Langmuir 2008, 24, 5245-5248
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Kinetic Stages of Single-Component Colloidal Crystallization Yaw Koon Koh,*,† Chan Hoe Yip,† Yet-Ming Chiang,‡ and Chee Cheong Wong†,§ Singapore-MIT Alliance, N3.1-01-36, 65 Nanyang DriVe, Singapore 637460, School of Materials Science and Engineering, Nanyang Technological UniVersity, N4.1 Nanyang AVenue, Singapore 639798 and Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts AVenue, Cambridge, Massachusetts 02139 ReceiVed March 5, 2008 To harness the full potential of colloidal self-assembly, the dynamics of the transition between colloids in suspension to a colloidal crystalline film should be better understood. In this report, the structural changes during the self-assembly process in a vertical configuration for colloids in the size range 200-400 nm are monitored in situ, using the transmission spectrum of the colloidal assembly treated as an emergent photonic crystal. It is found that there are several sequential stages of colloidal ordering: in suspension, with a larger lattice parameter than the solid state, in a close-packed wet state with solvent in the interstices, and, finally, in a close-packed dry state with air in the interstices. Assuming that these stages lead continuously from one to another, we can interpret colloidal crystallization as being initiated by interparticle forces in suspension first, followed by capillary forces. This result has implications for identifying the optimum conditions to obtain high-quality nanostructures of submicrometer-sized colloidal particles.
Introduction Self-assembly in colloidal systems has been utilized to produce long-range ordered structures (on the length scale of the colloidal particles). In particular, submicrometer-sized particles have the potential to form ordered structures (colloidal crystals) for applications such as photonic band-gap materials,1,2 sensors,3,4 and cell scaffolds.5 Extensive study of the equilibrium phase behavior of monodisperse colloidal systems has shown that, above a threshold volume fraction, face-centered cubic (fcc) packing is the equilibrium structure,6 and its stability provides a driving force for colloidal crystallization.7,8 Multicomponent colloids have also been shown to exhibit a wide array of possible crystal structures in equilibrium.9 The use of interaction forces to assemble nanostructures has also been applied in other types of systems including self-assembled monolayers (SAM) of various macromolecules10 as well as biomaterials.11 In static systems, microscopic interaction forces can be manipulated to produce a rich variety of short-range ordered structures. However, the growth of these short-range units into extended structures is extremely sensitive to macroscopic changes in their environment, especially for submicrometer-sized particles. In particular, as most of these techniques involve a final drying process, capillary forces can affect the self-assembly process significantly. Therefore, dynamic systems with continuous environmental changes must be taken into account when designing processes aimed at achieving long*
[email protected]. † Singapore-MIT Alliance. ‡ Massachusetts Institute of Technology. § School of Materials Science and Engineering, Nanyang Technological University. (1) Norris, D. J.; Vlasov, Y. A. AdV. Mater. 2001, 13, 371. (2) Lo´pez, C. AdV. Mater. 2003, 15, 1679. (3) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829. (4) Prasad, T.; Mittleman, D. M.; Colvin, V. L. Opt. Mater. 2006, 29, 56. (5) Kotov, N. A.; Liu, Y.; Wang, S.; Cumming, C.; Eghtedari, M.; Vargas, G.; Motamedi, M.; Nichols, J.; Cortiella, J. Langmuir 2004, 20, 7887. (6) Monovoukas, Y.; Gast, A. P. J. Colloid Interface Sci. 1989, 128, 533. (7) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340. (8) Woodcock, L. V. Nature 1997, 385, 141. (9) Maskaly, G. R.; Garcia, R. E.; Carter, W. C.; Chiang, Y.-M. Phys. ReV. E 2006, 73, 11402. (10) Ulman, A. Chem. ReV. 1996, 96, 1533. (11) Zhang, S. Nat. Biotechnol. 2003, 21, 1171.
range ordered structures that may be technologically useful. There has been little work done in combining the understanding of microscopic interaction and macroscopic boundary forces to provide a more complete model of colloidal self-assembly. When the macroscopic forces are considered along with microscopic forces, there can be two situations based on the relative size of the particles. In the case for larger particles, the particles will experience the effect of macroscopic boundaries before they have the opportunity to be assembled by the microscopic forces. For such a situation, the self-assembly process becomes solely a function of the capillary forces. Another situation occurs when the particles are much smaller in relation to the volume in which they are confined. The particles are then able to be driven to assemble by the microscopic interaction forces before they are affected by the macroscopic boundary forces. Here, we study a meniscus-driven colloidal self-assembly process12 in the second situation, using an optical in situ structural monitoring method. From the results, a model illustrating the key kinetic stages of colloidal self-assembly is developed.
Experimental Section A popular technique for obtaining dried colloidal crystals is vertical deposition, whereby a substrate is vertically submerged in a colloidal suspension and the colloidal crystal is deposited at the receding meniscus as the solvent evaporates. At the meniscus region, there is a constant arrival flux of particles due to solvent convection driven by evaporation.13 The particles that arrive at this region can either stay at the meniscus region or sediment back into the bulk suspension. The tendency to sediment is characterized by the Peclet number Pe ) mBgR/kT, where mB is the buoyant mass of a particle with radius R and g is the gravitational acceleration. For particles used in our experiments, this number is ∼10-3, which means that the particles will not sediment over the time scale of the experiment. In the case of nonsedimenting particles, the volume fraction increases locally over time. As the local volume fraction exceeds the threshold for crystallization, interaction forces, which we elucidate later, provide the driving force for crystallization. Here, we take advantage of the (12) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132. (13) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827.
10.1021/la800702d CCC: $40.75 2008 American Chemical Society Published on Web 04/25/2008
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Figure 1. Schematic of the setup used. The suspension is allowed to evaporate in a plastic cuvette with a glass substrate on one side. Due to the difference in wettability, the contact line is higher at the substrate, and this provides a clear line of sight for the transmitted beam. The whole apparatus is kept in a temperature-controlled chamber during the experiment.
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Figure 3. The calculated DLVO potential of the colloidal suspension used in our experiments, plotted against the surface-to-surface separation between the spheres. The surface potential is taken as the measured zeta potential of -38 mV at an ionic strength of 0.1 mM KCl. The dashed vertical line denotes the separation equal to 2 times the Debye length. The energy barrier has a magnitude of ∼15 kT.
featureless due to the absence of ordering. Random scattering of the light by the disordered structure ensures that no light is transmitted. As the volume fraction increases with evaporation, a first feature (A) appears in the transmission spectrum (Figure 2). This feature corresponds to the onset of order in the colloidal suspension and is the first kinetic stage of ordering we observe. At this stage, the particles are fully submerged in solvent and the driving force for ordering is the interaction forces between the particles. This happens as the average distance between the particles decreases, because of rising particle volume fraction to the point where the interaction forces causing ordering overwhelm the randomizing Brownian forces. As usual, we treat the interaction potential between two particles in a solvent using DLVO theory where the total potential is taken as the sum of the repulsive and attractive forces.14 Figure 2. Transmission spectra showing the appearance of the features A (608 nm), B (491 nm), and C (462 nm). These spectra are taken at different intervals [t1 ) 300 min, t2 ) 320 min, t3 ) 400 min, t4 ) 770 min, t5 ) 800 min] from the beginning of the experiment. Two features are observed simultaneously at times t2 and t4. A schematic of the corresponding structural changes is shown in Figure 6. The spectra are offset vertically for clarity.
fact that the ordered structure gives rise to photonic band-gap (PBG) properties that can be spectroscopically monitored. In our previous work, a reflectance measurement was used to probe the structure at the edge of the sessile drop.14 For the vertical deposition configuration, a transmission measurement is more convenient. Monitoring the transmission spectra during growth allows classification of various kinetic stages of self-assembly. A schematic of our transmission setup is shown in Figure 1). The light source used is a balanced deuterium tungsten halogen source (Ocean Optics DH-2000-BAL), and the spectrometer is a linear silicon CCD array coupled to gratings for the wavelength range 300-900 nm (Ocean Optics USB2000). The whole setup is housed in a temperature-controlled chamber. The collection area for the transmission measurement is 300 µm in diameter. The colloids used are polystyrene particles suspended in water. They are synthesized by surfactant-free emulsion polymerization. The surface charges on the particles are negative due to the sulfate-type initiator used, and the measured zeta potential is -38 mV in deionized water (∼10-6 M) with particle concentration of 0.1 vol % (Brookhaven Instrument Corporation ZetaPlus). This value is taken as the surface potential for subsequent calculation of the interaction potential. The starting bulk suspension for the selfassembly experiment has particle concentration of 0.5 vol %.
Results and Discussion Initially, the experiment is set up such that the meniscus is above the light path. Here, the transmittance spectrum is (14) Koh, Y. K.; Wong, C. C. Langmuir 2006, 22, 897.
VDLVO )
64πacoΓ2okT 2
κ
exp(-κr) -
Aa 12r
where a is the particle radius, co is the concentration of ions, k is the Boltzmann constant, T is the temperature, κ is the inverse Debye length, r is the separation between the particles, and A is the Hamaker constant. The first term on the right side is the repulsive part of the DLVO is provided by the electrostatic forces between similarly charged particles, while the second term arises from attractive Van der Waals forces. The surface potential of the particles appears as
( )
Γο ) tanh
zeΦο 4kT
where z is the valence of the counter ions, e is the electronic charge, and Φo is the surface potential. The calculated DLVO potential vs particle surface-to-surface separation for the present experimental system is shown in Figure 3. One important feature of the DLVO potential is the presence of an energy barrier against irreversible agglomeration, which is closely related to the electric double layer. The magnitude of this barrier can range from 0 to 102 kT depending on the suspension parameters. The appearance of a diffraction feature (Figure 2) can be correlated with the photonic band-gap structure of the ordering crystal. The equilibrium structure of the colloidal crystal in suspension is known to be fcc,6 and although the self-assembly process is dynamic in nature, it is assumed here that any ordering in suspension is able to equilibrate. More elaborate experiments like confocal microscopy (albeit with larger particles) can be done to confirm this. For fcc colloidal crystal, a pseudogap appears
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Figure 4. Top view of the colloidal crystal showing that the (111) plane is parallel to the substrate. The incident beam is perpendicular to this plane in the optical measurement.
Figure 6. Three distinct stages in the self-assembly process. As the meniscus recedes, a transition structure is first observed with a large lattice parameter shown in the transmission spectra as feature A. After the meniscus has passed, this structure collapses to a smaller lattice parameter but continues to retain water in its interstices, giving rise to feature B in the transmission spectra. Finally, a dried colloidal crystal corresponding to feature C is obtained.
Figure 5. Calculated central wavelength of the photonic bandgap at different lattice constant for a fcc colloidal crystal in water with light incident on the (111) plane. It is plotted against the average separation between the spheres for comparison with Figure 3. The colloidal particles are 195 nm polystyrene particles with a dielectric constant of 2.64. The vertical dashed vertical line denotes the separation equivalent to 2 Debye lengths. The equilibrium colloidal crystal in air has a central wavelength at 463 nm.
at the second and third bands of the photonic band-gap.15 This manifests itself as a feature in the optical transmission spectrum of the colloidal crystal. Calculation of the position of this feature can be done by solving Maxwell’s equation; here, the fully vectorial eigenmodes of Maxwell’s equations with periodic boundary conditions are computed by preconditioned conjugategradient minimization of the block Rayleigh quotient in a planewave basis, following the method of Johnson et al.16 In the present case, the growing crystal has a preferred orientation due to the presence of the substrate. As the particles (sulfate-polystyrene) and substrate (glass) are both negatively charged, the growing crystal orients its close-packed plane parallel to the flat substrate. SEM imaging (Figure 4) of the colloidal crystals grown in this study confirmed that the (111) plane is parallel to the substrate. Thus, this provides a reference direction for calculation of the photonic band-gap. The lattice parameter of the colloidal crystal can be inferred from comparison of the experimental results with the calculation. The calculated central wavelength of the photonic bandgap at different lattice constants for a fcc colloidal crystal in water is plotted in Figure 5. We find that the position of feature A corresponds to a fcc colloidal crystal, but one with a lattice parameter (368 nm) that (15) Israelachvili, J. N. Intermolecular and surface forces; Academic Press: London, 1992. (16) Ho, K. M.; Chan, C. T.; Soukoulis, C. M. Phys. ReV. Lett. 1990, 65, 3152.
is larger than expected for equilibrium colloidal crystal (276 nm) formed by hard-sphere packing of the polystyrene particles with diameter of 195 nm. This is a transition structure, stabilized by the interparticle forces, in which the barrier in the DLVO potential (Figure 3) prevents the particles from coming into direct contact resulting in a larger surface-to-surface separation. For the colloidal suspensions here, the value of the Debye length is 32 nm, and if we assume that the interparticle separation in the fcc structure has this dimension, the resulting fcc structure has a lattice parameter of 366 nm, in close agreement with the wavelength of the observed feature A in the transmission spectrum. This stage of colloidal self-assembly has not been previously observed in larger particles; the conventional view is that colloidal selfassembly at liquid menisci is driven solely by capillary forces.11 Our observation suggests that the self-assembly of particles can be initiated by the interaction forces between the particle, provided that the sizes of the particles are small relative to the volume that is confined by the macroscopic boundaries. However, the capillary forces clearly should become more important as the solvent continues to evaporate. Previous work by Kralchevsky et al.17 showed that, for floating particles in a wetting fluid, lateral capillary forces are negligible for particles smaller than 10 µm. Thus, lateral capillary forces should not affect the transition structure in the first stage, but at the thinning edge of the meniscus, where the transition structure is compressed against the substrate by the meniscus, the capillary forces increase. The lateral capillary forces due to the local curvature of the meniscus at the contact line with individual particles is significantly greater than that of floating particles; calculation with Krachevsky’s model17 shows a much stronger lateral capillary force than in the case of floating particles, even for particles as small as 10 nm. In our case, the energy due to these capillary forces can increase to ∼105 kT for meniscus recession below the top of the particles by as little as a few nanometers. (17) Johnson, S.; Joannopoulos, J. Opt. Express 2001, 8, 173.
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The capillary force is now enough to overcome the energy barrier present in the DLVO potential, bringing the particles into direct physical contact, and reaching the equilibrium state corresponding to the primary minimum of the DLVO potential curve. Krachevsky’s analysis is valid for a 2D particle array, but in our case, it has to be extended to 3D crystals. A possible mechanism for the final 3D packing process is proposed as follows. The effect of the capillary force is first felt by the top layer of the transition structure. However, the abrupt collapse of the double layer around the particles in the top layers causes the counter ions to diffuse downward, thus increasing the local ionic strength of the adjacent underlying layers. This increase is enough to lower the DLVO energy barrier below the thermal energy, causing the layers below to also come into direct contact. The collapse of the double layer thus cascades down through the layers to the substrate, creating a final equilibrium 3D structure of colloidal particles in direct contact. The following experimental results suggest that the double layers do collapse sequentially from the transition structure to the final colloidal crystal. With continued growth of the crystal, a second feature (B) appears at a shorter wavelength (Figure 2). The position of this feature corresponds to a fcc colloidal crystal with the colloidal particles in direct physical contact (zero separation) with water in the interstices. The interstices in the colloidal crystal are capillary pores that should retain water even after the meniscus has receded below the deposited crystal. We deduce that this is the case from the appearance of a later blue shift, feature C, that can be correlated with the dielectric contrast change as water in the interstices is replaced by air. The coexistence of the two features A and B in the transmission spectrum is likely due to the simultaneous existence of the transition structure and wet colloidal crystal during the final packing by the capillary forces. As the meniscus recedes further, feature B continues to grow in intensity at the expense of feature A, as the area of the collapsed colloidal crystal grows. Finally, feature B alone is seen, and is stabilized for a long period of time (more than 15 times the lifetime of feature A) because of the continued wicking of water into the interstices long after the meniscus has receded. This therefore is a second stage of colloidal self-assembly, where strong lateral immersion capillary forces collapse the electric double layer, bringing particles into direct contact, with solvent trapped in the interstices. After the meniscus has receded far enough that the wicking action of the interstitials can no longer sustain the flow of solvent, final drying occurs. This stage appears as feature C in Figure 2, blue-shifted in wavelength due to the increased dielectric contrast of the colloidal crystal when the water in the interstices is replaced by air. Photonic band-gap calculation of the shift is 27 nm and corresponds well to the observed difference between the two (18) Kralchevsky, P. A.; Nagayama, K. Particles at fluids interfaces and membranes: attachment of colloid particles and proteins to interfaces and formation of two-dimensional arrays; Elsevier: Amsterdam, 2001.
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features. Feature C also grows at the expense of feature B. The width of feature C is also observed to be larger in the dried colloidal crystal due to the increased dielectric contrast, consistent with the photonic band-gap calculation for increased dielectric constrast. A schematic diagram summarizing the structural changes with respect to the position of the meniscus is shown in Figure 6. The stability of the structure in the second stage was investigated by injecting more solvent into the system after feature C appears. There was no increase in the lattice parameter as the meniscus creeps up to above the collection aperture. Subsequent retraction of water also left the position of the features unchanged in the transmission spectra. The results show that the structure remains stable once the particles are in their primary minimum. This also suggests that the resulting colloidal crystals are robust enough to go through subsequent liquid infiltration processing, for example, with functional materials. Some directions toward improving the quality of submicrometer-sized colloidal crystals grown by meniscus-driven methods can be inferred from the self-assembly process described above. First, the presence of an energy barrier to avoid irreversible agglomeration into disordered agglomerates is important. A glassy phase will remain if the subsequent capillary forces are not strong enough to rearrange the disordered agglomerates, and long-range order will be very difficult to achieve. A second consideration is that the electric double layer around each particle should be as thin as possible while still preventing premature aggregation. During the final collapse of the double layer (A to B), this will result in lower shrinkage stresses. Shrinkage stresses are known to give rise to macroscopic cracks12 and, in extreme cases, may destroy the order of the colloidal crystals. Combining the two considerations, the optimum solvent conditions for high-quality colloidal crystal growth should be those that result in intermediate electric double-layer thicknesses.
Conclusion The self-assembly of submicrometer-sized colloidal particles to form dry, long-range ordered structures has been observed to occur in three stages. It is shown that that first instance of ordering is driven by the interparticle forces in suspension, followed by packing driven by capillary forces, followed by a final drying stage. It should be noted that the process described applies only when the size of the particles is much smaller relative to the volume in which they are confined, i.e., the meniscus. An assumption is that the colloidal crystal in suspension is able to equilibrate, which can be confirmed with more elaborate experiments. Despite these shortcomings, the observations here can provide guidance for the optimization of fabrication parameters for high-quality colloidal crystals of submicrometersized particles. LA800702D
