Assembling Ellipsoidal Particles at Fluid Interfaces using Switchable Dipolar Capillary Interactions

The fabrication of novel soft materials is an important scientific and technological challenge. We investigate the response of magnetic ellipsoidal particles adsorbed at fluid-fluid interfaces to external magnetic fields. By exploiting previously discovered first-order orientation phase transitions we show how to switch on and off dipolar capillary interactions between particles, leading to the formation of distinctive self-assembled structures and allowing dynamic control of the bottom-up fabrication of reconfigurable novel-structured materials


DOI: 10.1002/adma.201402419
creation of menisci around particles, and these particle-induced interface deformations, called capillary charges, interact with one another analogously to electric charges. [ 13,14 ] The height of the interface deformation, h, due to the presence of a particle obeys Young's equation, 0 2 h ∇ = , which can be solved using a multipole expansion. [ 8,15,16 ] Heavy particles deform the interface symmetrically in a monopolar fashion leading to log r interaction potentials between particles, where r is the inter-particle distance. [ 8,11,12 ] However, for micron-sized particles, gravitational forces are usually small compared to surface-tension forces. [ 8 ] Non neutrally-wetting micron-sized ellipsoidal particles adsorbed at fl uid-fl uid interfaces contort the interface around them in a quadrupolar fashion purely because of their shape: [ 8,17 ] the interface is depressed more at the tips than it is elevated at the sides, leading to orientation-dependent interaction potentials between particles. [ 8,[15][16][17] The resulting capillary interaction energies can be several orders of magnitude larger than the thermal energy, ~10 5 E kT B , providing a strong driving force for self-assembly. [ 8,17 ] However, neither the monopolar nor the quadrupolar interactions are dynamically tunable. Dipolar capillary charges are created by anisotropic particles infl uenced by torques. External torques can be caused by particles with uneven mass distributions interacting with gravity, complex surface chemistries (e.g. Janus particles) interacting with fl uids, [18][19][20] or-the focus of this Communication-embedded dipoles interacting with external magnetic fi elds, opening up new routes for the manipulation of particle monolayers.
Materials science advances [ 6,21 ] have enabled the production of anisotropic particles with embedded ferromagnetic dipoles [ 22 ] or (super)-paramagnetic dipoles [ 23,24 ] so that particles can interact with external magnetic fi elds.
Bresme et al. [ 2 ] investigated the behaviour of magnetic ellipsoidal particles adsorbed at fl uid-fl uid interfaces under the action of a magnetic fi eld, predicting that particles undergo a discontinuous, fi rst-order phase transition from a tilted state to a vertical state if a critical dipole-fi eld strength is reached. [ 3 ] Davies et al. [ 1 ] provided further evidence that the transition exists and also showed that particle-induced interface deformations signifi cantly affect the transition.
When a magnetic prolate spheroidal particle with dipole moment, μ μ, is adsorbed at a fl uid-fl uid interface and subjected to an external magnetic fi eld, H H, directed normal to the interface, it experiences a torque, T T H H μ μ = × , which attempts to align the particle with the external fi eld. Surface-tension forces oppose the magnetic torque, and so for a given dipole-fi eld strength, B B H H μ μ =| || |, the particle is tilted with respect to the external fi eld, rather than aligned with it. When the particle is The fabrication of novel soft materials is an important scientifi c and technological challenge. We investigate the response of ellipsoidal particles adsorbed at fl uid-fl uid interfaces to external magnetic fi elds. By exploiting previously discovered fi rst-order orientation phase transitions, [1][2][3] we show how to switch on and off dipolar capillary interactions between particles, leading to the formation of distinctive self-assembled structures and allowing dynamical control of the bottom-up fabrication of novel-structured materials.
Particles adsorb strongly at fl uid-fl uid interfaces: detachment energies of spherical particles can be orders of magnitude greater than the thermal energy, k T B . [ 4,5 ] Once particles are adsorbed at an interface, competing hydrodynamic, electromagnetic and capillary interactions can lead to particles selfassembling into materials with specifi c mechanical, optical, or magnetic properties. [ 6,7 ] Capillary interactions [ 8 ] have attracted interest for their role in assembling mosquito eggs adsorbed at air-water interfaces, [ 9 ] suppressing the coffee ring effect, [ 10 ] and aggregating Cheerios. [ 11,12 ] Capillary interactions occur because of the tilted with respect to the interface, the constant contact-angle condition stipulated by Young's equation means that the particle deforms the interface: [ 1 ] the interface is depressed on one side and elevated on the other, as shown in Figure 1 .
When a critical dipole-fi eld strength, B c , is reached, however, the magnetic torque overcomes surface-tension forces and the particle undergoes a fi rst-order phase transition and fl ips from a tilted orientation to a vertical orientation, with respect to the interface. In the vertical orientation, interface deformations are absent because of the rotational symmetry of the three-phase contact-line in this confi guration.
The interface deformations that occur before the particle transitions to the vertical state are important because they are analogous to electrostatic charges, with a twist; depressions attract depressions, elevations attract elevations, and depressions repel elevations: opposites repel, rather than attract. Therefore, if more than one particle is adsorbed at a fl uid-fl uid interface and under the infl uence of an external magnetic fi eld such that the dipole-fi eld strength is less than the critical dipole-fi eld strength, B < B c , we expect these capillary charges to interact with each other.
Due to the anti-symmetric, dipolar nature of the interface deformations, these interactions are orientation dependent and will give rise to torques orthogonal to the interface causing inplane rotation and ordering. Further, since the magnitude of the interface deformations depend on the dipole-fi eld strength, it is possible to tune the strength of these dipolar capillary interactions by changing the strength of the external fi eld, particle dipole moment, or both.
We employed lattice-Boltzmann simulations [ 1,[25][26][27][28][29][30][31][32][33][34][35][36] to investigate magnetic prolate spheroidal particles with aspect-ratio 2 α = adsorbed at a liquid-liquid interface under the infl uence of a magnetic fi eld applied parallel to the interface normal, implemented in our LB3D code [ 37 ] with the same model and parameters as described in Davies et al. [ 1 ] In our simulations, the dipole-fi eld strength, B , is dominated by a strong external magnetic fi eld and weak dipole moment so that magnetic dipole-dipole interactions are neglected. This means that the structures we observe are purely a result of dipolar capillary interactions between particles.
In Figure 2 we show the particles undergoing a fi rst-order transition into the vertical orientation by exceeding the critical dipole-fi eld strength for a single particle, B c , demonstrating the unique phenomenology of the dipolar capillary interaction mode. The particles begin randomly oriented on the interface (Figure 2 a). An external fi eld is applied such that the dipole-fi eld strength is 0.5 B B c = , creating capillary charges and causing the particles to interact with each other (Figure 2 b). The particles assemble into "capillary caterpillars", which we analyse further in Figure 3 . Finally, the dipole-fi eld strength is increased beyond the single particle critical dipole fi eld, B B c > , where the particles transition into the vertical confi guration (Figure 2 c and 2 d) and capillary interactions are spontaneously switched off.
After the particles have transitioned to the vertical orientation, they order according to a complex balance of other forces, such as magnetic dipole-dipole interactions, thermal fl uctuations, and van der Waals forces, which depend strongly on different combinations of external fi eld strength, dipole moment, particle size and shape, surface packing fraction and fl uid properties, making fi nal structures in the absence of capillary interactions diffi cult to predict. Figure 2 d illustrates a situation in which thermal fl uctuations are greater than magnetic dipoledipole interactions, and the particles order randomly.
The above mentioned parameters can be varied to observe the transition experimentally. For a typical system with a superparamagnetic particle of long-axis radius ≈ μ R 1 m , saturated Adv. Mater. 2014, 26, 6715-6719 www.advmat.de www.MaterialsViews.com  μ ≈ − and surface-tension γ ≈ − 0.05 Nm 1 , a magnetic fi eld strength H T < 1 should suffi ce to observe the fi rst-order phase transition. [ 2 ] In Figure 3 we present a systematic investigation of the intermediate dipole-fi eld strength regime before the particles have transitioned to the vertical confi guration i.e. the particles are tilted with respect to the interface, for several surface-fractions, where N is the number of particles adsorbed at the interface, A p is the interface cross sectional area of a single particle, and A is the area of the interface. We fi nd that the self-assembled structures depend strongly on the dipole-fi eld strength. For weak fi elds, , particles show some ordering, orienting in the side-by-side and tip-to-tip confi guration (Figure 3 b, 3 g, and 3 l). As the dipolefi eld strength is increased to 0.5 B B c = the particles begin to form long, curved ordered chains, or "capillary caterpillars", in which particles strongly prefer to orient side-by-side (Figure 3 (Figure 3 b, 3 g, and 3 l). A possible explanation is as follows. For a larger dipole-fi eld strength, the particles' tilt-angle with respect to the interface increases. [ 1 ] Particles prefer to align with their dipole axes parallel with one another. The sharper corners are simply changes to the in-plane components of the dipole-dipole angle due to the larger tilt-angles, however, a more thorough investigation of the formation and properties of individual capillary caterpillars is needed to confi rm this hypothesis.
Only once individual capillary caterpillars have formed do the particles in each caterpillar arrange tip-tip with particles in other caterpillars. Fully understanding dipolar capillary-induced chain formation is a priority for future study. For quadrupolar capillary interactions, tip-tip confi gurations occur when electrostatic repulsion between particles exists, and capillary arrows can form when the particles are of unequal size. [ 9,17,38 ] The effect of particle size, aspect-ratio, contact-angle, charge and magnetic moment remain unexplored for the dipolar capillary interactions we report here. By using magnetic anisotropic particles interacting with external magnetic fi elds, we have shown how to dynamically tune dipolar capillary interactions between particles by varying the dipole-fi eld strength, and how to switch these dipolar capillary interactions on and off by making the particles undergo a fi rst-order orientation transition. Our simulations reveal novel self-assembled structures that depend on the surface coverage of particles and the dipole-fi eld strength. We observed the formation of "capillary caterpillars", in which particles align in side-side confi gurations, and "capillary couples" where particles in individual caterpillars align in tip-tip chains with particles in other caterpillars, due to the anti-symmetric menisci formation. In addition to providing motivation for new experiments on the bottom-up fabrication of new materials, the novel assembly behaviour reported here should also be observable in colloid-liquid crystal mixtures, [ 40,41 ] and has implications for liquid crystals in general. Further, the discontinuous transition of the prolate spheroidal particles and the on-off tunability of capillary interactions could fi nd applications in photonic systems that require dynamic control of optical properties, such as e-readers. [ 42 ] Finally, the sensitivity of the fi rst order orientation transition, and hence the assembly process, to the particle size and shape, external fi eld strength and interface surface tensions has potential applications in colloidal metrology for sensors that respond to small changes in interface properties.