (20 °C). The same sample was studied by AFM and SEM. With MoS2, the effects of temperature and concentration were studied by increasing the former by 10 °C, i.e., from 20 to 30 °C, and the latter by a factor of 10 to 10-5 mol L-1. II-5. Substrate Characteristics. HOPG and MoS2 substrates are quasi-2D solids or layer compounds and have very flat and inert surfaces parallel to the basal plane. In HOPG, the surface planes are hexagonal lattices of carbon atoms (lattice constant 2.45 Å) with two atoms per cell. In MoS2 substrates, the surface planes are hexagonal lattices of sulfur atoms (lattice constant 3.16 Å). These two substrates were cleaved in air just prior to use. II-6. Results Obtained on Amorphous Carbon Used as a Substrate. In our previous papers,1,3,4,19 self-organizations in 2D and 3D superlattices were obtained by deposition of silver
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Figure 2. SEM images obtained by using HOPG as the substrate recorded on the border (A, C, and E) and on the center (B, D, and F). [particle] ) 10-6 mol L-1, T ) 20 °C. At zero angle (A and B) and by 60° tilt (C-F). sulfide coated particles on amorphous carbon. The formation of monolayer, organized in a compact hexagonal network of particles with an average distance between particles of 1.8 nm, was shown by using transmission electron microscopy (TEM). 3D superlattices organized in FCC structure were observed in the vicinity of the monolayers. The aggregates are surrounded by holes, i.e., parts of the surface not covered by particles (Figure 1A). By TMAFM, similar behavior (Figure 1B) was observed with formation of aggregates having sizes similar to those observed by TEM. It must be noted that the AFM experiments were made on a HOPG substrate whereas the TEM was on amorphous carbon. To a first approximation, it was concluded that the selforganizations observed with HOPG and amorphous carbon are similar. However, as we report here, the morphology of the selforganized film changes when HOPG is replaced by MoS2.
III. Experimental Results In our previous paper,4 it was demonstrated that the preparation mode of the sample induces changes in the self-organization of the particles. To avoid this problem, the same particle deposition procedure, as described that in the Experimental Section, was used for each substrate. SEM and AFM measurements were made on the same sample. The observed self-assemblies differ with the substrate used. In the following, we compare the patterns obtained by deposition of 5.8 nm silver sulfide nanocrystals. III-1. HOPG Used as a Substrate. The SEM patterns in Figure 2A,B are characterized by various contrasts: dark areas surround large aggregates (white), and large islands having a low contrast are located outside these
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dark areas. Taking into account the previously obtained results (Figure 1), it can be deduced that the dark areas are holes whereas the low contrast areas are monolayers. The number of aggregates, their height and morphology, and the domains of the monolayers differ between the border (parts A, C, and E of Figure 2) and the center of the substrate (parts B, D, and F of Figure 2). Because of these differences in the behavior between the border and the center of the sample, the two regions were explored: (i) In the center of the substrate large monolayers are formed. In the regions not covered by particles, called holes, aggregates are observed. The average width and height of the aggregates are between 4 and 8 µm and 2 and 4 µm, respectively. (ii) At the border of the substrate, some information can be deduced from parts A and C of Figure 2. As at the center, the aggregates are surrounded by holes. The average aggregate widths are about the same as those in the center (from 4 to 8 µm) whereas the height is smaller (below 1 µm). The holes surrounding the aggregates are interconnected and form a continuous pathway whereas the monolayers of particles form islands. Inside the monolayer, further substructures in the form of small holes are observed (Figure 2A). The differences in the SEM patterns on going from the center to the border of the substrate are the holes are larger, the aggregates are shorter, and the monolayer domains are smaller at the border compared to the center. However, the overall pictures and structure remain the same. The aggregates are always surrounded by holes, and they never grow on the top of a monolayer. The differences between the border and the center can be attributed to a change in the local number of nanocrystals dispersed in heptane: the capillary forces tend to push the solution to the center of the sample. As mentioned, the same sample was used in AFM and SEM. The formation of a dense layer with the appearance of rather small numbers of holes (black points) and small aggregates (white points) is shown on a large AFM scale in Figure 3A. The cross section (inset of Figure 3A) along the line shows that the depth of a hole is about 6 nm, indicating a very dense monolayer. No particles are observed in the holes at high-resolution AFM. This is not a direct proof that the AFM pattern shown in parts A and B of Figure 3 is a monolayer (it could be dense multilayers). However, taking into account the similarity of the TEM and AFM patterns observed on amorphous carbon and HOPG (Figure 1), it is concluded, to a first approximation, that a dense monolayer is formed on HOPG used as a substrate. This was made more convincing by using MoS2 as the substrate (see below). The invariance of the signal over a large range of cross section confirms the high density of the monolayer. The peak observed on the cross section indicates formation of very small aggregates [white points on the AFM pattern (Figure 3A)]. Their average size is between 100 and 200 nm and the height is in the 10-15 nm range, corresponding to bi- or trilayers. In the overall pattern given in Figure 3A, holes (black points) with areas from 120 to 5600 nm2 are observed. Figure 3B shows a high-resolution image of the monolayer shown in Figure 3A. The particles are organized in a hexagonal network. This indicates that locally, on HOPG (AFM experiment) and amorphous carbon (TEM experiment), the particles are organized similarly. On this scale the monolayer appears highly dense. However, inside the monolayer some vacancies consisting of a few particles are observed. The average periodicity between particles (center to center) is around 8.0 nm. Taking into account the average diameter of
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Figure 3. Monolayer images of 5.8 nm Ag2S nanocrystals deposited on HOPG observed by AFM over a long range (A) and with high resolution (B).
particles determined from TEM (around 6 nm), the average distance between organized particles is approximately 2 nm. This is in good agreement with data obtained in our previous papers.1,3,4,19 It must be noted that a similar average particle-particle distance was obtained with silver particles coated with dodecanethiol and deposited either on HOPG6 or on gold surface.22 Because of the vacancies and other defects inside the array, the monolayer is formed of differently oriented domains. In other words, only a limited range of perfectly ordered islands which are characterized by high-symmetry directions typical of a hexagonal network can be defined. The orientation of one of the three high-symmetry directions is measured for each ordered island on a few micron-sized squares of monolayers (Figure 4A). The number of ordered particles characterizes each direction. When the number of particles versus the various orientations (Figure 4B) is plotted, these islands are characterized (22) Taleb, A.; Silly, F.; Gusev, A. O.; Charra, F.; Pileni, M. P., to be submitted.
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Figure 4. Directions (B) measured on monolayers deposited on HOPG substrate (A) from high-resolution AFM images as shown in Figure 2B. Arrows in A show two types of vacancies inside monolayers.
by preferential orientations: two main directions are observed, which are at 0° (and the equivalent at 120°) and 30° of an arbitrary origin direction (Figure 4C). Such results suggest that, despite the large differences between the substrate and the monolayer lattice parameters, these monolayers are at least partly oriented along the substrate directions. These directions can be attributed to [100] and [110] directions of the basal plane of HOPG. The difference between lattice constants clearly induces an easy formation of vacancies (see arrows in Figure 4A), which are connected to the relatively limited size of the ordered islands. It can be noted that the measurements made on other areas give the same result. Hence, high-resolution AFM experiments show two preferential directions of the monolayers deposited on the HOPG substrate. No selective direction of particles is observed with amorphous carbon as the substrate. This is the major difference between HOPG and amorphous carbon used as the substrate. III-2. MoS2 Used as a Substrate. With MoS2 as a substrate, the SEM patterns differ markedly. Large interconnected domains made of monolayers, where a large number of smaller holes can be discerned inside these domains, are shown in parts A and C of Figure 5. Conversely to what is observed with HOPG, aggregates build on the top of monolayers (Figure 5C). They are small compared to those obtained with HOPG and are characterized by an average width of 1.6-2.3 µm. Their height cannot be measured by SEM. However, these small aggregates have been observed by AFM (Figure 5E). Their cross section indicates a width similar to that previously seen and an average height of 150 nm (Figure 5F). Hence, with HOPG the growth of the aggregates takes place on the holes whereas with MoS2 it seems to occur on the monolayer. The AFM pattern shown in Figure 6A at a large scale confirms data observed with SEM (Figure 5A): Rather large holes are trapped inside the monolayer (Figure 6A). The cross section of the monolayer AFM pattern (inset of Figure 6A) shows the presence of small aggregates corresponding to bi- or trilayers, and the depth of the holes is similar to the particle size. The high-resolution AFM pattern (Figure 6B) confirms formation of monolayers of particles arranged in a hexagonal network. The average periodicity between particles is 8 nm. As mentioned above, this is in agreement with many values obtained with nanocrystals coated by dodecanethiol on various sub-
strates. However, Figure 6B clearly shows that the monolayers form smaller islands of ordered particles (with a maximum number of 20 particles inside the islands). They are separated by large holes with areas from 100 nm2 to 0.5 µm2. It can be noted that no particles are visible inside the holes. This confirms the existence of only one layer of particles. Hence, the high-resolution AFM pattern clearly shows that the monolayers on MoS2 are less dense (Figure 6B) than those observed with HOPG (Figure 3B). Because of the presence of these large holes, it is rather difficult to make quantitative measurements of the preferential orientations of the particles when they are deposited on a MoS2 substrate. Because the aggregate size is not detectable by SEM, the experimental conditions were changed. The temperature and particle concentration (10-5 mol L-1) were increased by 10 °C (30 °C instead of 20 °C) and 1 order of magnitude, respectively. Parts B and D of Figure 5 show the formation of aggregates having an average width and height between 5 and 8 µm and 2 and 5 µm, respectively. Again it is clearly observed that the aggregates grow on top of the monolayer (arrows in Figure 5B,D show the holes on the SEM patterns). Under these experimental conditions, because of the presence of this large number of aggregates, it was difficult to obtain good resolution of the monolayer with AFM. However, SEM patterns suggest that the monolayer is denser than those observed at the lower temperature and concentration. IV. Parameter Determination As mentioned above, the experimental conditions in depositing silver sulfide nanocrystals on MoS2 or HOPG were the same: particle deposition procedure, particle concentration, solvent, and temperature. Hence, the major parameter that plays a role in the various morphologies observed by SEM and AFM has to be correlated to the substrate. To explain the differences described above, we have to take into account various parameters: the wetting properties of the two substrates, the particle-particle and particle-substrate van der Waals forces involved under deposition, and capillary forces. IV-1. Wetting Properties. In ambient air or in any case at vapor pressures below saturation (in order to allow the solvent to evaporate), a droplet of solution placed on HOPG forms a small but finite contact angle of about
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Figure 5. SEM images of aggregates obtained on MoS2. A and C: [particle] ) 10-6 mol L-1 and T ) 20 °C at zero (A) and on 60° tilt (C). B and D: [particle] ) 10-5 mol L-1 and T ) 30 °C at zero (B) and on 60° tilt (D). E and F: AFM image of the sample described in A and C and cross section along an aggregate.
5-10°. On MoS2, the solution spreads to a much smaller contact angle which cannot be measured. In this situation of nonzero contact angle (HOPG), at some value of the thickness, the film becomes unstable and splits into droplets of holes that grow in the film and can extend up to a macroscopic range of sizes. This is the
well-known Marangoni effect23 which is driven by surface tension gradients. This is induced by a concentration gradient in the solution.24 (23) Fanton, X.; Cazabat, A. M. Langmuir 1998, 14, 2254. (24) Yaminsky, V.; Motte, L.; Maillard, M.; Pileni, M. P., to be submitted.
Self-Assemblies of Silver Sulfide Nanocrystals
Langmuir, Vol. 16, No. 8, 2000 3809 Table 1. Various Parameters Used to Calculate Hamaker Constant, Interaction Energies, and Capillary Forces A. Parameters Used to Calculate Hamaker Constants Ag2S (medium 1) heptane (medium 2) MoS2 (medium 3) HOPG (medium 3)
n
ν (rad s-1)
ref
2.8 1.5 4.33 1.35
2.92 2 18.7 5.78
5.24 × 1015 1.6 × 1016 3 × 1015 2.73 × 1016
29, 30 31 32, 33 34, 35
B. Parameters Used to Calculate Capillary Force surface tension of heptane γ 20.14 dyn cm-1 Table 2. Hamaker Constants, Interaction Energies between Silver Sulfide Particles and Various Substrates, Ap-o-s and Ep-o-s, and Interaction Forces (in Limiting Forms)
Figure 6. Monolayer images of 5.8 nm Ag2S nanocrystals deposited on MoS2 observed by AFM over a long distance (A) and with high resolution (B).
IV-2. Hamaker Constants. The various Hamaker constants were calculated using Lifshitz theory.25,26 Details of the calculation are given in the appendix. For particle-particle (Ap-o-p) and particle-substrate (Ap-o-s) interactions, calculations were done for a threecomponent system consisting of either two particles or particle-substrate, both separated by heptane. The dodecanethiol alkyl chains are chemically similar to the solvent and were not taken into account for the calculations. However, this coating agent is very important for the energy interaction calculation (see below) because it drastically changes the minimum approach distance between particles and between particles and substrate. Using a solvent as the intermediate medium, we assumed that the major process takes place in the solvent, before the particles are dried. This is shown rather clearly in the (25) Mahanty, J.; Ninham, B. W. Dispersion forces; Academic Press: London, 1976. (26) Israelachvili, J. N. Intermolecular and surface forces, 2nd ed.; Academic Press: New York, 1991.
substrate
MoS2
HOPG
Ap-o-s (kT) Ep-o-s (kT) Fp-o-s (dyn)
89 -25.7 2.2 × 10-5
-15 4, 3 -0.37 × 10-5
experiments because once the solvent is evaporated, the system remains very stable. The parameters used to calculate the Hamaker constants are given in Table 1. The Hamaker constant between particles dispersed in oil, Ap-o-p, is 60kT. Table 2 gives the Hamaker constant calculated for the interaction between one particle dispersed in oil and substrate, Ap-o-s. Through comparison between Ap-o-p and Ap-o-s, it is clear that with MoS2 Ap-o-p and Ap-o-s are in the same order of magnitude whereas with HOPG Ap-o-p is significantly higher than Ap-o-s. The negative value of Ap-o-s obtained with HOPG indicates repulsive interactions between particles and substrate. IV-3. Interaction Energies and Forces. The interaction energy is calculated from eqs 3 and 4 given in the appendix. The force was obtained by derivation of the interaction energy. The interaction energy and the force between two particles dispersed in oil, having a diameter of 5.8 nm, surrounded by dodecanethiol and at 1.8 nm (interparticle separation measured by TEM) from each other are -1.25kT and 1.8 × 10-6 dyn, respectively. Table 2 gives the interaction energies between particles, dispersed in oil, having a diameter of 5.8 nm, surrounded by dodecanethiol and at 0.9 nm from a substrate. This distance was chosen on the assumption that the particlesubstrate distance is half the measured separation between each particle. The forces involved between coated particles and particle-substrate were calculated. Table 2 shows drastic changes in the forces depending on the substrate: with MoS2 attractive interactions between particle-substrate are stronger than those between particles. Hence, the particles tend to adhere to the substrate. Conversely, repulsive interactions between particles and substrate take place with HOPG. The particles tend to leave the substrate and to attract each other. IV-4. Capillary Forces. During the solvent evaporation process, when the thickness of the film is similar to the particle diameter, capillary forces arise. They depend on the contact angle (θ) of the solvent meniscus (surface tension γ) between two neighboring particles (radius b). The capillary force is then evaluated as27 (27) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley-Interscience: New York, 1997.
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Figure 7. Sketch of formation of monolayer and multilayer on HOPG substrate.
F ) 4πbγ cos θ Note that the capillary forces, when they act, are stronger than those described above which involve particle-particle and/or particle-substrate interactions. As an example, the capillary force for a contact angle of 10° is 7.5 × 10-5 dyn, which is larger than the van der Waals forces (see section IV-3). V. Discussion To understand the change in the behavior between HOPG and MoS2 used as a substrate, let us summarize the major differences seen with these two surfaces: (i) On HOPG, formation of dense and large monolayers of particles (Figure 2B) is observed whereas on MoS2 the
monolayer forms smaller islands with a lower particle density (Figure 6B). (ii) Holes percolate on HOPG whereas it is the monolayers that percolate on MoS2. (iii) On HOPG, the 3D aggregates are surrounded by holes (the monolayers tend to form islands). On MoS2 they are observed on the monolayers. (iv) The 3D aggregates are larger on HOPG (Figure 1E,F) than on MoS2 (Figure 5F). (v) With HOPG the contact angle of the solution is around 5-10° whereas it cannot be detected with MoS2. The particles are coated with alkyl chains (dodecane) which contain “bound” oil taken up in the surfactant tails. We call these coated particles “dressed” nanocrystals.
Self-Assemblies of Silver Sulfide Nanocrystals
When heptane containing “dressed” nanocrystals is deposited on a substrate, the whole surface is covered by the solution. Evaporation occurs, and the film gets thinner. At this point the behavior differs with HOPG and MoS2. On the basis of calculations, two scenarios, depending on the substrate used, can be proposed in order to explain the observed differences. V-1. HOPG Used as the Substrate. With HOPG there are repulsive forces between the particles and the substrate (-3.7 × 10-6 dyn) whereas the particles tend to attract each other (1.8 × 10-6 dyn). Moreover, holes open because of the Marangoni effect.24 The growth of the holes tends to assemble the particles. Because of the particleparticle attractive interactions and the repulsive interactions between particles and substrate, this process is enhanced and dense-packed monolayers are formed. The holes do not contain particles. Hence, simultaneously, the holes tend to grow progressively until percolation takes place and the particles are expelled to the external and internal parts of the holes. Between two holes the particles are expelled28 (Figure 7 B). Taking into account the location of the particles, two different behaviors are observed. (i) The particles located outside of the holes are all pushed together. As long as there is a large excess of solvent, capillary forces between particles do not act. However, when the thickness of the film becomes the same order of magnitude as the particle diameter, these forces become predominant. As an example, for 5.8 nm nanocrystals, the capillary force, corresponding to a contact angle of 10°, is 1 order of magnitude larger than the attractive forces between particles. This tends to form compact islands of “dressed” particles. Further evaporation induces a release of “bound” oil from the alkyl chains. There are attractive interactions between tails, and the nanocrystals tend to interdigitate to reach a total overlap. (ii) Particles squeezed in the center part of the percolating holes (Figure 7C) cannot be expelled. The pressure imposed on the particles by the meniscus along the perimeter of the holes is rather large. Furthermore, the “dressed” nanocrystals do not have enough room to pack in monolayers. At this point, the particles tend to form 3D superlattices (Figure 7C). This process can be related to the collapse of a Langmuir film when the pressure imposed on the molecules is too high. Hence, the collapse of the “dressed” particles is favored. As described above, further drying makes possible particle interdigitation, and this now takes place in 3D instead of 2D. As a result of this process, the 3D superlattices are organized in a “pseudo” crystalline phase with a FCC structure.3,4 The size distribution of the aggregates is homogeneous (4-8 µm), indicating that the areas corresponding to the joints between holes have similar sizes. Hence, nucleation (monolayer formation) and growth (aggregates formation) are simultaneous processes. The (28) Cassin, G.; Badiali, J. P.; Pileni, M. P. J. Phys. Chem. 1995, 99, 12941. (29) Bennett, J. M.; Stanford, J. L.; Ashley, E. J. J. Opt. Soc. Am. 1970, 60, 224. (30) Willig, F.; Schwarzburg, K.; Tro¨sken, B.; Mahrt, J.; Motte, L.; Pileni, M. P. Fine Particles Science and Technology from Micro- to Nanoparticles; Pelizetti, E., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996. (31) Ninham, B. W.; Parsegian, V. A. Biophys. J. 1970, 10, 646. (32) Evans, B. L.; Young, P. A. Proc. R. Soc. London 1965, A284, 402. (33) Neville, R. A.; Evans, B. L. Phys. Status Solidi B 1976, 73, 597. (34) Taft, E. A.; Philipp, H. R. Phys. Rev. 1965, 138, A197. (35) Ergun, S. In Chemistry and Physics of Carbon; Walker, P. L., Jr., Ed.; Dekker: New York, 1968; Vol. 3, p 45.
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3D aggregates result from high concentrations of particles on some small surface areas that join several percolating holes. A sketch of nucleation and growth processes is in Figure 7. Very few and small aggregates of two or three layers of particles can be seen in Figures 2E and 3A. This formation of these 3D superlattices can be attributed to particle-particle interactions when the monolayer is formed. V-2. MoS2 Used as a Substrate. With MoS2, because the particles are subjected to Brownian motion, they randomly collide with the substrate. During such collisions, because the particle-substrate interaction (-25.7kT) is higher than that between particles (-1.25kT), the nanocrystals remain fixed at the surface. During evaporation, the particle-substrate interactions are large enough to keep the particles adhering to the substrate. At this point, this random process would induce a nonordered monolayer. However, because of surface diffusion and attractive particle-particle interactions (van der Waals and/or capillary forces), small islands of ordered particles are formed. This creates low-density interconnected monolayer domains separated by holes. Once the MoS2 surface is covered by monolayers of particles, the particle-substrate interactions do not play any role in the aggregate growth. The particles interact and tend to form small aggregates because of, in some areas, high local particle concentrations. On increasing temperature and particle concentration, larger flat aggregates are formed on a dense monolayer (Figure 4B,D). This suggests a layer by layer growth following the monolayer formation. VI. Conclusion In the present paper, we demonstrate that deposition on various substrates of 5.8 nm silver sulfide nanocrystals induces marked changes in the self-organization of the particles in 2D and 3D superlattices. These changes appear to be correlated to the wetting properties of the substrates, to the different van der Waals interactions between the particles and the substrate, and to capillary forces. Acknowledgment. The authors thank O. Araspin (CEA Saclay, DRECAM/SCM) for SEM images. Appendix 1. Hamaker Constant.25,26 For three media (1-3), the Hamaker constant is given by
A123 )
3 2
∞′
kT
[
][
]
1(iνn) - 2(iνn) 3(iνn) - 2(iνn)
∑ n)0,1,... (iν ) + (iν ) 1
n
2
n
3(iνn) + 2(iνn)
(1)
where (iνn) are the dielectric constants for the three media at imaginary frequencies iνn, where νn (s-1) ) (2πkT/h)n ≈ 4 × 103n at T ) 300 K and where the prime over the summation (∑′) indicates that the zero frequency term (n ) 0) is multiplied by 1/2. Replacing the sum by the integral26 ∞
kT Then
h
∑ f 2π ∫ν n)1,2,...
∞ 1
dν
3812
Langmuir, Vol. 16, No. 8, 2000
Motte et al.
[ ][ ] ∫ [ ][ ∫ [ ][
1 - 2 3 - 2 3 kT + 4 1 - 2 3 + 2 3h ∞ 1(iνn) - 2 (iνn) 3(iνn) - 2(iνn) dν ≈ 4π ν1 1(iνn) + 2(iνn) 3(iνn) + 2(iνn) 3h ∞ 1(iνn) - 2(iνn) 3(iνn) - 2(iνn) dν (2) 4π ν1 1(iνn) + 2(iνn) 3(iνn) + 2(iνn)
A123 )
]
]
with 1, 2, and 3 the static dielectric constants for the three media (n ) 0). The (iνn) values are that of at imaginary frequencies.25 2
(iνn) ) 1 +
(n - 1) 2
2
(1 + ν /νe )
)1+
Ap-o-s b b R-b + + ln 6 R-b b+R R+b
[
(
Ep-o-p ) -
Ap-o-p b 12 l
Ep-o-s ) -
Ap-o-s b 6 l
()
and
N (1 + ν2/νe2)
(
)]
Ap-o-p 2b2 4b2 2b2 + + ln 1 Ep-o-p ) 6 R2 - 4b2 R2 R2
()
This corresponds to adhesive force:
()
Fp-o-p )
Ap-o-p b 12 l2
Fp-o-s )
Ap-o-s b 6 l2
and
(3)
The interaction energy between a particle (medium 1) surrounded by medium 2 (oil) and located at a distance l from a wall (medium 3) is given by
)]
(4)
where R is the distance from the particle center to the wall (R ) b + l). If b . l, the interaction energies become respectively
2
where νe is the electronic absorption frequency and n the refractive index of the medium in UV-visible. 2. Interaction Energies. The interaction energy between two particles dispersed in oil, characterized by a radius, b, and separated by a center to center distance, R (R ) 2b + l, with l the distance of separation), is given by25
[
Ep-o-s ) -
LA9908283
()
