Mesoscopic Solid Structures of 11-nm Maghemite, γ-Fe2O3

Synthesis and Characterization of the Superparamagnetic Fe3O4/Ag Nanocomposites. R. Ramesh , M. Geerthana , S. Prabhu , S. Sohila. Journal of Cluster ...
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Langmuir 2005, 21, 10234-10239

Mesoscopic Solid Structures of 11-nm Maghemite, γ-Fe2O3, Nanocrystals: Experiment and Theory† A. T. Ngo, J. Richardi, and M. P. Pileni* Universite´ Pierre et Marie Curie, Laboratoire des Mate´ riaux Mesoscopiques et Nanome´ triques, LM2N, U.M.R. 7070, BP 52, 4 place Jussieu, 75005 Paris, France Received April 28, 2005. In Final Form: July 18, 2005 Solid structures made of collapsed cylinders organized in hexagonal, stripes and wavy line-like structures are fabricated by slow evaporation of maghemite nanocrystals dispersed in hexane and subjected to an applied field perpendicular to the substrate. The sizes of the experimental structures are well described by a theory based on the minimization of the total free energy. Comparison between experiment and theory shows that the structures are explained by a labyrinthine instability enabled by a colloidal liquid-gas phase transition during the evaporation process. From the theoretical model and experimental data, it is concluded that the height determines the radius of the cylinders, whereas the phase ratio of the magnetic to the total volume and the field strength have little influence under the conditions studied here.

1. Introduction Instability phenomena enable the fabrication of new solid structures on micrometric and submicrometer scales. For example, nanocrystals can be organized in rings using the Marangoni instability.1-3 Several new instabilities such as the labyrinthine instability exist only in the case of magnetic and dielectric fluids. For magnetic nanocrystals, the organization by instability is of great interest because the structures can be tuned by a magnetic field. This opens a new pathway to the fabrication of artificially tailored structures on submicrometer scales, which are of interest both for fundamental research and technological applications. Recently,4-7 mesoscopic structures of cobalt nanocrystals were produced by applying a rather high magnetic field (from 0.1 to 0.8 T) during the solvent evaporation of the solution containing nanocrystals. Experiments and theory7,8 indicated that these structures are formed in the concentrated liquid phase induced by a colloidal liquid-gas phase transition.9 Similar structures were previously observed in ferrofluid systems using Hele-Shaw cells.10-14 Experiments with cobalt nanocrystals demon†

Part of the Bob Rowell Festschrift special issue. * To whom correspondence should be addressed. E-mail: [email protected]. (1) Ohara, P. C.; Gelbart, W. M. Langmuir 1998, 14, 3418. (2) Kurrika, V.; Shafi, P. M.; Felner, I.; Mastai, Y.; Gedanken, A. J. Phys. Chem. B 1999, 103, 3358. (3) Maillard, M.; Motte, L.; Ngo, A. T.; Pileni, M. P. J. Phys. Chem. B 2000, 104, 11871. (4) Legrand, J.; Ngo, A. T.; Petit, C.; Pileni, M. P. Adv. Mater. 2001, 13, 53. (5) Leo, G.; Chushkin, G. Y.; Luby, S.; Majkova, E.; Kostic, I.; Ulmeanu, M.; Luches, A.; Giersig, M.; Hilgendorff, M. Mater. Sci. Eng. C 2003, 23, 949. (6) Germain, V.; Pileni, M. P. J. Phys. Chem. B 2005, 109, 5548. (7) Germain, V.; Richardi, J.; Ingert, D.; Pileni, M. P. J. Phys. Chem. B 2005, 109, 5541. (8) Richardi, J.; Pileni, M. P. Phys. Rev. E 2004, 69, 016304. (9) Andersen, V. J.; Lekkerkerker, H. N. W. Nature 2002, 416, 811. (10) Cebers, A.; Maiorov, M. M. Magnetohydrodynamics 1980, 16, 21. (11) Rosensweig, R. E.; Zahn, M.; Shumovich, R. J. Magn. Magn. Mater. 1983, 39, 127. (12) Bacri, J. C.; Perzynski, R.; Salin, D. Endeavour 1988, 12, 76. (13) Elias, F.; Flament, C.; Bacri, J. C.; Neveu, S. J. Phys. I 1997, 7, 711. (14) Hong, C. Y.; Jang, I. J.; Horng, H. E.; Hsu, C. J.; Yao, Y. D.; Yang, H. C. J. Appl. Phys. 1997, 81, 4275.

strate that columns are mainly produced when the size distribution of nanocrystals is rather low (∼13%), whereas the fusion of these columns to form labyrinths is favored at higher values (>17%). These structures are often damaged by capillary forces at the end of the evaporation process.6 Here, we describe the mesoscopic structures obtained with maghemite (γ-Fe2O3) to demonstrate the influence of the magnetic material on these structures. Some similarities and differences with the study using cobalt nanocrystals6,7 are pointed out. 2. Method 2.1. Chemicals. Sodium dodecyl sulfate, Na(DS), and hexane were from Fluka, whereas iron chloride, Fe(Cl)2, and dimethylamine, (CH3)2NH2OH, were from Merck. Dodecanoic acid, C11H23COOH, was from Aldrich. Iron dodecyl sulfate, Fe(DS)2, was made as described in ref 15. 2.2. Apparatus. The solid structures were produced with an electromagnet (Oxford Instruments N38). Scanning electron microscopy (SEM) was done with a JEOL model JSM-5510 LV. The magnetization curve at room temperature was determined with a commercial SQUID magnetometer (Cryogenic S600). 2.3. Synthesis of γ-Fe2O3 Nanocrystals. The maghemite (γ-Fe2O3) nanocrystals are synthesized by using normal micelles as described elsewhere.16,17 Ferrous dodecyl sulfate, [Fe(DS)2] ) 1.3 × 10-2 M, is solubilized in aqueous solution and kept at 28.5 °C. Dimethylamine, [(CH3)2NH2OH] ) 8.5 × 10-1 M, is added to the micellar solution under vigorous stirring for 2 h. A magnetic precipitate appears. The solid and solution phases are separated by centrifugation, and the precipitate is washed and redispersed in ethanol. Dodecanoic acid, [CH3(CH2)10COOH] ) 0.5 M, is added to the solution, which is sonicated for 2 h at 90 °C. The resulting precipitate is washed with a large excess of ethanol, and the powder is dried in air. The nanocrystals coated with dodecanoic acid are dispersed in hexane. This leads to the synthesis of γ-Fe2O3 nanocrystals with an average diameter and polydispersity of 11 nm and 22%, respectively. 2.4. Fabrication of Structures of γ-Fe2O3 Nanocrystals. The structures are obtained by using a procedure similar to that for cobalt nanocrystals described elsewhere.4,7 Briefly, 200 µL of a concentrated solution of γ-Fe2O3 nanocrystals (9.5 × 10-3 mol (15) Moumen, N.; Veillet, P.; Pileni, M. P. J. Magn. Magn. Mater. 1995, 149, 67. (16) Ngo, A. T.; Pileni, M. P. J. Phys. Chem. B 2001, 105, 53. (17) Lalatonne, Y.; Richardi, J.; Pileni, M. P. Nat. Mater. 2004, 3, 121.

10.1021/la051149x CCC: $30.25 © 2005 American Chemical Society Published on Web 08/30/2005

Mesoscopic Solid Structures of 11-nm γ-Fe2O3

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L-1) is injected above a freshly cleaved 5 × 5 mm2 HOPG (highly oriented pyrolithic graphite) substrate placed at the bottom of a glass beaker. The beaker is then covered with Parafilm to reduce the evaporation rate. The solution is dried in the absence and in the presence of a magnetic field perpendicular to the substrate surface with various strengths (0.17, 0.33, 0.46, and 0.59 T). The morphology of the obtained solid structures is visualized with a scanning electron microscope. 2.5. Theory. Recently, a free-energy approach was developed to predict the hexagonal structures made of magnetic nanocrystals, which are observed after evaporation in a perpendicular field.7,8 Within the framework of this theory, the hexagonal structures are idealized as a hexagonal array of cylinders made of magnetic nanocrystals. The cylinder radius, r0, is a function of the external field, H0, the ratio of the magnetic phase to the total volume, Φ, and the cylinder height, L. For a given set of H0, Φ, and L, r0 is obtained by minimization of the free energy fh per surface area10,11,18

Fm 2L σ+ r0 sh

fh ) Φ

(1)

where sh is the surface area per cylinder. According to this equation, the structures form because of the competition between the surface and magnetic energy. The surface energy is characterized by the interfacial tension, σ, between the magnetic cylinders and their environment. Because of the relatively large height of the structures (>1 µm), the entropy term is neglected.18 The height is kept constant, and only r/0 ) r0/L is varied to find the optimal value. Therefore, the gravitational term is also constant and can be thus ignored. The height is probably determined by a complex interplay of solvent evaporation and dewetting, and our model is not applicable to explain the height of cylinders. As discussed in ref 8, the magnetic energy is calculated from the following equation:

Fm )

∫ ∫ HB ′ dBB′ drb - µ HB ∫ MB drb - µ HB ∫ HB drb µ µ H B M B dr b- ∫ H B dr b (2) 2∫ 2 B

Vm

0

0

0

0

Vm

0

0

Vm

0

Vm

d

Vm

()

dc 1 d 0.638mdF(γ-Fe2O3) p

volume-averaged magnetization is used during the evaluation of the demagnetization field.19 All calculations were carried out using the homemade Fortran package HEXALAB,20 which is available on request. 2.6. Procedure to Determine the Variation of the Parameters Controlling the Mesostructures. We focus on the study of the hexagonal structures because their geometry is more accurately measured than those of the others. For the comparison between experimental data and the theoretical model, some parameters such as the radius r0, the height L of the cylinders, and the phase ratio Φ are required to characterize the micrometric patterns. The ratio of the magnetic phase to the total volume (Φ) is calculated from the cylinder radius and their separation a.

d

2 d

The magnetic induction B B (r b) at a point b r in the hexagonal structure is calculated from the magnetization M B (r b) and the total magnetic field H B (r b): B B (r b) ) µ0(H B (r b) + M B (r b)). µ0, H B d(r b), and Vm are the magnetic permeability of vacuum, the demagnetization field, and the volume occupied by the magnetic liquid, respectively. In ref 8, we demonstrate the equivalence of eq 2 and the usual form of the magnetic energy. Equation 2 is used to obtain numerically stable values. The magnetization is calculated from the total magnetic field using the experimental magnetization curve of a deposition of γ-Fe2O3 nanocrystals without a field. The experimental curve was measured at room temperature using a SQUID (Figure 1). No remnant or coercive field is observed. This indicates that the nanocrystals are in a superparamagnetic state at room temperature. The measured total magnetization of the sample is divided by the volume occupied by the nanocrystal film. This volume is estimated from the equation

Vd )

Figure 1. Experimental room-temperature magnetization curve for maghemite nanocrystals deposited on HOPG without an applied field.

3

(3)

where md is the mass of the deposited nanocrystals. F (γ-Fe2O3) ) 4.85 103 kg m-3 is the mass density of γ-Fe2O3. dp and dc are the particle diameter (11 nm) and the approximate center-tocenter distance of the γ-Fe2O3 nanocrystals (12 nm), respectively. Both values are deduced from TEM images.17 The total field, H B(r b), within the hexagonal structure is reduced with respect to the external field, H B 0, due to the negative demagnetization field, H B d(r b). The calculation of the demagnetization field and the correct treatment of the long-range dipolar interactions are explained elsewhere.18,19 The approximation of (18) Richardi, J.; Ingert, D.; Pileni, M. P. Phys. Rev. E 2002, 66, 046306. (19) Richardi, J.; Pileni, M. P. Eur. Phys. J. E 2004, 13, 99.

Φ)

πr02

( )

x3 2 a 2

(4)

These geometrical parameters are measured on the SEM images. The radius and the height are obtained by measuring the average width and length of the cylinders lying on the flat substrate. To determine Φ, we need to measure the center-to-center distance a between cylinders. For this, two methods are used: (i) The distance between two cylinders on the SEM pictures is measured. (ii) The average surface area per cylinder is measured by counting the cylinders in a given large area on the substrate. From the average surface area, sh ) (x3/2)a2, a is calculated. These two methods give the same values within experimental error. The errors are calculated by taking into account the precision of the measurement and the size distribution of the cylinders. From the model described in section 2.5, the interfacial tension σ in eq 1 is obtained. From these values, the mechanism of the mesostructure formation is deduced. To study the influence of the experimental conditions (H0, Φ, and L) on the size of the structures observed experimentally, an average interfacial tension is used. The theoretical values of r/0,theory ) r0,theory/L are calculated for the experimental H0, Φ, and L using the average σ value and are compared to the experimental value (r/0,exp). We consider structures characterized by similar heights and phase ratios for the study of the influence of the magnetic field strengths. (20) The Fortran package HEXALAB is a highly optimized code of about 10 000 statements that calculates the geometry and energy of magnetic fluid patterns. These are not restricted to hexagonal or labyrinthine patterns. HEXALAB was developed by J. Richardi at the LM2N (direction: M. P. Pileni).

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Figure 3. SEM images of solid structures made of maghemite nanocrystals deposited on HOPG with a nonzero applied field of 0.17 T during the deposition process.

Figure 2. SEM images of solid structures made of maghemite nanocrystals deposited on HOPG without an applied field at 45° tilt (a) and with a nonzero applied field of 0.59 T during the deposition process at zero angle (b, d-g) and at 45° tilt (c, h).

3. Results and Discussion γ-Fe2O3 nanocrystals are deposited as described above on a substrate. During solvent evaporation, the system is subjected or not to an applied field perpendicular to the substrate. For deposition with no applied field, on tilting the sample by 45°, the SEM image (Figure 2a) shows inhomogeneous structures forming islands without a well-defined shape. By applying a magnetic field during the deposition process, the SEM images change markedly. In the range of the investigated field, its strength markedly modifies the structural shape with respect to the structure with no field. Figures 3, 4, and 2b-h show the structures obtained when the applied magnetic fields are 0.17, 0.46, and 0.59 T, respectively. Similar behavior is observed for a 0.33 T applied magnetic field. In all cases, four different structures are observed: (i) A local array of hexagonal structures made of elongated aggregates are observed (Figures 2b, 3a, and 4a). By tilting the samples, it is shown that cylinders are formed (Figure 2c). (ii) The cylinders are interconnected in head-to-tail lines with and without preferential orientations (Figures 2d and e, 3b and c, and 4c). (iii) The cylinders are organized in a dense array of hexagonal structures (Figures 2f and 4b). (iv) Two cylinders are associated to give stripes (Figures 2g, 3d, and 4d).

Figure 4. SEM images of solid structures made of maghemite nanocrystals deposited on HOPG with a nonzero applied field of 0.46 T during the deposition process.

At a very high applied magnetic field (0.59 T), in some regions the fallen cylinders are closely packed (Figure 2h). For any applied field strength, the observed cylinders are uniform in size in a given domain. Their average lengths vary from 2 to 5 µm from one domain to another on the substrate. No preferential length or structure is observed with the strength of the applied magnetic field during the evaporation process. In the following text, we concentrate our study on isolated and well-defined cylinders as represented in Figures 2b, 3a, and 4a. Parameters such as the radius r0 and height L of the cylinders and their center-to-center distance a are measured from the SEM images. We assume that the cylinders are upright during the formation of the structures and collapse because of capillary forces at the end of evaporation as shown by video with cobalt nanocrystals.6 The first objective is to determine the formation mechanism of the mesostructure. This is reached by estimating the interfacial tension value. The phase ratio Φ is calculated by using the various measured parameters (see above). Table 1 shows the average parameter values obtained at various strengths of the applied magnetic field. The errors are calculated by taking into account the precision of the measurement and the size distribution of the cylinders. The original data are the cylinder radius r0,

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Table 1. Values of the Radius (r0), Height (L), Separation (a), and Phase Ratio (Φ) of the Cylinders for Structures of Maghemite Nanocrystals Obtained at Various Field Strengthsa

a

sample number

magnetic field [T]

r0 [µm]

L [µm]

a [µm]

Φ

σ [N m-1]

1 2 3 4 5 6 7 8 9

0.17 ( 0.02 0.33 ( 0.02 0.33 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.59 ( 0.02 0.59 ( 0.02

0.49 ( 0.06 0.35 ( 0.03 0.47 ( 0.06 0.62 ( 0.07 0.67 ( 0.06 0.47 ( 0.06 0.62 ( 0.06 0.55 ( 0.09 0.65 ( 0.06

2.28 ( 0.12 1.98 ( 0.08 2.16 ( 0.15 3.75 ( 0.12 3.87 ( 0.12 3.89 ( 0.12 4.00 ( 0.15 2.92 ( 0.12 3.30 ( 0.10

2.94 ( 0.26 2.10 ( 0.19 2.82 ( 0.24 4.76 ( 0.33 4.61 ( 0.43 4.61 ( 0.50 5.05 ( 0.46 3.66 ( 0.21 3.77 ( 0.38

0.10 ( 0.04 0.10 ( 0.03 0.10 ( 0.04 0.06 ( 0.02 0.08 ( 0.03 0.04 ( 0.02 0.06 ( 0.02 0.08 ( 0.03 0.11 ( 0.03

1.9 × 10-4 1.4 × 10-4 2.4 × 10-4 3.0 × 10-4 3.2 × 10-4 1.9 × 10-4 2.8 × 10-4 3.0 × 10-4 3.5 × 10-4

Surface interfacial tensions (σ) are obtained by a comparison of theory with experiments. Table 2. Values of the Reduced Radius (r/0,exp) and Reduced Separation (a*) of the Cylinders for Structures of Maghemite Nanocrystals Obtained at Various Field Strengthsa

a

sample number

magnetic field [T]

L [µm]

Φ

r/0,exp

r/0,theory

a*

1 2 3 4 5 6 7 8 9

0.17 ( 0.02 0.33 ( 0.02 0.33 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.46 ( 0.02 0.59 ( 0.02 0.59 ( 0.02

2.28 ( 0.12 1.98 ( 0.08 2.16 ( 0.15 3.75 ( 0.12 3.87 ( 0.12 3.89 ( 0.12 4.00 ( 0.15 2.92 ( 0.12 3.30 ( 0.10

0.10 ( 0.04 0.10 ( 0.03 0.10 ( 0.04 0.06 ( 0.02 0.08 ( 0.03 0.04 ( 0.02 0.06 ( 0.02 0.08 ( 0.03 0.11 ( 0.03

0.22 ( 0.04 0.18 ( 0.03 0.22 ( 0.05 0.17 ( 0.04 0.17 ( 0.03 0.12 ( 0.04 0.16 ( 0.03 0.19 ( 0.05 0.20 ( 0.03

0.25 0.24 0.22 0.15 0.15 0.14 0.14 0.17 0.16

1.28 ( 0.18 1.06 ( 0.14 1.30 ( 0.20 1.23 ( 0.12 1.19 ( 0.15 1.19 ( 0.17 1.26 ( 0.16 1.25 ( 0.12 1.14 ( 0.15

The theoretical reduced radius (r/0,theory) is calculated using a surface tension of 2.5 × 10-4 N m-1.

the height L, and the cylinder distance a, which have experimental errors of about 10, 5, and 10%, respectively. The larger errors of about 20% for r/0 ) r0/L are due to the fact that they include the errors in both L and r0. The error in Φ is even larger because it depends as a quadratic function of both r0 and a according to eq 4. The interfacial tension used to reproduce the experimental parameters is calculated as described above. From Table 1, the interfacial tension varies from 1.4 × 10-4 to 3.5 × 10-4 N m-1. To study how the experimental errors in H0, L, Φ, and r/0 influence the interfacial tension, σ is recalculated for all structures by varying H0, L, Φ, and r/0 within experimental errors. It is observed that σ is only slightly modified by the experimental errors in H0, L, and Φ. However, the errors in r/0 drastically change the interfacial tension values. For example, a variation between 1.6 × 10-4 and 4.2 × 10-4 N m-1 is obtained for structure 7. This shows that the variation of σ observed in Table 1 can be mainly explained by the experimental errors in r/0. These values are close to those expected for a liquid-gas phase transition.21 This confirms data previously obtained with cobalt nanocrystal fluids and demonstrates that the mechanism proposed by the Rosenweig instability22,23 cannot be retained. In the latter case, the surface tension of the solution is expected to be close to that of the solution in contact with air (which is close to that of the pure solvent, 0.0184 N m-1 for hexane;24 see the discussion in ref 7). In the following text, we study the change in r/0 with various parameters. Let us first compare the calculated and measured r/0 values. Taking into account the average interfacial tension calculated from the σ value in Table 1 (2.5 × 10-4 N m-1), the theoretical r/0 ) r0/L values are (21) de Hoog, E. H. A.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1999, 103, 5274. (22) Cowley, M. D.; Rosensweig, R. E. J. Fluid Mech. 1967, 30, 671. (23) Zahn, M. J. Nanopart. Res. 2001, 3, 73. (24) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, U.K., 2001.

obtained from the experimental H0, Φ, and L. Table 2 shows good agreement between experimental and calculated values. Note that the experimental r/0 of structure 2 deviates considerably from the theoretical value. For the same H0 and Φ and L values similar to those in structure 2, structure 3 yields a larger r/0 that agrees well with the theoretical result. Therefore, the deviation of structure 2 might be due to statistical fluctuations and does not necessarily indicate a systematic failure of the model. The variation of the theoretical r/0 value with the applied magnetic field, H0, is calculated at fixed L and Φ values and compared to that obtained experimentally. From Table 1, structures (1, 2, 3), (4, 7), and (8, 9) are characterized by similar L and Φ values such as (L ) 2.2 µm, Φ ≈ 0.1), (L ) 3.9 µm, Φ ≈ 0.06), and (L ) 3.1 µm, Φ ≈ 0.1), respectively. Figure 5a shows a monotonic decrease in theoretical r/0 with the applied magnetic field. Because of the rather large experimental error, only poor agreement between the experimental and calculated values is obtained. The variation of r/0 with the ratio of the magnetic phase to the total volume, Φ, is calculated at a fixed applied field (0.46 T) and at two different L values (2.2 and 3.9 µm, respectively). Figure 5b shows that the experimental data are the same order of magnitude as the theoretical values. Let us consider a geometrical model taking into account the separation between cylinders. At low phase ratios, the separation between cylinders a is rather large, and it can be considered to be isolated. In such a case, the influence of the surroundings of the cylinders on their radii can be neglected, and then a and r/0 are expected to be independent. This is confirmed in Table 2 showing clearly a change in r/0 from one structure to another, whereas the reduced cylinder separation a* ) a/L remains constant (around 1.2). Therefore, a geometrical relation between r/0 and Φ can be used to explain the experimental

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Figure 6. Comparison of the experimental and theoretical variation of the reduced radius as a function of the cylinder height. The stars denote the r/0 recalculated from the theory at H0 ) 0.33 T and Φ ) 0.1 using the σ values given for each structure in Table 1.

Figure 5. (a) Dependence of the reduced cylinder radius r/0 in hexagonal patterns on the external field. The theoretical curves for different heights L and phase ratios Φ are compared to the experimental data points. (b) Dependence of the reduced cylinder radius r/0 in hexagonal patterns on the phase ratio. The theoretical curves for two different heights are compared to the experimental data points. The dashed-dotted line shows the reduced radius calculated from eq 5 using an average a* of 1.2.

data. This relation is obtained from eq 4 rewritten in the following form:

r*0 )

x

x3 Φa* 2π

(5)

Using 1.2 as an a* average value, the r/0 as a function of Φ calculated from eq 5 is shown in Figure 5b. The experimental data are well described by this curve, indicating that the dependence of r/0 as a function of Φ is explained by a geometrical model with r/0 going to zero for Φ f 0, in contrast to the other theoretical curves. In Figure 6, the theoretical evolution of r/0 as a function of L is shown for three different conditions. Theory predicts that the reduced radius decreases with increasing height. The experimental data were mostly obtained at field strengths and phase ratios different from the values of H0 and Φ used for the theoretical curves. Therefore, theoretical and experimental values cannot be directly compared. To cope with this problem, we recalculated theoretical r/0 values at 0.33 T and Φ ) 0.1 using the individual interfacial tensions in Table 1 obtained for each structure. Please recall that if the actual experimental conditions had been used to recalculate r/0 we would have obtained the experimental values. Therefore, the comparison between the experimental and recalculated r/0 values indicates the variation in r/0 caused by the different field strength and phase ratio, which is small in comparison

with the experimental error. The comparison of the theoretical curve obtained at 0.33 T and Φ ) 0.1 and the recalculated values indicated the quality of the theoretical model in predicting the experimental data. We conclude that experiment and theory actually indicate a slight but significant decrease of the reduced radius with the height. Similar studies were performed with cobalt nanocrystals dispersed in hexane.7 In both cases, rather good agreement for the mesostructure mechanism is observed. From the experimental parameter obtained with hexagonal patterns and from the minimization of the free energy, it is deduced that columns are formed in the concentrated solution of nanocrystals induced by a liquid-gas phase transition. In the case of cobalt nanocrystals, the pattern formation is observed by video microscopy.6 The observed phenomenon agrees well with a gas-liquid transition. Thus, it is found that the cylinders form within the solvent layer during the evaporation process and migrate to form a hexagonal array. The surface tension determined in both cases is very low compared to that of the solution in contact with air. In both cases, the reduced radius slightly decreases with the height of the columns. Some differences are observed. Let us first list them: (i) Using the same experimental setup and nanocrystal concentration, a marked difference in the mesostructure is observed. With γ-Fe2O3 nanocrystals, the structures are less dense. This involves a larger distance between the cylinders (i.e., a decrease in the magnetic volume fraction, Φ, in the present case). (ii) With γ-Fe2O3, most structures are in fact cylinders isolated or bound to others. Conversely, with cobalt nanocrystals the size distribution of nanocrystals plays a crucial role in column production.25 Under the experimental conditions described in this article (22% size distribution), only labyrinths are formed with cobalt nanocrystals, whereas with γ-Fe2O3 nanocrystals cylinders are produced. It is now rather difficult to explain such differences. Of course, the magnetic material used is not the same, but in the theoretical model this was taken into account. We also have to point out that the accuracy of the model does not allow us to predict what type of mesostructure could be expected by taking into account the size of the nanocrystals and the magnetic energy. In the future, other types of magnetic nanocrystals have to be taken into account for a better understanding of these systems. (25) Germain, V.; Pileni, M. P. Adv. Mater. 2005, 17, 1424.

Mesoscopic Solid Structures of 11-nm γ-Fe2O3

4. Conclusions The behavior of a magnetic fluid of γ-Fe2O3 nanocrystals evaporated in magnetic fields perpendicular to the substrate surface is analyzed by SEM measurements. Collapsed cylinders organized in hexagonal, stripe, and wavy line-like structures are formed. No influence of the magnetic field strength on the morphology of the structure is experimentally noted. For hexagonal structures, we used a recently developed theoretical model based on the minimization of the total free energy. In this theory, the cylinder radius is a function of the field, the phase ratio, and the cylinder height. Within the accuracy of the experimental data, general agreement between experiment and theory is found as previously observed for depositions of cobalt nanocrystals. From a comparison of theoretical values with experimental data, an average interfacial surface tension of 2.5 × 10-4 N m-1 is calculated.

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It is deduced that the formation of the structures is due to labyrinthine instabilities enabled by a colloidal gasliquid transition. Under the conditions studied here, the size of the structures is mainly controlled by the height, whereas the phase ratio and the field strength have only a small influence. In the future, it will be of interest to investigate whether a decrease in the height, which may be realized by reducing the initial nanocrystal concentration, will enable the fabrication of structures on scales of