Formation of Highly Ordered Spherical Aggregates from Drying

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Formation of highly-ordered spherical aggregates from drying microdroplets of colloidal suspension Mariusz Wo#niak, Giennadiy Derkachov, Krystyna Kolwas, Justice Archer, Tomasz Wojciechowski, Daniel Jakubczyk, and Maciej Kolwas Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b01621 • Publication Date (Web): 27 Jun 2015 Downloaded from http://pubs.acs.org on July 4, 2015

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Formation of highly-ordered spherical aggregates from drying microdroplets of colloidal suspension M. Wo´zniak,∗ G. Derkachov, K. Kolwas, J. Archer, T. Wojciechowski, D. Jakubczyk, and M. Kolwas Institute of Physics, Polish Academy of Sciences, Al.Lotnik´ ow 32/46, 02-668 Warsaw, Poland E-mail: [email protected] Phone: +48 22 116 32 77

Abstract Formation of highly-ordered spherical aggregates of silica nanoparticles by evaporation of single droplets of aqueous colloidal suspension levitated (confined) in the electrodynamic quadrupole trap is reported. The transient and the final structures formed during the droplet evaporation have been deposited on a silicon substrate and then studied with SEM. Various successive stages of the evaporation-driven aggregation of nanoparticles have been identified: formation of the surface layer of nanoparticles, formation of the highly-ordered spherical structure, collapse of the spherical surface layer leading to the formation of densely packed spherical aggregate, as well as the rearrangement of the aggregate into the final structure of a stable 3D quasi-crystal. The evaporation-driven aggregation of submicron particles in spherical symmetry leads to sizes and morphologies of the transient and the final structure significantly different than in case of aggregation on a substrate. The numerical model presented in the ∗

To whom correspondence should be addressed

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paper allows to predict and visualize the observed aggregation stages, their dynamics and the final aggregates observed with SEM.

Introduction Ordered assemblies of colloidal particles of micrometer to nanometer length scales became a recent focus of many studies as such assemblies can be used for construction of various periodic and quasi-periodic material structures. 1–4 In particular, the aggregation phenomenon allows to create composites whose physical properties are determined not only by their chemical composition but also by the specific morphology. 5–8 The new kind of structures, known as metamaterials, 2,9 exhibit unique (optical) properties not present in conventional materials. Significant attention has recently been paid to precisely pattern the morphology of nanoparticle films and self-assembled monolayers of nano-crystals by evaporation of dropdeposited colloids on substrates (e.g. 10–14 and references therein). It is known, that the presence of a substrate dramatically influences the process of particles aggregation. Much less is known about the particles ordering in unsupported evaporating droplets of colloidal suspensions. 15–19 Evaporation-driven ordering process in such systems is free of substrate influence. The spherical symmetry of the evaporating droplet provides exceptional conditions for assembly of 3D photonic structures with spherical symmetry of significantly different morphologies than those observed for the structures assembled on substrates. 20 Finite packing of such particles (e.g. 21–23 ) adopts symmetries different from the long-range ordering. Better understanding of how finite number of spheres can organize in stable structures may help to control the arrangement of matter at different length scales. In work, 22 aggregates which adopt packing that minimize the second moment of the mass distribution have been observed. The authors identified structures containing sphere doublets, triplets, tetrahedra and polyhedra which had not been previously found in infinite lattice packing or minimumpotential energy clusters. Few studies have been reported on aggregation of large, highly


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regular assemblies of spheres and their transient and final morphologies. 17,18,24 Final aggregates of highly regular morphology, built of much smaller particles and generated by means of the fast spray drying method, were investigated in. 25,26 Significantly more studies have been devoted to the self-assembly of nanoparticles in liquid suspensions (see e.g. 12,19,21,27 and references therein). Some systematic studies on the influence of the various aggregation parameters on the morphology of the final structures have also been performed. 28,29 It is worth noticing, that in order to investigate nanoparticle aggregates, a variety of methods have been proposed, such as: static light scattering, 30,31 small-angle X-rays scattering, 32–35 dynamic light scattering (DLS), 36 TEM and SEM 12,37 as well as electron tomography method. 27,38 Particularly valuable are these, which provide real time analysis of colloidal assembly in situ, i.e. light and X-ray scattering and spectroscopic methods. Some of these methods are able not only to determine the position of the surface particles on the cluster but also the location of the particles within the cluster at any stage of the aggregation. As an example, in 35 the authors described the transition from isotropic droplet to the core-shell structure during the SAXS investigation of drying of a single suspended droplet of a nanosilica suspension. The goal of the current study was to provide a new method of production of highlyordered spherical aggregates of nanoparticles by evaporation-driven aggregation of colloidal droplets. The main cause of aggregation are the strong capillary (surface tension) forces exerted on the suspended particles by the shrinking interface of evaporating liquid. We investigated the successive states of the transient aggregates and put emphasize on diagnostics of the final 3D structures. The transient and the final aggregates were deposited on a substrate and investigated with Scanning Electron Microscope (SEM).


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Dynamic of droplet evaporation and aggregation of colloidal particles; an introduction Studies on the formation of highly regular spherical aggregates and diagnostics of the aggregated structures presented in this paper are the consequence of our former studies on the evaporation of pure liquids, see e.g. 39,40 and mixtures of liquids, see e.g. 41,42 Therefore, in this section we briefly summarize our earlier research and provide the necessary background related to droplet evaporation, evaporation-driven aggregation of nanoparticles as well as formation and slow drying process of highly spherical aggregates. Finally, we describe the physical background of our numerical modeling of evaporation-driven aggregation.

Evolution of droplet size Single evaporating droplets of suspensions levitated in the electrodynamic quadrupole trap 43–46 have been produced and optically studied in the experimental setup built in our laboratory. 18,39 Droplets were injected into the trap with the droplet-on-demand injector and charged on injection by charge separation in the external field of the trap. The vertical position of the droplet was stabilized at the trap center by balancing the weight of the droplet with the DC field. The trap was kept in a small climatic chamber which allowed us to control (stabilize) parameters of the internal atmosphere by choosing ambient gas and adjusting temperature. We used simultaneously two coaxial, counter-propagating laser light beams for droplet illumination: the red vertically polarized and the green horizontally polarized in respect to the scattering plane. Two linear polarizes were used in the detection channel enabling observation of the interference pattern associated with horizontally and vertically polarized incident light. Scattering patterns were recorded with CCD camera. In order to find droplet radius evolution a(t) we applied the Mie Scattering Lookup Table Method (see 39 ) which is based on fitting of the complete Mie theory predictions (stored in the lookup table) to the 4 ACS Paragon Plus Environment

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experimentally obtained scattering patterns. It provides accuracy of radius determination of ±10 nm. Simultaneously, as an supplementary method of finding a(t), we used an electrostatic weighting. This method utilizes the analysis the evolution of DC voltage supplying the DC field balancing the droplet (aggregate) weight. The analysis is based on a simple mathematical relation between volume, weight and density of a spherical object. 39 The electrostatic weighting is less accurate than the Mie Scattering Lookup Table Method. However, its application is essential since it can be used not only to analyze spherical liquid droplets satisfying the Mie scattering assumptions but also to aggregates of nanoparticles observed after evaporation of liquid. Figure 1 shows an example of the evolution of the droplet radius of silica suspension found in experiment together with the numerical results from our evaporation model 41,47 for pure water and for water with solid inclusions (fraction of inclusions ∼ 0.1% in volume). The experimental evolution was obtained with a combination of the Mie Scattering Lookup Table Method and the electrostatic weighting. For more details on the both methods see. 39 Our analytical model of evaporation used in this work was discussed in details in. 39,41,47–49 It assumes rapid liquid mixing, implicating also no temperature gradients (which turns out to be a good approximation even for relatively fast evaporation rates 50 ) and makes use of the Köhler equation. 51 The Köhler equation formally requires a uniform distribution of particles in liquid, but this kind of parameterization reproduces the observed droplet evolution well. The droplet evolution can be perceived as driven by the difference between the equilibrium vapor pressure at the temperature of the droplet surface and the actual vapor pressure far from the droplet. The evaporation of micrometer sized droplet into a centimeter sized chamber void of vapor does not change the vapor content in the chamber in any significant way. The equilibrium vapor pressure is directly responsible for the volatility of the liquid (the lower equilibrium vapor pressure, the lower volatility) and is an (approximately) exponential function of temperature (hotter droplets evaporate much faster). For small concentration of suspended nanoparticles the modification of equilibrium vapor pressure (via Koehler term 51 )


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Figure 1: Example evolutions of radius of evaporating droplets: solid line - evolution found experimentally for water with silica (fraction of silica inclusions ∼ 0.1% in volume). Corresponding evolutions found from the model: triangles - pure water, circles - water with solid inclusions (fraction of ∼ 0.1% in volume). is negligible. Therefore, the evolution of the radius of a droplet of suspension closely resembles the evolution of a pure liquid droplet. 48,52 At the late evaporation stage, when the concentration of nanoparticles in the droplet becomes significant both curves significantly deviate. For the experimental data shown in Figure 1 it takes place when the droplet radius becomes smaller than ∼ 4 µm, i.e. when the fraction of inclusions exceeds ∼ 20% in volume. Finally, the evolution of colloidal droplet stops when the liquid evaporates and only the solid aggregate remains in the trap. At this stage significant fluctuations can be seen in the evolution obtained from the experimental data.

Stages of evaporation driven aggregation of colloidal particles The dynamics of evaporation-driven nanoparticles aggregation, as well as the geometry of the semi-final and the final structures, depend on thermodynamic parameters which influence the evaporation of the droplet of nanoparticles suspension. 51,53 Changes of the distribution of nanoparticles during evaporation can be found with the numerical modeling 17 which describes the movement of individual nanoparticles. Characteristic stages of the evolution are


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shown in Figure 2, which consists of snapshots from a representative simulation (droplet size is scaled freely for image clarity). The presented evolution scenario was inferred on the basis of the light scattering measurements 17 supported by the analysis of the surface pressure isotherm described in details in. 18 We distinguished several regions of the surface pressure isotherm, which, in view of the evolution scenario, were associated with various thermodynamic phases of the surface layer of nanoparticles. More insight about the evolution of the droplet surface investigated with light scattering methods can be found in. 24,54 The evolution scenario presented in current work is supported also by the numerical modeling. At the very beginning of the droplet evaporation, nanosilica particles are distributed uniformly inside the droplet volume (see Figure 2a). The initial concentration of nanoparticles in the suspension is relatively low (usually not higher that ∼1%). The shrinking surface of

(a)

(b)

(c)

(e)

(d)

Figure 2: Snapshots from a numerical simulation of the evaporation-driven aggregation of nanoparticles: (a) evaporation of homogeneous droplet suspension, (b) formation of surface aggregates on the shrinking interface (hydrodynamic compression), (c) formation of highlyordered surface layer, (d) dense packing of spherical aggregate (critical volume), (e) slow drying process of the final colloidal crystal. Droplet size is scaled freely for image clarity. an evaporating droplet gathers up nanoparticles from the evaporated volume which leads to 7 ACS Paragon Plus Environment

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an increase of concentration of nanoparticles just below the droplet surface. As the result, a film of surface nanoparticles starts to be formed. Nanoparticles residing near the interface modify the effective surface tension and the (local) curvature of the interface. When the volume fraction of nanoparticles is still small (less than 3%), surface nanoparticles are well separated. Subsequently, with further evaporation, their concentration increases and the growing surface islands are formed (see Figure 2b). Further evaporation of liquid increases the number of nanoparticles near the surface and compresses the surface structures to the point of formation of the densely packed regular shell with still diluted structure below (Figure 2c). With further progress of evaporation and shrinking of the droplet, the surface layer becomes overfilled and the shell collapses. The density of nanoparticles within the droplet can increase until a certain critical droplet volume VC is reached (Figure 2d). Below the critical volume the droplet surface becomes corrugated 21 and the nanoparticles emerge from the liquid. Further rearrangement takes place due to the van der Waals forces acting between the nanoparticles. Further drying of the structure results in formation of a solid, highly-ordered crystal-like structure (see Figure 2e). The average size of the final aggregate depends on the initial concentration of nanoparticles in the suspension as well as the initial size of the droplet.

Formation of aggregates Packing of spherical particles inside the droplet can be related to the well known problem of the atomic microclusters packing or the number of nucleons in an atom. The issue of stability of these structures was explained by introduction of ”magic numbers” of atoms (or nucleons in the atomic nucleus) that results in complete atomic (nuclear) shells. In particular, exceptionally stable clusters with ”magic numbers” of atoms were proved experimentally to exist, using mass spectra analysis. 55–57 The densely-packed and self-assembled structures of silica nanoparticles arranged in a regular hexagonal-pentagonal surface lattice, produced by means of spray drying, were re8 ACS Paragon Plus Environment

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ported by Onofri et. al. 26 The morphology of the final aggregates, observed initially with SEM, was described with the empirical model based on the assumption that an icosahedron constitutes the basic geometrical structure of the aggregate. Contrary to the attempts focussed on modelling of the final structures, our numerical model presented below, describes the dynamics of structural changes of an aggregate at the successive evaporation stages. Moreover, the model allows to study morphologies 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 be observed.

Numerical modeling of evaporation-driven aggregation of nanoparticles Aggregation of nanoparticles in colloidal suspension is usually described with the DLVO theory. 58 It specifies the forces between charged surfaces interacting through a liquid medium. The DLVO combines the effects of the van der Waals forces and the electrostatic repulsive forces appearing due to the formation of a double layer of counterions. For a pair of likecharged colloidal nanoparticles in a liquid DLVO predicts a purely repulsive electrostatic interaction. However, it has been proved experimentally, that for a colloidal suspension of high concentration, the effective potential between the particles might exhibit a long-range attractive component. 59,60 Similar behaviour has been shown for particles confined within charged glass walls. 61,62 There is still an open discussion in the literature about an exact explanation of the observed phenomenon. Our experimental results (both the light scattering and SEM measurements) show that the like-charged colloidal nanoparticles build stable aggregates. The energy of Brownian motion of particles as well as the energy of the electrostatic interaction between them is smaller than 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 to predict the final stable structures, we decided to neglect the electrostatic long-range interaction and the Brownian motion of nanoparticles. Instead, we 9 ACS Paragon Plus Environment

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used an effective Lenard-Jones potential which accounts for processes present during the aggregation but not introduced explicitly into the model, such as Brownian motion, long-range interaction and electrostatic interaction. It is believed that for the aggregated structures, short-range van der Waals forces strongly dominate and provide stability of the aggregate. The dynamics of evaporation driven aggregation of interacting nanoparticles was simulated with the use of the dedicated software in MATLAB and SIMULINK (see ref. 63 ) developed in our laboratory. We were able to study the dynamics of aggregates of 70 to 1700 monodisperse spherical silica nanoparticles, with diameter of 450 nm, suspended in an evaporating water droplet. Such numbers of nanoparticles correspond approximately to the experimental observations. Our model primarily describes the aggregation phenomenon for slow drying regime, where most the considered system is close to equilibrium. However, the irreversibly moving interface (shrinking droplet) introduces a non-equilibrated forces. The dynamics of the modeled evaporation process was predetermined by the time-scale and evaporation rates found experimentally (see e.g. Figure 1). The applied description introduces the forces essential in formation of evaporation driven aggregates. Simulation of movements of each nanoparticle inside the evaporating droplet uses the classical Newton’s equation of motion 64 (integrated with the Runge-Kutta iterative method):

mi

d2 ri = Fsph,i + Fbound,i + Fv,i , dt2

i = 1, 2, ...N

(1)

where ri and mi describe the position and the mass of the i-th nanoparticle respectively. Fsph,i and Fv,i are respectively the force acting on i-th particle resulting from interaction with other particles and with evaporating droplet boundary. Fv,i is the viscosity force and N is the number of nanoparticles inside the droplet. The interaction force Fsph,i was derived from the interaction potential: Fsph,i = −∇Ui ,


(2)

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where Ui was modeled with the Lenard-Jones potential: 64

Ui =

N ∑

[( ϵ

j=1

2Rsph ri,j

where Rsph is nanoparticles’ radius, ri,j =

)12

( −2

2Rsph ri,j

)6 ] ,

(3)

√ (xi − xj )2 + (yi − yj )2 + (zi − zj )2 is the dis-

tance between the centers of nanoparticles and ϵ is the depth of the potential well. The parameter ϵ has been further adjusted to reproduce the observed morphologies and was equal to ϵ = 1.58 · 10−24 [J]. To avoid oscillations between the colliding nanoparticles, it is necessary to introduce the dissipative force. In our case, it was introduced as the liquid viscosity force Fv,i , which conforms to Stokes’ law: Fv,i = −6πµRsph ui ,

(4)

where µ is the dynamic viscosity coefficient of the liquid (here: water) and ui is the velocity of a nanoparticle, assumed to be zero at the first iteration step. We assumed that the droplet boundary force and the interaction force between nanoparticles satisfy Fbound,i > Fsph,i . It physically means that the nanoparticles are not able to pass the liquid-air interface. The action of the surface tension and shrinking of the droplet surface due to liquid evaporation is described by Fbound,i which is the main driving force of the aggregation process:

Fbound,i

 ( ) √ √   −k a − x2 + y 2 + z 2 for a − x2 + y 2 + z 2 ≤ Rsph , i i i i i i = eˆr √   0 for a − x2i + yi2 + zi2 > Rsph ,

(5)

where eˆr is the unit radial vector, xi , yi , zi are the coordinates of the i-th nanoparticle, a is the radius of evaporating droplet, k = 1.73 · 10−10 [kg/s2 ] is the spring force coefficient found from the expected surface tension of liquid. Additionally, we performed simulations for small number of spheres (down to 2) to verify physical behavior of nanoparticles. The radius of an evaporating droplet used during the simulations was a time dependent value resulting from the experimental data. 11 ACS Paragon Plus Environment

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A movie illustrating the full dynamics of the evaporation process, parameterized by the droplet radius evolution obtained from the experiment (see Figure 1), can be found on the website. 63

Experimental section Experimental setup Figure 3 shows schematic of the experimental setup for aggregate formation and deposition. It consists of the linear quadrupole electrodynamic trap with 4 rod electrodes in vertical alignment, the climatic chamber, the laser system and 2 CCD cameras. The extended lower part of the quadrupole with the silicon substrate at the bottom, serves as a guide for particle deposition. The deposition substrate can be moved vertically along the trap. The electrodes provide the alternating (AC) electric field in a quadruple configuration which constrains droplets (aggregates) horizontally to a narrow vertical linear region. The annular electrodes placed around the vertical ones provide static (DC) field balancing particles (droplets) weight. We work primarily with single droplet (aggregate). The geometry of the trap allows us to progressively reduce DC field without changing AC field in order to stabilize the droplet (aggregate) vertical position and then to soft-land the aggregated structure on the silicon substrate at the bottom of the chamber. Structures deposited at a selected stage of the aggregate formation are further analyzed with SEM. The trap is contained in a small climatic chamber (Peltier element cooled/heated, not shown in Figure 3), which allows us to control parameters of the internal atmosphere by choosing ambient gas and adjusting temperature. Droplets are injected into the trap with the droplet-on-demand injector (developed in our laboratory; see 39 ) and charged by charge separation in the field between two small annular electrodes located before and behind of the tip of the injector nozzle. Thus, the sign and the approximate value of the charge are adjusted on demand. Our experimental setup imposes some important restriction concerning the charge of the levitating droplet. To remain within 12 ACS Paragon Plus Environment

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Green laser beam ( =528 nm) Rod electrodes

CCD camera (in focus image) On-demand droplet injector

Droplet position analysis Optical system DC control system

CCD camera (in focus image) Silicon substrate for landing particles

Figure 3: Schematic of the experimental setup.


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the stability region of the trap, a levitating droplet should carry from 105 to 6·105 elementary charges. In this range we did not observe any effects 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 pseudo-minimum of the trapping potential). Laser light scattered by the droplet/aggregate enables stabilization of the vertical position using CCD cameras and a PID-type loop driving DC voltage of annular electrodes.

Experimental procedure A single droplet of nanoparticle suspension injected into the trap was steadily kept at the desired location. The progress of evaporation was monitored with optical examination. At the chosen moment, the droplet was deposited in a controlled 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 of nanoparticles contributing to aggregate formation. This was done by adjusting the initial concentration of the nanosilica particles and the initial size of the droplet. The concentration was controlled by the dilution of a selected commercial silica suspension. The initial size of the droplet was adjusted by changing parameters of the electric signal triggering the piezoelectric injector. The experiment was conducted at the temperature of 293.2 K, the initial humidity of ∼95% and the atmospheric pressure of 1006 hPa. We used aqueous suspension of SiO2 spheres with diameter of 450 nm (produced by Corpuscular Inc). The suspension obtained from the manufacturer (initial mass and volume concentrations equal to ∼ 5% and ∼ 2.6% respectively) was diluted with ultrapure water (Milli-Q Plus, Millipore) in 2.6:1 and 26:1 proportions resulting in the volume concentration of nanoparticles of ∼1% and ∼0.1% respectively. Stabilizing agent introduced by the manufacturer was not removed.


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Results and discussion An overview SEM image of various aggregates, built of 450 nm diameter silica spherical nanoparticles, deposited on the silicon substrate is shown in Figure 4 which show some examples of highly-ordered spherical structures (1)-(4) with external diameter ranging from 3.5 to 3.7 µm, aggregates (5)-(7) with diameter ranging from 4.1 to 4.3 µm and an aggregate (8) with diameter ∼ 5.8 µm. The external diameters of the aggregates presented in Figure 4 and in the following figures (5 and 6) were estimated directly from the SEM with dedicated software. Diverse diameters of final aggregates result from various sizes of injected droplets and various initial concentrations of nanoparticles.

Figure 4: An overview SEM image of several aggregates built of 450 nm diameter silica deposited on a silicon substrate. Diameter of the aggregates: (1)-(4) 3.5-3.7 µm, (5)-(7) 4.1-4.3 µm and (8) ∼ 5.8 µm. All the aggregates presented in Figure 6 exhibit spherical shape and highly-regular ordering of the single layer of nanoparticles on their surfaces. The highly-regular surface is preserved from the smallest observed structures with the external diameter ∼ 3.5 µm up to the largest one with diameter ∼5.8 µm. On the surface of certain aggregates shown in 15 ACS Paragon Plus Environment

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Figure 4 some small defects (see 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 of nanoparticles on the surface of aggregate does not satisfy geometrical conditions required for a uniform distribution of nanoparticles. The appearance of large dips, according to the most possible scenario, should be associated with strong capillary forces on the surface of the evaporating droplet. The aggregation of nanoparticles starts from the surface, therefore at a certain aggregation stage we observe a highly-organized surface structure, with much looser structure below (see Fig. 2c). Further evaporation pulls the surface particles inward. The surface pressure significantly increases then (effect observed with the light scattering methods and reported in our previous works 18,24 ). However, a partially empty shell can easily warp inside under the capillary forces. In that case, a large dip on the surface of aggregate appears. We infer from the aggregation mechanism and some experimental evidences (e.g. SEM images of disintegrated aggregates) that the highly-ordered shells are not empty inside. However, both their internal compactness and the ordering are lower than on the surface layer. We expect that it should be a fractal-like structure with high fractal dimension, below 3 but close to. In order to investigate the influence of the initial parameters of colloidal droplets on the final morphology of aggregates we compared the experimentally obtained SEM images with the structures resulting from our numerical model. Figure 5 shows various aggregates observed with SEM (left column) and the aggregates numerically predicted with our code (right column). Aggregates contain from ∼70 (Figure 5a) to ∼1700 (Figure 5d) spherical silica nanoparticles with the diameter of 450 nm. The aggregate shown in Figure 5a (left column) was obtained by evaporation of the aqueous nanosilica suspension with the initial concentration of ∼0.1% in volume. The initial diameter of the droplet injected into the trap was equal to ∼19 µm, hence after evaporation of the liquid, the external diameter of the final aggregate is equal to ∼ 2.1 µm. In such case the concentration of nanoparticles was too small to form a regular film on the surface during


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


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the evaporation process. This conclusion is supported by our optical diagnosis 24 based on the analysis of the temporal Fano profile of the light scattered during the liquid evaporation. Thus, the aggregate in 5a forms a compact volume structure formed at the very end of the evaporation driven process. It contains approximately 70 nanospheres. For slightly smaller droplets (the initial diameter of ∼16 µm) but made of suspension with nanosilica concentration of ∼ 1%, the final aggregate took the form presented in Figure 5b. It contains ∼500 nanospheres and its external diameter is ∼4.0 µm. By increasing the diameter of the droplet injecting into the trap up to ∼ 20 µm, larger aggregates, with diameter of ∼ 5.0 µm, containing ∼1000 nanospheres were obtained. Figure 5c shows an aggregate with the external diameter of ∼ 5.1 µm. Further increasing of the droplet initial diameter leads to the formation of still larger final aggregates. As an example, Figure 5d shows an aggregate with the external diameter of ∼6.1 µm, containing approximately 1700 nanospheres. However, the deposited aggregate was found less stable and with large number of defects. Therefore, the final surface collapsed. We inferred from our numerical modeling and the optical observations that at the time of deposition the aggregate shown in Figure 5d contained still some fraction of water. Therefore, after the deposition, the highly-ordered surface layer of the aggregate collapsed. Further drying on the flat substrate resulted in the significant deformation of the aggregate and translation from the spherical to translational symmetry. In contrast to the completely dried, highly-ordered aggregates shown in Figure 5a-c, Figure 6 demonstrates the effect of deposition of various transient aggregation products. Figure 6a corresponds to a droplet deposited at an early stage of aggregation. Due to the significant content of water, deposited structure splashed on the substrate and, after water evaporation, formed a thin, irregular layer of silica nanoparticles with some fractallike structures in the center. Figures 6b and 6c show two aggregates containing ∼4000 and ∼10000 nanoparticles respectively. It can be inferred from SEM images that at the time of deposition both structures still contained a significant fraction of water which evaporated


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(a)

(b)

(c)

Figure 6: SEM image of (a) a residue of a droplet of the nanosilica suspension deposited at an early stage of aggregation, (b) an aggregate not fully dried before deposition containing ∼4000 silica nanoparticles and (c) and an aggregate not fully dried before deposition containing ∼10000 silica nanoparticles.


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after landing. In Figure 6b we can see a collapsed surface layer of nanoparticles with some circular traces around the aggregate left by evaporated liquid. It can be inferred, that at the time of deposition, a well-organized structure, foreseen by our numerical model, was already formed. However, the large aggregates presented in Figure 6b and 6c collapsed under their own weight. Therefore, some dimples on the top and significant deformations at the footing appeared. Nevertheless, the interaction forces between the nanoparticles within the aggregate were strong enough to maintain the stability of the deformed structures and suppress further disintegration.

Conclusion We have investigated formation of highly-ordered aggregates of spherical silica nanoparticles in evaporating droplets of aqueous colloidal suspension. An assembly of nanoparticles develops from water suspension in spherical symmetry, mainly due to the surface tension of evaporating droplet. The process leads to highly-regular spherical aggregates of significantly different size and morphology than that observed when aggregation takes place on a substrate. Combining modeling with experimental observations, we were able to examine and describe consecutive states of the aggregate formation. Our numerical model can predict various aggregation stages and their dynamics. This includes the formation and collapse of the regular surface layer of nanoparticles, the formation of highly-ordered spherical aggregates and the rearrangement of the drying assembly. It is also worth noticing that morphology of the final structures significantly depends on the drying rate. We observed the process of evaporation, which, from the thermodynamic point of view, was stationary and close to equilibrium. Under these conditions (centimeter sized climatic chamber with stabilized temperature, pressure and humidity) no temperature gradient is observed. We expect that a droplet levitating inside the electrodynamic trap rotates randomly (analog to Brownian motions), thus it dries uniformly and no other effect should be seen. Our experimental setup


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allows to deposit the aggregating structures at the selected stages of aggregation. It enables us to analyze the resulting aggregates with SEM and compare the results with the optical scattering measurements. 17,24,39,54 Thus, the presented scenario of aggregate formation seems to be confirmed by our SEM observation 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 nano- to micro- regime. Such aggregates can remain stable and highly regular after deposition on a substrate. Further manipulation, even in case of very large structures is possible. The stability and arrangement of structures depend on the number of surface and volume defects which can be controlled by the initial concentration of colloidal droplet, the droplet initial size and the size of spherical inclusions.

Author information Corresponding Author *E-mail: [email protected].

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

Notes The authors declare no competing financial interest.

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


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Supporting Information Available A movie illustrating the full dynamics of the evaporation-driven aggregation in the evaporating droplet of aqueous suspension containing 1500 silica nanoparticles with 450 nm diameter, parameterized by the droplet radius evolution obtained from the experiment. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry Electrodynamic quadrupole trap

DC control system AC control system

Laser beam

Levitating droplet of suspension

Aggregate deposition SEM analysis


Formation of Highly Ordered Spherical Aggregates from Drying

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