Lluis
Balcells
a,
Igor
Stanković
*b,
Zorica
Konstantinović
c,
Aanchal
Alagh
a,
Victor
Fuentes
a,
Laura
López-Mir
a,
Judit
Oró
a,
Narcis
Mestres
a,
Carlos
García
d,
Alberto
Pomar
a and
Benjamin
Martínez
a
aInstitut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus de la UAB, 08193 Bellaterra, Catalonia, Spain
bScientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, 11080 Belgrade, Serbia. E-mail: igor.stankovic@ipb.ac.rs
cCenter for Solid State Physics and New Materials, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
dDepartamento de Física & Centro Científico Tecnológico de Valparaíso-CCTVal, Universidad Técnica Federico Santa María, Av. España 1680, Casilla 110-V, Valparaíso, Chile
First published on 20th May 2019
Knowing the interactions controlling aggregation processes in magnetic nanoparticles is of strong interest in preventing or promoting nanoparticles’ aggregation at wish for different applications. Dipolar magnetic interactions, proportional to the particle volume, are identified as the key driving force behind the formation of macroscopic aggregates for particle sizes above about 20 nm. However, aggregates’ shape and size are also strongly influenced by topological ordering. 1-D macroscopic chains of several micrometer lengths are obtained with cube-shaped magnetic nanoparticles prepared by the gas-aggregation technique. Using an analytical model and molecular dynamics simulations, the energy landscape of interacting cube-shaped magnetic nanoparticles is analysed revealing unintuitive dependence of the force acting on particles with the displacement and explaining pathways leading to their assembly into long linear chains. The mechanical behaviour and magnetic structure of the chains are studied by a combination of atomic and magnetic force measurements, and computer simulation. The results demonstrate that [111] magnetic anisotropy of the cube-shaped nanoparticles strongly influences chain assembly features.
Here, we report on the spontaneous self-assembly of magnetic nanoparticles into macroscopic chains. We show that dipolar interactions, proportional to the particle volume, are the key driving force behind the formation of macroscopic aggregates for particle sizes above about 20 nm; however, aggregates’ shape and size are strongly influenced by topological ordering. 1-D macroscopic chains of several μm lengths are obtained with 25 nm magnetic iron/iron-oxide cube-shaped magnetic nanoparticles fabricated by using a modified gas-aggregation technique, which allows particles to assemble in flight without the influence of the medium. Self-assembled chains represent an excellent paradigmatic system to explore the self-assembly process of individual particles and a unique model system to study the behaviour of complex agglomerates without dumping of the medium (i.e., only conservative interparticle forces are present) at the nano- and mesoscale ranges. Since magnetic cores and shells may have different magnetic anisotropies, a detailed characterisation of the NPs is required for understanding the magnetic structure of the nanocubes. We have used an exact analytical theory to predict the energetically favourable configurations. Our results reveal a complex energy landscape leading to non-intuitive force distance characteristics. Then, to validate the developed model, a series of magnetic and atomic force microscopy measurements and computer simulations were performed. Applying both techniques simultaneously, the processes governing self-assembly of magnetic cubes into single-stranded chains are unveiled.
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Fig. 1 Magnetic assembly of nanocubes in a single strand. (a) SEM and (b) TEM images of the micrometre long single-stranded core/shell iron NP chain. (c) TEM image of a chain segment. |
The particle-size characterisation was determined by scanning electron microscopy (SEM) using a QUANTA FEI 200 FEG-ESEM microscope. TEM, HRTEM and scanning TEM (STEM) in the high angle annular dark field (HAADF) mode were used to study the crystallinity, morphology, size, and dispersion of the samples. TEM images were obtained using a JEOL JEM 1210 transmission electron microscope operating at 120 kV. HRTEM and STEM images were acquired in a FEI Tecnai F20 microscope operating at 200 kV. Digital diffraction patterns (DDP) of power spectra were obtained from selected regions in the micrographs. No electron-beam-induced changes were observed in any of the analyzed particles.27 Energy dispersive X-ray (EDS) spectra were acquired using an EDAX super ultrathin window (SUTW) X-ray detector.
Micro-Raman spectra were obtained by using a Jobin–Yvon T64000 monochromator with a liquid nitrogen cooled charge-coupled detector. The excitation light was a 514.5 nm line from an Ar-ion laser. The incident and scattered beams were focused by an Olympus microscope using a ×50 objective to give a spot size of ca. 2 μm. Unpolarised Raman spectra were measured due to the polycrystalline nature of the samples.
MFM measurements were performed with an MFP-3D Asylum Research microscope using ASYMFM-HC probes with CoPt/FePt (30 nm) coating. In MFM the phase shift near the cantilever resonance was used to map stray fields by measuring in the amplitude modulation AFM (AM-AFM) mode and keeping the cantilever at a constant height (57 nm) from the surface. Variable field module (VFM2) from Asylum Research, which was a special holder with a rotating permanent magnet, was used to apply a magnetic field of up to 1 T in the in-plane direction.
The John et al.29 and Zhang et al.30 models are modified in two ways: first, instead of only one central dipole, 9 were used (cf. illustration in Fig. S5†). In this way, we have reproduced the potential energy profile of the two cubes calculated analytically (see comparison in Fig. S6†). Also, additional dipoles take into account the interaction of the touching corners of the cubes, which is important for the stability of the chain under extension (see ESI Movies†). If we analyse a case of extreme extension, the magnetic energy of two [111] magnetised cubes with aligned magnetisation touching on the corner, which comes from the two adjacent corner cubes , is two times larger than the energy stemming from the interaction between the central cubes (radius d/2), i.e.,
. And second, an additional 24 spheres were placed inside of the cube edges in order to make a smooth surface and avoid pinning during mechanical manipulation. The geometrical contact between two cubes is simulated using the WCA potential for the spheres (truncated and shifted Lennard-Jones potential, elsewhere called also soft-sphere model) (see ESI).†
We study the mechanical behaviour of the model system by means of molecular dynamics computer simulations: the cubes are represented by the WCA potential and carry nine-point dipoles as described in Fig. S5.† This model was the basis for zero temperature molecular dynamics simulation. The simulations of the breaking of the chains were performed by different forces exerted on the chain ends. Molecular dynamics was used to study mechanical manipulation of the free-standing chain composed of magnetic cubes. The total force was the conservative force of inter-particle interactions, i.e., contact WCA potential of 33 (overlapping) spheres and 9 dipoles. The dipolar interactions were treated with cut-off at rcut/d = 8 (cf. ref. 24), and a non-periodic simulation box was used. The constituent spheres within the cube were moved as rigid body data structures in every time step. The rotational degrees of freedom are also governed by the equations of motion for torque and angular velocity of the spheres. The total force and torque on each cluster representing one cube are computed as the sum of the forces and torques on its constituent particles at each time step. The dipole orientation is accordingly rotated with the cube as a single entity. The rotation was implemented by creating internal data structures for each rigid body and performing time integration on these data structures.32,33 The mass of the cuboid corresponded to a 25 nm iron cube and was distributed over constitutive dipolar particles. MD step was t = 4 ps and the total length of the MD simulation 400 ns.
In the present work, for a 5 cm travel distance, a large number of shell only particles were obtained with an average particle size of about 8 nm. Meanwhile, for an 8 cm travel distance, an increase of the average particle size to 15 nm is observed at the expense of the number of generated particles (see Fig. S2).† In addition, particles produced in the latter case were mainly of a core/shell structure (see Fig. 2a). Further increase of the travel distance resulted in a small increase in the particle size: for a 11 cm travel distance, the average size was 16 nm, while for 13 cm, the average size was 17 nm. When the oxidation process is dominated by the Cabrera–Mott-like mechanism, initial oxidation rapidly develops a 4 nm-thick oxide shell around the Fe core. A similar effect has been observed in the synthesis of iron core/shell cubes from solution,36 where a partial oxidation promoted the formation of core/shell nanostructures with an iron core trapped inside the oxide shell. Following this procedure, single crystalline iron NPs covered by a crystalline Fe3O4 shell can be fabricated. For small enough NPs, i.e. below about 9–10 nm, the Cabrera–Mott like oxidation mechanism produces hollows. In contrast, for particles above 12 nm, a core/shell structure is obtained (see Fig. S3).† This evolution can be clearly observed in Fig. 2a. To promote spontaneous self-assembly, stronger interactions between core/shell magnetic cubes are required, i.e., a strongly magnetised iron core is necessary. Therefore, nanocube dimensions should be larger than 12 nm in order to have a core/shell structure with a strongly magnetised core.
A high-resolution Z-contrast TEM image is shown in Fig. 2b. A well-defined square shape of the particle with a sharply defined 4 nm shell can be appreciated. The reflections of the power spectrum pattern (see Fig. 2c and d) obtained by TEM can be indexed using the corresponding reflections of cubic Fe for the core and the spinel structure for the shell. Since TEM and electron diffraction techniques cannot distinguish between the different oxide phases, Raman spectroscopy was used to identify them. Different bands in the Raman spectrum correspond to specific frequency vibration modes, allowing distinguishing different oxide phases. In particular, maghemite differs from magnetite because it contains no divalent iron species. Due to the fact that the ionic radius of Fe(II) is larger than that of Fe(III), Fe(II)–O bonds are longer and weaker than Fe(III)–O bonds; this shifts up the vibration frequency in the Raman spectrum, and hence, Raman analysis allows distinguishing between these two phases. In the Raman spectrum displayed in Fig. 2e, the main band centred at 668 cm−1 and the weaker peaks at ca. 539 and 317 cm−1 have been assigned to A1g, T2g, and Eg vibrational modes of magnetite, respectively.39 EDX line profile analysis of one single particle shows the absence of oxygen at the core and the progressive increase at the surface (Fig. 2f), thus giving further support for the idea of core/shell nanostructures of Fe/Fe3O4.
The magnetic dipolar attraction of particles above 25 nm is strong enough to form long single stranded chains, while for particles less than 25 nm, only individual particles and clusters are detected (see Fig. 1). Individual particles are not observed, which implies that the growth of chains is completed before being deposited on the substrate. Therefore, the substrate does not influence chain formation. The emergence of chains is actually driven by interplay of the geometrical contact between two cubes and the magnetic dipolar interaction. It is worth mentioning that both contact and dipolar interaction are anisotropic. The nanometer-sized iron cubes display a fixed and permanent magnetic dipole moment that is strong enough to form single strand chains.
The chain morphology provides an insight into the particle magnetic anisotropy. The magnetic moment of magnetically anisotropic materials tends to align with an easy axis, which is an energetically favourable direction of spontaneous magnetisation. Actually, the direction of the easy axis of the magnetic cube can be controlled by the core to shell ratio. There are indeed two possible magnetic easy axes: one governed by the magnetite shell lying in the [111] direction and the other governed by the iron core along the [001] direction.17,37,40 Since hollow, i.e., magnetite shell-only, cubes have dimensions below 12 nm, dipolar interactions are small and therefore no chains are formed along the [111] orientation. It is evident that the direction of the net magnetic orientation relative to the cube geometry changes the structure of the observed chains (see Fig. 3a and b). For chains of nanocubes, the assembly mechanism drives the particles to adopt structures that create a head–tail configuration, very much like chains of magnetic beads. In the case of [001] direction, this leads to deep central minimum of magnetic potential energy with respect to the lateral movement of the magnetic particles and consequently to quite stiff configuration (cf., ESI Movie 1†). On the contrary, when the magnetisation is along the principal axis, i.e., [111] direction, the structure becomes more flexible (cf., ESI Movie 2†). The configuration with minimal energy has a zig-zag dipole vector placement (cf., the top left panel where particles are placed in face-to-face configuration in Fig. 3b) of the magnetic cubes, and the system can extend to a head–tail configuration by relative rotation of the cubes (cf., also ref. 24). The relative rotation is taking place along the bottom of the circular valley shown in Fig. 3b. The valley is denoted as a white circle and is tilted towards the centre of mass (c.m.) of the bottom particle. The highest point of the valley is when the c.m. of the upper particle is above the edge corner of the particle below. This corresponds to head–tail placement of the dipoles. Head–tail configuration of dipoles shows about a 20% energy increase along the valley. At the minimum energy point (zig-zag configuration), the distance between their centres of mass Δr2 is equal to the cube size Δr2 = d. At the furthest point of the circular minimum valley (i.e., when c.m. of one particle is above the corner of the other), the centres of mass of the particles are 22% further apart than at global minimum (as shown in Fig. 4, , i.e., Δr2 = 30.6 nm for 25 nm particles).
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Fig. 3 The energy landscape obtained analytically and a schematic view of the chain of the particles for [001] (a) and [111] (b) easy magnetisation axis directions. Interaction energy per particle u2 for pure iron particles is scaled with the reference interaction energy ε = 25 eV (see also Fig. S4†). The contour of the bottom cube is shown with the black solid line in the energy diagrams. The white solid line circle in the energy diagram for the [111] magnetisation direction represents the bottom of the circular potential valley. Three representative configurations with [001] magnetisation directions are shown with side views in the upper panels of (a). From left to right: centre of mass (c.m.) of one particle in the middle of the edge of the other, one particle on top of the other, and c.m. of one particle on the corner of the other. Four representative configurations with [111] magnetisation are shown with top and side views. The configurations are shown in the upper panels of (b), from left to right: (i) zig-zag configuration, where the particles are above each other with the surfaces placed face-to-face (the zig-zag configuration is the most stable one), (ii) c.m. of the upper particle is at the edge of the contour of the lower particle, (iii) head–tail configuration when the upper particle's c.m. is at the edge of the bottom particle and (iv) the so-called unstable configuration, when c.m. of the upper particle is furthermost from the contour of the bottom. |
Fig. 4a gives the calculated dependence of the magnetic restoring force on the distance between the centres of mass of the two particles. We see that there are two maximums of the force (roughly equal in size). The first peak, which is very narrow, locks particles in a zig-zag position while the second broad peak keeps the chain connected. The reason for the existence of the first narrow maximum is that particles have first to move laterally in order to come out of the zig-zag position (see also Fig. 2b). The shape of the magnetic potential energy valley further enhances the flexibility of the whole structure. The contour of the potential valley crosses the edge of the bottom cube, and a large part of it lies outside of the contour of the bottom cube. In this area, the two-particle system becomes unstable. This means that one cube can flip over the edge of the other cube and change in the other equivalent position on the different side of the cube (see ESI Movie 3†). This is also a local minimum of the restoring force (cf., Δr2 = 30 nm) (Fig. 4a). Also, during extension, cubes can partially detach when they are in a head–tail configuration, i.e., stay only attached by the corner-to-corner contact, i.e., at . In the corner-to-corner configuration, the parts of the chain have a large rotational freedom. This is also a configuration from which we observe that the chain finally detaches (breaks). Still, the local maximum of the force is at roughly Δr2 ≈39 nm, and at this point, particles are still overlapping.
The response of the chain of magnetic cubes to strain is shown in Fig. 4b. We observe that the chain is extending and contracting quasi-elastically (see ESI Movie 4†). The energy u follows a parabolic curve, and the elastic force acting on the ends of the chain increases linearly with the extension of the chain. The estimated elastic coefficient of the chain is 0.21 ± 0.05 meV nm−2. The elastic extension of the chain continues up to the point where the maximal force per particle approaches roughly 3 pN (see Fig. 4a) at roughly Δr2 = 40 nm. It is also observed that there is a pinning of the parts of the chain in an energetically less favourable configuration, and as a result, the energy depends on the history of the mechanical manipulation.
In Fig. 5, we show the magnetisation dependence of individual cubes of a representative part of a chain on the external magnetic field. The stray magnetic field generated by the chain is small when no external magnetic field is initially applied (cf. AFM topography and MFM41,42 measurement in Fig. 5a and c, respectively). A computer generated configuration with similar morphology as in the experiment is also shown in Fig. 5b. The magnetic field necessary to rotate the magnetisation direction of the cubes is larger than 0.1 T (cf., no significant difference between Fig. 5c and d). The small differences in the two figures are a consequence of local reorientation of magnetisation due to the applied field. Still the field is not strong enough to determine magnetisation of all particles.
A sequence of MFM measurements at magnetic field −0.5 T, 0 T, 0.5 T, and 0 T is depicted in Fig. 6. In order to study magnetisation reversal in an external magnetic field, a field larger than that necessary to rotate the magnetisation direction of the cubes was applied. It is found that at −0.5 T, the magnetisation of the chain is completely aligned along the external field direction (see Fig. 6a). Therefore, we can conclude that the local magnetic field generated by cubes in the chain is less than 0.5 T. In fact, the analytical results for uniformly magnetised iron cubes give 0.35 T in the centre of the neighbouring cube placed face-to-face in a zig-zag configuration and 0.15 T in the head–tail configuration (see ESI†). Initially, a −0.5 T external magnetic field was applied to magnetise the chain in one direction and then the external magnetic field was turned off so that a spontaneous reordering of magnetisation can take place. No remanence is found when the external field is set back to zero, as observed in Fig. 6a and b. The magnetisation direction, after the external field is switched off, is along the chain backbone. The magnetisation orientation is determined by the previously applied external magnetic field, as it can be observed at the corners in Fig. 6b. In the next step, a 0.5 T external field is applied in the opposite direction. As one would expect, after the magnetic field is switched off, the resulting configuration shows that the pole north and south of the individual cubes and the chain as whole have interchanged their positions. The visualisation of the sequence obtained from the computer simulation is shown in the right panels of Fig. 6.
The magnetic configuration of a broken chain is also shown in Fig. 7a. The MFM images illustrate that one end corresponds to the a north pole and other end to a south pole (the north and south poles are differentiated in the figure as light and dark contrasts), which is indicative of the magnetic moment aligned along the chain. This can be compared with the simulation results in Fig. 7e; the snapshots just before and after chain break-up are shown as well as the magnetic field perpendicular to the substrate plane. A constant force of 3 pN was applied on the terminal cubes. The initial configuration was a zig-zag magnetisation configuration where cubes are in face-by-face contact, seen on the right side of the panel in Fig. 7b. The transitions between these phases create the stray field. When the chain is finally broken, we observe at the two ends the stray field pointing up and down, similar to Fig. 7a.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/C9NR02314C |
This journal is © The Royal Society of Chemistry 2019 |