ARTICLE
Spontaneous Pattern Formation of Surface Nanodroplets from Competitive Growth Shuhua Peng,† Detlef Lohse,‡,§ and Xuehua Zhang*,†,‡ †
Soft Matter and Interfaces Group, School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, VIC 3001, Australia, ‡Physics of Fluids Group, Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, and § Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany
ABSTRACT Nanoscale droplets on a substrate are of great interest because of their
relevance for droplet-based technologies for light manipulation, lab-on-chip devices, miniaturized reactors, encapsulation, and many others. In this work, we establish a basic principle for symmetrical arrangements of surface nanodroplets during their growth out of oversaturated solution established through solvent exchange, which takes place under simple and controlled flow conditions. In our model system, nanodroplets nucleate at the rim of spherical cap microstructures on a substrate, due to a pulse of oversaturation supplied by a solvent exchange process. We find that, while growing at the rim of the microcap, the nanodroplets self-organize into highly symmetric arrangements, with respect to position, size, and mutual distance. The angle between the neighboring droplets is 4 times the ratio between the base radii of the droplets and the spherical caps. We show and explain how the nanodroplets acquire the symmetrical spatial arrangement during their competitive growth and why and how the competition enhances the overall growth rate of the nucleated nanodroplets. This mechanism behind the nanodroplet self-organization promises a simple approach to control the location of droplets with a volume down to attoliters. KEYWORDS: surface nanodroplets . self-organization . diffusive interaction . solvent exchange
P
atterns spontaneously emerge in nature over all length scales. Although not as precise as man-made structures, regular patterns occur from local chemical concentration gradients in the environment. For example, a seashell pattern is a response to the sea conditions,1,2 and the morphology of the sea floor is a record of the ice age glaciers.3 Plant-like structures of mineral precipitates form in chemical gardens.4,5 Recently highly complex designed crystal microstructures have been realized by precisely modulating chemical gradients as the reactions proceeded.6,7 Up to now, little research has been carried out to investigate spontaneous pattern formation of nanodroplets at the very early stage of their nucleation and growth. Such nanodroplet patterns, if formed, will have significant implications for a wide range of advanced technologies in light manipulation,810 high-throughput analysis and single bimolecular diagnosis,1113 miniaturized chemical reactors,13,14 or compartmentalized microcontainers for sequential PENG ET AL.
separation and detection processes.15 The regular nanodroplet patterns may also act as simple and effective precursors for ordered porous microstructures1619 and microparticles with unconventional shapes.20 In this work, we investigate the spontaneous pattern formation of nanodroplets in a process of diffusive-driven droplet growth. In heterogeneous nucleation theory, at least three stages can be identified in droplet nucleation and growth: the initial droplet nucleation on the sites characterized by their chemical and geometric properties, the growth of each individual nucleated droplet out of the surrounding, and the competition between growing droplets close by and subsequent diffusive interaction and possible merging.2127 We explore such diffusive interactions between evolving droplets to modulate their growth, following the inspiration from the regular pattern formation in nature.1,2 In our system, the evolution of an oil nanodroplet (e.g., dissolution or growth) modifies the local concentration profile of dissolved oil, imposing effects on VOL. 9
’
NO. 12
’
* Address correspondence to
[email protected]. Received for review July 17, 2015 and accepted October 26, 2015. Published online October 26, 2015 10.1021/acsnano.5b04436 C 2015 American Chemical Society
11916–11923
’
2015
11916 www.acsnano.org
ARTICLE Figure 1. Spherical cap microstructures on the substrate and the formation of nanodroplets by solvent exchange. (a) AFM topography image of microcaps. (b) Cross-sectional profiles of three representative caps. (c) Contact angle versus the microcap base diameter. (d) Sketch of the solvent exchange process on a microcap-decorated substrate. The flow direction was from left to right, as indicated by the arrow. The flow rate was 100 μL/min in all the experiments. (e) Sketch of three oversaturation pulses. The oil oversaturation ζ(t) depends on time t during the solvent exchange, and the maximal level of the pulse is determined by the oil concentration in the solutions.
the concentration gradient that are felt by the neighboring nanodroplets. Remarkably, spatially symmetric arrangements emerge from the competition among growing nanodroplets around a microcircle. To the best of our knowledge, this is the first time that spontaneous formation of nanodroplet patterns through diffusion is observed and quantified directly. RESULTS AND DISCUSSION The solid substrates in our experiments are decorated with micrometer-sized spherical caps (Figures 1ac). Three prevalent features of the substrate are essential for the nanodroplet nucleation. (i) The wettability of the droplet liquid on the immersed substrate and the shape of the microcaps were selected so that the droplets preferred to nucleate around the microcap rim rather than on the flat area, due to a low nucleation energy barrier.28,29 (ii) There is no difference for the droplet nucleation anywhere around the base circumference of the same cap and (iii) also little difference at the rim of different-sized caps, due to the comparable size (note that the curvature in azimuthal direction is dependent on the cap size) and very similar contact angle of these microcaps shown in Figures 1b and c. On this substrate, nanodroplets of a polymerizable oil were produced by the protocol of solvent exchange, shown in the schematic drawing in Figure 1d. The oil droplets nucleate all over the surface with preference at the rim of the microcaps. As reported recently,30 the nanodroplets grow from the oversaturation (also called supersaturation) pulse ζ(t) = c¥(t)/cs(t) 1, as the moving front passes by (see Figure 1e). Here, cs(t) is the oil solubility of the (exchanged) liquid and c¥(t) the oil concentration far away from the droplets. The size and arrangement of evolving nanodroplets were obtained by “freezing” them by polymerization at different times during the solvent exchange process (ti) or upon full completion (tf). PENG ET AL.
Figures 2ac show how one nanodroplet is situated on the cap rim at time tf. The SEM image shows that the nanodroplet is partly overlaid on the side of the microcap. How much the nucleated droplets “creep” on the microcap, i.e., the force balance in the radial direction, can be understood from the respective interfacial tensions between droplet, liquid, and surface and will be discussed in future work. We now examine the most intriguing configurations of multiple nanodroplets around one microcap, as shown in Figures 2di. The nanodroplets are produced from lower oversaturation levels, indicated by the blue and red saturation profiles in Figure 1e. The oversaturation level was controlled by the oil concentration in the first solution during the solvent exchange. In these cases the droplet number around the same-sized microcap increases with a decrease in the final nanodroplet size, resulting from a lower saturation level. For any given saturation level, the probability distribution function (PDF) of the droplet footprint sizes was obtained by analyzing their cross-sectional profiles in AFM images, as detailed in the Supporting Information. Figure 3a shows that the size distribution of nanodroplets at the rim is independent of the droplet number around a single cap. However, the nanodroplets on the rim are clearly larger than isolated droplets. This holds not only for one droplet per cap, but also for prior phases with N droplets per cap. We will show later in the paper that the larger size is a consequence of the competitive growth of the nanodroplets confined around the rim of the microcap. Remarkably, those droplets at the rim possess high symmetry in their spatial arrangement. We found that most frequently twin nanodroplets are aligned on a straight line across the center of the microcap, i.e., at two opposing poles. Triplets occupy the three ends of an equal-side triangle, while the quadruplets sit on the four corners of a square. The same spatial symmetry in VOL. 9
’
NO. 12
’
11916–11923
’
11917
2015 www.acsnano.org
ARTICLE Figure 2. Spatial arrangement of the nanodroplets around the microcap. (a, b) AFM and SEM images of one nanodroplet sitting on a microcap. (c) Notation of the nanodroplet and the microcap. (di) AFM images of multiple nanodroplets around one microcap. Symmetric N-gons with N = 2 (d, doublet), N = 3 (e, triplet), N = 4 (f, quadruplet), N = 5 (g, pentagon), N = 6 (h, hexagon), N = 7 (i, heptagon). Scale bar: 5 μm. These AFM images were taken on different microcaps at time tf, i.e., after the solvent exchange process was completed. Compared to panels (a) and (b), the oversaturation levels for the growth of these droplets were lower.
the location was also observed for N > 4 droplets in a unit: they form a regular N-gon, with high symmetry both in the azimuthal position and in the droplet size. The azimuthal characteristics of the droplets is quantified by measuring the angle spanned by the two lines through the centers of two adjacent nanodroplets and the cap. It is plotted as a function of the droplet number (N) in a unit in Figure 3b. For a given N, the angle scatters in a relatively narrow range around its average, which is φh = 2π/N by definition. This shows that the location of the nanodroplets relative to each other is solely determined by their total number around the microcap. Clearly, the growing nanodroplets in the same circle interact with each other, positioning themselves in a highly symmetrical spatial arrangement. Such symmetry allows the nanodroplets to acquire a maximal distance from each other while they are arrested at the microcap rim. This kind of spatial distribution is reminiscent of an animal circle around their feed, while each competes for the maximal amount of food, and indeed, here the growing droplets are fed, namely, out of the oil-oversaturated pulse. PENG ET AL.
How many nanodroplets a microcap rim can accommodate is determined by the cap size relative to the droplet size. Specifically, the actual number of nanodroplets in a unit increases with the ratio between the footprint radii of the cap and those of the nanodroplets, as shown in the plot in Figure 3c. Here three saturation levels were achieved by varying the initial solution concentration, and the images for the analysis were taken at time tf, i.e., after completion of the solvent exchange. The red points were from the lowest oversaturation level, and the black from the highest, with the blue in between, corresponding to the colors of the oversaturation pulses sketched in Figure 1e. The average slope obtained from linear fittings for three oversaturation levels was ∼0.62. Remarkably, this slope is universal, followed by all nanodroplets that were produced at all different saturation levels at the final time (tf). The linear relations of Figure 3c and their slopes can readily be understood from an estimate of the lateral space a nanodroplet of radius r requires (in Figure 3d): This is 4r, namely, the diameter of 2r plus concentration boundary layers of width r on each side, which is the appropriate concentration boundary layer width VOL. 9
’
NO. 12
’
11916–11923
’
11918
2015 www.acsnano.org
ARTICLE Figure 3. Size and spatial symmetry of nanodroplets at the rim. (a) PDF for the footprint diameter of the isolated droplets and droplets at the rim from the same saturation level. The droplet number per cap is indicated in the inset by the same color. (b) Angles between two nanodroplets as a function of the droplet number N. The definition of the angle for a given droplet number per microcap is shown in the inset. (c) Plot of the ratio between the footprint radii R of the microcaps and the radii r of the droplets as a function of N. The droplets were produced at three saturation levels, where the red points are from the lowest oversaturation level and the black from the highest, with the blue in between. (d) Sketch of the boundary layer of growing droplets.
around a cylinder for low flow rates as applicable in our experiments. (For large flow rates the boundary layers become smaller.30) As the circumference around the microcap equals 2πR, we have space for N = 2πR/(4r) drops, implying φh ¼
2π r 4 N R
(1)
or R/r ≈ (2/π)N ≈ 0.64N, just as seen in Figures 3(b) and (c). To understand how these symmetric configurations evolve during the droplet growth, we first examine the droplet formation in situ. Figure 4a shows the time course snapshots at different stages during the solvent exchange. (In situ movies are provided in the Supporting Information.) Initially, many tiny droplets form at the rim, and all of them grow simultaneously as the solvent exchange proceeds. The time scale for the evolution of the droplet size is on the order of minutes, implying a quasi-static growth driven by diffusion. For a detailed morphological characterization of the growing nanodroplets, they were polymerized at different intermediate times (ti) of the solvent exchange. The AFM image at t1 shown in Figure 4 reveals the spatial arrangement of nanodroplets at a very early stage of their growth when their volume was as small as ∼2 attoliters. As soon as these nanodroplets were observed, they are already in a highly symmetrical configuration. Throughout the solvent exchange process, the angles between two neighbor droplets remain close to the average value φh = 2π/N, as shown in PENG ET AL.
Figure 5a, while N decreases with time. Therefore, the symmetry in the droplet location is already acquired at the initial stage of the droplet formation and is maintained throughout the whole growth process. As for the droplets around the same microcap, their size is not perfectly the same, as shown in Figures 5b and c. The plot shows the average of two angles formed by a droplet with its two neighbors as a function of the ratio between the droplet radius r and the microcap radius R. The angle increases linearly with the ratio r/R, following a slope of 3.99, close to the value 4 suggested by eq 1. To account for the observed patterns of growing nanodroplets, we assume that all droplets start to nucleate and grow at the same time, roughly when the liquid around the microcaps starts to be oil-oversaturated. The average size of the nanodroplets on the rim is determined by the local oversaturation level and the duration, just as it holds for droplets on the flat area. We assume that the interaction between the droplets is purely given by diffusion, either through the bulk liquid or through diffusion along the surface.31 Additional electrostatic interaction between the droplets may be important when the droplets are very small and closely spaced. The reason for the potential electrostatic interaction is that the oilwater interface is charged,32 leading to mutual droplet repulsion, analogous to the interactions among periodic domains in phospholipid monolayers elaborated in refs 3336. As long as the droplets in the circle are far away from each other, the local oversaturation level is externally given. However, VOL. 9
’
NO. 12
’
11916–11923
’
11919
2015 www.acsnano.org
ARTICLE Figure 4. Morphological characteristics of growing nanodroplets. (a) Optical images of growing nanodroplets. The blue dots on the sketch correspond to the location of the nanodroplets resolved in the images. (b) AFM images of growing nanodroplets at different times. t1 ≈ 5 s, t2 ≈ 20 s, t3 ≈ 40 s, and tf ≈ 200 s (i.e., after completion of the solvent exchange). The insets are representative AFM images of nanodroplets around a microcap with R = 5 μm. The droplet volume at t1 is around 2 attoliters. Scale bars are 20 and 4 μm (insets), respectively.
once the drops have grown large enough, they will start to interact with each other through their respective concentration fields, namely, once their distance (from center to center) becomes on the order of the sum of their diameters. As the size of the droplets at the rim is not exactly the same, the coarsening process sets in.37 Smaller nanodroplets become the victims, due to a larger Laplace pressure around them and thus the larger oversaturation at their edge. Thus, larger neighboring droplets will grow toward the smaller ones and “cannibalize” them, filling the emerging gap; see the sketch in Figure 5d. In other words, the center of the larger droplet shifts toward the small droplet victims; hence the symmetry of the spatial arrangement is maintained while the droplet number decreases. This pattern formation process is similar to the coarsening of compartmentalized shaken granular matter.38 The diffusive interactions among droplets in a circle can also explain why the droplets growing in competition are larger than the isolated ones shown in Figure 3a. Exposed to an enhanced local concentration gradient, the droplets at the rim can scavenge more from their neighboring droplets that are later “cannibalized” by diffusion and Ostwald ripening. This enhanced growth by competition is also reflected by the growth rate in Figure 6a, where we show the PENG ET AL.
probability distribution functions of the droplet sizes for the four different times shown in Figure 4b: The sizes of the droplets at the rims are initially almost the same as those of the isolated ones. The size difference occurs only later and increases with time. (In principle, there is a possibility that earlier nucleation of droplets on the rim may contribute to the larger droplet size. However, the difference between the droplet size on the rim and that on flat areas is not obvious at the initial stage t1. Clearly, the preferential or early growth of droplets on the rim cannot be the main cause for the larger final size on the rim.) This also becomes clear from the time dependence of the mean droplet size: While the size of the isolated droplets scales with r(t) ∼ t0.30, i.e., with an exponent close to the 1/3 exponent suggested by Lifshitz and Slyozov23 for Ostwald ripening, the droplets at the rim grow faster, namely, with r(t) ∼ t0.38 (see Figure 6b and c). Figure 6d shows the time evolution of the droplet number N(t) at the rim of the same-sized microcap (R ≈ 5 μm), which indeed scales as N(t) ∼ 1/r(t) ∼ t0.38, as eq 1 suggests. CONCLUSIONS In conclusion, we have shown that surface nanodroplets spontaneously form highly symmetrical arrangements during the droplet growth around a microcap VOL. 9
’
NO. 12
’
11916–11923
’
11920
2015 www.acsnano.org
ARTICLE Figure 5. Symmetry of evolving nanodroplets. (a) Plot of the angle between the nanodroplets at three intermediate times (t1 < t2 < t3) of the solvent exchange versus the droplet number per microcap. The preferred angle is 2π/N, labeled by the bars. (b) AFM image of nine droplets around a cap and the two angles associated with a given droplet. The angle φhi is φhi = (φi þ φiþ1)/2 with cyclic permutations. (c) Plot of the angles φh defined in (b) as a function of the ratio r/R. (d) Illustration of the dynamics process of the droplet cannibalization during the competitive growth. The initial location of three droplets (1, 2, and 3) is indicated with the blue solid circles, and they evolve into positions indicated with black dotted circles. The victim droplet is droplet 3, and the cannibalizer is droplet 1.
Figure 6. Enhanced growth rate from the competition. (a) PDFs of the footprint radius r of isolated droplets (dashed lines) and droplets at the rim of the microcaps (solid lines) at different solvent exchange times ti shown in AFM images in Figure 4b. The colors of the curves correspond to different times during the solvent exchange process. Black for t1, red for t2, blue for t3, and pink for tf. The standard deviation of the droplets at times t1, t2, and t3 is 0.16, 0.26, and 0.34 μm for the isolated droplets and 0.20, 0.29, and 0.38 μm for the droplets at the rim. (b and c) Double logarithmic plots of the mean droplet diameter 2r(t) for droplets growing on the rim (b) and for isolated droplets (c) as a function of the solvent exchange time. Note the considerable error bar in determining the passing time of the front, which varies from droplet to droplet. (d) Number of droplets N on the rim as a function of solvent exchange time. The microcap radius R was fixed at ∼5 μm. In (b), (c), and (d) it is seen that the solvent exchange process was completed at ∼200 s. From then on the droplets do not further grow; that is, their sizes became constant. PENG ET AL.
VOL. 9
’
NO. 12
’
11916–11923
’
11921
2015 www.acsnano.org
location, and distance and (ii) an enhanced growth rate, as compared to isolated droplets on the flat area. The basic principle for the nanodroplet pattern formation observed and quantified directly for the first time in this work is universal in nature, providing opportunities for nanodroplet patterning in simple flow conditions.
METHODS
and D.L. from the NWO MCEC program and from an ERC Advanced Grant. We thank Shuying Wu for technical assistance in SEM imaging. We thank Helmuth Moehwald for very stimulating discussion.
Chemicals. Octadecyltrimethylchlorosilane (OTS, >90%), polymerizable oil (1,6-hexanediol diacrylate, HDODA), and photoinitiator (2-hydroxy-2-methylpropiophenone, HMPP) were purchased from Sigma-Aldrich. Organic solvents including chloroform (AnalaR), toluene (AnalaR), and ethanol (100%) were from Merck Pty Ltd. All chemicals were used without further purification unless otherwise specified. Preparation of Spherical Cap Microstructures on Substrates. The flat OTS-Si was prepared by following the procedure in the literature.39 The spherical cap microstructures were prepared by the protocol of ref 10. In brief, they were obtained by photopolymerization of the HDODA microdroplets on a flat OTS-Si substrate and served as the microstructures to nucleate the surface nanodroplets. Both microcaps and the flat background area were coated homogeneously with the same material, the physical roughness of which was on the order of 2 nm. The height of the microcaps is less than 0.5 μm. The macroscopic advancing and receding contact angles of the droplets on the flat immersed substrate were 26 and 18, respectively. The contact angle of the oil droplet is around 7 on the flat substrate in water. Solvent Exchange to Produce Surface Nanodroplets. The solvent exchange was applied on the substrate decorated with spherical cap microstructures. The substrate was placed inside a narrow fluid channel (0.33 mm), where the flow rate was constant in all experiments (∼100 μL/min). To prepare the solution, the polymerizable oil HDODA was first dissolved in a 50 vol % ethanol aqueous solution (a good solvent) with different concentrations (i.e., 2, 3, and 4 vol %). The monomer concentrations in the first solution were 2, 3, and 4 vol %, corresponding to three saturation levels (red, blue, and black lines) in the sketch in Figure 1e. The above mixture was then displaced by water (a poor solvent). During the solvent exchange process, an oil-oversaturation pulse induces the nucleation of oil nanodroplets on the surface and subsequent growth as the oil-rich solution is displaced by an oil-insoluble liquid.30,39 The final droplet size at the completion of the solvent exchange is mediated by the initial oil concentration in the first solution. The second solution was injected at a flow rate of 100 μL per min. Solution B was entirely replaced at time tf ≈ 200 s, beyond which the droplet size did not change with further extension of the exchange time. Characterization. At different times during the solvent exchange process or upon full completion (tf), the substrate was exposed to UV to photopolymerize the nanodroplets for characterization. The polymerized microdroplets were imaged in air by using an MFP-3D atomic force microscope (Asylum Research, Santa Barbara, CA, USA). The cross-sectional profiles of the polymerized droplets were extracted from the AFM topography images. Scanning electron microscopy (SEM) analysis was performed using a FEI Nova NanoSEM, equipped with an Oxford X-MaxN 20 energy dispersive X-ray detector, operating at 15 kV and a 5 mm working distance. Samples were coated with about 5 nm Au before imaging. Conflict of Interest: The authors declare no competing financial interest. Acknowledgment. X.H.Z. acknowledges the support from the Australian Research Council (FT120100473, DP140100805, NWO MCEC program), S.P. from an ARENA Research Fellowship,
PENG ET AL.
ARTICLE
on the substrate. The droplet number around the rim and the mean angle between neighboring droplets are universally determined by the ratio between the microcap radius and the droplet radius. The spatial arrangements of the nanodroplets emerge through diffusive interactions between evolving droplets, which results in (i) high symmetry with respect to size,
Supporting Information Available: The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b04436. Additional figures (PDF) Movie (AVI)
REFERENCES AND NOTES 1. Ball, P. The Self-Made Tapestry: Pattern Formation in Nature; OUP Oxford: Oxford, 2001. 2. García-Ruiz, J. M.; Melero-García, E.; Hyde, S. T. Morphogenesis of Self-Assembled Nanocrystalline Materials of Barium Carbonate and Silica. Science 2009, 323, 362–365. 3. Crowley, J. W.; Katz, R. F.; Huybers, P.; Langmuir, C. H.; Park, S.-H. Glacial Cycles Drive Variations in the Production of Oceanic Crust. Science 2015, 347, 1237–1240. 4. Haudin, F.; Cartwright, J. H. E.; Brau, F.; De Wit, A. Spiral Precipitation Patterns in Confined Chemical Gardens. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 17363–17367. 5. Nagatsu, Y.; Ishii, Y.; Tada, Y.; De Wit, A. Hydrodynamic Fingering Instability Induced by a Precipitation Reaction. Phys. Rev. Lett. 2014, 113, 024502. 6. Noorduin, W. L.; Grinthal, A.; Mahadevan, L.; Aizenberg, J. Rationally Designed Complex, Hierarchical Microarchitectures. Science 2013, 340, 832–837. 7. Steinbock, O. Complexity from Precipitation Reactions. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 17346–17347. 8. Wang, Z.; Guo, W.; Li, L.; Luk'yanchuk, B.; Khan, A.; Liu, Z.; Chen, Z.; Hong, M. Optical Virtual Imaging at 50 nm Lateral Resolution with a White-light Nanoscope. Nat. Commun. 2011, 2, 218. 9. Chen, Y.; Elshobaki, M.; Gebhardt, R.; Bergeson, S.; Noack, M.; Park, J.-M.; Hillier, A. C.; Ho, K.-M.; Biswas, R.; Chaudhary, S. Reducing Optical Losses in Organic Solar Cells using Microlens Arrays: Theoretical and Experimental Investigation of Microlens Dimensions. Phys. Chem. Chem. Phys. 2015, 17, 3723–3730. 10. Zhang, X. H.; Ren, J. M.; Yang, H. J.; He, Y. H.; Tan, J. F.; Qiao, G. G. From Transient Nanodroplets to Permanent Nanolenses. Soft Matter 2012, 8, 4314–4317. 11. Ziauddin, J.; Sabatini, D. M. Microarrays of Cells Expressing Defined cDNAs. Nature 2001, 411, 107–110. 12. Flaim, C. J.; Chien, S.; Bhatia, S. N. An Extracellular Matrix Microarray for Probing Cellular Differentiation. Nat. Methods 2005, 2, 119–125. 13. Hong, J.; Edel, J. B.; deMello, A. J. Micro- and Nanofluidic Systems for High-Throughput Biological Screening. Drug Discovery Today 2009, 14, 134–146. 14. Shao, N.; Jiang, S.-M.; Zhang, M.; Wang, J.; Guo, S.-J.; Li, Y.; Jiang, H.-W.; Liu, C.-X.; Zhang, D.-B.; Yang, L.-T.; Tao, S.-C. MACRO: A Combined Microchip-PCR and Microarray System for High-Throughput Monitoring of Genetically Modified Organisms. Anal. Chem. 2014, 86, 1269– 1276. 15. Guo, M. T.; Rotem, A.; Heyman, J. A.; Weitz, D. A. Droplet Microfluidics for High-Throughput Biological Assays. Lab Chip 2012, 12, 2146–2155.
VOL. 9
’
NO. 12
’
11916–11923
’
11922
2015 www.acsnano.org
PENG ET AL.
39. Zhang, X.; Ducker, W. Formation of Interfacial Nanodroplets through Changes in Solvent Quality. Langmuir 2007, 23, 12478–12480.
VOL. 9
’
NO. 12
’
11916–11923
’
ARTICLE
16. Connal, L.; Qiao, G. Preparation of Porous Poly(dimethylsiloxane)-Based Honeycomb Materials with Hierarchal Surface Features and Their Use as Soft-Lithography Templates. Adv. Mater. 2006, 18, 3024–3028. 17. Mendez-Vilas, A.; Jodar-Reyes, A. B.; Gonzalez-Martin, M. L. Ultrasmall Liquid Droplets on Solid Surfaces: Production, Imaging, and Relevance for Current Wetting Research. Small 2009, 5, 1366–1390. 18. Hernandez-Guerrero, M.; Stenzel, M. H. Honeycomb Structured Polymer Films via Breath Fgures. Polym. Chem. 2012, 3, 563–577. 19. Mu~ noz-Bonilla, A.; Fernández-García, M.; Rodríguez-Hernández, J. Towards Hierarchically Ordered Functional Porous Polymeric Surfaces Prepared by the Breath Figures Approach. Prog. Polym. Sci. 2014, 39, 510–554. Topical Issue on Composites. 20. Kraft, D. J.; Hilhorst, J.; Heinen, M. A. P.; Hoogenraad, M. J.; Luigjes, B.; Kegel, W. K. Patchy Polymer Colloids with Tunable Anisotropy Dimensions. J. Phys. Chem. B 2011, 115, 7175–7181. 21. Epstein, P. S.; Plesset, M. S. On the Stability of Gas Bubbles in Liquid-Gas Solutions. J. Chem. Phys. 1950, 18, 1505– 1509. 22. Lohse, D.; Zhang, X. Surface Nanobubbles and Nanodroplets. Rev. Mod. Phys. 2015, 87, 981–1035. 23. Lifshitz, I.; Slyozov, V. The Kinetics of Precipitation from Supersaturated Solid Solutions. J. Phys. Chem. Solids 1961, 19, 35–50. 24. Viovy, J. L.; Beysens, D.; Knobler, C. M. Scaling Description for the Growth of Condensation Patterns on Surfaces. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 37, 4965–4970. 25. Rogers, T. M.; Elder, K. R.; Desai, R. C. Droplet Growth and Coarsening during Heterogeneous Vapor Condensation. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 5303–5309. 26. Narhe, R. D.; Beysens, D. A. Nucleation and Growth on a Superhydrophobic Grooved Surface. Phys. Rev. Lett. 2004, 93, 076103. 27. Widawski, G.; Rawiso, M.; Francois, B. Self-Organized Honeycomb Morphology of Star-Polymer Polystyrene Films. Nature 1994, 369, 387–389. 28. Nowakowski, B.; Ruckenstein, E. A Kinetic Treatment of Heterogeneous Nucleation. J. Phys. Chem. 1992, 96, 2313– 2316. 29. Qian, M.; Ma, J. Heterogeneous Nucleation on Convex Spherical Substrate Surfaces: A Rigorous Thermodynamic Formulation of Fletcher's Classical Model and the New Perspectives Derived. J. Chem. Phys. 2009, 130, 214709. 30. Zhang, X.; Lu, Z.; Tan, H.; Bao, L.; He, Y.; Sun, C.; Lohse, D. Formation of Surface Nanodroplets under Controlled Flow Conditions. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 9253–9257. 31. Steyer, A.; Guenoun, P.; Beysens, D.; Knobler, C. M. Growth of Droplets on a Substrate by Diffusion and Coalescence. Phys. Rev. A: At., Mol., Opt. Phys. 1991, 44, 8271–8277. 32. Beattie, J. K.; Gray-Weale, A. Oil/Water Interface Charged by Hydroxide Ions and Deprotonated Fatty Acids: A Comment. Angew. Chem., Int. Ed. 2012, 51, 12941–12942. 33. Miller, A.; Knoll, W.; Möhwald, H. Fractal Growth of Crystalline Phospholipid Domains in Monomolecular Layers. Phys. Rev. Lett. 1986, 56, 2633–2636. 34. Miller, A.; Moehwald, H. Diffusion Limited Growth of Crystalline Domains in Phospholipid Monolayers J. Chem. Phys. 1987,86.4258 35. Helm, C. A.; Moehwald, H. Equilibrium and Nonequilibrium Features Determining Superlattices in Phospholipid Monolayers. J. Phys. Chem. 1988, 92, 1262–1266. 36. Moehwald, H. Phospholipid and Phospholipid-Protein Monolayers at the Air/Water Interface. Annu. Rev. Phys. Chem. 1990, 41, 441–476. 37. Marqusee, J. A.; Ross, J. Theory of Ostwald Ripening: Competitive Growth and Its Dependence on Volume Fraction. J. Chem. Phys. 1984, 80, 536–543. 38. van der Meer, D.; van der Weele, K.; Lohse, D. Coarsening Dynamics in a Vibrofluidized Compartmentalized Granular Gas. J. Stat. Mech.: Theory Exp. 2004, 4, P04004.
11923
2015 www.acsnano.org
