Article pubs.acs.org/Langmuir
Spatial Ordering of Colloids in a Drying Aqueous Polymer Droplet Erkan Senses,† Matthew Black,‡ Thomas Cunningham,† Svetlana A. Sukhishvili,§ and Pinar Akcora*,† †
Department of Chemical Engineering and Materials Science, Stevens Institute of Technology, Hoboken, New Jersey 07030, United States ‡ Department of Bioengineering, University of Maryland, College Park, Maryland 20742, United States § Department of Chemistry, Chemical Biology and Biomedical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030, United States S Supporting Information *
ABSTRACT: We explore the role of polymer chains on deposition of colloidal particles at solid surfaces from drying aqueous drops and show that the kinetics of phase separation of colloids and polymers can be explained by spinodal decomposition of binary systems. Concentrations of polymer solutions and polymer chain lengths were varied to understand the aggregation dynamics of colloidal particles via a polymer bridging mechanism. We show that when polymer concentration in the droplet is increased, particles spatially order upon drying due to a combination of the phase separation of highly bridged particles and the Marangoni flow effect. The demonstrated effect of particle-adsorbing, water-soluble polymers on the coffee-ring formation opens up new ways of creating highly ordered, long-range patterned surfaces using a facile, template-free approach.
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the outward flow moves the polymer chains from the center to the edges, resulting in the formation of thicker coffee rings.7 In this study, we demonstrate that flow-controlled concentration profiles can be used to deposit colloidal particles as ordered patterns. The process of drying a drop of polymer solution is used in inkjet printing14,15 and holds a critical role in controlling the particle deposition; the particles can influence the velocity fields in a drying droplet. In the case of solution mixtures of colloidal particles and nonadsorbing polymers at concentrations below the critical overlap concentration of polymer coils (denoted c*), competition between the colloidrich and polymer-rich phases has been shown to result in spontaneous demixing (spinodal decomposition).16−19 In this work, we study the effect of water-soluble, adsorbing polymer chains on patterns of colloidal particle deposition during solvent evaporation. The coffee-ring concept is applied to dispersions of colloidal particles in polymer solution, and polymer chain length and concentration are shown to be important factors controlling the particle deposition. We experimentally report, for the first time, the kinetics of phase separation within Marangoni eddies near the contact line. Drying of aqueous dispersions of colloidal poly(styrene) (PS) microbeads in poly(N-vinylpyrrolidone) (PVP) solutions produced a unique flow-driven, spatially ordered, colloid-rich and polymer-rich phases near the droplet edge. The kinetics of
INTRODUCTION Bare colloidal particles in aqueous solutions tend to deposit on hydrophilic substrates nonuniformly, typically leaving a ringshaped pattern. The formation of so-called “coffee rings” in colloidal suspensions is attributed to a combined effect of pinning of the contact line and an increased evaporation flux near the droplet edge.1−3 The resulting outward capillary flow drags colloidal particles from the center of the drying droplet to its perimeter, resulting in an increased particle concentration next to the droplet edge. The coffee-ring phenomenon has been widely studied since the last decade, and various evaporationinduced structures have been successfully demonstrated in colloidal systems.4−9 The effect of the particle shape on droplet evaporation has also been investigated.10,11 For example, when micrometer size ellipsoids rather than spheres were used, the capillary outward flow effect could be eliminated.10 Colloidal particles carried to the air/water interface can “feel” the strong long-range interactions between anisotropic particles deforming the interface, and uniformly distributed particles are obtained.10 The coffee-ring effect can also be suppressed by using electrowetting12 or by depositing smaller droplets to achieve faster liquid evaporation.6 It has been found that when the solvent evaporation is faster than the particle movement, the ring formation stops.6 This phenomenon has been used to deposit uniform, closely packed monolayers of nanoparticles at solid surfaces.5 The capillary flow effect has also been employed in a confined environment (a sphere contacting a flat surface) to form regular lines or patterns of quantum dots.13 On the other hand, for particle-free polymer droplets, it was shown that © XXXX American Chemical Society
Received: January 4, 2013 Revised: January 28, 2013
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Figure 1. (a) Chemical formula of PVP and schematic representations of dispersed and aggregated PS beads (0.1 vol %) in low and high PVP concentrations. (b) Dynamic light scattering results and ζ-potential measurements for PS beads in PVP solutions in water prepared at different concentrations and molecular weights of PVP.
potential of PS particles with increased PVP concentrations. It is seen that the higher the molecular weight of PVP, the stronger the polymer effect on both hydrodynamic size and ζ potential of dispersed PS beads. For the shortest PVP chains (Mw = 2.5 and 55 kg/mol), colloidal dispersions remain stable and particles do not aggregate, as indicated by the DLS measurements (Figure 1b). At the same time, the initial highly negative ζ-potential value of PS particles in the absence of a polymer (−60 mV) becomes less negative in PVP solutions. This is indicative of adsorption of PVP at the surface of PS particles, resulting in effective steric stabilization of colloidal dispersion. Note that the PVP concentration required for a monolayer particle coverage is estimated to be 0.01 mg/mL using the equation, cads = (3/ πNA)(ϕMw)/(RRg2), where NA is Avogadro’s number, ϕ the volume concentration of the spheres (ϕ = 0.001), R and Rg refer to the radius of colloidal spheres and the radius of gyration of polymer coils in solution, with the assumption that after binding with the colloidal particle polymer coils remain unperturbed. Hydrodynamic size (Rh) as determined from DLS was used to predict Rg. For all molecular weights, the ζ potential of PVP-coated PS particles saturated at concentrations significantly exceeding that required for a monolayer coverage of PS particles with polymer chains.20 Larger changes in the hydrodynamic diameter and ζ potential of PS particles occur when the molecular weight of PVP was increased to 360 and 1300 kg/mol. One possible explanation of the particle aggregation is the depletion effect,21 but this effect should be significantly suppressed in the case of the sterically stabilized colloidal dispersions studied here. Note also that the critical overlap concentration of polymer coils for 2.5, 55, 360, and 1300 kg/mol PVP was determined to be ∼1000, 100, 2, and 0.2 mg/mL, respectively using c* = (3/4πNA)(Mw/Rg3). Beyond c*, the volume fraction of polymer chains exceeds the volume fraction of monomers inside each isolated coil, and the polymer coils start interpenetrating by forming a transient network (entanglement).22 Thus, the observed onset of aggregation of PS beads in solutions of higher molecular weight PVP occurs at c > c* and, therefore, is likely to be due to the bridging effect of the entangled polymers. For the purpose of this study, we
phase separation, studied by video microscopy and Fourier transform analysis of time-resolved images, suggest that the early stages of phase growth can be quantitatively described by spinodal decomposition kinetics.
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EXPERIMENTAL PROCEDURE
Solution Preparation. We performed the experiments with aqueous suspension of colloidal polystyrene (PS) particles with diameters of 1000 ± 50 nm purchased from Polysciences Inc. The particle size distributions were verified by using dynamic light scattering (DLS) and determined to be 1041 ± 14 nm. PS bead concentration was fixed at 0.1 vol %. Water-soluble PVP (Mw = 2.5, 55, 360, and 1300 kg/mol) was purchased from Sigma Aldrich and used as received. Polymers were dissolved in deionized (DI) water (18.2 MΩ, Direct-Q Millipore), and the suspensions of PS-beads were mixed with a vortex mixer for ∼2 h. Measurements and Data Analysis. The hydrodynamic sizes of samples at different concentrations and molecular weights were monitored by dynamic light scattering (DLS) using a Zetasizer NanoZS (Malvern, Inc.) at 25 °C. Zeta potentials were obtained from electrophoretic mobility values measured with a Zetasizer Nano-ZS using the Smoluchowski approximation. All measurements were repeated three times on separately prepared solutions. Precleaned glass slides (Ted Pella Inc.) were further sonicated in DI water for 10 min and rinsed several times to obtain dust-free surfaces. Cleaned wafers were completely wettable by DI water. Contact angle experiments were performed using a goniometer (KVS Instruments) in a closed chamber. Average contact angles were determined from measurements with five separate sessile droplets on clean glass substrates. The droplet volumes were ∼0.05 μL, resulting in a droplet diameter of 1−3 mm. Optical images and real time videos were recorded by a Nikon OPTIPHOT 2 POL optical microscope in transmission mode at magnifications ranging from 5 to 140×. The grayscale intensities were obtained using Image-J and the Fourier transform analysis of the line intensities was performed using FastFourier Transform (FFT) in MATLAB.
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RESULTS AND DISCUSSION We first studied the stability of colloidal dispersions of PS beads in the presence of the polymer. The chemical formula of PVP and the effect of polymer concentration on aggregation of PS beads are schematically presented in Figure 1a. Figure 1b shows evolution of the hydrodynamic diameter and the zeta (ζ) B
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Figure 2. (a) Deposition of PS beads (0.1 vol%) from 55 kg/mol PVP aqueous solutions at varying concentrations (0−5 mg/mL). (b) The normalized inverted grayscale intensities along the radial lines. The width of the peaks shows that the ring thickness increases with the polymer solution concentration, resulting in more uniform deposition. (c) A closer look at the particle deposition without and with PVP near the droplet edge.
focused on 55 kg/mol PVP solutions, which enable working with high particle and polymer concentrations in the region c < c*, where demixing can easily occur. Other molecular weights of PVP, lower and higher than 55 kg/mol, will be used to compare the results. Figure 2a presents optical images and normalized grayscale intensities of the PS beads deposited from 55 kg/mol PVP solutions. The inverse of the grayscale in the transmission mode of the optical microscope is proportional to the transmitted light intensity and allows estimating the width of the ring.23 In the absence of PVP, the PS beads closely pack at the pinned contact line, demonstrating a classical coffee ring deposition scenario. When PVP is added to the solution, the ring thickness is monotonically increased up to PVP concentration of 5 mg/mL. A previous study by Cui et al.24 suggested that with the addition of hydrosoluble polymers such as PEO and PVP, the viscosity increase opposes the capillary flow and results in suppression of the coffee-ring formation. While this hypothesis is intuitively valid for our PVP system, we suggest that local bridging of the adsorbed chains can provide an additional resistance to the radial flow. A closer look at the optical microscope images of the contact line shows that with the PVP addition, the PS beads are loosely packed next to the edge. We suggest that entanglement of adsorbed chains with free polymers facilitates depinning, which leads to more uniform particle deposition at high polymer concentrations. Because of the movement of the three-phase line toward the center, concentration of the deposited particles at the edge increases as shown in the optical images for 2 mg/mL PVP solutions (Figures 2, panels a and b). In 5 mg/mL PVP solutions, concentric rings are observed due to discontinuities
in the motion of the contact line due to its pinning and depinning. When the concentration of 55 kg/mol PVP is further increased to 10 mg/mL, a unique, highly periodic radial deposition of the colloids occurred (Figure 3). High-
Figure 3. Drying of aqueous mixtures of PS beads (0.1%) and 55 kg/ mol PVP (10 mg/mL): radial stripes developed at the periphery, and aggregates observed in the center.
magnification images taken from the boxed areas show aggregation at the central region and a periodic radial pattern elsewhere. Because solutions become highly concentrated at late stages of evaporation, aggregated particles are jammed in the center. We will discuss the formation of unusual ordered radial patterns in the next section. C
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To further elucidate the chain length effect on capillary flow, we prepared colloidal solutions with different molecular weights of PVP. Figure 4 shows the different deposition patterns
suggesting that the chain-length-dependent polymer mobility controls the flow-induced patterns during droplet evaporation. Importantly, with 55 kg/mol PVP solutions, at concentrations well below the overlap concentration (100 mg/mL), we observed the formation of unusual radial periodic patterns. Figure 6 shows an intermediate time of evaporation after
Figure 6. A snapshot of the evaporating droplet: the contact line moves toward the center, and particles circulate at the contact line, depositing within radially oriented stripes. The circulation region in the contact line and the arrow showing the direction of contact line movement are depicted schematically.
Figure 4. Deposition of PS beads (0.1 vol%) from 10 mg/mL PVP solutions of different molecular weights.
depinning (tdepin < t < tdry), where ordered colloid-rich and polymer-rich phases move toward the center of the droplet. The phase separation patterns are highly stable and persist over long distances (typically millimeters), as new particles join in the circulation region and a fraction of them are being deposited as the contact line recedes. Movie S1 of the Supporting Information visualizes the motion of the phaseseparated region and is highly recommended to the reader. Next, we monitor the development of droplet patterns. Figure 7a presents snapshots taken at different times during early stages of evaporation from 10 mg/mL of 55 kg/mol PVP solutions (see Movie S2 of the Supporting Information). It is seen that particles started to circulate by Marangoni eddies after the pinning of the contact line by 3−4 rows of close-packed PSspheres. The concentration fluctuations increased within the first 20−25 s of evaporation, giving rise to directional phase separation along the contact line. We calculated the inverted grayscale intensity along the yellow line (in-line with the contact boundary) to better visualize the growth in amplitude and periodicity of the stripes. As the particles are forced to circulate in the narrow region, the frequency of collisions increases and particles aggregate due to the bridging effect of the adsorbed polymer. In time, more particles collide with these aggregates, and the system eventually phase separates. Two main reasons might account for the stability of this phase separation. First, there is an ultralow interfacial tension between the polymer and polymer-coated particles, which scales as γ ∼ kBT/d2, where d is particle diameter and kB is the Boltzmann constant.25,26 With d = 1 μm and T = 298 K, γ is estimated to be ∼0.004 μN/m. The corresponding capillary length estimated from L = (γ/Δρg)1/2 gives ∼2 μm, assuming that Δρ = 120 kg/ m3. This value is close to the periodicity of the patterns, suggesting that the capillary waves might play a role in this type of phase separation. Furthermore, when the polymer and particles are phase separated, there is a surface tension gradient which may drive local transverse Marangoni flow from polymer-rich (low surface tension) to particle-rich (high surface tension) domains. This local Marangoni flow effect
obtained. For 2.5 kg/mol PVP, “treelike” ring-shaped patterns occur due to pinning−depinning of the contact line caused by Marangoni eddies. Still et al.23 reported similar structures of micrometer-sized PS beads observed after addition of a SDS surfactant. They showed that the concentration gradient of SDS next to the contact line and the outward capillary flow, a result of pinning, resulted in Marangoni eddies. We observe here that a similar effect is caused by 2.5 kg/mol PVP: an increase in polymer concentration near the edge results in a surface tension gradient, which then generates the Marangoni eddies. Such short and highly mobile polymer chains are unable to bridge the particles, and the drying droplet behavior is similar to that observed with a simple short-chain surfactant. For highmolecular weight polymers (360 and 1300 kg/mol PVP), uniform particle deposition is observed. As the c* concentration is readily exceeded in their concentrated solutions, polymer mobility becomes restricted and capillary flow effects diminish. In addition, we prepared mixtures of solutions containing two different molecular weights (Figure 5). The treelike structures in the outer region and radial stripes in the center are observed,
Figure 5. Deposition profile of PS beads evaporated from a mixture of 2.5 and 55 kg/mol PVP 10 mg/mL solutions (1:10 by volume). The stripes are formed at the central region, while tree-ring structures are seen at the outer regions. D
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Figure 7. (a) Top view of the droplet edge showing a real-time development of periodic patterns in a droplet containing PS beads (0.1 vol %) and 10 mg/mL PVP (55 kg/mol) solution. (b) Inverted grayscale intensity (proportional to particle density) determined along the yellow line (shown in a), indicating growth of periodic patterns from small concentration gradients. The intensity curves are shifted for better visualization. (c) Schematic representation of the phase separation and the formation of spinodal-like patterns: a small concentration fluctuation along the angular direction creates polymer-rich and particle-rich regions. Marangoni flow occurs from the polymer-rich (low surface tension) to the particle-rich (high surface tension) regions.
Figure 8. (a) Fourier transform (FT) of the intensity profiles presented in Figure 7b. The system becomes ordered with a periodicity equivalent to 10 particle sizes (10 μm). (b) The FT intensity (a measure of particle concentration) at this periodicity presents an exponential growth in time until the contact line depins. This behavior is similar to the phase growth on spinodal decomposition at the early stages of the transformation. After depinning, the amplitude growth stops suggesting that pinning is required for eddy formation. (c) The average particle concentration is constant with time, implying that more particles are joining the circulation region.
separation in polymer−colloid mixtures are quantitatively similar. The early growth of phases in spinodal decomposition is described by the Cahn−Hilliard theory.29,30 The solution to Cahn’s diffusion equation with the concentration-dependent gradient is given by the following equation: c(x,t) − c0 = A(β,t) exp(iβx), where A(β,t) is the amplitude of the Fourier Transform (FT) of the concentration fluctuations around the average concentration (c0), and β is the wavenumber related to wavelength as λ = 2π/β. The amplitude changes exponentially in time and can be expressed in terms of the initial amplitude as A(β,t) = A(β,0)exp[R(β)t], where R(β) is called the amplification factor. The solution suggests that when R(β) becomes positive, the amplitude grows exponentially, while it decays in all other cases. Because R(β) has a maximum value at
favors a spinodal-like phase separation (Figure 7c). Second, once the colloid- and polymer-rich phases start to develop, facilitated by interparticle bridging, the clusters can also be stabilized by the osmotic pressure exerted by polymer-rich regions. This additional stabilization effect is similar to depletion-induced phase separation in nonadsorbing polymer and colloidal mixtures;21 however, the effect is seen at the micrometer scale in our work. Such fine microstructures are common in kinetically driven spinodal decompositions of binary mixtures and are also theoretically and experimentally explored for the case of polymer−colloid suspensions.19,27,28 We studied kinetics of phase separation in our polymer−colloid system and found that the spinodal decomposition and the evaporation-driven phase E
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βmax = βc/√2 (or equivalently at λm = √2λc), certain wavelengths grow much faster than others, and this leads to the formation of fine and uniform microstructures. We analyzed the growth kinetics in Cahn−Hilliard’s framework by calculating the FT of the inverted grayscale intensity (proportional to particle concentration) profiles presented in Figure 7b (without shifting). Figure 8a shows the FT peaks in frequency domain (inverse μm, in this case) for different times of evaporation. It is clear that the system becomes gradually ordered with a periodicity equivalent to 10−12 particle sizes (10−12 μm) in ∼25 s. The FT intensity at this particular periodicity presents an exponential growth in time (Figure 8b), until the contact line depins. The maximum amplification factor is found to be 0.0533 s−1 (Figure 8b). After depinning, the growth of the amplitude stops as the contact line moves toward the center. We tested the growth of the phases with larger-sized droplets (see Figure S1 of the Supporting Information) and found that the phases continue growing since the depinning time lag (tdepin − tpin) of ∼100 s is longer for larger-sized droplets. However, the average particle concentration is found to be weakly dependent on time, suggesting that particle concentration slowly increases during phase separation. This can be explained by the presence of a stagnation region in front of the circulation region where the outward capillary flow meets with the backward Marangoni flow. The stagnation region can be visualized in Figure 6 and Movie S2 of the Supporting Information and also reported by Still et al.23 for PS spheres in SDS solutions. The stagnation region creates particles depletion in front of the eddies and prevents the flow of particles from center to the circulation region. Thus, the average particle concentration during phase growth remains less affected during pinning and truly represents phase separation of colloidal particles inside the Marangoni. However, as the contact line moves, some particles join the eddies while others are left behind as traces. This process keeps the phases active over large distances. We also studied the effect of extreme polymer concentrations on the particle deposition pattern. Figure S2 of the Supporting Information shows that the phase separation in PS dispersions gradually fades away as the concentration of 55 kg/mol PVP solution is increased to c* values (∼100 mg/mL). This is because strong interparticle bridging during evaporation provides an energy barrier to phase separation at these polymer concentrations. On the other hand, when the particle concentration is decreased below 0.1 vol % (for the same high concentration of 55 kg/mol PVP), the pinning does not occur and the droplet shrinks freely without giving rise to Marangoni eddies (Figure S3 of the Supporting Information). Conversely, as the particle concentration exceeds 0.1 vol %, the particles become highly crowded near the contact line, and relatively fewer polymer chains are unable to initiate Marangoni eddies, resulting in uniform deposition rather than spatially ordered particle patterns. Thus, the phase separation occurs in a narrow range of concentrations of particles and polymer. Weon et al.31 have recently demonstrated formation of fingerlike patterns in bidisperse mixture of micro- and nanoparticles. The formation of these features has been attributed to the interplay of temperature-driven Marangoni flow and coffee-ring effects in decalin droplets. They used fluorophore on the colloids which may act as surfactants, and nanoparticles essentially behave as low surface tension sites which accumulate at the edge and facilitate the Marangoni flow. The finger patterns, which are not valid for aqueous solutions,
seem to appear close to the edge, while our demonstration provides a prolonged and dynamic pattern formation towards the center of the aqueous polymer droplet. It would be very interesting to extend our study to deposition of nanoparticles from droplets of polymer solutions. Studies of polymer dynamics effect on flow-induced nanoparticle ordering might provide better understanding of fundamental issues underlying particle aggregation during evaporation. Organization of surface-functionalized nanoparticles with ligands and/or grafted polymers can be enhanced with the consideration of dynamical particle−polymer interactions during solvent evaporation that will lead to patterned particle depositions at micrometer scales. Moreover, application of controlled, yet facile, drying strategies to create ordered nanoparticle patterns might have important implications for fabrication of optoelectronic and photoconductive devices.
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CONCLUSIONS We studied the effect of adsorbing polymer chains on the deposition profile of the colloidal particles and spinodal decomposition of homogeneous PVP-PS microsphere suspensions upon solvent evaporation. For moderate polymer concentrations (up to 5 mg/mL), the ring thickness is found to be controlled by formation of Marangoni eddies near the pinned contact line. Further increase in polymer concentration induces stable growth of colloid-rich and polymer-rich phases. Kinetics of the phase separation is explained within a Cahn− Hilliard framework, where the amplitude of the fastest-growing wavelength is exponential, and the critical wavelength is on the order of the capillary length. The segregated phases first form lines in the direction of flow and move toward the center, leaving a fraction of particles deposited along moving stripes. The phases are highly stable due to strong interparticle bridging in the colloid phase and the depletion forces due to surrounding polymer-rich regions. Our study presents, for the first time, a real-time observation of phase separation in colloid−polymer mixtures under an internal flow field. Further theoretical and experimental studies will help to expand this study to nanoparticle−polymer systems.
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ASSOCIATED CONTENT
S Supporting Information *
Optical image of a large droplet, optical images of samples prepared with various polymer and particle concentrations, and movies on particle organization and deposition at different stages. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Stevens Institute of Technology, Department of Chemical Engineering & Materials Science, McLean 415, Hoboken, NJ 07030. Tel: (201) 216-5060. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Stevens Institute of Technology for start-up funds. We also thank Prof. Dilhan Kalyon for the use of the optical microscope. F
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hydrosoluble polymer additives. ACS Appl. Mater. Interfaces 2012, 4 (5), 2775−2780. (25) Aarts, D. G. A. L.; Dullens, R. P. A.; Lekkerkerker, H. N. W. Interfacial dynamics in demixing systems with ultralow interfacial tension. New J. Phys. 2005, 7 (1), 40. (26) Aarts, D. G. A. L.; Schmidt, M.; Lekkerkerker, H. N. W. Direct visual observation of thermal capillary waves. Science 2004, 304 (5672), 847−850. (27) Bailey, A. E.; Poon, W. C. K.; Christianson, R. J.; Schofield, A. B.; Gasser, U.; Prasad, V.; Manley, S.; Segre, P. N.; Cipelletti, L.; Meyer, W. V.; Doherty, M. P.; Sankaran, S.; Jankovsky, A. L.; Shiley, W. L.; Bowen, J. P.; Eggers, J. C.; Kurta, C.; Lorik, T., Jr.; Pusey, P. N.; Weitz, D. A. Spinodal decomposition in a model colloid-polymer mixture in microgravity. Phys. Rev. Lett. 2007, 99 (20), 205701. (28) Fuchs, M.; Schweizer, K. S. Structure of colloid-polymer suspensions. J. Phys.: Condens. Matter 2002, 14 (12), R239. (29) Cahn, J. W. On spinodal decomposition. Acta Metall. 1961, 9 (9), 795−801. (30) Cahn, J. W.; Hilliard, J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 1958, 28, 258. (31) Weon, B. M.; Je, J. H. Fingering inside the coffee ring. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2013, 87, 1.
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