Particles dispersed in one fluid generally assemble at the interface with a second, immiscible fluid to reduce the interfacial tension, g, and the free energy of the system. If bound strongly enough, the particles form a monolayer that, with a slight reduction in the interfacial area, jam, precluding further interfacial compression. The jamming kinetically traps particle-stabilized liquid-in-liquid structures in metastable, i.e., excess interfacial area shapes, as has been demonstrated for Pickering emulsions1, emulsion gels2, and 3D-printed liquids3. While this particle layer endows the interface with an elastic modulus, the interface has little ability to recover or self-heal its original shape due to its kinetically trapped nature. Large-scale liquid structures are, therefore, delicate, as any perturbation could destroy them. The gold standard for shaping liquids would be to produce conditions where the assemblies are in thermodynamic equilibrium and the destruction of the liquid structure would be followed by its rapid reformation.
The conditions of particle adsorption are at odds with the formation of large-scale liquid structures, due to the reduction in the interfacial tension. Shaking a mixture of oil and water containing excess interfacially active particles disperses droplets of one liquid in the other. The increase in the interfacial area leads to droplet coalescence or coarsening to decrease the interfacial free energy. This reduction densifies and eventually jams the interfacial particle assemblies4,5,6. Such dispersed droplets coalesce or coarsen either by a direct liquid transfer or indirect liquid transfer by Ostwald ripening. During the former, liquid is transported through a liquid bridge connecting the droplets. If the droplet surfaces are covered by particles, a large energetic penalty, associated with generating monolayer openings, must be overcome for a bridge to form. This penalty is sufficiently large that liquid bridges are essentially absent for droplets covered by jammed monolayers. Ostwald ripening, the alternate mechanism, is slow, particularly when the dense particle layers protect much of the droplet surface area. Therefore, interfacially bound particles are anticipated to be highly effective emulsifying agents, rather than enabling formation of structured liquids.
We find that the strong binding and two-dimensional assembly of ferromagnetic particles at a liquid-liquid interface not only suppresses emulsification, but in a container, causes the macroscale interface to adopt the shape of a Grecian urn. The literature results (Table S1) show that nonmagnetic, micron-sized particles stabilize emulsion droplets that are tens-of-microns in size, slightly less than that calculated for jamming, a discrepancy reflecting stabilization of the emulsion droplets at particle areal densities somewhat below those required for particle jamming7,8,9.
Based on these principles, applying a magnetic field to interfaces bearing strongly bound magnetic particles might seem to offer a robust means to manipulate emulsions and other structured liquid systems10. To probe this possibility, a mixture of oil and water was prepared in an open glass vessel by combining water containing well-dispersed ferromagnetic nickel particles (with an oxide surface layer) with an equal volume of dichloromethane (DCM) containing 100 mM of tetrabutylammonium perchlorate (TBAP). As shown in Figure 1(a), the particles, as expected, segregate to the DCM-water interface. Keane et. al.11 explained that the large hydrophobic cations of TBAP and small hydrophilic anions partition differently across an oil-water interface, generating a surface potential on the water side that attracts negatively charged particles dispersed in this phase. Due to the magnitude of the potential in this study, the nickel particles were electrostatically bound, essentially irreversibly, to the interface with binding energies reaching ~102 kT11. Figure 1(b) and Video S1 (Supporting Information) show that after agitating the DCM-water mixtures containing nickel particles, the heuristic for nonmagnetic particles is violated. The DCM droplets rapidly coalesce into container-sized liquid phases separated by an interface shaped like a Grecian urn. The densities of DCM and water are significantly different, 1.33 and 1.00 g/cm3, respectively, and when the average particle size is varied from tens of nanometers to tens of microns, no noticeable impact on interfacial behavior was observed. The rapid phase growth implies a coalescence/coarsening mechanism different from that of a conventional Pickering emulsion, i.e., one made with nonmagnetic particles.
Figure 2a shows an optical microscope image of the DCM-water interface, where the nickel particles are found to assemble into a heterogeneous interfacial network due to their attractive (and anisotropic) interactions. Irregular areal cavities, or voids, are evident. These open surface features could reduce, or even eliminate, the particle-rearrangement barriers that impede the direct transfer of liquid between droplets. Hard-sphere dipoles confined to the surface of a larger sphere were simulated using Morpho, a software for shape optimization12. The mobile dipoles were constrained in the simulations to fixed, random orientations, as justified by the long dipole re-orientation timescale, while energy was minimized with respect to dipole position. Figure 2(b) illustrates the formation of a network-like particle organization, akin to that observed experimentally in Figure 2(a); this organization is driven by interfacial interparticle attractions produced by cooperative local dipole alignment. Structures similar to those in Figure 2(a) and (b) were previously reported for magnetic particles bound to a planar liquid interface13,14.
As envisaged in the Gibbs adsorption isotherm8, accumulation of a soluble species at a liquid interface reflects a difference between the bulk and interfacial chemical potentials. Assuming a binary system with ideal mixing in the bulk and at the interface, the model suggests that adsorption, i.e., a positive surface excess, always leads to a lowering of the interfacial tension g 8. The pendant drop tensiometry experiments in Figure 2(c) show the opposite behavior when the nickel particles accumulate at the DCM-water interface, where g increases by ~50%, visibly altering the droplet shape. However, ideal mixing is not maintained at the interface, where ferromagnetic particles are known to have a negative second virial coefficient due to attractive in-plane magnetic interactions15. Consequently, the particles do not bind to the interface to reduce g but rather to reduce the overall free energy, which incorporates an additional energy associated with the network observed in Figure 2(a).
To confirm that network cavities facilitate droplet coalescence, an emulsion combining the ferromagnetic nickel particles and negatively charged, nonmagnetic silica nanoparticles (NPs) was prepared. Since the binding energy for the NPs is smaller than for the nickel particles, NP adsorption does not alter the nickel particle network. Figure 3 shows that in the mixed particle emulsion, silica NPs fill the interfacial cavities, blocking droplet coalescence; and the mixed emulsion is stable for months. Without magnetic particles, NP adsorption at the same NP concentration was too limited to block coalescence or stabilize the emulsion11, demonstrating a particle synergy not further explored in this study. Interestingly, the mixed particle emulsion does not flow freely due to a strong affinity between the stabilized water droplets.
To investigate the liquid structures formed in the presence of magnetic particles, equal volumes (2 ml) of a DCM/TBAP solution and water containing magnetic particles were combined in a glass-walled cylindrical vessel made either hydrophobic (by silanization) or hydrophilic (by immersion in a base bath). In the first case, irrespective of starting condition, the liquids rapidly re-arranged to establish a slightly concave, horizontal DCM-water interface, as shown in Figure 4(a). Most of the particles adsorbed to this concave interface, depleting the water of particles, as evidenced by the clarity of the water above the DCM-water contact line. The bottom phase was the higher density DCM, so this curvature met the expectation for preferential DCM wetting of the vessel. In the second case, presented in the same figure, a thin layer of water surrounded a single large DCM phase at the bottom of the vessel, reflecting the preferential wetting of the vessel by water.
The shapes of the separated liquid domains are seen to vary as either oil or water is added or removed. When sufficient water is removed to reduce the distance between the DCM droplet and the water-air interface, Figure 4(b) shows the transformation of the compact droplet into a Grecian urn. Further DCM additions raise the catenoid-like neck of the urn. Subsequently, as seen in Figure 4(c), when adding water, the open water surface advances upward until the Grecian Urn pinches off, leaving an oil droplet at the bottom of the vial and a layer of oil at the top. The maximum possible height of a stable neck is independent of the order of the liquid addition/withdrawal or the particle and TBAP concentrations. The urn is also reformed by withdrawing water afterwards. Thereby, urn formation is a rapid, fully reversible process.
The preceding discussion suggests that the liquid-liquid interface is at equilibrium. The experimentally observed urn shape quantitatively agrees with the shape calculated for a pendant drop subjected to a uniform pressure at its bottom (Figure 1(b), right); the calculation details are given in Supplementary Information. In Figure 1(b) the predicted and observed shapes of the interface shapes are superposed where g is assigned the value measured by pendant drop tensiometry (see Figure 2(c)). The magnetic particles, therefore, acted only to modify interfacial tension and facilitate a rapid re-equilibration of the perturbed liquid structure.
Due to the anisotropy of their interactions, the ground state of a finite number of ferromagnetic particles confined to a plane corresponds to string-like rings of maximum size14. Adding a slight size polydispersity, larger particles serve as branch-points between rings, assembling an interfacial network with heterogeneities on the scale of tens-of-particle diameters14. These expectations align well with the curved interface simulations given in Figure 2(b), as well as the experimental results shown in Figure 2(a). The observed network void sizes also agree with those found in previous studies14, and, as these sizes were much smaller than the interfacial radii of curvature, they did not affect interface shape. Absent an external magnetic field, ordering of spherical ferromagnetic particles of diameter d and magnetic moment m is governed by a dimensionless coupling parameter J, the ratio of the pairwise magnetic interaction energy m2/d3 to the thermal energy kT. When J≲1, only disorder is anticipated, but when J>>1, equilibrium order will approach that predicted for the ground state. Stable emulsification by magnetic particles was previously reported only for J»10 (11), but here J is much larger, ~105, explaining why the reported phenomena were not seen before. Under a strong magnetic field, differences between magnetic and non-magnetic systems are evident even at small J, so external fields changed the urn shape. By various placements of a magnet, the interface was deformed into asymmetric shapes, and the entire shape spun when placed on a magnetic stirrer(Video S2, Supporting Information).
In summary, interfacially active magnetic particles stabilize immiscible liquid mixtures against emulsification, due to long-lived heterogeneities imposed on the liquid interfaces by in-plane magnetic particle interactions. The energies of these interactions are large, attractive, and directional, i.e., dependent on interparticle orientation, so the stabilization occurred concurrently with an increase in interfacial tension. These effects run counter to the typical behavior of a Pickering emulsion made with nonmagnetic particles, which pack nearly like hard spheres. The dipolar anisotropy in magnetic interactions creates a string-like particle surface network with openings large enough to enable facile liquid transfer between contacting droplets. The particles thereby bolster the equilibration and re-equilibration of structured liquid interfaces, as evidenced by the urn-shaped phase that forms in a cylindrical vessel; only the wetting conditions of the liquid surface and the vessel walls affect shape.