Article pubs.acs.org/cm
Fluid Networks Assembled from Endoskeletal Droplets Tamás A. Prileszky and Eric M. Furst* Center for Molecular and Engineering Thermodynamics, Department of Chemical and Biomolecular Engineering, University of Delaware, Allan P. Colburn Laboratory, 150 Academy Street, Newark, Delaware 19716, United States S Supporting Information *
ABSTRACT: Anisotropic endoskeletal droplets are produced continuously in a microfluidic device. The device temperature is controlled such that droplets are formed in a fluid state and subsequently cooled to crystallize an internal network that retains an anisotropic shape. Droplets that are forced to collide after crystallizing partially coalesce to form linear droplet superstructures with tunable rigidity. Superstructure filaments can be folded into larger, three-dimensional percolating fluid networks with tunable porosity and size, which can be further controlled by temperature. The results of this work provide a means of generating hierarchical porous structures with continuous liquid interfaces on demand in a process similar to three-dimensional printing.
1. INTRODUCTION Porous networks of one or more solids, including polymer foams, bicontinuous polymer blends,1 and zeolites,2 are valuable materials in catalysis,3 biology,4 separations,5 and environmental science6 because they provide large surface areas, small characteristic transport length scales,7 and outstanding mechanical properties.8 Liquid systems that mimic the interconnected matrices of porous solids belong to a class of materials called percolating fluid networks. Bicontinuous, interfacially jammed emulsion gels, or bijels, are among the first examples of stable, percolating fluid networks9−11 and are promising material templates, tissue scaffolds, and microreactors.12−14 Bijels consist of two miscible liquids that phase separate through spinodal decomposition in the presence of nanoparticles. The interfacial area of the separating fluids decreases until nanoparticles that partition at the liquid−liquid boundary jam into an elastic, semipermeable membrane. In all percolating fluid networks, some similar structural framework must kinetically arrest the liquid conformations to limit the demixing driven by their thermodynamic instability. The functionality of fluid networks can be expanded by producing the materials through alternative approaches, introducing directionally oriented structures, liquid−liquid interfaces unobstructed by adsorbed particles, and greater freedom in materials selection. Adapting existing additive manufacturing methods to engineer new percolating fluid networks allows greater control of the final structures. No current additive manufacturing technique is designed to assemble fluid networks; however, features of additive manufacturing that are useful in other systems may be drawn upon to accommodate and exploit the properties of liquids. Two of the most common three-dimensional (3D) printing principles incorporate liquids into the production of solid © XXXX American Chemical Society
materials: fused deposition modeling, the deposition of a melted polymer filament through extrusion;15 and robocasting, the accretion of solid particles suspended in liquid media.16 In this work, a printing method with roots in both robocasting and fused deposition modeling is presented using partially crystalline droplets formed in a microfluidic device as building blocks to create internally reinforced filaments and larger percolating fluid networks. These “endoskeletal droplets”, nonspherical oil-in-water emulsions, have been shown to change shape in response to changes in temperature and surfactant concentration.17,18 Additionally, endoskeletal droplets resist coalescence, forming droplet superstructures that preserve the shapes of the component droplets rather than forming spheres.19 In this work, we discuss the formation of endoskeletal droplets in microfluidics and their assembly into super droplet structures and, finally, percolating fluid networks, by controlled partial coalescence. Once formed, the structure of such networks can be further tailored by coarsening at higher temperatures.
2. EXPERIMENTAL METHODS 2.1. Emulsion Materials. Internally reinforced percolating fluid networks consist of at least two phases, one of which contains an internal network that provides structural support. In the percolating fluids described here, the unstructured phase is an aqueous surfactant solution of 10 mM sodium dodecyl sulfate (SDS) (OmniPur, 99%) in ultrapure water (resistivity of >18.2 MΩ cm). The concentration of SDS is greater than the critical micelle concentration under experimental conditions.20 Received: February 2, 2016 Revised: May 13, 2016
A
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials The structured oil phase consists of hexadecane (Fisher Scientific, 99%) reinforced with petrolatum (Unilever Vaseline) at weight percentages ranging from 60 to 80% petrolatum, where greater petrolatum fractions correspond to droplets with higher yield stresses.18 The two oil phase components are mixed by heating a vial containing weighed quantities of both materials in a water bath at 80 °C, which is greater than the melting temperature range of petrolatum (40−55 °C). Once the petrolatum has melted, the components are incorporated by vortex mixing the vial. Before the mixture recrystallizes, it is drawn into a heated glass syringe to prevent inhomogeneities caused by crystallization of high-melting point components. 2.2. Microfluidic Device. Figure 1 is a schematic representation of the microfluidic device used to generate endoskeletal droplets. Similar
mixture is maintained using a metallo-ceramic heater (Thorlabs HT24S) mounted beneath the glass slide. The edge of the heater is aligned with the nonaqueous fluid channel and T-junction (cf. Figure 1) and heats the region of drop breakup to approximately 60 °C, measured by a thermocouple. A dc power supply (OTE Instruments HY3005-3) provides 0.2 A at 5.6 V to the heater, which is allowed to equilibrate on the device for 15 min before operating. The fluid drops continue to flow in a crystallization channel that cools the droplets until the internal networks form. The partially crystalline droplets are ejected into a recovery reservoir, where individual droplets can be recovered or droplet superstructures can be formed. Each device is fabricated from a master on a silicon wafer made by soft lithography. Silicon wafers are spin coated with SU-8 (MicroChem), a negative photoresist, leaving a layer with a uniform thickness. The coated wafer is baked prior to exposure to UV light so the photoresist solvent evaporates and the film hardens. Afterward, a negative lithographic mask is adhered to a glass sheet with water and then placed printed-side down on the hardened SU-8 film. The wafer and mask are placed under a shuttered UV lamp, which is then opened for a time depending on film thickness and irradiance power. The exposed wafer is returned to a hot plate for a postexposure bake to complete curing. Subsequent to the second heat treatment, the wafer is placed in the SU-8 developer (MicroChem) and gently agitated. Silicon masters are used to pattern polydimethylsiloxane (PDMS) (Dow Corning Sylgard 184) devices. PDMS is mixed with a curing agent in a 10:1 ratio until the mixture is milky in appearance, followed by degassing to remove bubbles. The clear PDMS is poured over a master wafer and cured at 150 °C for 10 min. After curing, the PDMS is leeched to remove non-cross-linked oligomers and enhance hydrophilicity: the PDMS slab is placed in two chloroform baths followed by two acetone baths, each bath lasting 2 h. Residual solvents are removed from the PDMS by placing the leeched slab in a 65 °C oven under circulating dry air for 8 h. Individual microfluidic devices are cut from the PDMS slab as needed. Ports for fluid interfacing are punched with blunted hypodermic needles. Ported devices are bound to glass slides by exposing both the slide and feature side of the PDMS to air plasma for 30 s and then bringing the two into conformal contact; the plasma treatment also renders the channel surfaces hydrophilic, which is necessary for producing oil droplets in a continuous aqueous phase. Microfluidic devices are imaged on an inverted microscope (Axiovert 200, Zeiss), and videos are captured using a high-speed camera (Phantom version 5.1, Vision Research). Polarized light microscopy is used to highlight crystallinity in droplets: crossed polarization makes crystallites appear bright relative to the background intensity, while parallel polarizers make them appear dark. The microscope was adapted for polarized light by placing a polarizer before the condenser and an analyzer after the objective in the microscope light path. Both the analyzer and the polarizer are mounted on goniometers, allowing the optical axes of both polarizers to be rotated relative to the microfluidic device. 2.3. Operating Conditions. The ratio of dispersed and continuous phase flow rates determines the size of droplets that are produced in a T-junction.22 However, changing the mass fraction of petrolatum added to the endoskeletal droplet mixture affects the viscosity of the hot dispersed phase and changes the size of droplets produced. Correspondingly, we have developed a new scaling relationship for predicting the size of droplets produced in a Tjunction as a function of the dispersed and continuous phase flow rate as well as the dispersed phase viscosity:23
Figure 1. Overview of the experimental setup used to continuously produce structured emulsion droplets. (a) Layout of devices used to control the temperature and flow of materials to the microfluidic device. (b) Representation of the T-junction, cooling channel, and placement of the metallo-ceramic heater. microfluidic systems with a modular layout have been conceived for producing larger droplets of crystallized fats.21 The current devices reduce dimensions, fabrication times, and complexity, allowing all components to be incorporated onto a single chip. The apparatus consists of the following features. First, a circulating water bath at 80 °C heats the petrolatum/hexadecane mixture and feed tube to 65 °C, preventing the oil phase from crystallizing throughout the pumping stage. A syringe pump pushes fluid from the heated reservoir to the microfluidic device. There, a T-junction breaks up the nonaqueous stream as droplets are dispersed in a second, water stream. To ensure a liquid oil phase during droplet breakup, a temperature above the crystallization temperature of the hexadecane/petrolatum
Q L = θ0 + θ1 D W Q CμD
(1)
where L is the droplet length, W is the droplet width, QD and QC are dispersed and continuous phase flow rates, respectively, μD is the dispersed phase viscosity, and θ0 and θ1 are fit parameters. Flow rates for the dispersed nonaqueous phase range from 0.5 to 2 μL/min, while the continuous aqueous phase flows at a rate of 2−5 μL/min. Flow rates are chosen such that the T-junction operates in the dripping B
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials regime.24 Increasing the petrolatum fraction increases the dispersed phase viscosity, leading to a decrease in droplet size at a constant flow rate ratio. The dimensions of the microfluidic channels are small. The channel widths vary between 40 and 100 μm, and the channel depth is 25 μm. The small sizes of the microfluidic channels reduce the characteristic times for heat, momentum, and mass transfer compared to those of macroscale fluid flows. The Péclet number, Pe, which relates the rates of advective and diffusive transport, is small. The heat transfer Péclet number is defined as Pe = Lu/α, where L is a characteristic channel dimension, u a velocity, and α the thermal diffusivity. The Pe values of experimental devices are on the order of unity: the fluid and droplet temperature is always nearly equilibrated with that of the surrounding channel. Controlling the temperature profile over the length of the channel, as well as the droplet residence time in the channel, provides the means of controlling the crystallinity of the droplets. The temperature profile along the crystallization channel is measured by adhering a PDMS slab to a glass slide and placing a thermocouple probe through prepunched holes that extend perpendicularly from the heater edge. This approach measures the approximate temperatures experienced by droplets as they pass through the channel. The measured temperature profile is plotted in Figure 2 along with a fit of eq 2. The profile follows the form ⎛ T − Tambient ⎞ ln⎜ ⎟= ⎝ Tmax − Tambient ⎠
hL ̅ 2 ξ kd
3. RESULTS AND DISCUSSION 3.1. Endoskeletal Droplets. The melted hexadecane/ petrolatum mixture is a Newtonian fluid and flows smoothly, which is required for droplet breakup in the T-junction to occur. As newly formed droplets flow through the cooling channel, the decreasing temperature leads to crystallization once they reach the solidification temperature. Although the droplets span the channel, lubricating hexadecane and aqueous layers surround the droplet internal network and allow them to continue flowing as they crystallize, provided the channel is straight and has a uniform cross section. The increasing yield stress that accompanies the increasing crystallinity maintains droplets in the shape of the channel cross section as they proceed through the device. The crystallization process results in a petrolatum-scaffolded droplet that becomes stronger over time, which can be seen by the increasing crystallinity shown in Figure 3a. By monitoring the transmittance of polarized light through a crystalline droplet, we obtain information about the drop crystallization kinetics. We measure the fraction of incident light, J0, that is depolarized by the crystalline sample. From this, the total optical retardation of droplets, DE, is calculated by
(2)
Figure 2. Temperature profile of microfluidic chips. Error bars and gray fit uncertainty are calculated at the 95% level.
where h̅ is an average heat transfer coefficient, ξ is a dimensionless length, L is the overall length, and k is the thermal conductivity. Assuming PDMS is a good insulator, the calculated average heat transfer coefficient for passive convection on the underside of the microfluidic chip is 17 W m−2 K−1, within the range predicted by heat transfer coefficient correlations.25 The temperature range of the device allows fully liquid droplets to crystallize along the length of the lowtemperature outlet channel, corresponding to a residence time of 1−2 s.
Figure 3. (a) Crystalline droplet viewed under crossed polarizers (left column) and bright field microscopy (right column). The residence time in the cooling channel increases from top to bottom. The flow rates are QD = 1 and QC = 2 μL/min. Under crossed polarizers, the droplets appear bright because of the birefringence of the developing internal crystalline structure. Crossed polarizer images are enhanced to improve contrast. The scale bar is 100 μm. (b) Total optical retardation of droplets as a function of residence time in the cooling channel. C
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials DE = −ln(1 − J0 )
(3)
as a metric for quantifying crystallinity, where D is the average optical retardation of a single birefringent plate and E is the average number of birefringent plates in the light path.26 DE values calculated for endoskeletal droplets as a function of residence time in the cooling channel are plotted in Figure 3b; while DE is not linearly related to the degree of crystallinity, it is indicative of the quantity of crystalline material in the light path. Correspondingly, the plateau at residence times of >2 s suggests a saturation of the crystallization kinetics. The fast kinetics of this process allows droplets to be produced rapidly, at rates ranging from tens to hundreds per second. As droplets flow through the channel, recirculation of the dispersed phase can affect the internal structure; however, the final crystalline structure of the droplets has randomly oriented crystallites, which suggests the internal flow has negligible effects on the ultimate droplet network. Partially crystalline endoskeletal droplets maintain a shape imposed by the channel cross section after ejection into the recovery reservoir. Representative droplets are shown in Figure 4. The rectangular channels of the microfluidic devices produce rounded cuboid droplets with surface area:volume ratios significantly larger than those of spheres of an equivalent volume. Depending on the device design and flow rates, droplets are 40−100 μm wide, approximately 30 μm deep, and anywhere from tens to hundreds of micrometers long. Hence, the droplets encompass a range of sphericity values, defined as the ratio of the surface areas of a sphere and a nonspherical particle of equal volume, ψ = (π1/36Vd2/3)/Ad, where Vd is the droplet volume and Ad is the droplet area. Typical sphericity values are in the range of 0.5−0.8. Interestingly, on the basis of droplet curvature, the microfluidic device produces endoskeletal droplets that are substantially stronger than those formed using glass capillaries in previous studies.18 The endoskeletal droplets shown in Figure 4 have three principal regions of curvature: a highcurvature region at the end caps, a medium-curvature region at the sides, and a low-curvature region at the tops and bottoms. The surface traction forces are greatest at the end caps and sides, where the curvatures are highest. The radii of curvature measured for the droplets in Figure 4d give maximal Laplace pressures in excess of 1000 Pa, with typical values in the hundreds of pascals, as shown in Figure 5e for an idealized droplet with a 15 μm radius edge, a 30 μm radius end, and a 10 mN/m surface tension.27 These pressures are roughly 1 order of magnitude higher than the yield stress of the crystallized hexadecane/petrolatum mixture, which is reported to range from 20 to 160 Pa.18 We attribute the mechanical stability of the ejected droplets to a larger yield stress of the crystalline network. The rapid temperature quench rate of the droplets as they flow through the device, which reduces the crystallization times from 15 min in previous studies to ∼1 s in this work, leads to high nucleation rates and many smaller crystallites. The yield stress of a network composed of crystallites with radius a is expected to scale as ∼1/a2.28 On the basis of their birefringence, we estimate that the crystallites are on the order of 10 μm in the microfluidic device, while they are hundreds of micrometers long when formed slowly in a capillary. The difference in crystallite size accounts for the increased mechanical strength of droplets produced in the microfluidic channels.
Figure 4. Droplets ejected from a microfluidic device. Images a−c provide different perspectives on the anisotropic droplets formed at 60% petrolatum, and panel d is a schematic representation of a droplet with typical dimensions. The scale bar is 100 μm.
3.2. Superdroplet Assembly. The structural framework that supports shape anisotropy in endoskeletal droplets also contributes to their interesting coalescence behavior. When spherical, Newtonian emulsion droplets coalesce, the shape characteristics of the component droplets are superseded by those of the final, larger spherical droplet that replaces them. In contrast, the shapes of coalescing endoskeletal droplets are preserved to an extent that is determined by the yield stress of their internal networks.19 Two spherical endoskeletal droplets, for instance, will coalesce to form dumbbell shapes at high petrolatum fractions and ellipsoids at low petrolatum fractions, high- and low-yield stress conditions, respectively. Controlling the yield stress is essential for the assembly of droplet superstructures. While variation of the composition of droplets directly affects yield stress, it is not trivial to vary droplet composition in the microfluidic device. Instead, it is more convenient to exploit the kinetics of the crystallization to tune coalescence. Decreasing D
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials
Figure 5. Varying droplet superstructures formed on the basis of outlet and crystallinity conditions: (a) scorpion tail structures and (b) a flexible chain. The scale bar is 250 μm.
the droplet residence time in the crystallization channel of the microfluidic devices reduces droplet crystallinity upon ejection, increasing coalescence. Controlling residence time provides precise control over droplet crystallinity as well as providing a means of tuning yield stress without compromising the strength of the final structure by decreasing the petrolatum fraction. As droplets move into the recovery reservoir, they assemble into suprastructures, forming “scorpion tail” structures (Figure 5a) or long droplet chains shown in Figure 5b. The length of scorpion tails can be controlled by varying the shear stress applied at the device outlet: increasing flow rate increases the stress acting on droplets, which leads to greater droplet deflection and shorter suprastructures. In addition to residence time and reservoir conditions, the current microfluidic devices have control over droplet size, which improves the management of droplet assembly properties. Droplet size affects both the process of forming assemblies and their ultimate morphologies. When droplet aspect ratios are increased over the short droplets of Figure 5, the ordered, alternating pattern gives way to a more disordered droplet sheet. As a result, droplet joints in sheets are not regularly distributed throughout the droplet assembly, which reduces the flexibility of the superstructure. In droplet chains, droplet length has little effect on the assembly process, but the flexibility of the final chain is reduced. Where Figure 5b portrays a smoothly curved droplet chain comprising short droplets, longer droplets form chains that crease along joints to reduce stress. In this way, droplet chains resemble macroscopic linear polymers. Polymers can be divided into Kuhn segments over which the chain is approximately flexible; similarly, endoskeletal droplet chains are discretized by the individual droplets where joints provide flexibility. Longer droplets correspond to longer Kuhn segments, implying stiffer chains. 3.3. Percolating Fluid Networks. Percolating fluid networks are built from smaller droplet superstructures produced continuously. In a process similar to fiber spinning, fluid networks emerge as droplet chains, sheets, and ribbons fold in on themselves, forming random, porous networks. Figure 6 shows how fluid networks are built from a single droplet chain. Over 0.2 s, 20 droplets are produced and the resulting droplet chain folds back and forth, weaving the network. The bending of the droplet chain demonstrates that the flexibility of the superstructures that compose the threedimensional networks dictates the density of packing of the
structured phase: more rigid materials are less prone to folding, so the size scales of pores increase accordingly. The most flexible constituents, droplet chains, form the assembly in the first panel of Figure 7, which is characterized by short distances between filaments in the final assembly. When chains are replaced with sheets, structures are more difficult to discern as a result of the random orientations of droplets in each sheet, but the width of droplet sheets limits their flexibility to bending normal to the flat face, thereby increasing the porous volume of the networks. Finally, producing percolating fluid networks from fully coalesced ribbons yields a structure that has significantly increased distances between filaments as a result of decreased ribbon flexibility. Moreover, as the width of filaments increases at a constant thickness, the direction of bending becomes more selective because the amount of material that must stretch and compress increases along the thicker direction, leading to preferential bending normal to the wider face of the droplet assemblies. While it is possible to tune the size scales of percolating fluid networks during the assembly process, the response behavior of endoskeletal droplets allows dynamic restructuring of fluid networks in situ. At low temperatures, the petrolatum internal network of endoskeletal droplets is fully crystalline; as temperatures increase, the network begins to melt, reducing the yield stress of the droplets. Thus, an increasing temperature reduces the interfacial curvature that droplets can support, resulting in collapse. On the scale of percolating fluid networks, the curvature reduction occurs across the entire interface as the temperature increases, culminating in coarsening of the fluid network. During this process, filaments coalesce to form larger threads and pores grow in size. Figure 7 depicts a fluid network assembled from endoskeletal ribbons collapsing in response to increased temperature. It is possible to arrest the coarsening of the network at any point by reducing the temperature, which allows the droplet internal network to re-form and support the existing curvature, resulting in a new percolating fluid network with properties distinct from those of the source structure. Similar behavior is expected as a result of increased surface tension when the surfactant concentration is decreased, but it is more difficult to control coarsening through this method.
4. CONCLUSIONS Additive manufacturing provides a conceptual framework for building structures that applies over a wide range of materials E
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials
Figure 7. Melting of a percolating fluid network demonstrates coarsening of an endoskeletal droplet assembly in situ. The black lines indicate a reference frame for the network as the images progress over time. Remnants of the porous structure are visible in light-colored holes in the coarsened network, indicative of trapped water. The scale bar is 500 μm.
and operating conditions. To date, however, these principles have applied exclusively to solids. Since the concept of percolating fluid networks was conceived with the inception of bijels, alternative methods and materials that are capable of expanding the functionality and availability of fluid networks have been sought. Here, we have demonstrated a unique additive manufacturing methodology capable of weaving fluid networks reinforced with a soft crystalline solid that draws from existing 3D printing processes. Like bijels, these materials contain two liquid phases distributed co-continuously. Unlike the case in existing percolating fluid networks, however, elasticity arises from a temperature sensitive agglomeration of petrolatum crystallites rather than nanoparticles jammed at a liquid interface. The resulting materials are able to selectively coarsen as a result of the temperature sensitivity of the underlying structure, allowing porous fluid networks to change size scale and surface area on demand. These new percolating fluid networks are an interesting alternative to bijels that can be improved through the use of new materials or parallelized production. New materials would allow greater resilience of the fluid network structure as well as increased functionality. Via incorporation of polymerizable species into one phase, the structure could be permanently retained by reacting the monomers. Parallelizing production would allow the production of structures larger than the structure that is possible with a single microfluidic device. A linear increase in the level of production would accompany an increase in the number of cooperating devices, improving the production of milliliters of percolating fluids over the course of several minutes to significantly larger volumes in less time.
Figure 6. Percolating fluid network assembled from a droplet chain. As the chain forms, it weaves back and forth, bending around droplet joints. The strength of droplet joints is an important factor that contributes to chain flexibility, where increased coalescence produces thicker joints that are less prone to bending, yielding more rigid droplet chains. The scale bar is 100 μm. F
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials
■
(13) Lee, M. N.; Mohraz, A. Bicontinuous Macroporous Materials from Bijel Templates. Adv. Mater. 2010, 22, 4836−4841. (14) Haase, M. F.; Stebe, K. J.; Lee, D. Continuous Fabrication of Hierarchical and Asymmetric Bijel Microparticles, Fibers, and Membranes by Solvent Transfer-Induced Phase Separation (STRIPS). Adv. Mater. 2015, 27, 7065−7071. (15) Crump, S. S. Apparatus and Method for Creating ThreeDimensional Objects. US5121329 A, 1992. (16) Ceserano, J., III; Calvert, P. D. Freeforming objects with lowbinder slurry. US6027326 A, 1997. (17) Caggioni, M.; Lenis, J.; Bayles, A. V.; Furst, E. M.; Spicer, P. T. Temperature-Induced Collapse, and Arrested Collapse, of Anisotropic Endoskeleton Droplets. Langmuir 2015, 31, 8558−8565. (18) Caggioni, M.; Bayles, A. V.; Lenis, J.; Furst, E. M.; Spicer, P. T. Interfacial stability and shape change of anisotropic endoskeleton droplets. Soft Matter 2014, 10, 7647−7652. (19) Pawar, A. B.; Caggioni, M.; Hartel, R. W.; Spicer, P. T. Arrested coalescence of viscoelastic droplets with internal microstructure. Faraday Discuss. 2012, 158, 341−350. (20) Mukerjee, P.; Mysels, K. Critical micelle concentrations of aqueous surfactant systems. J. Pharm. Sci. 1972, 61, 222. (21) Kim, J.; Vanapalli, S. A. Microfluidic Production of Spherical and Nonspherical Fat Particles by Thermal Quenching of Crystallizable Oils. Langmuir 2013, 29, 12307−12316. (22) Garstecki, P.; Fuerstman, M. J.; Stone, H. A.; Whitesides, G. M. Formation of droplets and bubbles in a microfluidic T-junction− scaling and mechanism of break-up. Lab Chip 2006, 6, 437. (23) Prileszky, T. A.; Ogunnaike, B. A.; Furst, E. M. Statistics of droplet sizes generated by a microfluidic device. AIChE J. 2016, n/a− n/a. (24) De Menech, M.; Garstecki, P.; Jousse, F.; Stone, H. A. Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 2008, 595, 141−161. (25) Ç engel, Y. A.; Ghajar, A. J. Heat and Mass Transfer: Fundamentals & Applications; McGraw-Hill: New York, 2011; p 924. (26) Ziabicki, A. Transmission of light through a statistical system of birefringent plates. J. Opt. A: Pure Appl. Opt. 2005, 7, 774−782. (27) Kim, D.; Oh, S.; Cho, C. Effects of Cs and Na ions on the interfacial properties of dodecyl sulfate solutions. Colloid Polym. Sci. 2001, 279, 39−45. (28) Buscall, R.; Mills, P. D. A.; Goodwin, J. W.; Lawson, D. W. Scaling behaviour of the rheology of aggregate networks formed from colloidal particles. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4249.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b00497. Video of droplets coalescing into linear secondary suprastructures, corresponding to the chains in Figure 6 (AVI) Video of a droplet network coarsening, corresponding to the network melting in Figure 7 (AVI)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by National Science Foundation Grant CBET-1336132.
■
REFERENCES
(1) Kimber, R. G. E.; Walker, A. B.; Schröder-Turk, G. E.; Cleaver, D. J. Bicontinuous minimal surface nanostructures for polymer blend solar cells. Phys. Chem. Chem. Phys. 2010, 12, 844−851. (2) Wheatley, P. S.; Chlubná-Eliásǒ vá, P.; Greer, H.; Zhou, W.; Seymour, V. R.; Dawson, D. M.; Ashbrook, S. E.; Pinar, A. B.; McCusker, L. B.; Opanasenko, M.; Č ejka, J.; Morris, R. E. Zeolites with Continuously Tuneable Porosity. Angew. Chem., Int. Ed. 2014, 53, 13210−13214. (3) Rosen, J.; Hutchings, G. S.; Jiao, F. Ordered Mesoporous Cobalt Oxide as Highly Efficient Oxygen Evolution Catalyst. J. Am. Chem. Soc. 2013, 135, 4516−4521. (4) Wu, S.; Liu, X.; Yeung, K. W.; Liu, C.; Yang, X. Biomimetic porous scaffolds for bone tissue engineering. Mater. Sci. Eng., R 2014, 80, 1−36. (5) Duan, J.; Higuchi, M.; Krishna, R.; Kiyonaga, T.; Tsutsumi, Y.; Sato, Y.; Kubota, Y.; Takata, M.; Kitagawa, S. High CO2/N2/O2/CO separation in a chemically robust porous coordination polymer with low binding energy. Chem. Sci. 2014, 5, 660−666. (6) Gao, X.; Xu, L.-P.; Xue, Z.; Feng, L.; Peng, J.; Wen, Y.; Wang, S.; Zhang, X. Dual-Scaled Porous Nitrocellulose Membranes with Underwater Superoleophobicity for Highly Efficient Oil/Water Separation. Adv. Mater. 2014, 26, 1771−1775. (7) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms. J. Am. Chem. Soc. 1951, 73, 373−380. (8) Tan, J. C.; Bennett, T. D.; Cheetham, A. K. Chemical structure, network topology, and porosity effects on the mechanical properties of Zeolitic Imidazolate Frameworks. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 9938−9943. (9) Stratford, K. Colloidal Jamming at Interfaces: A Route to FluidBicontinuous Gels. Science (Washington, DC, U. S.) 2005, 309, 2198− 2201. (10) Herzig, E. M.; White, K. a.; Schofield, a. B.; Poon, W. C. K.; Clegg, P. S. Bicontinuous emulsions stabilized solely by colloidal particles. Nat. Mater. 2007, 6, 966−971. (11) Kim, E.; Stratford, K.; Adhikari, R.; Cates, M. E. Arrest of fluid demixing by nanoparticles: A computer simulation study. Langmuir 2008, 24, 6549−6556. (12) Lee, M. N.; Thijssen, J. H. J.; Witt, J. a.; Clegg, P. S.; Mohraz, A. Making a Robust Interfacial Scaffold: Bijel Rheology and its Link to Processability. Adv. Funct. Mater. 2013, 23, 417−423. G
DOI: 10.1021/acs.chemmater.6b00497 Chem. Mater. XXXX, XXX, XXX−XXX
