Defined core-shell particles as the key to complex interfacial self-assembly.

The two-dimensional self-assembly of colloidal particles serves as a model system for fundamental studies of structure formation and as a powerful tool to fabricate functional materials and surfaces. However, the prevalence of hexagonal symmetries in such self-assembling systems limits its structural versatility. More than two decades ago, Jagla demonstrated that core-shell particles with two interaction length scales can form complex, nonhexagonal minimum energy configurations. Based on such Jagla potentials, a wide variety of phases including cluster lattices, chains, and quasicrystals have been theoretically discovered. Despite the elegance of this approach, its experimental realization has remained largely elusive. Here, we capitalize on the distinct interfacial morphology of soft particles to design two-dimensional assemblies with structural complexity. We find that core-shell particles consisting of a silica core surface functionalized with a noncrosslinked polymer shell efficiently spread at a liquid interface to form a two-dimensional polymer corona surrounding the core. We controllably grow such shells by iniferter-type controlled radical polymerization. Upon interfacial compression, the resulting core-shell particles arrange in well-defined dimer, trimer, and tetramer lattices before transitioning into complex chain and cluster phases. The experimental phase behavior is accurately reproduced by Monte Carlo simulations and minimum energy calculations, suggesting that the interfacial assembly interacts via a pairwise-additive Jagla-type potential. By comparing theory, simulation, and experiment, we narrow the Jagla g-parameter of the system to between 0.9 and 2. The possibility to control the interaction potential via the interfacial morphology provides a framework to realize structural features with unprecedented complexity from a simple, one-component system.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces.

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Interfacial self-assembly of SiO2-PNIPAM core-shell particles with varied crosslinking density.

Spherical particles confined to liquid interfaces generally self-assemble into hexagonal patterns. It was theoretically predicted by Jagla two decades ago that such particles interacting via a soft repulsive potential are able to form complex, anisotropic assembly phases. Depending on the shape and range of the potential, the predicted minimum energy configurations include chains, rhomboid and square phases. We recently demonstrated that deformable core-shell particles consisting of a hard silica core and a soft poly(N-isopropylacrylamide) shell adsorbed at an air/water interface can form chain phases if the crosslinker is primarily incorporated around the silica core. Here, we systematically investigate the interfacial self-assembly behavior of such SiO2-PNIPAM core-shell particles as a function of crosslinker content and core size. We observe chain networks predominantly at low crosslinking densities and smaller core sizes, whereas higher crosslinking densities lead to the formation of rhomboid packing. We correlate these results with the interfacial morphologies of the different particle systems, where the ability to expand at the interface and form a thin corona at the periphery depends on the degree of crosslinking close to the core. We perform minimum energy calculations based on Jagla-type pair potentials with different shapes of the soft repulsive shoulder. We compare the theoretical phase diagram with experimental findings to infer to which extent the interfacial interactions of the experimental system may be captured by Jagla pair-wise interaction potentials.

Pattern formation in two-dimensional hard-core/soft-shell systems with variable soft shell profiles.

Hard-core/soft shell (HCSS) particles have been shown to self-assemble into a remarkably rich variety of structures under compression due to the simple interplay between the hard-core and soft-shoulder length scales in their interactions. Most studies in this area model the soft shell interaction as a square shoulder potential. Although appealing from a theoretical point of view, the potential is physically unrealistic because there is no repulsive force in the soft shell regime, unlike in experimental HCSS systems. To make the model more realistic, here we consider HCSS particles with a range of soft shell potential profiles beyond the standard square shoulder form and study the model using both minimum energy calculations and Monte Carlo simulations. We find that by tuning density and the soft shell profile, HCSS particles in the thin shell regime (i.e., shell to core ratio ) can form a large range of structures, including hexagons, chains, squares, rhomboids and two distinct zig-zag structures. Furthermore, by tuning the density and r1/r0, we find that HCSS particles with experimentally realistic linear ramp soft shoulder repulsions can form honeycombs and quasicrystals with 10-fold and 12-fold symmetry. Our study therefore suggests the exciting possibility of fabricating these exotic 2D structures experimentally through colloidal self-assembly.

Amphiphile-Induced Anisotropic Colloidal Self-Assembly.

Spherical colloidal particles typically self-assemble into hexagonal lattices when adsorbed at liquid interfaces. More complex assembly structures, including particle chains and phases with square symmetry, were theoretically predicted almost two decades ago for spherical particles interacting via a soft repulsive shoulder. Here, we demonstrate that such complex assembly phases can be experimentally realized with spherical colloidal particles assembled at the air/water interface in the presence of molecular amphiphiles. We investigate the interfacial behavior of colloidal particles in the presence of different amphiphiles on a Langmuir trough. We transfer the structures formed at the interface onto a solid substrate while continuously compressing, which enables us to correlate the prevailing assembly phase as a function of the available interfacial area. We observe that block copolymers with similarities to the chemical nature of the colloidal particles, as well as the surface-active protein bovine serum albumin, direct the colloidal particles into complex assembly phases, including chains and square arrangements. The observed structures are reproduced by minimum energy calculations of hard core-soft shoulder particles with experimentally realistic interaction parameters. From the agreement between experiments and theory, we hypothesize that the presence of the amphiphiles manipulates the interaction potential of the colloidal particles. The assembly of spherical colloidal particles into complex assembly phases on solid substrates opens new possibilities for surface patterning by enriching the library of possible structures available for colloidal lithography.

Anisotropic Self-Assembly from Isotropic Colloidal Building Blocks.

Spherical colloidal particles generally self-assemble into hexagonal lattices in two dimensions. However, more complex, non-hexagonal phases have been predicted theoretically for isotropic particles with a soft repulsive shoulder but have not been experimentally realized. We study the phase behavior of microspheres in the presence of poly(N-isopropylacrylamide) (PNiPAm) microgels at the air/water interface. We observe a complex phase diagram, including phases with chain and square arrangements, which exclusively form in the presence of the microgels. Our experimental data suggests that the microgels form a corona around the microspheres and induce a soft repulsive shoulder that governs the self-assembly in this system. The observed structures are fully reproduced by both minimum energy calculations and finite temperature Monte Carlo simulations of hard core-soft shoulder particles with experimentally realistic interaction parameters. Our results demonstrate how complex, anisotropic assembly patterns can be realized from entirely isotropic building blocks by control of the interaction potential.

Magnetic cylindrical colloids at liquid interfaces exhibit non-volatile switching of their orientation in an external field.

We study the orientation of magnetic cylindrical particles adsorbed at a liquid interface in an external field using analytical theory and high resolution finite element simulations. Cylindrical particles are interesting since they possess multiple locally stable orientations at the liquid interface so that the orientational transitions induced by an external field will not disappear when the external field is removed, i.e., the switching effect is non-volatile. We show that, in the absence of an external field, as we reduce the aspect ratio α of the cylinders below a critical value (αc≈ 2) the particles undergo spontaneous symmetry breaking from a stable side-on state to one of two equivalent stable tilted states, similar to the spontaneous magnetisation of a ferromagnet going through the Curie point. By tuning both the aspect ratio and contact angle of the cylinders, we show that it is possible to engineer particles that have one, two, three or four locally stable orientations. We also find that the magnetic responses of cylinders with one or two stable states are similar to that of paramagnets and ferromagnets respectively, while the magnetic response of systems with three or four stable states are even more complex and have no analogs in simple magnetic systems. Magnetic cylinders at liquid interfaces therefore provide a facile method for creating switchable functional monolayers where we can use an external field to induce multiple non-volatile changes in particle orientation and self-assembled structure.

ABC triblock copolymer micelles: spherical versus worm-like micelles depending on the preparation method.

Well-defined ABC triblock copolymers based on two hydrophilic blocks, A and C, and a hydrophobic block B are synthesized and their self-assembly behavior is investigated. Interestingly, at the same solvent, concentration, pH, and temperature, different shape micelles are observed, spherical and worm-like micelles, depending on the preparation method. Specifically, spherical micelles are observed with bulk rehydration while both spherical and worm-like micelles are observed with film rehydration.

Influence of magnetic field on the orientation of anisotropic magnetic particles at liquid interfaces.

We study theoretically the influence of an external magnetic field on the orientation of an ellipsoidal magnetic particle adsorbed at a liquid interface. Using the finite element program Surface Evolver, we calculate the equilibrium meniscus shape around the ellipsoidal particle and its equilibrium tilt angle with respect to the undeformed interface θt when a magnetic field B is applied perpendicular to the interface. We find that as we increase field strength, θt increases and at a critical magnetic field Bc1 and tilt angle θc1, the particle undergoes a discontinuous transition to the 'perpendicular' orientation (θt = 90°). Our results agree qualitatively with the simplified theory of Bresme and Faraudo [F. Bresme and J. Faraudo, J. Phys.: Condens. Matter, 2007, 19, 375110] which assumes that the liquid interface is flat, while they agree quantitatively with recent lattice-Boltzmann simulations of Davies et al. [G. Davies et al., Soft Matter, 2014, 10, 6742] which account for the deformation of the liquid meniscus. We also show for the first time that upon reducing the external magnetic field, at a critical magnetic field Bc2 < Bc1, the particle undergoes a second discontinuous transition from the perpendicular orientation to a finite tilt angle θc2 < θc1. In other words, for micron-sized particles where the thermal energy kBT is negligible compared to the interfacial energy, the tilt angle vs. magnetic field curve exhibits hysteresis behaviour. Due to the higher degree of accuracy of the Surface Evolver method, we are able to analyse the behaviour of the particles near these orientational transitions accurately and study how the critical quantities Bc1, Bc2, θc1 and θc2 vary with particle aspect ratio and contact angle.

Self-assembly of two-dimensional colloidal clusters by tuning the hydrophobicity, composition, and packing geometry.

We study the structure of binary monolayers of large (3 µm diameter) very hydrophobic (A) and large (3 µm diameter) hydrophilic (B) or small (1 µm diameter) hydrophilic (C) silica particles at an octane-water interface. By tuning the composition and packing geometry of the mixed monolayer, we find that a rich variety of two-dimensional hexagonal superlattices of mixed A/B or A/C clusters are formed, stabilized by short-ranged electrostatic induced dipole interactions. The cluster structures obtained are in excellent agreement with zero temperature calculations, indicating that the self-assembly process can be effectively controlled.

Water-in-water emulsions based on incompatible polymers and stabilized by triblock copolymers-templated polymersomes.

Aqueous solutions containing a mixture of polyethylene glycol (PEG) and dextran homopolymers form an aqueous two-phase system which can be emulsified to give a water-in-water emulsion. We show how these emulsions can be stabilized using triblock polymers containing poly[poly(ethylene glycol) methyl ether methacrylate] (PEGMA), poly (n-butyl methacrylate) (BuMA), and poly[2-(dimethylamino) ethyl methacrylate] (DMAEMA) blocks of general structure Pp-Bb-Dd, in which the middle BuMA block is hydrophobic. Low-energy input stirring of mixtures containing equal volumes of PEG- and dex-rich aqueous phases plus 1 wt % of Pp-Bb-Dd stabilizer all form dex-in-PEG emulsions (for the range of Pp-Bb-Dd triblock polymers used here) which have a polymersome-like structure. In favorable cases, the emulsion drop (or templated polymersome) sizes are a few micrometers and are stable for periods in excess of 6 months. The emulsions can be inverted from dex-in-PEG to PEG-in-dex by increasing the volume fraction of dex-rich aqueous phase. We demonstrate that both high and low molecular weight fluorescent solutes "self-load" into either the dex- or PEG-rich regions and that solute mass transfer across the water-water interface occurs on a timescale of less than 1 min.

Two-dimensional colloidal alloys.

We study the structure of mixed monolayers of large (3 µm diameter) and small (1 µm diameter) very hydrophobic silica particles at an octane-water interface as a function of the number fraction of small particles ξ. We find that a rich variety of two-dimensional hexagonal super-lattices of large (A) and small (B) particles can be obtained in this system due to strong and long-range electrostatic repulsions through the nonpolar octane phase. The structures obtained for the different compositions are in good agreement with zero temperature calculations and finite temperature computer simulations.

Correction to "Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces".

[This corrects the article DOI: 10.1021/acsomega.8b01818.].

Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces.

Magnetic ellipsoidal particles adsorbed at a liquid interface provide exciting opportunities for creating switchable functional materials, where self-assembly can be switched on and off using an external field [Davies et al., Adv. Mater., 2014, 26, 6715]. In order to gain a deeper understanding of this novel system in the presence of an external field, we study the capillary interaction and self-assembly of tilted ellipsoids using analytical theory and finite element simulations. We derive an analytical expression for the dipolar capillary interaction between tilted ellipsoids in elliptical polar coordinates, which exhibits a 1/r 2 power law dependence in the far field (i.e., large particle separations r) and correctly captures the orientational dependence of the capillary interactions in the near field. Using this dipole potential and finite element simulations, we further analyze the energy landscape of particle clusters consisting of up to eight tilted ellipsoids in contact. For clusters of two particles, we find that the side-to-side configuration is stable, whereas the tip-to-tip configuration is unstable. However, for clusters of more than three particles, we find that circular loops of side-to-side particles become globally stable, whereas linear chains of side-to-side particles become metastable. Furthermore, the energy barrier for the linear-to-loop transition decreases with increasing particle number. Our results explain both thermodynamically and kinetically why tilted ellipsoids assemble side-to-side locally but have a strong tendency to form loops on larger length scales.

Interaction between colloidal particles on an oil-water interface in dilute and dense phases.

The interaction between micron-sized charged colloidal particles at polar/non-polar liquid interfaces remains surprisingly poorly understood for a relatively simple physical chemistry system. By measuring the pair correlation function g(r) for different densities of polystyrene particles at the decane-water interface, and using a powerful predictor-corrector inversion scheme, effective pair-interaction potentials can be obtained up to fairly high densities, and these reproduce the experimental g(r) in forward simulations, so are self consistent. While at low densities these potentials agree with published dipole-dipole repulsion, measured by various methods, an apparent density dependence and long range attraction are obtained when the density is higher. This condition is thus explored in an alternative fashion, measuring the local mobility of colloids when confined by their neighbors. This method of extracting interaction potentials gives results that are consistent with dipolar repulsion throughout the concentration range, with the same magnitude as in the dilute limit. We are unable to rule out the density dependence based on the experimental accuracy of our data, but we show that incomplete equilibration of the experimental system, which would be possible despite long waiting times due to the very strong repulsions, is a possible cause of artefacts in the inverted potentials. We conclude that to within the precision of these measurements, the dilute pair potential remains valid at high density in this system.