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Formationofhighly-orderedsphericalaggregatesfromdryingmicrodropletsofcolloidalsuspension.

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Formation of Highly Ordered Spherical Aggregates from DryingMicrodroplets of Colloidal SuspensionM. Wozniak,* G. Derkachov, K. Kolwas, J. Archer, T. Wojciechowski, D. Jakubczyk, and M. Kolwas

Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland

*S Supporting Information

ABSTRACT: The formation of highly ordered sphericalaggregates of silica nanoparticles by the evaporation of singledroplets of an aqueous colloidal suspension levitated(confined) in the electrodynamic quadrupole trap is reported.The transient and final structures formed during dropletevaporation have been deposited on a silicon substrate andthen studied with SEM. Various successive stages of theevaporation-driven aggregation of nanoparticles have beenidentified: formation of the surface layer of nanoparticles,formation of the highly ordered spherical structure, collapse ofthe spherical surface layer leading to the formation of densely packed spherical aggregates, and rearrangement of the aggregateinto the final structure of a stable 3D quasi-crystal. The evaporation-driven aggregation of submicrometer particles in sphericalsymmetry leads to sizes and morphologies of the transient and final structures significantly different than in the case ofaggregation on a substrate. The numerical model presented in the article allows us to predict and visualize the observedaggregation stages and their dynamics and the final aggregates observed with SEM.

■ INTRODUCTION

Ordered assemblies of colloidal particles on micrometer tonanometer length scales became a recent focus of many studiesas such assemblies can be used for the construction of variousperiodic and quasi-periodic material structures.1−4 In particular,the aggregation phenomenon allows to create compositeswhose physical properties are determined not only by theirchemical composition but also by the specific morphology.5−8

The new kind of structures, known as metamaterials,2,9 exhibitunique (optical) properties not present in conventionalmaterials. Significant attention has recently been paid toprecisely pattern the morphology of nanoparticle films and self-assembled monolayers of nanocrystals by the evaporation ofdrop-deposited colloids on substrates (e.g. refs 10−14 andreferences therein). It is known that the presence of a substratedramatically influences the process of particles aggregation.Much less is known about the particle ordering in unsupportedevaporating droplets of colloidal suspensions.15−19 Theevaporation-driven ordering process in such systems is free ofsubstrate influence. The spherical symmetry of the evaporatingdroplet provides exceptional conditions for the assembly of 3Dphotonic structures with spherical symmetry of significantlydifferent morphologies than those observed for the structuresassembled on substrates.20 Finite packing of such particles (e.g.refs 21−23) adopts symmetries different from the long-rangeordering. A better understanding of how a finite number ofspheres can organize in stable structures may help to controlthe arrangement of matter on different length scales. In ref 22,aggregates which adopt packing that minimize the secondmoment of the mass distribution have been observed. The

authors identified structures containing sphere doublets,triplets, tetrahedra, and polyhedra which had not beenpreviously found in infinite lattice packing or minimum-potential energy clusters. Few studies have been reported onthe aggregation of large, highly regular assemblies of spheresand their transient and final morphologies.17,18,24 Finalaggregates of highly regular morphology, built of much smallerparticles and generated by means of the fast spray dryingmethod, were investigated in refs 25 and 26. Significantly morestudies have been devoted to the self-assembly of nanoparticlesin liquid suspensions (e.g. refs 12, 19, 21, and 27 and referencestherein). Some systematic studies on the influence of thevarious aggregation parameters on the morphology of the finalstructures have also been performed.28,29

It is worth noticing that in order to investigate nanoparticleaggregates, a variety of methods have been proposed, such asstatic light scattering,30,31 small-angle X-rays scattering,32−35

dynamic light scattering (DLS),36 TEM, SEM12,37 and electrontomography.27,38 Those that provide a real-time analysis ofcolloidal assembly in situ (i.e., light and X-ray scattering andspectroscopic methods) are particularly valuable. Some of thesemethods are able to determine not only the position of thesurface particles on the cluster but also the location of theparticles within the cluster at any stage of the aggregation. As anexample, in ref 35 the authors described the transition from anisotropic droplet to the core−shell structure during the SAXS

Received: May 6, 2015Revised: June 26, 2015

Article

pubs.acs.org/Langmuir

© XXXX American Chemical Society A DOI: 10.1021/acs.langmuir.5b01621Langmuir XXXX, XXX, XXX−XXX

investigation of the drying of a single suspended droplet of ananosilica suspension.The goal of the current study was to provide a new method

of producing highly ordered spherical aggregates of nano-particles by the evaporation-driven aggregation of colloidaldroplets. The main cause of aggregation are the strong capillary(surface tension) forces exerted on the suspended particles bythe shrinking interface of the evaporating liquid. Weinvestigated the successive states of the transient aggregatesand emphasized the diagnostics of the final 3D structures. Thetransient and final aggregates were deposited on a substrate andinvestigated with a scanning electron microscope (SEM).

■ DYNAMIC OF DROPLET EVAPORATION ANDAGGREGATION OF COLLOIDAL PARTICLES: ANINTRODUCTION

Studies on the formation of highly regular spherical aggregatesand diagnostics of the aggregated structures presented in thisarticle are a consequence of our former studies on theevaporation of pure liquids39,40 and mixtures of liquids.41,42

Therefore, in this section we briefly summarize our earlierresearch and provide the necessary background related todroplet evaporation, evaporation-driven aggregation of nano-particles, and the formation and slow drying process of highlyspherical aggregates. Finally, we describe the physical back-ground of our numerical modeling of evaporation-drivenaggregation.Evolution of Droplet Size. Single evaporating droplets of

suspensions levitated in the electrodynamic quadrupoletrap43−46 have been produced and optically studied in theexperimental setup built in our laboratory.18,39 Droplets wereinjected into the trap with the droplet-on-demand injector andcharged on injection by charge separation in the external fieldof the trap. The vertical position of the droplet was stabilized inthe center of the trap by balancing the weight of the dropletwith the dc field. The trap was kept in a small climatic chamberwhich allowed us to control (stabilize) the parameters of theinternal atmosphere by choosing ambient gas and adjusting thetemperature.We simultaneously used two coaxial, counter-propagating

laser light beams for droplet illumination: the red verticallypolarized and the green horizontally polarized with respect tothe scattering plane. Two linear polarizers were used in thedetection channel, enabling the observation of the interferencepattern associated with horizontally and vertically polarizedincident light. Scattering patterns were recorded with a CCDcamera. To find droplet radius evolution a(t), we applied theMie scattering lookup table method39 which is based on thefitting of the complete Mie theory predictions (stored in thelookup table) to the experimentally obtained scatteringpatterns. It provides an accuracy of the radius determinationof ±10 nm. Simultaneously, as a supplementary method forfinding a(t), we used an electrostatic weighting. This methodutilizes the analysis of the evolution of dc voltage supplying thedc field balancing the droplet (aggregate) weight. The analysisis based on a simple mathematical relationship among thevolume, weight, and density of a spherical object.39 Theelectrostatic weighting is less accurate than the Mie scatteringlookup table method. However, its application is essentialbecause it can be used to analyze not only spherical liquiddroplets satisfying the Mie scattering assumptions but alsoaggregates of nanoparticles observed after liquid evaporation.

Figure 1 shows an example of the evolution of the dropletradius of a silica suspension found in the experiment together

with the numerical results from our evaporation model41,47 forpure water and for water with solid inclusions (fraction ofinclusions ∼0.1% by volume). The experimental evolution wasobtained with a combination of the Mie scattering lookup tablemethod and the electrostatic weighting. For more details onboth methods, see ref 39. Our analytical model of evaporationused in this work was discussed in detail in refs 39, 41, and47−49. It assumes rapid liquid mixing, also implicating notemperature gradients (which turns out to be a goodapproximation even for relatively fast evaporation rates50),and makes use of the Kohler equation.51 The Kohler equationformally requires a uniform distribution of particles in liquid,but this kind of parametrization reproduces the observeddroplet evolution well.The droplet evolution can be perceived as driven by the

difference between the equilibrium vapor pressure at thetemperature of the droplet surface and the actual vaporpressure far from the droplet. The evaporation of micrometer-sized droplets into a centimeter-sized chamber void of vapordoes not change the vapor content in the chamber in anysignificant way. The equilibrium vapor pressure is directlyresponsible for the volatility of the liquid (the lower theequilibrium vapor pressure, the lower the volatility) and is an(approximately) exponential function of temperature (hotterdroplets evaporate much faster). For a small concentration ofsuspended nanoparticles, the modification of equilibrium vaporpressure (via the Koehler term51) is negligible. Therefore, theevolution of the radius of a droplet of suspension closelyresembles the evolution of a pure liquid droplet.48,52 In the lateevaporation stage, when the concentration of nanoparticles inthe droplet becomes significant, both curves deviate signifi-cantly. For the experimental data shown in Figure 1 it takesplace when the droplet radius becomes smaller than μ∼4 m(i.e., when the fraction of inclusions exceeds ∼20% by volume).Finally, the evolution of colloidal droplet stops when the liquidevaporates and only the solid aggregate remains in the trap. Atthis stage significant fluctuations can be seen in the evolutionobtained from the experimental data.

Figure 1. Example evolutions of the radius of evaporating droplets:solid line, evolution found experimentally for water with silica (fractionof silica inclusions ∼0.1% by volume). Corresponding evolutionsfound from the model: triangles, pure water; circles, water with solidinclusions (fraction of ∼0.1% by volume).

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Stages of Evaporation-Driven Aggregation of Colloi-dal Particles. The dynamics of evaporation-driven nano-particle aggregation and the geometry of the semifinal and thefinal structures depend on thermodynamic parameters whichinfluence the evaporation of a droplet of nanoparticlesuspension.51,53 Changes in the distribution of nanoparticlesduring evaporation can be found with the numerical modeling17

which describes the movement of individual nanoparticles.Characteristic stages of the evolution are shown in Figure 2,which consists of snapshots from a representative simulation(droplet size is scaled freely for image clarity). The presentedevolution scenario was inferred on the basis of the lightscattering measurements17 supported by the analysis of thesurface pressure isotherm described in detail in ref 18. Wedistinguished several regions of the surface pressure isotherm,which, in view of the evolution scenario, were associated withvarious thermodynamic phases of the surface layer ofnanoparticles. More insight about the evolution of the dropletsurface investigated with light scattering methods can be foundin refs 24 and 54. The evolution scenario presented in currentwork is also supported by the numerical modeling.At the very beginning of the droplet evaporation, nanosilica

particles are distributed uniformly inside the droplet volume(Figure 2a). The initial concentration of nanoparticles in thesuspension is relatively low (usually not higher than ∼1%). Theshrinking surface of an evaporating droplet gathers upnanoparticles from the evaporated volume which leads to anincrease in the concentration of nanoparticles just below thedroplet surface. As a result, a film of surface nanoparticles startsto be formed. Nanoparticles residing near the interface modifythe effective surface tension and the (local) curvature of theinterface. When the volume fraction of nanoparticles is stillsmall (less than 3%), surface nanoparticles are well separated.Subsequently, with further evaporation, their concentrationincreases and growing surface islands are formed (Figure 2b).

Further evaporation of liquid increases the number ofnanoparticles near the surface and compresses the surfacestructures to the point of formation of the densely packedregular shell with the still diluted structure below (Figure 2c).With further progress in the evaporation and shrinking of thedroplet, the surface layer becomes overfilled and the shellcollapses. The density of nanoparticles within the droplet canincrease until a certain critical droplet volume VC is reached(Figure 2d). Below the critical volume, the droplet surfacebecomes corrugated21 and the nanoparticles emerge from theliquid. Further rearrangement takes place because of the vander Waals forces acting between the nanoparticles. Furtherdrying of the structure results in the formation of a solid, highlyordered crystal-like structure (Figure 2e). The average size ofthe final aggregate depends on the initial concentration ofnanoparticles in the suspension as well as the initial size of thedroplet.

Formation of Aggregates. The packing of sphericalparticles inside the droplet can be related to the well-knownproblem of atomic microcluster packing or the number ofnucleons in an atom. The issue of stability of these structureswas explained by the introduction of “magic numbers” of atoms(or nucleons in the atomic nucleus) that results in completeatomic (nuclear) shells. In particular, exceptionally stableclusters with “magic numbers” of atoms were provenexperimentally to exist using mass spectra analysis.55−57

The densely packed and self-assembled structures of silicananoparticles arranged in a regular hexagonal−pentagonalsurface lattice, produced by means of spray drying, werereported by Onofri et al.26 The morphology of the finalaggregates, observed initially with SEM, was described with theempirical model based on the assumption that an icosahedronconstitutes the basic geometrical structure of the aggregate.Contrary to the attempts focused on the modeling of the

final structures, our numerical model presented below describes

Figure 2. Snapshots from a numerical simulation of the evaporation-driven aggregation of nanoparticles: (a) evaporation of a homogeneous dropletsuspension, (b) formation of surface aggregates on the shrinking interface (hydrodynamic compression), (c) formation of a highly ordered surfacelayer, (d) dense packing of spherical aggregates (critical volume), and (e) slow drying process of the final colloidal crystal. The droplet size is scaledfreely for image clarity.

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the dynamics of structural changes of an aggregate in successiveevaporation stages. Moreover, the model allows us to study themorphologies of aggregates not restricted to the assumed ones.For example, structures with some defects in the volume and/or on the surface of the dried crystal-like structure can beobserved.Numerical Modeling of Evaporation-Driven Aggrega-

tion of Nanoparticles. The aggregation of nanoparticles in acolloidal suspension is usually described with DLVO theory.58

It specifies the forces between charged surfaces interactingthrough a liquid medium. DLVO combines the effects of thevan der Waals forces and the electrostatic repulsive forcesappearing due to the formation of a double layer ofcounterions. For a pair of like-charged colloidal nanoparticlesin a liquid, DLVO predicts a purely repulsive electrostaticinteraction. However, it has been proved experimentally thatfor a colloidal suspension of high concentration the effectivepotential between the particles might exhibit a long-rangeattractive component.59,60 Similar behavior has been shown forparticles confined within charged glass walls.61,62 There is stillan open discussion in the literature about an exact explanationof the observed phenomenon. Our experimental results (boththe light scattering and SEM measurements) show that the like-charged colloidal nanoparticles build stable aggregates. Theenergy of the Brownian motion of particles as well as theenergy of the electrostatic interaction between them is smallerthan the capillary forces exerted by the droplet surface(nanoparticles do not escape through the droplet surface).Therefore, in order to simplify the aggregation model and topredict the final stable structures, we decided to neglect theelectrostatic long-range interaction and the Brownian motion ofnanoparticles. Instead, we used an effective Lenard-Jonespotential which accounts for processes present during theaggregation but not introduced explicitly into the model, suchas Brownian motion, long-range interaction, and electrostaticinteraction. It is believed that for the aggregated structures,short-range van der Waals forces strongly dominate andprovide stability to the aggregate.The dynamics of evaporation-driven aggregation of interact-

ing nanoparticles was simulated with the use of the dedicatedsoftware in MATLAB and SIMULINK (see ref 63) developedin our laboratory. We were able to study the dynamics ofaggregates of 70 to 1700 monodisperse spherical silicananoparticles, with a diameter of 450 nm, suspended in anevaporating water droplet. Such numbers of nanoparticlescorrespond approximately to the experimental observations.Our model primarily describes the aggregation phenomenonfor the slow drying regime, where most of the consideredsystem is close to equilibrium. However, the irreversiblymoving interface (shrinking droplet) introduces nonequili-brated forces. The dynamics of the modeled evaporationprocess was predetermined by the time scale and evaporationrates found experimentally (Figure 1). The applied descriptionintroduces the forces essential in the formation of evaporation-driven aggregates. The simulation of movements of eachnanoparticle inside the evaporating droplet uses the classicalNewton’s equation of motion64 (integrated with the Runge−Kutta iterative method)

= + + =mt

i Nr

F F Fdd

, 1, 2 ,...ii

i i i

2

2 sph, bound, v, (1)

where ri and mi describe the position and the mass of the ithnanoparticle, respectively. F isph, and Fv,i are respectively theforces acting on the ith particle resulting from interaction withother particles and with the evaporating droplet boundary,respectively. F iv, is the viscosity force, and N is the number ofnanoparticles inside the droplet. The interaction force F isph, wasderived from the interaction potential

= −∇UF i isph, (2)

where Ui was modeled with the Lenard-Jones potential64

∑= ϵ −=

⎡

⎣⎢⎢⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥U

R

r

R

r

22

2i

j

N

i j i j1

sph

,

12sph

,

6

(3)

where Rsph is the nanoparticle radius, ri,j = [(xi − xj)2 + (yi −

yj)2 + (zi − zj)

2]1/2 is the distance between the centers ofnanoparticles, and ϵ is the depth of the potential well.Parameter ϵ has been further adjusted to reproduce theobserved morphologies and was equal to ϵ = × −1.58 10 [J]24 .To avoid oscillations between the colliding nanoparticles, it isnecessary to introduce the dissipative force. In our case, it wasintroduced as the liquid viscosity force F iv, , which conforms toStokes’ law

πμ= − RF u6i iv, sph (4)

where μ is the dynamic viscosity coefficient of the liquid (here,water) and ui is the velocity of a nanoparticle, assumed to bezero at the first iteration step. We assumed that the dropletboundary force and the interaction force between nanoparticlessatisfy >F Fi ibound, sph, . This physically means that the nano-particles are not able to pass the liquid−air interface. The actionof the surface tension and the shrinking of the droplet surfacedue to liquid evaporation are described by F ibound, which is themain driving force of the aggregation process

=

− − + + | − + + |≤

| − + + | >

⎧

⎨⎪⎪

⎩⎪⎪

e

k a x y z a x y z

R

a x y z R

F

( ) for

0 for

i r

i i i i i i

i i i

bound,

2 2 2 2 2 2

sph

2 2 2sph (5)

where er is the unit radial vector, xi, yi, zi are the coordinates ofthe ith nanoparticle, a is the radius of an evaporating droplet,and = × −k 1.73 10 [kg/s ]10 2 is the spring force coefficientfound from the expected surface tension of liquid. Additionally,we performed simulations for a small number of spheres (downto 2) to verify the physical behavior of nanoparticles. Theradius of an evaporating droplet used during the simulationswas a time-dependent value resulting from the experimentaldata.A movie illustrating the full dynamics of the evaporation

process, parametrized by the droplet radius evolution obtainedfrom the experiment (Figure 1), can be found on the Website.63

■ EXPERIMENTAL SECTIONExperimental Setup. Figure 3 shows a schematic of the

experimental setup for aggregate formation and deposition. It consistsof the linear quadrupole electrodynamic trap with four rod electrodesin vertical alignment, the climatic chamber, the laser system, and twoCCD cameras. The extended lower part of the quadrupole with thesilicon substrate at the bottom serves as a guide for particle deposition.

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The deposition substrate can be moved vertically along the trap. Theelectrodes provide the alternating (ac) electric field in a quadrupleconfiguration which constrains droplets (aggregates) horizontally to anarrow vertical linear region. The annular electrodes placed around thevertical ones provide the static (dc) field-balancing particle (droplet)weight. We work primarily with single droplets (aggregates). Thegeometry of the trap allows us to progressively reduce the dc fieldwithout changing ac field in order to stabilize the droplet (aggregate)vertical position and then to soft land the aggregated structure on thesilicon substrate at the bottom of the chamber. Structures deposited ata selected stage of aggregate formation are further analyzed with SEM.The trap is contained in a small climatic chamber (Peltier elementcooled/heated, not shown in Figure 3), which allows us to control theparameters of the internal atmosphere by choosing ambient gas andadjusting the temperature. Droplets are injected into the trap with thedroplet-on-demand injector (developed in our laboratory; see ref 39)and charged by charge separation in the field between two smallannular electrodes located before and behind the tip of the injectornozzle. Thus, the sign and the approximate value of the charge areadjusted on demand. Our experimental setup imposes some importantrestrictions concerning the charge of the levitating droplet. To remainwithin the stability region of the trap, a levitating droplet should carryfrom 105 to ×6 105 elementary charges. In this range we did notobserve any effects on aggregation related to the charge of the droplet.The droplet is illuminated by the control laser beam along the

vertical axis of the trap (associated with the pseudominimum of thetrapping potential). Laser light scattered by the droplet/aggregateenables stabilization of the vertical position using CCD cameras and aPID-type loop driving the dc voltage of annular electrodes.Experimental Procedure. A single droplet of a nanoparticle

suspension injected into the trap was steadily kept at the desiredlocation. The progress of evaporation was monitored via opticalexamination. At the chosen moment, the droplet was deposited in acontrolled manner on a silicon substrate.The final size of an aggregate can be precisely predetermined by

careful sample preparation in order to vary the number ofnanoparticles contributing to aggregate formation. This was done byadjusting the initial concentration of the nanosilica particles and theinitial size of the droplet. The concentration was controlled by thedilution of a selected commercial silica suspension. The initial size ofthe droplet was adjusted by changing the parameters of the electricsignal triggering the piezoelectric injector.The experiment was conducted at a temperature of 293.2 K, an

initial humidity of ∼95%, and an atmospheric pressure of 1006 hPa.We used an aqueous suspension of SiO2 spheres with a diameter of450 nm (produced by Corpuscular Inc.). The suspension obtained

from the manufacturer (initial mass and volume concentrations equalto ∼5% and ∼2.6% respectively) was diluted with ultrapure water(Milli-Q Plus, Millipore) in 2.6:1 and 26:1 proportions, resulting involume concentrations of nanoparticles of ∼1% and ∼0.1%,respectively. The stabilizing agent introduced by the manufacturerwas not removed.

■ RESULTS AND DISCUSSIONAn overview SEM image of various aggregates, built of 450-nm-diameter silica spherical nanoparticles, deposited on the siliconsubstrate is shown in Figure 4, which shows some examples of

highly ordered spherical structures (1−4) with externaldiameter ranging from 3.5 to 3.7 μm, aggregates (5−7) withdiameter ranging from 4.1 to 4.3 μm, and an aggregate (8) withdiameter ∼ 5.8 μm. The external diameters of the aggregatespresented in Figures 4−6 were estimated directly from theSEM with dedicated software. Diverse diameters of finalaggregates result from various sizes of injected droplets andvarious initial concentrations of nanoparticles.All of the aggregates presented in Figure 6 exhibit a spherical

shape and highly regular ordering of the single layer ofnanoparticles on their surfaces. The highly regular surface ispreserved from the smallest observed structures with anexternal diameter of ∼3.5 μm up to the largest one with adiameter of ∼5.8 μm. On the surface of certain aggregatesshown in Figure 4 some small defects (e.g., aggregates (5) and(8)) or even larger dips can be seen (e.g., aggregates (1) and(2)). In our opinion, small defects appear when the number ofnanoparticles on the surface of an aggregate does not satisfy thegeometrical conditions required for a uniform distribution ofnanoparticles. The appearance of large dips, according to themost possible scenario, should be associated with strongcapillary forces on the surface of the evaporating droplet. Theaggregation of nanoparticles starts from the surface; therefore,at a certain aggregation stage we observe a highly organizedsurface structure, with much looser structure below (Figure 2c).Further evaporation pulls the surface particles inward. Thesurface pressure significantly increases (effect observed with thelight scattering methods and reported in our previousworks18,24). However, a partially empty shell can warp insideunder the capillary forces. In that case, a large dip on the surfaceof the aggregate appears. We infer from the aggregationmechanism and some experimental evidence (e.g., SEM imagesof disintegrated aggregates) that the highly ordered shells arenot empty inside. However, both their internal compactness

Figure 3. Schematic of the experimental setup.

Figure 4. Overview SEM image of several aggregates built of 450-nm-diameter silica deposited on a silicon substrate. Diameter of theaggregates: (1−4) 3.5−3.7 μm, (5−7) 4.1−4.3 μm, and (8) ∼ 5.8 μm.

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and the internal ordering are lower than on the surface layer.We expect that it should be a fractal-like structure with a highfractal dimension, below but close to 3.To investigate the influence of the initial parameters of

colloidal droplets on the final morphology of aggregates wecompared the experimentally obtained SEM images with thestructures resulting from our numerical model. Figure 5 shows

various aggregates observed with SEM (left column) and theaggregates numerically predicted with our code (right column).Aggregates contain from ∼70 (Figure 5a) to ∼1700 (Figure 5d)spherical silica nanoparticles with a diameter of 450 nm.The aggregate shown in Figure 5a (left column) was

obtained by the evaporation of the aqueous nanosilicasuspension with an initial concentration of ∼0.1% by volume.The initial diameter of the droplet injected into the trap wasequal to ∼19 μm, hence after evaporation of the liquid, theexternal diameter of the final aggregate is equal to μ∼2.1 m. In

such case the concentration of nanoparticles was too small toform a regular film on the surface during the evaporationprocess. This conclusion is supported by our optical diagnosis24

based on the analysis of the temporal Fano profile of the lightscattered during liquid evaporation. Thus, the aggregate inFigure 5a forms a compact volume structure formed at the veryend of the evaporation-driven process. It contains approx-imately 70 nanospheres.For slightly smaller droplets (with an initial diameter of ∼16

μm) made of a suspension with a nanosilica concentration of∼1%, the final aggregate took the form presented in Figure 5b.It contains ∼500 nanospheres, and its external diameter is ∼4.0μm. By increasing the diameter of the droplet injected into thetrap to up to μ∼20 m, larger aggregates with a diameter of

μ∼5.0 m containing ∼1000 nanospheres were obtained. Figure5c shows an aggregate with an external diameter of μ∼5.1 m.Further increases in the droplet initial diameter lead to theformation of still larger final aggregates. As an example, Figure5d shows an aggregate with an external diameter of ∼6.1 μm,containing approximately 1700 nanoparticles. However, thedeposited aggregate was found to be less stable and had a largenumber of defects. Therefore, the final surface collapsed. Weinferred from our numerical modeling and the opticalobservations that at the time of deposition the aggregateshown in Figure 5d contained still some fraction of water.Therefore, after the deposition, the highly ordered surface layerof the aggregate collapsed. Further drying on the flat substrateresulted in a significant deformation of the aggregate andtransition from spherical to translational symmetry.In contrast to the completely dried, highly ordered

aggregates shown in Figure 5a−c, Figure 6 demonstrates theeffect of the deposition of various transient aggregationproducts. Figure 6a corresponds to a droplet deposited at anearly stage of aggregation. Because of the significant content ofwater, the deposited structure splashed on the substrate and,after water evaporation, formed a thin, irregular layer of silicananoparticles with some fractal-like structures in the center.Figure 6b,c shows two aggregates containing ∼4000 and∼10 000 nanoparticles, respectively. It can be inferred fromSEM images that at the time of deposition both structurescontained a significant fraction of water which evaporated afterlanding. In Figure 6b we can see a collapsed surface layer ofnanoparticles with some circular traces around the aggregateleft by evaporated liquid. It can be inferred that at the time ofdeposition a well-organized structure, foreseen by ournumerical model, was already formed. However, the largeaggregates presented in Figure 6b,c collapsed under their ownweight. Therefore, some dimples on the top and significantdeformations at the footing appeared. Nevertheless, theinteraction forces between the nanoparticles within theaggregate were strong enough to maintain the stability of thedeformed structures and suppress further disintegration.

■ CONCLUSIONS

We have investigated the formation of highly orderedaggregates of spherical silica nanoparticles in evaporatingdroplets of an aqueous colloidal suspension. An assembly ofnanoparticles develops from the water suspension in sphericalsymmetry, mainly due to the surface tension of the evaporatingdroplet. The process leads to highly regular spherical aggregatesof significantly different size and morphology compared tothose observed when aggregation takes place on a substrate.

Figure 5. SEM images of the experimentally obtained highly orderedaggregates built of 450-nm-diameter silica particles (left column) and avisualization of the numerically generated corresponding aggregates(right column): (a) 2.130 μm external diameter aggregate containing∼70 nanospheres and a numerically generated aggregate of exactly 70nanospheres, (b) 4.030 μm external diameter aggregate containing∼500 nanospheres and a numerically generated aggregate of exactly500 nanospheres, (c) 5.098 μm external diameter aggregate containing∼1000 nanospheres and a numerically generated aggregate of exactly1000 nanospheres, and (d) 6.057 μm external diameter aggregatecontaining ∼1700 nanospheres and a numerically generated aggregateof exactly 1700 nanospheres.

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Combining modeling with experimental observations, we wereable to examine and describe consecutive states of aggregateformation. Our numerical model can predict variousaggregation stages and their dynamics. This includes theformation and collapse of the regular surface layer ofnanoparticles, the formation of highly ordered sphericalaggregates, and the rearrangement of the drying assembly. Itis also worth noticing that the morphology of the finalstructures significantly depends on the drying rate. Weobserved the process of evaporation, which from thethermodynamic point of view was stationary and close toequilibrium. Under these conditions (centimeter-sized climaticchamber with stabilized temperature, pressure, and humidity)no temperature gradient is observed. We expect that a dropletlevitating inside the electrodynamic trap rotates randomly(analogous to Brownian motions), thus it dries uniformly andno other effect should be seen. Our experimental setup allowsus to deposit the aggregating structures at the selected stages ofaggregation. It enables us to analyze the resulting aggregateswith SEM and compare the results with the optical scatteringmeasurements.17,24,39,54 Thus, the presented scenario ofaggregate formation seems to be confirmed by our SEMobservation and optical studies.We showed that the evaporation-driven aggregation of

nanoparticles can be used as a method of formation of stable(quasi-) spherical, highly ordered crystal-like structures of sizes

in the nano- to micrometer regime. Such aggregates can remainstable and highly regular after deposition on a substrate.Further manipulation, even in the case of very large structures,is possible. The stability and arrangement of structures dependon the number of surface and volume defects, which can becontrolled by the initial concentration of the colloidal droplet,the droplet initial size, and the size of spherical inclusions.

■ ASSOCIATED CONTENT*S Supporting InformationA movie illustrating the full dynamics of the evaporation-drivenaggregation in the evaporating droplet of an aqueoussuspension containing 1500 silica nanoparticles with 450 nmdiameter, parametrized by the droplet radius evolution obtainedfrom the experiment. The Supporting Information is availablefree of charge on the ACS Publications website at DOI:10.1021/acs.langmuir.5b01621.

■ AUTHOR INFORMATIONCorresponding Author*Phone: +48 22 116 32 77. E-mail: mwozniak@ifpan.edu.pl.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the National Science Center,Poland, under grant number 2014/13/D/ST3/01882.

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Figure 6. SEM image of (a) a residue of a droplet of the nanosilicasuspension deposited at an early stage of aggregation, (b) an aggregatenot fully dried before deposition containing ∼4000 silica nanoparticles,and (c) and an aggregate not fully dried before deposition containing∼10 000 silica nanoparticles.

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