Tunable Formation of Ferromagnetic Nanoparticle Rings: Experiments

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Tunable Formation of Ferromagnetic Nanoparticle Rings: Experiments and Monte Carlo Simulations Wang-Feng Ding, Ziwei Li, Hang Zhou, Bo Zhao, Jian-guo Wan,* Fengqi Song, and Guang-Hou Wang National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, P. R. China S Supporting Information *

ABSTRACT: Anisotropic interactions in self-assembly of nanostructures always result in novel patterns. We demonstrate that, by the aid of high-power sonication, 16 nm ε-cobalt ferromagnetic nanoparticles (FMNPs) dispersed in dilute suspensions at room temperature would self-assemble into rings as small as ∼50 nm in diameter. The well-defined size and shape and the uniform surfactant coating layer of the cobalt nanoparticles enable quantitative calculations of particle−particle and particle−interface interactions. The experiments, in conjunction with cluster-moving Monte Carlo simulations mimicking the self-assembly in solution and dynamics during solvent evaporation, have revealed three key factors that influence the ring formation most, i.e., FMNP density, dipolar strength, and surfactant layers. Two very different mechanisms of the FMNP-ring formation are found by changing these factors. The results provide a guide to the fabrication of nanorings as well as diverse patterns assembled by FMNPs.

1. INTRODUCTION Ferromagnetic rings have attracted much attention in the past decade due to their unique magnetic properties and magnetoelectronic applications.1−16 Studies on microstructured magnetic rings show that in a flux-closure (FC) or “vortex” state the magnetization is orientated circularly without any domain walls.1,2,13 The chirality of the magnetization rotation, i.e., clockwise and anticlockwise, has been utilized to store a data bit.1 However, the sizes of these rings are far from their size minima, which depend on the remanence of magnetic materials, and therefore can be substantially reduced while still maintaining the FC state. Conventional means of fabricating nanosized rings are quite limited. Nevertheless, Tripp et al. have demonstrated that 27 ± 4 nm Co nanoparticles (NPs) can self-assemble into braceletlike rings with typically 5−12 particles.3 Evidence has shown that such highly localized positioning of nanoparticles is directed by the magnetic dipolar forces in competition with isotropic short-ranged interactions.15,16 Off-axis electron holographic images confirm that these ferromagnetic nanoparticle (FMNP) rings support the bistable FC state at room temperature.5,15 Moreover, the magnetic rings in the sub-100 nm range are supposed to display distinct magnetic properties as their dimensions are comparable to the exchange length of the magnetic material.13 For example, the bistable FC states of the bracelet nanorings could be reversed by coaxial magnetic pulses, a phenomenon unique to nanomagnetism.12 With the spatial confinement of both the excitons and magnetic fields, the magnetic nanorings are promising as quantum rings.17 Considerable efforts have been devoted to understand the solution-based assembly of magnetic NPs due to their unique © 2012 American Chemical Society

features, such as single domains and giant dipolar moments.18−32 Magnetic NPs under a critical volume are superparamagnetic at room temperature, and their assemblies in zero field are just like nonmagnetic nanoparticles.19,20,28 While under an external magnetic field, superparamagnetic NPs, with their magnetic moments getting aligned with the applied field, move and assemble via anisotropic dipolar forces in solution, yielding chains, rods, elongated superstructures, etc.18,27,30,31 Magnetic NPs above the superparamagnetic limit (e.g., 10 nm for Co33), on the other hand, are ferromagnetic and possess substantial dipolar moments as individual nanomagnets at 300 K.29 For example, in the absence of external magnetic fields, Co NPs with diameters of 10.0−11.2 nm display distinct assembly patterns from those formed by nonmagnetic NPs.32 For larger magnetic NPs with strong anisotropic interactions, notable dipolar structures such as linear chains, necklace-like rings, and branched assemblies have been observed.10,22,23 In spite of the numerous studies on magnetic NP assemblies, reports on the FMNP rings are much fewer than those on other forms of arrangements, and these rings reported usually consist of FMNPs with sizes around 30−40 nm.11,14,16 This is because underlying the seemly straightforward dipole-directed formation of nanorings are subtle nanoscopic interactions of great complexity.34,35 FMNPs in solution are subjected to various dynamic forces such as compressive or shear stresses, gravity, and magnetic or electric fields.36−40 Even in a static equilibrium Received: March 2, 2012 Revised: April 11, 2012 Published: April 25, 2012 10805

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Figure 1. (a) Scheme of the particle−particle, the particle−liquid−air interface, and the particle−substrate interactions modeled in the simulation. (b) Dependence of the interaction potentials on the interparticle distance. The dipolar, the sum of steric and van der Waals (vdW), and the total potentials between two particles with diameter d = 16 nm and coating layer thickness δ = 2 nm are plotted. For the dipolar interaction, the most stable head−tail configuration is chosen.

state, interparticle interactions other than the dipolar force would have great impacts on the nanoring formation.24,34,35 So to assemble nanostructures driven by a specific force requires the reduction of other interactions to their minima. The formation of FMNP rings has also been predicted by theoretical simulations, most of which were performed in twodimensional (2D) planes or three-dimensional (3D) boxes.4,32,41−43 Since nanostructures observed in experiments are always attached to substrates, there are no such ideal substrates like the 2D planes in simulations. Besides, though cryo-transmission electron microscopy (cryo-TEM) studies on vitrified ferrofluids have provided some information on the FMNPs in solution phase,22,23 there still lacks direct observation techniques on the thermodynamical states under ambient conditions. Consequently, significant discrepancies arise between these simulations and experiments. In this work, we have investigated three key factors, i.e., FMNP concentration, magnetic dipolar moment, and surfactant coating layer, that affect the FMNP-ring formation most, by means of both experiments and cluster-moving Monte Carlo simulations. In the experiments, nanorings mainly composed of 5−8 ε-cobalt FMNPs with the size ∼16 nm were prepared by introducing a crucial step of high-power sonication. Changes applied on either the suspension concentration or particle size would greatly change the assembly patterns. Simulations on both the self-assembling process in solution and dynamics during the solvent evaporation were performed to understand the observed assemblies as well as to predict morphologies of the colloidal systems with different parameters.

Co2(CO)8 in the reaction, the average size of the Co NPs can be controlled. 2.2. Preparation and Characterization of Nanoparticle Assemblies. The black colloidal suspensions extracted from reacting flask were diluted by pure cyclohexane and centrifuged at 7000 rpm for 5 min to remove the excess of surfactants and particles much smaller than the average size. Then the sediments were redispersed in DCB to different concentrations. The high-power sonication was carried out in an ultrasonic cell crusher, which has a demagnetized amplitude lever with fine adjustable power output. Sample dispersions (8 mL) were sonicated intermittently at 10 W for 5 min, with the temperature controlled under 40 °C. Afterward, the transparent (or light brown depending on the NP density) suspensions were aged for 3 min in air and then drop-cast to 400 mesh carbon-coated copper grids. The grids were rested on filter papers with the side of carbon films downward, so that each mesh served as a reservoir for the solvent, which was allowed to evaporate steadily in air for 10−20 min. For a very dilute suspension, the drop-cast procedure was repeated several times to ensure a proper density of the NPs. Note that the evaporation speed of solvent depends critically on the temperature. A rapid evaporation would introduce various dynamic forces to the system, making the assembling process unsteady and complicated. Here, all the self-assembling processes were carried out at room temperature (∼296 K) with a relative humidity of 30−40%, where the evaporation of nonvolatile DCB (with a boiling point of 454 K) was slow and steady. The samples were characterized in a Tecnai F20 transmission electron microscope integrated with Gatan’s third generation of postcolumn energy filters (GIF Tridiem), with the field emission gun operated at 200 kV. The three energy windows used for elemental mapping in the EFTEM image were 714, 754, and 799 ± 20 eV for cobalt and 484, 514, and 547 ± 15 eV for oxygen. 2.3. Monte Carlo Simulations. A model taking account of the particle−particle, particle−liquid−air interface, and particle−substrate interactions has been established on the basis of the experiments. As depicted in Figure 1a, the system consists of monodisperse particles in a 3D box. The particle has a core with diameter d and magnetic moment m and is coated with a surfactant layer of thickness δ. As widely applied in the context of colloidal magnetic NPs, the interaction forces between two particles are summarized into three terms, i.e., dipolar, steric, and vdW interactions;24,30 the total energy of the interparticle

2. METHODS 2.1. Synthesis of ε-Cobalt Nanoparticles. We have employed the standard thermodecomposition method to synthesize the colloidal ε-Co NPs.21 All the reagents were purchased from Alfa Aesar (Tianjin, China) and used without further treatments. In the case of 16 nm sized NPs, Co2(CO)8 (0.60 g, stabilized with 1−5% hexane) dissolved in odichlorobenzene (DCB) (4 mL, 99%) at room temperature was quickly injected into the refluxing bath of DCB (10 mL) in the presence of oleic acid (OA) (0.2 mL, 99%) and tri-noctylphosphine oxide (TOPO) (0.1 g, 98%). The mixture was kept up to 182 °C for 30 min in an oil bath. All the reactants were degassed prior to the argon-protected reactions. Both Xray diffraction and high-resolution TEM images confirmed the ε-phase of the cobalt nanocrystals. By varying the dose of 10806

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Figure 2. (a) A representative bright-field TEM image of Co ferromagnetic nanoparticles (FMNPs) cast from suspension C1 on a carbon-coated copper grid. (b−d) High-resolution TEM images of three basic structures: (b) nanoring, (c) nanoraft, and (d) nanochain. In (b), the Co NP is measured to be 16 nm in diameter with a uniform coating layer of thickness 2 nm.

liquid−air interface, and the bottom as the substrate. With the liquid−air interface steadily moving downward, particles were confined below the interface due to the large energy increase for particles to cross the solvent surface.24 The particle− substrate interaction is defined by a steric repulsion due to the coating surfactants and a vdW interaction between a sphere and a half-space. (See the Supporting Information for detailed particle−interface interactions.) Here the dropping speed of the liquid−air interface in the simulations is much faster than that in the experiments, where the nonvolatile solvent DCB was used. Nevertheless, the morphologies obtained by choosing a wide range of evaporating speed are roughly the same, particularly when a system of low volume concentration is concerned.

interactions is calculated by summing the terms in eqs S1−S3 (see explicit formula in the Supporting Information). For parameters d = 16 nm and δ = 2 nm, the dipolar, the sum of steric and vdW, and the total potentials between two particles are plotted in Figure 1b, where the most stable head−tail configuration is chosen for the dipolar interaction. It is worth noting that the magnitude of the steric + vdW potential (with a minimum of −3.8 kT) is almost of 1 order smaller than that of the dipolar interaction. On the basis of the above model, we performed the simulations using a cluster-moving Monte Carlo algorithm.18,30 In each iteration of the simulation, a trial movement either on a particle or a cluster of particles as a whole is made randomly, which causes an energy difference of ΔU. The movement is accepted with the probability exp(−ΔU/kTeff), where we have introduced the effective temperature, Teff. In the process of sonication, the applied external energy source acts like thermodynamical fluctuations on the particle assembly, augmenting the value of Teff. Here all the simulations were started from corresponding configurations obtained at Teff = 1000 K, where no aggregation of particles occurred, and subsequently carried out in two steps at Teff = 300 K. First, the particles were allowed to self-assemble in the simulation box with periodic boundary conditions in each direction. The average number of trial movements, Ntry, before an actual one was made, was used to assess the equilibrium of the system. An equilibrium state of the system is characterized by a large Ntry. When the particles got highly localized through aggregations, the system came to a relatively stable state. Thereafter, simulations on solvent evaporation process were performed as the second step, with the top of the simulation box set as the

3. RESULTS AND DISCUSSION 3.1. Experiments. The as-synthesized 16-nm ε-cobalt FMNPs in DCB tend to aggregate into micrometer-sized grains immediately after being extracted from the reaction flask at room temperature, displaying strong interparticle attractions. On the edge of these aggregations randomly oriented chain-like structures are observed, indicating considerable anisotropic dipole−dipole interactions between NPs (see Supporting Information, Figure S1). The magnetic measurement on these aggregates by SQUID (superconducting quantum interface device) shows weak ferromagnetism at room temperature, with saturation magnetization of 89 emu g−1 and coercive field of 49 Oe (see the Supporting Information, Figure S2). Sonication is a routine method of dispersing NP suspensions.3,25 An appropriate sonicating power should completely disperse the aggregates in solution without any 10807

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in reactants, Co nanoparticles always grow with a uniform coating layer of about 2 nm in thickness. Considering the straight head-to-tail length of the OA structure, i.e., 1.917 nm as shown in Figure 3a, we believe that the Co NP is covered with a monolayer of the OA molecules. The energy-filtered TEM (EFTEM) elemental map in Figure 3b (red: cobalt; cyan: oxygen) also qualitatively supports this conclusion. Therefore, the size of magnetic cores can also be explicitly determined. Measurements over several hundred NPs give a narrow size distribution with an average diameter of 16 nm (Figure 3c). For suspensions with high concentrations, very different assemblies are observed. Figures 4a,b exhibit assemblies cast

damage to the NPs. Here the power density applied is much higher than that in conventional ultrasonic cleaners. As a key procedure, the sonication releases the FMNP systems from whatever trapped states when they were prepared. Thus, the well-dispersed Co FMNPs are allowed to self-assemble directed only by interparticle interactions, greatly simplifying the analysis. We have prepared suspensions with three different concentrations at room temperature, denoted as C1, C2, and C3, respectively. Their NP densities are estimated to be C1: 1 × 10−10, C2: 2 × 10−9, and C3: 6 × 10−9 mol L−1. Figure 2 shows a representative TEM image of the assemblies cast from suspension C1 on a carbon-coated TEM grid (more TEM images taken randomly over the same specimen are shown in Figure S3 of the Supporting Information). These images exhibit small clusters composed of a few discrete Co FMNPs on the substrate, mainly involving nanorings, nanorafts, and nanochains. Counting of the three basic structures over several meshes of the TEM grid indicates that clusters with 5−8 NPs are most likely to form the structure of rings, while larger ones tend to be closely packed. Here the diameters of both the Co FMNPs (∼16 nm) and the nanorings (∼50 nm for 6-NP rings) are much smaller than those ever reported.3,10,14,16 Typical structures of the three basic configurations, i.e., nanorings, nanorafts, and nanochains, are shown in Figures 2b−d, respectively. The interparticle distances of the rings and chains are slightly larger than those of the rafts. This can be attributed to the different approaches of pinning to the substrate related to their geometries. The particle size and the thickness of the surfactant layer are of great importance in the modeling of interactions between the Co FMNPs. From these enlarged TEM images in Figures 2b− d, one can observe a uniform coating layer on the surface of each NP, displaying a core−shell structure. Studies on the colloidal Co NPs synthesized by exactly the same method demonstrate that OA molecule chains get chemisorbed on the Co nanoparticle surface via covalent Co−O bond, as schematically illustrated in Figure 3a.21,44 We have found in experiment that when enough or an excess of OA was present

Figure 4. (a, b) Representative TEM images of the samples cast from the suspensions (a) C2 and (b) C3, respectively. The insets are enlarged images of typical structures deposited on substrate. (c, d) Typical assemblies obtained by the same treatments, as in Figure 2, of the as-synthesized (c) 14 nm and (d) 18 nm ε-Co nanoparticles.

from the suspensions C2 and C3, respectively. As seen from Figure 4a, the FMNPs have formed islands of nanoparticle monolayers (or 2D nanorafts), which are hexagonally closepacked on the substrate. This phenomenon is similar to those reported when the solvent of organic solution containing nonmagnetic metallic nanoparticles was evaporated.36,45 The only difference is that the nanorafts here possess noticeable defects in the form of hollows and cleavages, which imply the presence of anisotropic interactions. For larger assemblies resulting from the higher particle density (as in Figure 4b), the rafts get superposed in the center, displaying core−shell-like patterns in the TEM images. Despite the direct imaging of the FMNP assemblies, one should bear in mind that the structures confined on the substrate are far from the equilibrium of thermodynamics as in solution. The geometrical transformations from a solution phase to a deposited state are referred to the Simulations section. As the magnetic moments of the Co FMNPs depend critically on the particle volumes, the dipolar strength could be tuned accordingly. Following the same procedures with the only change of the dose of reactant Co2(CO)8, 14 and 18 nm Co NPs were synthesized, purified, diluted, and sonicated,

Figure 3. (a) Schematic of a Co FMNP coated with a monolayer of oleic acid (OA) molecules (top); chemical structure of OA with a straight head-to-tail length of 1.917 nm (bottom). (b) A bright-field TEM image of a 6-NP ring (left) with its corresponding energy-filtered TEM (EFTEM) elemental map (red: cobalt; cyan: oxygen) (right). (c) A statistical analysis of the Co FMNP size indicating a narrow distribution of the magnetic cores, with an average diameter of 16 nm. 10808

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Figure 5. Computational results for particles with diameter d = 16 nm and coating layer thickness δ = 2 nm. (a) Well-separated small clusters in solution phase for a volume fraction of 0.001 vol % and (b) corresponding deposits on substrate after solvent evaporation. The products for a higher concentration of 0.1 vol % are shown in (c) and (d), respectively.

respectively, in sequence. As seen from Figure 4c, for the 14 nm Co FMNPs, nanorafts prevail with few dipolar structures, suggesting the domination of van der Waals (vdW) attractions. In contrast, for the 18 nm Co FMNPs (as in Figure 4d), the nanorafts have almost disappeared, accompanied by an increase in the length of nanochains as well as the size of nanorings. However, despite of the enhancement of dipolar interactions, fewer rings were formed, and small nanorings with less than 10 NPs can barely be seen. 3.2. Simulations. We first studied systems of dipolar particles with d = 16 nm and δ = 2 nm. For an extremely low volume fraction (0.001 vol % in Figure 5a), the initially dispersed particles have aggregated into well-separated small clusters, which can be classified into three basic types: 1D chain, 2D ring, and 3D close-packed structure. As the process of aggregation was greatly slowed down by the low particle density, at the early stage of assembly, only metastable chains were formed, which would either grow longer by absorbing particles nearby or bend into rings with dipolar stability. When the cluster got larger (usually with more than 10 particles), it may transform into a 3D structure as time evolved. However, the sizes of clusters were much constrained by the low volume fraction. As shown in Figure 5a, very few of clusters have adopted the 3D configurations. The possibility for the small

clusters to coalesce was even smaller, even during the evaporation process where strong density fluctuations were present at nanoscale. Thus, the deposits after evaporation (as in Figure 5b) have kept the dispersity of the clusters in solution. Moreover, the dipolar structures of small sizes underwent little deformation during the pinning onto the substrate. Therefore, we believe that the experimental results in Figure 2 and Figure S3, to a large extent, reflect the thermodynamical structures of the clusters in solution. For a much higher particle density (0.1 vol % in Figure 5c), aggregates deposited on substrate differ dramatically from those in solution. Because of the high particle density, neighboring small clusters tend to coalesce into larger spheres with compact structures (Figure 5c). As a result, no evident dipolar structures are observed. The spherical clusters, or supraparticles, would transform into 2D close-packed arrays (or 2D rafts) on substrate (as in Figure 5d) during solvent evaporation. This transformation is revealed by the simulation as follows: as the liquid−air interface approached the spherical clusters in solution, they were driven out of equilibrium with distorted geometries; when the liquid surface was close to the substrate, the particles were confined in the narrow space between the two interfaces and finally “squeezed” into islands of monolayers by the repulsions from the interfaces. This explains why only 10809

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N show that: (a) Rings with more than four particles are always energetically more favorable than chains of the same size. The energy difference between the two types tops at N = 7. Nevertheless, the chains as metastable intermediates would coexist with the rings for a relatively long period due to the not very large energy differences. (b) Close-packed structures serve as lower energy alternatives for N > 9. With the growth of N, the energy difference between the rings and the close-packed structures increases remarkably, and the latter becomes the only geometric configuration in solution phase. It is intriguing to notice that even though the dipolar attraction is much stronger than that of the vdW (see Figure 1b), the latter seems to dominate the geometries of modestly large clusters. Though the compact structures lead to a large number of nearestneighboring contacts, which are favored by vdW interactions, dipoles are aligned head-to-tail as much as possible, lowering the magnetostatic energy.46 This is verified by the small net magnetic moments calculated for these configurations (Figure 6b). As a result, for clusters consisting of more than a dozen of particles, close-packed spheres are the final structures with thermodynamical stability. Since the formation of FMNP rings is driven by the dipole− dipole interactions, it is reasonable to expect more rings from magnetic particles with enhanced dipolar strength, which depends on the volume of particles for specific materials. Figures 7a−d present the computational results for particles

2D rafts are found experimentally (as in Figure 4a). For larger compact structures in solution, there may not be enough time for the particles to relax onto the substrate, and thus stackings of the rafts are formed in the center, which correspond to the experimental assemblies in Figure 4b. In addition, these 2D rafts bear similar defects to those observed experimentally (Figure 4), indicating the presence of anisotropic dipolar forces. From the above comparison, we can conclude that the topology of the chains and the rings are invariant to most deformations, while the 2D rafts on substrate have evolved from the 3D compact structures in solution. The observed structures of the FMNP clusters in the experiments could be understood from a thermodynamic perspective by calculating the numerical interparticle potentials. The well-defined size and shape and uniform coating layer of the ε-Co nanocrystals in the experiments enable numerical calculations of nanoscopic interactions in the colloidal systems, which make the quantitative understanding of the FMNP-ring formation possible. On the basis of the model of interactions for d = 16 nm and δ = 2 nm, arbitrary structures of the three basic types, i.e., 1D chains, 2D rings, and 3D compact structures, were relaxed at Teff = 300 K until relatively stable states were attained. Thereafter, potential energies were obtained by averaging over thousands of iterations. During the whole process, we ensured their dimensionalities were kept unchanged. In Figure 6a, the average energies of the three types are compared, where the energy deviations are attributed to the thermodynamics. The free energies as a function of cluster size

Figure 7. Final states of simulations performed for (a) d = 14 nm, (b) d = 16 nm, (c) d = 18 nm, and (d) d = 20 nm, with a uniform coating layer of δ = 2 nm. All the systems have the same particle density and were subjected to the same number of iterations.

with diameters d = 14, 16, 18, and 20 nm, respectively, and a constant coating layer thickness of δ = 2 nm. The magnetic moments for particles with d = 14, 16, 18, and 20 nm are calculated to be 1.27, 2.01, 3.00, and 4.28 × 10−18 A m2, respectively. All the systems have the same particle density of 0.01 vol % and were subjected to the same number of iterations. As seen from Figures 7a,c, the assemblies are similar to their corresponding experimental results (as in Figures 4c,d).

Figure 6. (a) Numerical potential energies for arbitrary structures of the rings, the chains and the compact spheres, respectively, as a function of cluster size N. The inset shows a larger scale of the cluster size. (b) Net magnetic moments of the close-packed clusters. Despite of the increased size, the cluster exhibits good magnetic stability, displaying a total dipolar moment within 3m0, where m0 is the moment of a single particle. Two poles of the dipolar particles are denoted by red and blue. 10810

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coating layers can be tuned by choosing alternatives with different molecule weights and lengths.10,14,29 A thicker coating layer increases the interparticle space and consequently reduces both vdW and dipolar interactions. But the short-ranged vdW attraction decreases more rapidly, and therefore the longranged dipolar force starts dominating as the coating thickness increases. Figures 9a−d are the computational results corresponding to 16 nm particles with coating layer thickness δ = 3, 4, 5, and 6

Both the experiments and simulations have shown that large magnetic moments do not necessarily result in more rings. Since nanoparticle chains are formed initially in the assembling process, the transition from the chains to the rings requires spontaneous bending of the former into the latter, dictated by thermodynamics. 34 A simple model of the transition, characterized by a bending angle θ from 0 to 2π, is illustrated in Figure 8a. The energy variations during the transition suggest

Figure 9. Computational results for particles with constant diameter d = 16 nm and a variation of the coating layer thickness δ: (a) 3, (b) 4, (c) 5, and (d) 6 nm. The same particle density and simulation steps are applied as in Figure 7. Figure 8. (a) A simple model of the transition from linear chains to rings characterized by the bending angle θ from 0 to 2π. (b) Energy variations in the transition as a function of θ. Clusters with 8 particles (●) and 16 particles (▲) are concerned respectively for both d = 16 (blue) and 20 nm (red).

nm, respectively. The same particle density and iterations are applied in the simulations as in Figure 7. Compared to the case of δ = 2 nm (Figure 7b), there is an increase in both the number and the average size of the rings for δ = 3 nm (Figure 9a) and δ = 4 nm (Figure 9b). Moreover, these rings have a broader size distribution and suffer larger distortions from thermodynamics. The loosely connected rings are signs of weak dipolar interactions. Since the vdW attractions between particles are reduced dramatically, few close-packed rafts are observed. With the surfactant thickness δ continuing to grow, even the long-ranged dipolar interactions are weakened remarkably. We have noticed in the simulations that, for both δ = 5 and 6 nm, no aggregations occurred in solution phase, while their corresponding deposits still feature some dipolar structures (Figures 9c,d). This is attributed to the weaker potentials required to overcome the unfavorable entropic effects accompanying self-assembly in more concentrated suspensions.35 In the final few nanometers of the evaporating solvent, the particles got temporarily high-concentrated, which drove the self-assembly near the substrate. Besides, at the final stage of evaporation, the thin liquid film served as a quasi-twodimensional plane, in which rings formed were less likely to get knotted or catenated. This, to some extent, explains the special self-assembled rings reported by Keng et al.10 The short chains and separated single particles present in Figures 9c,d are due to the relatively short time of the assembling process.

that an energy barrier must be overcome. As seen from Figure 8b, for relatively weak dipolar interactions, i.e., d = 16 nm, the height of the barrier is negligible compared to the thermodynamical energy kT. But for an eight-particle chain with d = 20 nm, a barrier of the magnitude of 2.2kT arises in the transition. For the self-assembly in equilibrium states, the thermodynamical energy solely may fail to overcome such a high barrier, consequently hampering the ring formation. Yet longer chains do not have this problem, since the energy barriers almost disappear for large N (see the smooth barriers for N = 16 in Figure 8b). So the assembly of large FMNP rings can always be realized by choosing FMNPs with large magnetic moments. On the contrary, small FMNP rings required rigid control of the dipolar strength, so that it is neither too weak to compete with isotropic interactions nor too strong to prevent the transformation from metastable chains. We further investigated the influence of the coating layer thickness on the morphology of FMNP assemblies. In experiments, colloidal NPs produced by wet chemical methods are always coated with surfactant layers, which control shortranged interactions such as vdW attraction. The thickness of 10811

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For the set of parameter values (d, δ) mentioned above, corresponding potential minimums of both the sum of steric and vdW forces, and the total interactions are given in Table S2.

Science Foundation of Jiangsu in China (Grant BK2008024). We thank Xiaoning Zhao and Yanbin Chen for valuable discussions.

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4. CONCLUSIONS The formation of Co FMNP rings at room temperature has been investigated by considering the three key factors, i.e., FMNP density, dipolar strength, and surfactant layer. The welldefined size and shape, and the uniform surfactant coating layer of the spherical cobalt nanoparticles, as well as the simulations taking account of dynamical evaporation process and substrate effects, promise a good agreement between the experiments and the theoretical calculations. For strongly correlated FMNPs, e.g., 16 nm or larger ε-cobalt NPs with a 2 nm surfactant layer, an extremely dilute suspension is required for the nanoring formation. These nanorings, mainly composed of 5 to 8 NPs, are stable in solution and can be preserved on substrate after solvent evaporation. High concentration of the suspension would cause 2D rings to coalesce into 3D structures, which subsequently transform into close-packed rafts on substrate after solvent drying. While the elimination of vdW attractions is much favored, modest dipolar strength is preferred, as the energy barrier in the transition from chains to rings increases with the dipolar strength. For FMNPs with weak dipolar interactions, short-ranged isotropic interactions such as vdW forces would dominate the morphologies. With the absence of these isotropic attractions, on the other hand, the weak dipolar forces are not sufficient to result in aggregations in dilute suspensions. However, particles get temporally high-concentrated within the final few nanometers of the evaporating liquid film, consequently driving selfassembly near the substrate. Considering the weak dipolar strength, these rings may display different magnetic properties from those with the FC state. In conclusion, low volume fractions, eliminations of isotropic attractions, and modest dipolar strengths are required for the self-assembly of the FMNP rings. The results presented in this work could be a guide to the fabrication of nanorings as well as diverse patterns assembled by FMNPs. A better understanding of nanoscopic interactions also makes theoretical simulations a powerful tool for exploring dynamics of systems at nanoscale.

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ASSOCIATED CONTENT

S Supporting Information *

TEM images and magnetic measurements of the samples, a list of potential minimums for various parameters (d, δ), and detailed calculations of interactions. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel: 86-025-8362-1202. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Key Projects for Basic Research of China (Grant 2010CB923401), the National Natural Science Foundation of China (Grants 11134005 and 50972055), the PAPD project, and the Provincial Nature 10812

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