Direct‐Write Freeform Colloidal Assembly

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Direct-Write Freeform Colloidal Assembly

Alvin T. L. Tan, Justin Beroz, Mathias Kolle, and A. John Hart*

A. T. L. TanDepartment of Materials Science and EngineeringMassachusetts Institute of Technology77 Massachusetts Ave, Cambridge, MA 02139, USAJ. Beroz, Prof. M. Kolle, Prof. A. J. HartDepartment of Mechanical EngineeringMassachusetts Institute of Technology77 Massachusetts Ave, Cambridge, MA 02139, USAE-mail: [email protected]

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.201803620.

DOI: 10.1002/adma.201803620

confinement to the evaporative assembly process, through techniques such as drop casting,[15,16] blade-casting,[17,18] and Langmuir–Blodgett drawing,[19,20] yields large area films suitable for applications such as electronics and optical displays. Confinement of colloids within liquid droplets and assembly upon evaporation yields spherical clusters of particles, such as photonic “balls” for optical applications such as visual displays[21–25] and crumpled balls of graphene for energy applications such as electrochemical storage.[26–28] Yet, with these established self-assembly tech-niques, the shape and geometry of the material is limited to planar shapes and discrete patterns.

Another emerging fabrication tech-nique, direct ink writing, has been used to build miniature antennae,[29] light-weight composites,[30] batteries,[31] and many other functional structures from

metallic, dielectric, polymer, and biomaterial inks. In this pro-cess, an ink is provided to a needle or nozzle, which is moved with three degrees of freedom with respect to a substrate, as the ink is extruded. The rheology of the ink is typically engineered to give it a well-defined yield stress, therefore requiring cohe-sion between particles in high-density suspensions.[32] How-ever, this inhibits long range crystalline ordering in the final structure.[33–35] If crystalline order can be achieved using col-loidal building blocks in a direct-write process, emergent prop-erties such as photonic[4,5] and electronic band gaps,[36] could be achieved. Moreover, the ability to select the feedstock of col-loidal particles and engineer the particle interactions and order by methods established for planar assembly could be extended to design 3D, macroscale colloidal materials and structures.

Here, we introduce direct-write colloidal assembly, as a new fabrication technique that combines the principles and advan-tages of evaporative colloidal assembly with the versatility and scalability of direct-write 3D printing. This approach allows for both local control of particle organization and global control of the shape of the structure. We demonstrate fabrication of col-loidal structures that exceed heights of 1 cm and aspect ratios of 10, and exhibit polycrystalline particle ordering. We model the build rate of the structures using a scaling argument and demonstrate examples of structures with properties relevant to photonic applications.

Direct-write colloidal assembly is performed using a custom-built apparatus wherein a colloidal solution is dis-pensed through a needle, with fine position control relative to a substrate, in a temperature-controlled environment (Figure 1a and Figure S1, Supporting Information). The formation of a

Colloidal assembly is an attractive means to control material properties via hierarchy of particle composition, size, ordering, and macroscopic form. However, despite well-established methods for assembling colloidal crystals as films and patterns on substrates, and within microscale confinements such as droplets or microwells, it has not been possible to build freeform colloidal crystal structures. Direct-write colloidal assembly, a process com-bining the bottom-up principle of colloidal self-assembly with the versatility of direct-write 3D printing, is introduced in the present study. By this method, centimeter-scale, free-standing colloidal structures are built from a variety of materials. A scaling law that governs the rate of assembly is derived; macroscale structural color is tailored via the size and crystalline ordering of polystyrene particles, and several freestanding structures are built from silica and gold particles. Owing to the diversity of colloidal building blocks and the means to control their interactions, direct-write colloidal assembly could therefore enable novel composites, photonics, electronics, and other mate-rials and devices.

Colloidal Assembly

Structural hierarchy, which involves the control of composi-tion and form across length scales, is a powerful strategy for creating functional natural and synthetic materials. In nat-ural materials, examples of hierarchical morphology can be found in, for instance: butterfly wings, which display intricate photo nic effects;[1] the xylem architecture of plants, which fea-ture optimized mass transport;[2] and the skeletal structure of sea sponges, which possess outstanding mechanical proper-ties.[3] In synthetic materials, colloidal particles can be assem-bled into crystals that exhibit unique optical,[4,5] chemical,[6,7] and mechanical[8,9] properties based on particle geometry, composition and arrangement. Colloidal assembly therefore enables materials design for diverse applications including optical coatings,[10] biological and chemical sensors,[11] and bat-tery electrodes.[12]

Evaporative self-assembly provides a pathway to estab-lish hierarchy in colloidal assembly.[13,14] For instance, planar

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colloidal structure is initiated by dispensing a small amount of suspension to form a liquid bridge between the substrate and the orifice of the needle. This liquid bridge provides confine-ment for the assembling particles that accumulate at the base of the liquid bridge. In turn, we observe accumulation of particles into a solid layer at the base of the liquid bridge and retract the substrate downward as the particles accumulate. Continuing, we move the substrate downward at a rate matched to the ver-tical growth rate of the particle structure; this enables construc-tion of high aspect ratio pillars (Figure 1, Movie S1, Supporting Information), which we call colloidal “towers”. The formation process can be terminated at any point by halting the flow from the needle, after which evaporation collapses the liquid bridge (Figure S2, Supporting Information); freestanding towers sev-eral millimeters tall can be easily drawn. The dispense rate (≈10−2 µL s−1) and motions of the substrate relative to the needle (≈1 µm s−1) are motor controlled, and the needle, tower, and substrate are viewed in situ with video microscope cameras.

The radius R of the colloidal towers is nominally set by the needle radius, and the local width and curvature of the

structure can be modulated by changing the dispense rate relative to the vertical rate of motion, as shown in Figure S3 in the Supporting Information. When the dispense rate is lesser than the rate of evaporation, the liquid bridge necks, as shown in region (i). When the dispense rate is greater than the rate of evaporation, the liquid bridge bulges, as shown in region (ii). The result is a structure of varying cross-section, as exemplified by the “hourglass” structure shown in Figure S3 in the Supporting Information.

As a first model system, we built colloidal towers using aqueous solutions of spherical polystyrene particles with radius ranging from a = 44 nm to a = 500 nm, at volume fraction φ1 ≈ 0.025. The diameters of the resulting towers range from 50 µm to 1 mm, and the heights range from 1 mm to 1 cm, as shown in Figure 2 and Figure S4 in the Supporting Informa-tion. Throughout this wide range of dimensions, towers built by direct-write colloidal assembly are polycrystalline, though the packing of the smallest particles (a = 44 nm) is less ordered due to broad size dispersity (CV = 11%). In general, we chose particle sizes that do not result in appreciable sedimentation

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Figure 1. Direct-write colloidal assembly of macroscale freestanding colloidal crystal structures. a) Direct-write colloidal assembly is performed by precision dispensing of a colloidal solution from a fine needle, followed by controlled downward or multi-axis substrate motion to build the structure, as shown in the schematic (top) and in the photograph (bottom). Scale bar: 2 mm. b) Scanning electron microscopy (SEM) image of a freestanding structure comprising of particles of radius a = 500 nm. Insets: close views of top and middle sections. c) 3D reconstruction of the interior of a free-standing colloidal structure, as imaged by X-ray microscopy. d) High-magnification view of a portion of the cross-section indicated in (c), revealing crystal defects such as vacancies, dislocations, and grain boundaries.



during the timescale of the experiment (≈1–2 h); calculations suggest this is a ≤ ≈1 µm for polystyrene, a ≤ ≈200 nm for silica (shown later), a ≤ ≈50 nm for gold (shown later).

X-ray microscopy permits nondestructive imaging of the particle arrangement within the structures. A 3D reconstruc-tion (Movie S2, Supporting Information) of an tower reveals an average grain size of ≈20 µm (Figure 1c). A cross-sectional slice of the imaged volume reveals grain boundaries, voids, and disloca-tions (Figure 1d), as can be expected within colloidal crystals.[37] We previously showed that freestanding towers can be built by precise dispensing of liquid containing ≈10 µm microparticles from a needle. However, the dominance of sedimentation at that larger particle size prevented long-range ordering of the assembled particles.[38]

Here, in situ video microscopy reveals that the colloidal towers precipitate wet, i.e., saturated with water between the particles, and then dry at a distance L below the bottom of the liquid bridge. The wet and dry sections, as well as a drying front in between, are easily distinguishable based on optical appearance—the wet section is darker than the dry section, and the drying front is opaque white (Figure 3a). The precipi-tation of the solid structure occurs by an influx of water and particles through the bottom of the liquid bridge. The water flowing into the wet section compresses the particles down-ward while the capillary pressure at the section’s outer surface, due to the liquid’s surface tension γ, provides lateral constraint. This capillary pressure drives water through the wet section to its outer surface, where the water evaporates. The water experi-ences a resistance to flow due to its viscosity µ as it travels in

the interstitial spaces between the particles packed at volume fraction φ2, driven locally by the pressure gradient ∇P. In all our experiments, the Reynolds number is Re ≤ 10–3, based on the dispense rates and particle sizes.

A quantitative understanding of the factors governing the build rate in direct-write colloidal assembly was obtained by performing a series of experiments where towers of constant radius R were built with various particle radii a. Experiments were performed with polystyrene spheres suspended in water, where the polystyrene particles occupy volume fraction φ1 ≈ 0.025.

For steady build of a vertical structure with uniform radius R, the wet length L is constant (Movie S3, Supporting Informa-tion) and the speed at which the substrate is withdrawn from the needle to build the structure z

• relates to the above-mentioned

quantities as follows. The energy change dewetting a particle of surface area Ap is u = (γap − γlp) Ap = γ cos θAp as its sur-face energy changes from liquid-particle γlp to air-particle γap; here Young’s law γap − γlp = γ cos θ defines the contact angle θ. The free energy change associated with dewetting a differential layer dz of the structure is therefore dF = (uφ2/Vp) πR2dz, Vp being the volume of a particle, and φ2 being the volume frac-tion of particles in the wet solid. The pressure difference PF of the liquid relative to atmosphere at the drying front is the negative of the change in free energy per cross-sectional areaP F z R aπ φ γ θ= − −(d /d )/ ~ cos /F

22 .

We assume that the average flux of water q through the liquid bridge into the structure is governed by Darcy’s law q = (−k/µ)∇P, where the permeability of the structure k

Adv. Mater. 2018, 1803620

Figure 2. Millimeter-scale structures built by direct-write colloidal assembly. Optical and corresponding SEM images of vertical columns built from a,d) a = 500 nm polystyrene particles, b,e) a = 250 nm polystyrene particles, c,f) a = 88 nm polystyrene particles.



must, on dimensional grounds, be of the form k = f(φ2)a2 and using the Kozeny–Carman equation[39] we approximate

( ) (1 ) /452 23

22f φ φ φ≈ − . The pressure at the top of the structure is

set by the capillary pressure of the liquid bridge ~ /BP Rγ , so

PP P

L La~ ~ cosF B

2φ θ γ∇ − − by P

P

R

a~ 1F

B

, and the build rate of

the structure is therefore

z Cf a

1 L1 2

1

φ φ γφ µ( )

( )≈−

(1)

Mass balance gives q z (1 )/2 1 1φ φ φ= − , φ2 ≈ 0.73 based on X-ray microscopy measurements, and the proportional factor C includes θ (Supporting Information). Experimentally, Equation (1) is shown to fit a range of experiments from par-ticle size a = 44 nm to a = 110 nm, over growth rates ranging from ≈0.5–3 µm s−1. This linear fit approximates C ≈ 22 for all structures built to heights ≥L. The build rate is inversely pro-portional to L because a shorter L means a greater pressure gradient and therefore greater flow by Darcy’s law. The intui-tion that a longer wet section implies a faster build rate, that is, more surface area implies greater total evaporation and greater flow rate through the needle, is true only for structures built to heights shorter than L.

Colloidal assemblies exhibit a diverse range of optical phe-nomena depending on their crystalline order. Well-ordered colloidal crystals are known to have photonic stopbands that enable the spectrally selective reflection of light,[40,41] which gives a sparkling, iridescent appearance. The spectral posi-tion of the stopband mainly depends on the particle size and packing.[25] Conversely, amorphous colloidal structures made by frustrating the assembly process[42] can exhibit nonirides-cent structural colors, and the building blocks can be chosen to exploit absorption and interference effects synergistically.[43–45] Such ordered and disordered materials can form the basis for lasers, optical sensors, waveguides, and structural color displays.[46]

Direct-write colloidal assembly therefore provides a route to build macroscale colloidal structures with tailored optical properties, such as by selecting the particle size and control-ling the packing within the structures. The ordered crystalline arrangements observed throughout the cross-section of assem-bled structures (Figure 1c,d) suggest that structures should exhibit structural coloration due to Bragg reflection occurring in the visible range of light. Structures made from monodis-perse particles of different size should therefore reflect dif-ferent colors when illuminated with white light. Upon white light illumination, towers formed from particles of radius a = 95, 105, 110, and 140 nm appear violet, blue, green, and red, respectively, as shown in Figure 4a. Reflectance spectroscopy reveals Bragg reflection peaks at λ = 420, 460, 510, and 620 nm, respectively. In towers built from suspension with mixed particle sizes (here, an equal proportion of a = 110 nm and a = 140 nm particles; Figure 4a), the slight mismatch in particle size leads to frustrated particle packing and no long-range order (Figure S5h, Supporting Information). Therefore, under white light illumination in an optical microscope, the mixed-particle towers appear whitish and the reflection spectrum is flat with a value of ≈0.2.

Complex freeform shapes can be built by coordinating additional degrees of freedom in the substrate’s motion. For example, to form a helical structure, we coordinated the cur-vilinear rate of growth of the structure with the rotational and vertical motion of the substrate, as illustrated in Figure 4b and shown in Movie S4 in the Supporting Information. Here, a slanted-tip needle was used so that the liquid bridge would be oriented in the direction of crystal growth, as shown in Figure S6, Supporting Information. The helical structure shown here has a pitch of 2.28 mm, circular radius of 0.34 mm, and is built from polystyrene particles with a = 44 nm.

While we have demonstrated that the rate of direct-write col-loidal assembly can be understood in terms of a scaling law, this does not capture the detailed kinetics of particle assembly which may influence the density of microstructural defects.

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Figure 3. Scaling of build rate in direct-write colloidal assembly. a) The structure (radius R) precipitates wet, and evaporation occurs from the surface of the wet section of length L, which drives an influx of liquid and particles through the liquid bridge. Scale bar: 200 µm. The inset illus-trates particles of radius a near the surface of a wet region of the solid, and the surface tension quantities on the air-liquid (γ), air-particle (γap), liquid-particle (γlp) interfaces. b) The steady state build rate z

• follows a simple scaling relationship with γ, a, L, the volume fraction of particles

in the suspension φ1, volume fraction of particles in the solid φ2, and viscosity of water µ. Calculation of error bars is detailed in the Supporting Information.



It may be possible to achieve structures with larger grain size by improving the monodispersity of the particle feedstock, and by tailoring the temperature and growth rate. The control of macroscale defects such as cracks is also important, and, interestingly our experiments show that the particle size and structure dimensions can determine whether the structures are cracked or fully crack-free.[47] Another area of further research is mechanical reinforcement of the colloidal structures. The as-fabricated colloidal structures are mechanically weak, held together only by van der Waals forces. The mechanical prop-erties of freestanding colloidal structures could possibly be improved by methods such as sintering, in situ precipitation of a matrix between the particles, and assembly of particles with functional moieties designed for interparticle bonding. Moreover, while the present process is quite slow (growth rates of ≈1–5 µm s−1), we expect it is possible to perform parallel assembly using microneedle arrays,[48] and to accelerate the rate by tuning the assembly parameters.

Further, we show that direct-write colloidal assembly can be straightforwardly applied to other colloidal building blocks. As an example, we assembled silica nanoparticles (a = 100 nm) and gold nanocrystals (a ≈ 40 nm) into millimeter-scale vertical towers, as shown in Figure 4c,d, respectively. This implies the

possibility of tailoring the properties of macroscale colloidal materials via direct-write colloidal assembly, in combination with deliberate choice of particle size and composition.

In conclusion, we have demonstrated the combination of evaporative self-assembly with a direct-write process, ena-bling the freeform construction of macroscale colloidal crystalline solids for the first time. Looking forward, we antici-pate this technique can build colloidal materials with tailored optical,[49,50] mechanical,[51,52] and acoustic[53] properties, and many other interesting emergent characteristics. Our technique may also serve as a model system to investigate meniscus-con-fined colloidal epitaxy,[54] and to build macroscale structures with a single crystallographic orientation. Direct-write colloidal assembly may also be applied to particles with even smaller sizes and from a wide range of materials, thereby combining materials design via self-assembly with the versatility of direct-write 3D printing.

Experimental SectionParticle Suspensions: Aqueous dispersions of polystyrene particles

were procured from Polysciences, Inc. and used as received

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Figure 4. Tailoring the properties of freeform colloidal structures by choice of particle size, build trajectory, and material. a) Freestanding cylindrical colloidal crystals with structural colors tunable by the radius of polystyrene particles (increasing from left to right), and corresponding reflectance spectra measured from the surface of each of the above structures. b) Optical image of a freestanding helical shaped structure, with circular diameter of ≈0.67 mm and height of ≈1.1 mm. The helical structure was built by simultaneously rotating (ω) and lowering (vz) the substrate. c) Optical and SEM images of image of a structure 3 mm tall assembled from a = 100 nm silica nanoparticles. d) Optical and SEM images of a structure 0.75 mm tall assembled from a ≈ 40 nm gold nanoparticles.



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(2.5 wt%), or procured from Bangs Laboratories and diluted to 2.5 wt% to keep the concentration of particles consistent between experiments. Measurement of the surface tension of each particle solution is outlined in Supporting Information. Gold nanoparticles, capped with carboxylic acid ligands, were procured from Nanopartz (Product number A11-100-NPC-25, Lot SPC359N). Silica nanoparticles were synthesized by the Stöber method.[55]

Liquid Dispensing Apparatus: Direct-write colloidal assembly was performed using a custom-fabricated benchtop system that comprised a glass syringe and needle mounted vertically above two parallel aluminum plates that created a uniform temperature environment for the particle structures (Figure S1, Supporting Information). The needle passed through a hole in the top plate, which was machined in half to expedite preparation for experiments, and the substrate rested on the bottom plate as shown. The top and bottom plates were uniformly heated by thermoelectric chips (standard square dimensions, Custom Thermoelectric), and the plate temperature was measured by embedded thermocouples (K-type) which fed to a temperature controller (PTC 10, Stanford Research Systems). The thickness of the top plate was chosen so that the particle suspension dispensed through the needle heats to the temperature of the plate while transiting its thickness for the dispense rates used in experiments. The dispense rate (≈0.01 µL s−1) and translational motions of the substrate relative to the needle (≈1 µm s−1) were motor controlled (0.078 µm step size: M-229.26S, Physik Instrumente), and the motors were controlled manually using joysticks (Pro Flight Throttle Quadrant from Saitek); it was found to be the most convenient way to match the structure’s evaporation and build rate, and enable fine adjustments. The motions of all the actuators were recorded for the duration of each experiment. Depending on the volume capacity of particle suspension required to build the structures, syringes with piston diameters [2.30, 3.26] mm were used that respectively corresponded to dispensing precisions of [0.3, 0.7] nL. The dispensing needles were made of glass for smaller sizes, ID/OD = [50/80, 82/120, 200/250, 400/500, 600/700] µm (Hilgenberg), and made of stainless steel for the largest size ID/OD = 0.84/0.127 mm. The diameters of the built structures were of approximately the needle ID. Building of the particle structures were observed in situ with two video microscope cameras. One views the needle orifice and liquid bridge with a 3× objective (Mitutoyo Telecentric 3× Objective, Edmund Optics stock #56-985) and 5 megapixel CCD (DCC 1645C, Thorlabs). The other views the needle and entire structure with a 1× objective (Mitutoyo Telecentric 1× Objective, Edmund Optics stock #56-984) and 10 megapixel CCD (EO-10012C, Edmund Optics). For each objective, the needle and structure were backlit with a telecentric lens (Techspec Telecentric Backlight Illuminator, Edmund Optics), and LED spotlights (Amscope LED-6W) were used to illuminate the front side of the structure facing the objectives. The video feeds from both CCDs were simultaneously recorded and displayed on a computer screen—the onscreen view was used to monitor the building of the structure and adjust the dispense rate and stage motion.

Microstructural Characterization: Imaging the surface of the structures was performed with a Zeiss Merlin SEM in high efficiency secondary electron imaging mode, at an acceleration voltage of 1 kV and probe current of 80 to 100 pA. X-ray Microscopy of the interior of the structure was performed courtesy of Dr. Steve Kelly of Carl Zeiss X-ray Microscopy, Inc. Zernike phase contrast images were acquired with a Zeiss Xradia 810 Ultra system, at photon energies of 5.4 keV and a total scan time of 25 h. The field of view for data acquisition was 65 µm × 65 µm and the voxel size was 64 nm. 3D reconstruction of the image slices was performed with ORS Visual SI Advanced software.

Reflectance Measurements: Vertical particle structures were constructed; they were broken at the base, and they were mounted on a flat adhesive substrate. The surface of the structure was illuminated through a microscope objective (Olympus, 20× objective lens, 0.4 N.A.) which also collected the light reflected from the sample. The reflected light passed through an optics train coupled to an optical fiber (Ocean Optics; 100 µm core) and was analyzed with a grating spectrometer (Ocean Optics; Maya Pro) controlled via the software IGOR.

Supporting InformationSupporting Information is available from the Wiley Online Library or from the author.

AcknowledgementsA.T.L.T. and J.B. contributed equally to this work. The authors thank Dr. Mostafa Bedewy for contributions to prior apparatus design and experimentation, Johan Villanueva for performing surface tension measurements, and Dr. Hari Katepalli for synthesis of silica nanoparticles. X-ray microscopy measurements and analysis were performed by Dr. Stephen Kelly of Carl Zeiss X-ray Microscopy, Inc. J.B. was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. A.T.L.T. was supported by a postgraduate fellowship from the Singapore Defence Science Organization. This work made use of the MRSEC Shared Experimental Facilities at MIT, supported by the National Science Foundation under award number DMR-14-19807. Funding for hardware and experiments was provided by a National Science Foundation CAREER Award to A.J.H. (CMMI-1346638).

Conflict of InterestThe authors declare no conflict of interest.

Keywordsadditive manufacturing, colloids, nanoparticles, self-assembly, structural color

Received: June 7, 2018Revised: July 3, 2018

Published online:

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