Adding new dimensions to the self-assembly of nanomagnets
Interactions between dipoles aligned by an external field depend on their mutual configuration. The dipoles strongly attract if placed head-to-tail (Figure 1a). The latter promotes formation of 1-dimensional chains consisting of many dipoles (Figure 1d). Adding a second dimension is a bit more tricky because aligned dipoles strongly repel each other in the side-to-side configuration. When a single dipole is aligned in the out-of-register position with a chain of two dipoles, the configuration shown in Figure 1b, the pair interaction energy reduces by a factor of four, but it still remains repulsive. Whereas, if a longer chain is formed and is aligned with the field then the situation changes. The interactions with more distant dipoles in the chain will stabilise a side dipole in the out-of-register position (Figure 1c). Sufficiently long chains can therefore attract each other side-to-side promoting the assembly of 2-dimensional close-packed sheets. There are no configurations possible which further extend the assembly process into the third dimension based solely on the dipolar interaction of parallel dipoles.
The dipole forces at the nanoscale work in exactly the same way but the situation is complicated by other factors such as screened Coulomb repulsion and van der Waals attraction between the particles, as well as the excluded volume entropy, which becomes increasingly important at higher concentrations. Luckily, thermal fluctuations at the nanoscale are strong enough to render colloids mobile and to let them search for the best configurations. Hence, if the interparticle interaction energies are properly scaled with each other, the self-assembly of nanoparticles proceeds spontaneously. Experiments at the ESRF revealed details of the self-assembly process on the scale of thousands of X-ray wavelengths.
Composite particles containing a magnetic magnetite core and a silica shell  with a diameter of about 200 nm were synthesised. The core-shell structure of the colloids is essential for several reasons. Firstly, it allows a particle size to be attained that is comparable to the wavelength of visible light so that the self-assembled structures are photonic and interact strongly with light. Secondly, the silica shell is optically transparent so that the optical properties are further improved since light absorption by the magnetite core is reduced. Thirdly, the non-magnetic silica shells ensure that the dipolar interactions are not too strong in comparison to the thermal energy kT. The particles can thus re-attach in their search for the best configuration.
The experiment was performed at beamline BM26 (DUBBLE) using a microradian X-ray diffraction setup  with compound refractive lenses. The suspension was placed in flat capillaries and left vertically for sedimentation under gravity. The magnetic field was applied orthogonally to the X-ray beam in the horizontal direction using a magnet provided by beamline ID02.
Examples of microradian X-ray diffraction patterns are given in Figure 2. The measurements were performed for different strengths of the magnetic field (increasing from left to right) and at different positions in the capillary. Because of the gravitational compression, the particle concentration increases from top to bottom. Figure 2 also depicts models of the particle self-assembly of 1D-, 2D- and 3D-type. At low concentration and low magnetic field strength (left-top corner) the self-assembly is mostly one-dimensional in the form of chains of magnetic nanoparticles. In the reciprocal space this ordering corresponds to equally-spaced vertical lines separated by a distance inversely proportional to the interparticle distance along the chains.
At higher field and higher concentration (middle row and top-right corner in Figure 2) the chains assemble into 2D hexagonal close-packed sheets. One can clearly see the development of features typical for hexagonal ordering. Note, however, that the vertical lines of scattering are still clearly visible because of the 2D character of the self-assembly. The 2D sheets of nanoparticles can rotate around the direction of the magnetic field. As a result, the periodicity along the external field is common for all orientations of the sheets while the apparent distances in the vertical direction are dependent on the rotation angle. Note also that high-order scattering features are clearly visible, which indicates that the positional interparticle correlations extend over large distances. At even higher concentration (the bottom row of patterns in Figure 2) the osmotic compression of the system overcomes the dipolar repulsion and the nanoparticles start to form 3D structures with well-defined d-spacings between planes of colloidal particles. The vertical stripes of scattering disappear from the scattering patterns and one can see small-angle diffraction patterns characteristic of 3D colloidal crystals.
In summary, our experiments revealed details of the self-assembly of core-shell magnetic colloids, which proceeds from 1D through 2D to 3D structures. This work sheds light on the creation of stimuli-responsive photonic structures, which could prove useful for novel applications.
The authors thank Albert Philipse and Jan Hilhorst for providing models of magnetic spheres.
Principal publication and authors
Colloidal crystallization and structural changes in suspensions of silica/magnetite core-shell nanoparticles, V. Malik (a), A.V. Petukhov (b), L. He (c), Y. Yin (c), M. Schmidt (a), Langmuir 28, 14777-14783 (2012).
(a) University of Wisconsin – Milwaukee (USA)
(b) Utrecht University (The Netherlands)
(c) University of California – Riverside (USA)
 J. Ge, Y. Hu, M. Biasini, W.P. Beyermann, Y. Yin, Angew. Chem. Int. Ed.46, 4342 (2007).
 A.V. Petukhov, J.H.J. Thijssen, D.C. ’t Hart, A. Imhof, A. van Blaaderen, I.P. Dolbnya, A. Snigirev, A. Moussaid, I. Snigireva, J. Appl. Cryst., 39, 137 (2006).