Segregation in Drying Binary Colloidal Droplets

When a colloidal suspension droplet evaporates from a solid surface, it leaves a characteristic deposit in the contact region. These deposits are common and important for many applications in printing, coating, or washing. By the use of superamphiphobic surfaces as a substrate, the contact area can be reduced so that evaporation is almost radially symmetric. While drying, the droplets maintain a nearly perfect spherical shape. Here, we exploit this phenomenon to fabricate supraparticles from bidisperse colloidal aqueous suspensions. The supraparticles have a core–shell morphology. The outer region is predominantly occupied by small colloids, forming a close-packed crystalline structure. Toward the center, the number of large colloids increases and they are packed amorphously. The extent of this stratification decreases with decreasing the evaporation rate. Complementary simulations indicate that evaporation leads to a local increase in density, which, in turn, exerts stronger inward forces on the larger colloids. A comparison between experiments and simulations suggest that hydrodynamic interactions between the suspended colloids reduce the extent of stratification. Our findings are relevant for the fabrication of supraparticles for applications in the fields of chromatography, catalysis, drug delivery, photonics, and a better understanding of spray-drying.

W hen a suspension droplet evaporates from a solid surface, the previously dispersed colloids remain on the surfaces. The structure of the deposited colloids depends on the wetting properties of the surface. If the suspension fully wets the surface, a film is formed (Figure 1a). Evaporation of films and the resulting film formation has been studied because of its relevance in applications such as painting, coating, film formation, etc. 1 Due to the spatial symmetry of the drying process, evaporation can be described by a single coordinate perpendicular to the substrate. 2−4 The evaporation of isolated drops occurring on partially wetted surfaces is more complex (Figure 1b). Dispersion evaporation is common in daily life and important for applications in printing, 5 washing, forensics, 6,7 or agriculture. 8 The evaporation dynamics and the final structure of the deposit have been widely investigated both experimentally and in simulations. 9,10 For partially wetting isolated drops, the evaporation is no longer homogeneous. If the apparent contact angle of the drop is below 90°more liquid evaporates at the periphery than in the center. The resulting radial flow of liquid enriches colloids at the periphery, where particles aggregate and finally form a ring-or doughnut-like structure. 11−17 As a result of line pinning at the periphery, drops often evaporate at a constant contact radius rather than at a constant contact angle.
Another important case is the evaporation of free droplets, which occurs, for example, in spray drying (Figure 1d). Spray drying is a widely used process to fabricate powders from solutions or suspensions. 18 −23 In the case of a free spherical drop, evaporation is radially symmetric and thus can also be described by a single coordinate.
During the past decade, water and oil repellent surfaces, socalled superamphiphobic surfaces have become available. 24,25 Liquid droplets on these surfaces can maintain a spherical morphology with a contact angle larger than 150°, while the interfacial area between liquid and solid is extremely small, i.e., ≪V 2/3 , where V is the volume of the drop (Figure 1c). Usually superamphiphobic surfaces are also porous, allowing the liquid to evaporate through the substrate. As a result, liquid evaporation is almost radially symmetric and the flow is suppressed. Furthermore, super-liquid-repellent surfaces allow for the fabrication of supraparticles. Such supraparticles are typically 100−1000 μm in diameter and consist of colloids that are 20−2000 nm in size. Supraparticles were first formed from aqueous dispersions on superhydrophobic surfaces. 26−35 Using superamphiphobic substrates, non-aqueous suspensions can be applied, surfactants can be added, and, due to the extremely low real contact area and the low adhesion, supraparticles can easily be removed from the surface, 36−38 allowing for the production of many supraparticles. Fabrication of supraparticles on a super liquid-repellent surface has the advantage that no surrounding processing liquid is required as in the case of microfluidics. In contrast to spray drying, the process can be carried out slowly under well-controlled boundary conditions so that more-complex supraparticles can be designed. Using super-liquid-repellent surfaces for the preparation of supraparticles may also help to improve our understanding of spray drying.
Previous experimental and simulation studies about drying colloidal droplets on super-liquid-repellent surfaces have focused on monodisperse colloids. 26,28,31,33,35 The final packing of the colloids depends on their interaction in suspension. For long-range repulsive interactions, the colloids tend to form a closed-packed crystalline structure. If at a certain level of concentration, attraction takes over, the colloids aggregate and form a random and more porous structure.
In this study, we aim to achieve more complex architectures of the supraparticles. We investigate both experimentally and in simulations the drying processes of a bidisperse colloidal suspension, i.e., the mixture of colloids of two distinct sizes, small (S) and large (L). Of particular interest is the distribution of colloids in the suprapaticles, i.e., whether they remain homogeneously distributed as in the initial suspension, or if they are able to form ordered structures. Previous experiments of bidisperse colloids in evaporating drops on superhydrophobic surfaces 26 and in acoustically levitated drops 39 suggested an enrichment of small colloids at the supraparticle surface, but the details and mechanisms of the colloid segregation remain largely unexplored.
The evaporation of such bidisperse suspensions has been studied in more detail for thin films experimentally 40−42 and in simulations. 40,43−49 It was found that depending on the particle size ratios, initial volume fraction and evaporation speed, the smaller colloids end up more to the top of the film. The larger colloids are pushed to the bottom, creating "inverted" stratification. Qualitatively, this segregation occurs because evaporation leads to a local increase of the colloid concentration near the film−air interface, which, in turn, translates to a chemical potential gradient for both colloid species. 44,45 Typically, this gradient is steeper for the large colloids than for the small ones because more volume is excluded to the large colloids. As a consequence, the large colloids experience a stronger driving force pushing the colloids away from the film−air interface. Inverted stratification then occurs if the mobility of the large colloids decrease slower than the driving force increases. The quantitative extent of stratification depends on the specific system, e.g., whether the dispersed particles are rigid colloids or flexible polymers 43,45,49 and whether or not hydrodynamic interactions are included in the theoretical description. 47−49 For a more comprehensive discussion on evaporating films, we refer to the recent review by Schulz and Keddie. 4 To study the stratification in spherical drops, we investigated the evaporation behavior of drying binary colloidal drops on a superamphiphobic surface. Aqueous suspensions of polystyrene (PS) colloids of mean diameters . With the help of scanning electron microscopy (SEM), we observed a significant enrichment of small colloids at the supraparticle surface with a concomitant depletion of large colloids in this region. Toward the center of the supraparticles the two species gradually mixed again. The extent of this separation became less pronounced when we decreased the evaporation speed. Computer simulations confirmed this dynamic stratification and provided additional information on the colloid distribution during the evaporation process. These results will help us to prepare supraparticles for various applications such as in chromatography, catalysis, or for making photonic crystals.

RESULTS AND DISCUSSION
Evaporation of Drops. The relevant parameter describing the evaporation process of a suspension is the Pećlet number (Pe). It characterizes the relative contributions of advection and diffusion to the motion of the colloids. For evaporating spherical droplets, Pe is the ratio of the typical time, a dispersed particle needs to diffuse one initial droplet radius, τ d , and the characteristic time of evaporation, τ ev . The evaporation time can be expressed as τ = R v / ev 0 ev , where R 0 is the initial droplet radius and v ev is the speed of the receding droplet-air interface. For (free) droplets, the evaporation is limited by the diffusion of water molecules through the surrounding air, 50 and the droplet volume V decreases as:

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Article where V 0 is the initial volume of the droplet and α is the rate of surface reduction. Taking the time derivative of eq 1, one obtains for the initial v ev the following expression: For a free, spherical droplet, α can be determined analytically, i.e.: Here, D air is the diffusion coefficient of vapor molecules in air, m is the mass of one vapor/liquid molecule, ρ is the density of the liquid, ΔP is the difference in pressure at the droplet surface and outside the film of vapor, and k T B is the thermal energy of the system. For sessile droplets which are shaped like a spherical cap, Picknett and Bexon 51 calculated the evaporation rate and found: with the contact angle θ, and f = 0.00008957 + 0.633θ + 0.116θ 2 − 0.08878θ 3 + 0.01033θ 4 for θ (rad) above 10°. The pressure difference ΔP in eqs 3 and 4 can be expressed in terms of relative humidity RH as Δ = − P P (1 RH) 0 with saturation vapor pressure P 0 . We indeed observed a linear decrease of V 2/3 for the evaporation of pure water droplets as well as the colloidal suspensions (Movie S1 and Figure S1). Using eq 4 for pure water droplets at our experimental conditions (θ =°154 , =°T 23 C, = P 2810 Pa 0 , and = RH 24%) , w e fi n d α = μ s 1550 m / sessile 2 , which is in excellent agreement with the value of α = ± μ s 1482 7 m / 2 that we obtained from fitting our results with eq 1. Note that these values for α are roughly 30% smaller than the ones expected for completely free spherical droplets. Droplets of suspensions evaporated with the same kinetics as pure water droplets but with a slower rate of α = ± μ 1046 20 m /s 2 ( Figure S1d). We attribute the slight reduction in the evaporation rate to the reduced surface area of the droplets caused by colloids coating the surface.
The characteristic diffusion time can be expressed as where D p is the diffusion coefficient of the colloids. For a spherical particle with stick boundary conditions, D p can be estimated through the Stokes−Einstein relation, i.e., πη , with suspension viscosity η. For dilute suspensions of spherical particles, Cichocki 53,54 For the initial colloid volume fraction ϕ = 8%, we find that the suspension viscosity increases by roughly 24% compared to the neat solvent (water in our case).
In conclusion, we find 2/3 p for evaporating spherical droplets, which is independent of the initial droplet radius. It should be noted that the Pećlet numbers quoted in this work refer to the beginning of the evaporation process when the droplets have still their initial radius, R 0 , and their initial colloid volume fraction ϕ = 8%. As the droplet is drying, the (local) colloid volume fraction increases, resulting in a (local) increase of the suspension viscosity. Consequently, the Pećlet numbers increase over time and eventually become undefined once the colloids jam or crystallize. Nevertheless, the initial Pećlet numbers are useful quantities for characterizing the drying regime of the droplets.
Structure of Supraparticles. When the evaporation is completed, the final supraparticle assumes a nearly spherical shape. It took about 18 min for complete drying of a 2 μL L for the small and large colloids, respectively. Thus, diffusion is substantially slower than advection.
Small colloids were enriched at the surface of supraparticles (Figure 2a,b). The small colloids were assembled into close packed, crystalline regions with some line and dot defects between the highly ordered regions. Only a small area of the supraparticle surface was occupied by large colloids. These seemed to anchor in particular in the defective regions between the crystals formed by the small particles.
To further analyze the distribution of small and large colloids, we cut the supraparticles in half (with a WEDO leather knife) and imaged the internal structure using SEM. Segregation of the small and large colloids was observed. The outer shell of roughly 20 μm thickness contained almost exclusively small colloids (Figures 2a and S2b). They formed well-ordered 3D crystal structures. Only few of the large

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Article colloids were found in the shell. In contrast, the core part of the supraparticle consisted mostly of large colloids (Figures 2b,  S2c, and S3). The small colloids mainly filled the interstitial spaces. No crystallization was observed in this region. Stitching of a series of SEM pictures taken along a line from the edge to the center shows the transition between these two regions in detail (Figure 2b). The radial distribution of small and large colloids in the supraparticle (Figure 2c) shows the clear spatial segregation between the two colloid types, which manifests itself during evaporation. Note that the crystallization of the smaller colloids that is observed in the outer layer of the supraparticle does not contribute to the stratification effect but is rather a consequence of the segregation. Furthermore, we did not observe any indication of buckling or cracking of the dried supraparticles in our experiments, as it can occur during spray drying due to skin formation. 55 In experiments on the formation of supraparticles from monodispersed colloids, we could provoke crust formation only by pronounced acceleration of the evaporation process, using either temperatures close to the boiling point or applying vacuum (manuscript in preparation). Increasing the droplet volume to 10 μL leads to a flattening of the initial droplet due to gravity. As the droplet shrinks during evaporation, it becomes spherical again as its mass decrease. The evaporation rate of α = 884 μm 2 /s is slightly lower than for the small droplet. However, the final deposit is nonspherical, as during the much longer evaporation time, sedimentation of the PS particles sets in ( Figure S4). This sedimentation for larger drop can be mostly suppressed by density matching using D 2 O instead of H 2 O, leading to almost spherical supraparticles again ( Figure S5).
Comparison to Simulations. For a more-comprehensive understanding of segregation, we conducted complementary Langevin dynamics simulations with an implicit solvent. Initially, the colloids were uniformly distributed (Figure 3a and dotted line in Figure 3b). As the droplet dries, the small colloids accumulate near the surface (dashed and solid red lines in Figure 3b). A corona consisting almost exclusively of small colloids builds up. This shell is directly followed by a region enriched by large colloids (dashed and solid blue lines in Figure 3b), which extends over ∼15 μm in the final state. Additionally, there are a few large colloids trapped at the droplet-air interface, which are no longer able to move through the dense layer of small particles. The core of the supraparticle is seemingly unaffected by the evaporation, as we find the same composition and density of colloids like in the beginning of the simulation. This behavior can be rationalized by the large evaporation rate ( ≫ Pe 1 S and ≫ Pe 1 L ), which impedes diffusive mixing of the core and shell regions.
When overlaying the density of colloids after evaporation from the simulations with the experimental measurements, the results largely agree (Figure 4). Because the Pećlet number is independent of the drop radius, we scaled the radial coordinate and plotted both curves in one graph. Simulated colloid densities qualitatively agree with the experimental results. In both cases, we observe a higher density of large colloids in the core. At a distance of ∼80% of the supraparticle radius, the small colloids enrich and dominate the shell with the exception of a few large colloids pinned at the surface of the supraparticle.
A closer inspection of Figure 4 reveals that stratification is more pronounced in the simulations. This discrepancy likely stems from the lack of hydrodynamic interactions and liquid back flow in our simulation model. Indeed, for drying films, it has been shown that hydrodynamic interactions and liquid back flow can reduce the degree of stratification. 47−49 The missing local hydrodynamics in the particle interaction is certainly a limitation of our model. In contrast, large-scale hydrodynamics due to Marangoni flow, as it occurs for sessile drops with pinned contact line (coffee ring effect), 11−15 can be excluded in our evaporation situation with radial symmetry. Further note that the droplet radius, R d , in experiments and simulations differs by a factor of ∼6 (see the Experimental

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Article Methods section). Although the Pećlet numbers are identical in experiments and simulations, and thus qualitatively similar stratification behavior is expected, the local structuring of the dispersed colloids might be affected by the different size ratio between the colloids and the drop; each colloid takes up relatively more space in the simulations compared to the experiments, which could explain the more pronounced layering found in the simulations. The surface-to-volume ratio of the droplet is also bigger in the simulations, which further supports the stronger separation between large and small colloids in the simulations because stratification is driven by the receding boundary. Nonetheless, the agreement between experiments and simulations is rather good, underlining the robustness of the stratification process.
Low-Speed Evaporation of Binary Colloidal Droplets. For planar films, the extent of stratification depends on the evaporation speed. 4,40,44,56 To observe the effect of evaporation speed in radial symmetry, we repeated our experiments at an increased relative humidity of 68%. Increasing the humidity resulted in an increase in the evaporation time from 18 min to 2 h ( Figure S6). The Pećlet numbers for small and large colloids decreased to 27 and 110, respectively. Again, we observed a monotonic decrease of droplet volume over evaporation time, with a rate of α = ± μ 154 2 m /s 2 . Spherical supraparticles could still be obtained even after prolonged evaporation ( Figure S7a).
For slow evaporation, the colloids were distributed more evenly in the supraparticle surface. Each large colloid was surrounded by a similar volume of small colloids (Figure 5a,b).
The cross-section shows that the core region is enriched in large colloids and mixed with a low number of small colloids (Figure 5b). The difference is, however, not as pronounced as after fast evaporation. The shell between a radius of 220 and 280 μm was mostly occupied by small colloids. When crossing over this layer, the number of small colloids gradually decreased, while the density of large colloids increased ( Figure  5c). The small colloids did not crystallize in this case, presumably because their concentration was not high enough.
Such a weakening of the inverted stratification is consistent with simulation results ( Figure S8).

CONCLUSIONS
In this study, we demonstrate that stratification of evaporating binary suspensions occurs not only for film-like geometry but also for radial symmetric geometry. An almost-radial symmetry can be achieved by evaporating drops of suspensions from superamphiphobic surfaces. The distributions of small and large colloids in the supraparticles depend on the evaporation speed. For fast evaporation, small colloids form an outer shell, while the core is enriched by large colloids. The small colloids in the shell form crystallites with several point and line defects. Only a few large colloids are trapped at the surface of the supraparticle, primarily at the site of defects. For slow evaporation, large and small colloids form a disordered structure on the surface, followed by an intermediate layer that is mostly occupied by small colloids with several large colloids randomly distributed. At the center of the supraparticles, the concentration of small colloids gradually decreases, while large colloids are enriched.
Preparation of Soot-Template Superamphiphobic Surfaces. Glass slides were first cleaned with toluene, acetone, and ethanol by ultrasonication, then dried under nitrogen flow. After treatment of the glass slides with oxygen plasma (Diener Electronic Femto, 300 W for 5 min), candle soot was deposited on the glass slides. 58 Afterward, the soot-coated glass slides were placed in a desiccator together with two opened glass bottles containing 3 mL of TEOS and aqueous ammonia solution. The desiccator was closed, evacuated to 250 mbar, and then vented with ambient air to atmospheric pressure for chemical vapor deposition of TEOS (catalyzed with ammonia) for 24 h. After the soot was coated with a silica shell, the soot was burnt away at 550°C for 3 h. In this way, a fractal-like silica nanoparticle structure with overhangs was created. To achieve superamphiphobicity, the surface was further modified with trichloro (1H, 1H, 2H, and 2Hperfluorooctyl) silane by means of chemical vapor deposition. Silicacoated surfaces were put into a desiccator together with an opened glass bottle containing 0.1 mL of the silane. The desiccator was evacuated to 50 mbar and left for 3 h to finally obtain the soottemplate superamphiphobic surfaces. The superamphiphobic substrate exhibited good liquid repellent properties because it was constructed from fractal silica structure with overhangs ( Figure S9a) and further modified with perfluorosilane. Water and hexadecane droplets form a spherical morphology. Water droplets possess a contact angle over 170°( Figure S9b) with a sliding angle about 1°, while hexadecane droplets have a contact angle around 154°( Figure  S9c

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Article ϕ = 5.5% L and ϕ = 2.5% S , respectively. A total of 2 μL of this suspension were dropped onto the superamphiphobic surface. Drops were evaporated at 23°C, either at ambient conditions (relative humidity 24%), or at a relative humidity of 68% (measured with a TFA Digital Thermo-Hygrometer). High humidity was achieved by putting several opened water bottles around the superamphiphobic substrates in a chamber and by allowing the system to equilibrate for about 0.5 h before placing the drop.
Characterization. Static and sliding angles of 5 μL of water and hexadecane droplets on a superamphiphobic surface were measured with a goniometer, Dataphysics OCA35 (Data Physics Instruments GmbH, Germany). The morphology of the soot-template superamphiphobic surface and supraparticles were characterized by SEM (low-voltage LEO 1530 Gemini, Germany). The samples were sputter-coated with a 5 nm layer of Pt using a BalTec MED 020 coater prior to taking images to avoid charge buildup. The distributions of colloids in the supraparticles from the experiments were obtained by analyzing the SEM images using ImageJ software. The shape of the droplet during the evaporation process was recorded with a side view camera (IDS uEye USB camera). The polydispersity of the prepared PS colloids were characterized by dynamic light scattering (Malvern Zetasizer Nano S90).
Simulations. In the simulations, we modeled the colloidal suspension as a binary mixture of large and small colloids with the same size ratio ≈ d d Here, the spring constants k i effectively control the surface tension and were chosen as The harmonic form of eq 5 stems from geometric consideration of the change in surface area when a colloid is placed at the interface with a contact angle of 90°. This model neglects hydrodynamic interaction between colloids and interface but reflects repulsive interaction due to surface tension preventing a hydrophilic particle to cross the interface. Evaporation is mimicked by reducing R d according to eq 1 until the droplet reached its final size. Our treatment of the droplet−air interface using an external potential enforces a spherical droplet shape at all times and impedes buckling of the dried supraparticle. Note, however, that neither buckling nor cracking was observed in the experiments, which validates our simulation approach.
The initial droplet had a radius of = R 121.5 d μm, which is roughly six times smaller than the experimental system due to computational limitations (the total number of colloids in the simulations was = N 9 604 239). Note that this reduction in droplet size should not significantly alter the behavior of the system, as the simulations were conducted at the same Pećlet number as that used in the experiments.
The initial volume fractions of the large and small colloids were chosen in line with those in the experiments, i.e., ϕ = 5.5% L and ϕ = 2.5% S , respectively. The simulation time step was set to τ Δ = t 0.005 , and all simulations were performed using the HOOMD-blue software package. 61