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.


Introduction
Colloidal particles are useful building blocks to fundamentally study self-assembly phenomena 1-4 as well as to engineer functional materials with a defined structure at the nanoscale. [5][6][7] When adsorbed at a liquid interface, colloids are able to crystallize into ordered twodimensional lattices. 1, 8,9 Depending on the balance between attractive van der Waals and capillary forces (arising from contact line undulations 10 ) and repulsive electrostatic and dipole forces, monodisperse spherical colloidal particles typically form close packed or non-close packed arrangements with hexagonal symmetry. 3,11 These colloidal monolayers can be deposited onto a solid substrate, providing a strategy to create ordered nanoscale surface patterns in a simple and fast process over macroscopic dimensions. The deposited colloidal particles can further serve as templates and shadow-or etching masks to create more complex surface nanostructures, used for example in photonics, [12][13][14][15] phononics, 16,17 electronics, 18,19 liquid repellency 20,21 or to control cell-surface interactions. 22,23 However, the tendency of spherical colloidal particles to assemble into hexagonal lattices limits the available structural motifs for such surface nanostructures.
Ongoing research efforts therefore focus on manipulating the self-assembly process to create colloidal surface patterns with more complex symmetries. Changing the shape of the colloidal building blocks to cubic or octahedral enables the assembly of square lattices as the densest packing. 24,25 Introducing defined patches on spherical colloidal particles is another way to manipulate the symmetry of the assembly. 26,27 Manipulating the interaction potential by external electric [28][29][30] or magnetic fields [31][32][33] may induce dipoles and align the particles into chains oriented along the field lines. Similarly, the directionality of the capillary interaction forces can be manipulated with anisotropic particles 34,35 or a defined curvature of the liquid interface 36,37 to create square symmetries or particle chains. Further, liquid crystal interfaces can guide spherical colloids into 1D chains or 2D crystals. 38,39 Topographically prestructured 4 surfaces provide an alternative engineering to guide the assembly of colloids. [40][41][42] Common to all of these approaches is that the anisotropy of the final assembly is externally imposed onto the colloidal particles via process conditions, force fields, or the properties of the substrate.
Nearly two decades ago, Jagla predicted that even spherical particles with an isotropic interaction potential are able to assemble into anisotropic structures when confined in two dimensions. 43,44 The formation of such complex phases requires an isotropic repulsive interaction potential with two distinct length scales, consisting of a hard sphere potential at the particle core and a longer repulsive shoulder. When forced into contact by increase of the particle density, such systems minimize their free energy by fully overlapping their shells in some directions in order to avoid overlap in other directions. 43,[45][46][47] As a result, chain structures, square symmetries or even more complex structural motifs including quasi-crystals have been theoretically predicted as minimum free energy phases. [47][48][49][50][51][52] Recently, we devised an experimental system that showed structural similarities to the theoretical predictions by Jagla. We co-assembled spherical, polystyrene microspheres with soft poly(N-isopropylacrylamide) microgels and found that the microspheres self-assembled into anisotropic chains and phases with square symmetry at the air/water interface. 53 We attributed this non-intuitive phase behavior to the presence of a soft repulsion potential with a near-linear ramp profile interacting between the microspheres. The phase behavior was fully recovered by minimum energy calculations and Monte Carlo simulations using similar shapes of the interaction potential. We rationalized this interaction potential by assuming the formation of a two-dimensional, compressible microgel corona around the polymer microspheres in situ at the air/water interface. Accumulation repulsion 54 and elastic compressibility of this corona induce an effective repulsion of the microspheres, which may account for the postulated interaction potential. However, the system requires the microgel particles to be much smaller than the colloidal particles forming the anisotropic lattice, therefore limiting the observable structures to micron-sized particles.

5
Here, we aim to manipulate the interaction potential of smaller colloidal particles with sizes in the nanometer range by adopting a similar strategy. We hypothesize that other surface-active species may be similarly effective in manipulating the interaction potential between colloidal particles at the air/water interface, allowing the formation of complex assembly phases using isotropic, nanoscale colloidal particles.
We therefore investigate the assembly behavior of polystyrene (PS) colloidal particles in the presence of different types of molecular amphiphiles at the air/water interface, including classical surfactants, block copolymers and proteins. We characterize the self-assembly in situ by optical microscopy as well as after transfer to a solid substrate by scanning electron microscopy (SEM). For certain types of surfactants, we observe complex assembly phases, including chains and square lattices. We discuss criteria for the amphiphiles that are required to induce complex self-assembly structures and show that the observed structures agree with theoretical minimum energy calculations of hard spheres interacting via a soft-repulsion (Jagla) potential.

Results
We used surfactant-free emulsion polymerization to synthesize polystyrene (PS) colloidal particles with acrylic acid as comonomer and ensured that the colloidal dispersions were free of impurities by applying dialysis and centrifugation. As amphiphilic additives, we investigated commercially available surfactants (Triton X-100, sodium dodecyl sulfate (SDS)), low molecular weight ionic block copolymers (BCP) poly(acrylic acid)-block-poly(methyl methacrylate) (poly(AA15-block-MMA15)) 55 and the surface active protein bovine serum albumin (BSA). We premixed the colloidal dispersions with defined concentrations of an amphiphile, diluted the dispersions with 50 vol-% ethanol and spread them to the air/water interface of a Langmuir trough (Figure 1). To visualize the assembly as a function of the surface pressure (or, the particle density) we used two techniques: For small colloidal particles (d = 600 nm), we used the simultaneous compression and deposition method to transfer the interfacial monolayer onto a solid substrate while compressing (Figure 1). This procedure enables us to transfer the full phase diagram onto a single substrate, which can then be imaged by SEM. [56][57][58] For large colloidal particles (d = 1.1 µm) we directly visualized the assembly in situ by mounting the Langmuir trough set-up on top of a conventional optical microscope equipped with a camera.  Scale bar: 5 µm.
Next, we used the amphiphilic block copolymer (BCP) (poly(AA15-block-MMA15)). In its chemical composition, this block copolymer resembles the polymer colloids, which were synthesized using acrylic acid as the comonomer as well. At pH 7 the acrylic acid groups With increasing BCP concentration, this behavior became more pronounced, indicating that the interfacial properties were increasingly dominated by the BCP (Figure 3a, brown to green lines).
In contrast to the case of the commercial surfactants shown above, the BCP induced changes in the self-assembly behavior of the colloidal particles at the interface.  To understand the evolution of the complex interfacial arrangements of the BCP/colloid system in more detail, we investigated the phase behavior of the colloidal particles in the squareand chain region as a function of the surface pressure. Figure  However, small deformations occurring upon drying by capillary forces may cause the relatively small crystal sizes. As we cannot exclude artifacts from the drying process, we refrained from a quantitative analysis of the phase behavior. Qualitatively, all observed phases can be directly correlated to the phase behavior directly at the interface (see below), indicating that capillary forces do not dominate the structure formation process. The measured high surface pressure values have to be taken with care, as extra and deviatoric stresses can occur. 64 13 Figure 5 shows the surface pressure -area isotherm for the 0.1 wt% BCP/colloid system along with the transferred assembly structures. Similar to before, at lower surface pressures (Π < ~25 mN/m), the transferred colloidal structures appear inhomogeneous and partially agglomerated, which we attribute to capillary forces acting upon drying (Figure 5b  14 The small size of the colloidal particles prevents the direct observation of the structure of the monolayer formed at the air/water interface, requiring the indirect method of transferring the interfacial arrangement to a solid substrate to characterize the structure of the assembly by electron microscopy. This procedure, however, bears the risk that the structural arrangement is affected by capillary forces during the drying process. Indeed, images of the particle arrangements taken at lower transfer pressures show close packed structures and partial aggregation, which may have been caused by capillary forces (Figure 4b, Figure 5b). We increased the size of the colloidal particles (d = 1.1 µm) and integrated the Langmuir trough into a microscope setup to directly observe the interfacial arrangement by optical microscopy. 53 Figure 6 shows the interfacial assembly phases of these large polystyrene microspheres at the air/water interface in the presence of BCP molecules. We observed a similar surface pressurearea isotherm as for the smaller particles, albeit with the change in slope shifted to a higher surface pressure (Figure 6a). The interfacial assembly of pure microspheres showed hexagonal close packed structures (Figure 6b). In the presence of the BCP, the interfacial assembly of the microspheres was more complex and transitioned from non-close packed arrangements at low surface pressure (Figure 6c) to anisotropic chain phases at higher surface pressures ( Figure 6de). These results coincide with the assembly phases observed for the smaller colloids by electron microscopy, demonstrating that the interfacial assembly can be transferred to a solid substrate without altering its structure if the transfer is performed at high compression. At lower surface pressure, we observed non-close packed arrangements and chain structures at the interface, while the electron microscopy images showed close packed aggregates. We therefore conclude that ex-situ SEM imaging cannot be used to interpret the interfacial behavior at low surface pressures as capillary forces alter the structure of the assembly. It is noteworthy that the observed particle chains were preferentially aligned perpendicular to the barriers, similar to the case of smaller colloids investigated by SEM. The comparison of in-situ microscopy and electron microscopy underlines that it is possible to transfer the complex assembly phases to a 15 solid substrate, opening up avenues to create complex assembly structure for the nanostructuring of surfaces.

Discussion
Our experiments indicate that some molecular additives present at the air/water interface alter the self-assembly of colloidal particles at the air/water interface. These amphiphiles direct the colloidal particles into pseudo-square or chain phases, which is not expected for isotropic, spherical colloidal particles.
We discuss this complex phase behavior in the context of a change in the interaction potential acting between the colloidal particles. Previously, we demonstrated that polystyrene microspheres in the presence of soft microgels showed a similar phase behavior and underwent phase transitions upon compression from a non-close packed phase, to a chain phase, to a pseudo-square phase until finally forming a hexagonal close packed phase. 53 This phase behavior coincided with theoretical predictions based a long-range, linear repulsive contribution to the interaction potential between the microspheres. We rationalized this interaction potential by the in-situ formation of a two-dimensional corona of small particles around a large particle directly at the interface. This corona forms by adsorption of the microgels to the particles' surfaces and the presence of additional microgels surrounding this layer of adsorbed microgels. These microgels are forced to overlap upon decreasing the area available at the interface, which, in turn, creates a repulsive force as the polymer chains are forced into closer contact. The two-dimensional nature of this compressible shell translates into a linear increase in overlap area with decreasing distance between the microspheres -which we hypothesized to cause a linear increase in the repulsion, as required by the theoretical considerations to form the complex assembly phases. 53 The close similarity to the phase behavior we observe for smaller colloidal particles in the presence of some of the amphiphiles leads to the assumption that these amphiphiles affect the interaction potential in a similar way as the microgels (as schematically illustrated in Figure 9).
In analogy to the case of microgels, we hypothesize that the repulsive component of the interaction potential is caused by an accumulation of amphiphiles in between the colloidal particles at the air/water interface. In this picture, the amphiphiles adsorb to the particle surface and accumulate in between the particles, with the following consequences for the interaction potential. First, the accumulation of the amphiphiles itself causes an effective repulsion of the large particles, which are pushed apart from each other as amphiphiles accumulate in between the particles. This phenomenon is known as accumulation repulsion 54 and is directly observable from the microscopy investigations of the interfacial assemblies in Figure 6. In the presence of amphiphiles, the colloidal particles show a non-close packed arrangement at minimal compression, indicating a net repulsive character. Second, the two-dimensional layer of amphiphiles present in between the particles is forced into increasingly closer contact upon compression, which adds to the repulsive character of the system when we increase the overlap.
From these considerations, we deduce the following requirements for the additive to be able to alter the phase behavior of the colloidal particles.
Surface activity. The additive must adsorb to the air/water interface to form a twodimensional layer in between the colloidal particles. The two-dimensional nature of this shell surrounding the colloidal particles seems to be crucial to achieve the required (linear) shape of the interaction potential, since the area of overlap between the amphiphiles changes linearly upon compression in a two-dimensional layer. 53 This requirement seems trivial but is the reason why amphiphilic components need to be chosen as the additive to be co-assembled with the colloidal particles and why three-dimensional core-shell particles to not exhibit this behavior. 53,56,68,69 Homogeneous co-assembly with the colloidal species. The hypothesized change in interaction potential relies on the formation of a homogeneous, two-dimensional corona of amphiphilic molecules around the colloidal particles (Figure 1). The formation of this homogeneous layer requires an affinity between the two species at the interface. Phase separation of amphiphile and colloids therefore needs to be prevented. Irreversible adsorption. The amphiphile needs to adsorb strongly, almost irreversibly, to the air/water interface to enable compression without desorption into the subphase. The twodimensional corona formed around the particles can only contribute to the complex phase behavior if it the area per particle can be changed (i.e. by compression of the interface) without losing the corona by desorption from the interface.
Compressibility of the amphiphile layer. We hypothesize that the amphiphile corona needs to be compressible in order to generate a longer range repulsive shoulder between the particles, similar to the case of microgel additives. 53 Next, we argue how these criteria relate to the different interfacial species and discuss why some of the tested species do influence the assembly behavior while others do not. First, we note that all species fulfil criterion 1, i.e. they are all surface active in the presence of the colloidal particles as can be seen from the changes in the surface pressure -area isotherms of all mixed samples. Second, we note that the commercial surfactant Triton X-100 does not induce any change in the phase behavior of the colloidal particles (Figure 2a-c), but instead causes a macroscopic phase separation. The surfactant does not form a corona around the colloids and thus does not fulfill criteria two. The other tested commercial surfactant SDS does desorb from the air/water interface. The interfacial surfactant layer is therefore removed upon compression, preventing the formation of an irreversible corona around the PS colloids, described in criteria three. For the other surface-active species (block copolymer (BCP), and protein) we did not observe any phase separation or desorption from the interface. Both species also induced a complex phase behavior, supporting the criteria put forward above.
In a proof of principle experiment, we performed the interfacial assembly of BCP and colloids on a subphase with a defined amount of salt. We hypothesized that salt will screen the charges of the acrylic acid groups in the block copolymer and therefore decrease the repulsion in the system, forming more compact polymer coils and therefore reduce the compressibility at the 20 interface. With increasing salt addition, we observed that the surface pressure -area isotherm became steeper and less compressible (Figure 8), as predicted for the more compact polymer chains. The phase behavior of the colloidal particles observed after transfer to a solid substrate changed significantly with increasing salt concentration and chain formation was only observed in the absence of salt (Figure 8b-d), indicating that compressibility, i.e. the ability to force the surfactant layer into closer overlap, is important to observe the complex assembly phases as well. Finally, we discuss the effect of amphiphile concentration on the resulting interfacial assembly properties that we experimentally observe (Figure 3). With increasing concentration of block copolymer, the assembly phases at maximum compression shift from pseudo square packing to anisotropic chains, which subsequently become shorter and more widely spaced, until, at maximum BCP concentration, only individual, separated particles are observed. We note that there is a significant scatter in colloidal chain lengths, chain orientation and inter-chain distance, which only allows a qualitative discussion of these effects. 21 Within the framework of our simple core-shell model, an increase in the amphiphile concentration will increase the range of the soft repulsive shoulder, as more and more amphiphiles separate the colloidal particles. The assumed interaction potential should therefore be controlled by the amphiphile concentration.
Previously, we showed that the core-shell model could reproduce the experimental phase behavior for the case where shell thickness was fixed while the surface pressure/colloid area fraction was increased. 49 Here, we show that the model can also reproduce the phase behavior observed in Figures 3 and 7, i.e., where the surface pressure is fixed, but the shell thickness is increased.
We model the interaction between the core-shell particles using the Jagla potential with a linear ramp profile for the soft shoulder ( Figure 9a); this is equivalent to assuming that the soft shoulder profile parameter = 1. In Figure 9a, 0 , 1 are the range of the hard core and soft shoulder respectively (or equivalently the diameter of the hard core and soft shell respectively), while 0 is the potential shoulder height. As detailed elsewhere, 53  We performed a comprehensive exploration of the minimum energy structures containing one particle per unit cell (Figure 9b) in the NPT ensemble. Specifically, we determined the minimum energy configuration (MEC) for a given value of 1 0 ⁄ and by minimizing the enthalpy per particle with respect to the lattice parameters shown in Figure 9b. Note that the 22 MECs are relevant experimentally since in the experimental system 0 ≫ so that we are effectively in the zero temperature regime.
In Figure 9c, we sketch the minimum energy phase diagram for our theoretical core-shell particles in the 1 0 ⁄ vs.

Conclusion
In this study, we observed that the presence of block copolymer or protein changes the assembly behavior of the colloids confined at an air/water interface.
While pure colloids assemble into a hexagonal close packed lattice, the observed colloidal phases transition from a distorted square lattice, via chain structures to fully separated colloidal particles with increasing amount of amphiphiles. We further investigated the assembly behavior of the colloid/BCP mixture in situ at the air/water interface, where we observed a chain assembly even at low surface pressures, thus excluding possible artefacts during the deposition of the interfacial assembly onto a solid substrate.
The observed structures are in agreement with minimum energy calculations based on isotropic particles interacting via a long-range repulsive shoulder known as Jagla potential. We hypothesize that the repulsive component of the interaction potential may be caused by an accumulation of amphiphiles in between the colloidal particles at the air/water interface, which cause an effective repulsion of the large colloidal particles by accumulation repulsion. The twodimensional layer of amphiphiles around the colloids thus acts as soft corona separating the colloidal particles.
With increasing concentration of amphiphiles, this two-dimensional corona increases in size and therefore alters the phase behavior. The corona size -dependent phase behavior is reproduced by the theoretical model.
Our results provide an experimental simple pathway to direct the self-assembly of spherical colloids into complex anisotropic structures. This methodology opens pathways to increase the structural variety of nanoscale surface patterns created by colloidal lithography. added to the mixture. After 5 min the reaction was initiated with 0.1 g ammonium persulfate, dissolved in 5 mL Milli-Q water. The reaction was carried out for one day at 80 °C. After cooling to room temperature, the dispersion was filtered and purified by centrifugation and redispersion and applying dialysis against water for 2 months.
The detailed synthesis for the low molecular weight ionic block copolymers (BCP, Poly(AA15-block-MMA15)) is described in a previous publication. 55 In short, BCP were For in-situ observation of the particle assembly at the air/water interface we mounted the Langmuir trough set-up on an optical microscope (Leitz, Ergolutz) equipped with a CMOS camera (Thorlabs, DCC1645C). We used larger PS colloids (d = 1.1 µm) and a high compression trough with a glass window in the center and an area of 550 cm 2 . The images were taken as 8-bit-grey-scale images in transmission mode with a 50x objective (Leitz Wetzlar).
The barriers were compressed with a speed of 4 mm/min.