Article pubs.acs.org/Langmuir
Polloidal Chains from Self-Assembly of Flattened Particles Laura Mely Ramírez,† Charles A. Michaelis,† Javier E. Rosado,† Elias K. Pabón,† Ralph H. Colby,*,‡ and Darrell Velegol*,† †
Department of Chemical Engineering, 175 Fenske Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Materials Science and Engineering, 309 Steidle Building, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *
ABSTRACT: Chains of micrometer-size colloidal particles have been self-assembled that are flexible, mechanically stable, and observable in optical microscopy. The chains sometimes have more than 30 particles, and we call them “polloidal chains”. A key aspect of the work is the careful modeling of the interparticle forces between partially flattened polystyrene spheres. This modeling helped us to identify a narrow window of system conditions that produce interparticle physical bonds with a bond energy greater than 15kT, as well as a gap of fluid between particles that enables freely rotating bonds and flexible chains. The formation of the chains is well-modeled using linear condensation growth from classical polymer theory, suggesting that the chains might be used experimentally as largescale, relatively slow moving models for polymer chains.
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colloidal particles are flattened on one side,7,8 giving a large anisotropy in interaction energy (≈10−18kT) that enables a self-assembly of flexible polloidal chains in a narrow window of 25−30 mM KCl. The bonds are strong but retain flexibility, with ≈10 nm of fluid between the particles since each bond is in a secondary energy minimum with no particle contact. To flatten particles,8 we lower the glass transition temperature (Tg) of the polymer colloid to below room temperature (T = 20−25 °C) by adding toluene as a plasticizer. Amidinefunctionalized polystyrene colloids were electrostatically adhered in water to a negatively charged silicon wafer. After 24 h, the Si wafers were transferred to Nalgene beakers under ∼1 cm deep deionized water. Toluene (∼1 mL) was added at the top of the beaker to allow the toluene molecules to diffuse through the water phase at room temperature. When the toluene molecules reached the bottom of the beaker, the particles absorbed the toluene. The increasing absorption of toluene with time lowered the Tg of the polymer below room temperature. Thus, the polystyrene free volume increased and the particles spread onto the flat silicon substrate due to surface tension.7 After a controlled spreading time, which we determine from diffusion theory, we raise the Tg of the particles by rinsing off the plasticizer with a siphoning system. A plastic pipet was then used to detach the particles from the substrate. For 2 min, the particles were placed in an ultrasonicator, and as a result,
INTRODUCTION In this work we demonstrate the fabrication of colloidal chains that are flexible and mechanically stable. The chains spontaneously self-assemble with no applied external field, due to the careful modeling and detailed design of interparticle forces. The fabrication involves flattening individual colloidal spheresproducing a geometric asymmetry in the system and designing the colloidal forces to produce rotatable physical bonds stronger than 15kT. Since the chains can have a length of 30 particles or even more, we call the chains “polloids” or “polloidal chains”; they look like oligomers or polymers composed of micrometer-size “monomer” colloidal particles. Current methods for self-assembling nano- and microscale structures often use highly specific and reversible bonds. DNAfunctionalized colloids have been tailored to have programmable links (i.e., “DNA strands”) that hybridize under certain conditions to obtain the self-assembly of a target structure.1−3 Alternative binding mechanisms that self-assemble reversibly into chain-like structures have been explored. These include (1) grafting polymer molecules onto inorganic metal nanoparticles (≈50 nm)4 and (2) using Fischer’s lock-and-key principle with spherical particles that are buckled and spontaneously assemble via depletion or hydrophobic forces into chains up to eight particles long.5,6 These binding mechanisms show a successful assembly of reversible chainlike structures. However, these methods lack (1) chain flexibility, (2) mechanical stability over more than a day, or (3) a length greater than 10 monomers. The key to producing our chains is to develop a strong and anisotropic physical bond on one region of each particle. The © 2013 American Chemical Society
Received: April 2, 2013 Revised: July 20, 2013 Published: July 25, 2013 10340
dx.doi.org/10.1021/la401232g | Langmuir 2013, 29, 10340−10345
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Figure 1. DLVO theory modified for flattened spheres. The inset schematic displays flat−sphere (blue) and sphere−sphere (red) configurations of particles with radius a, flat radius s, and separation distance between the two particles δ. Secondary energy minima |2ndΦmin/kT| are shown for flat− sphere (blue) and sphere−sphere (red dashed) configurations with increasing salt concentration C(mM). In 25−30 mM salt (denoted by the vertical dashed lines), the flat−sphere state has a strong secondary energy minimum (≈15−18kT) compared with ≈7.4−8.8kT for the sphere−sphere configuration. The inset plot shows the pairwise energies (Φ/kT) for particles having a radius a = 1.1 μm and a flattened radius s = 0.65a in a flat− sphere configuration as a function of the dimensionless separation distance (κδ, where κ is the inverse Debye length11) between the two particles at 25 mM KCl (bright red), 31 mM KCl (purple), 32 mM KCl (orange), and 35 mM KCl (black). As the salt concentration is increased from 25 to 30 mM KCl, the depth of the secondary energy minimum increases. Above 30 mM KCl, the secondary energy minimum starts to decrease until it disappears above 32 mM KCl. At this point, the barrier has vanished and nonselective, irreversible aggregation dominates, as particle−particle bonds fall into their primary energy minimum (particle contact).
spherical colloids with a well-defined flat patch were suspended in water. This flattening technique produces electrostatically stable particles with excellent size control of the flattened regions (Figure 2a). The flattened particles remain deformed over a period of 2 months. We have used a similar technique to produce two flats on a particle on a v-shaped etched silicon wafer.7 More details on flattening particles are given in our two previous publications.7,8
typically have energy wells on the order of the thermal energy kT (k is Boltzmann’s constant and T is absolute temperature) in their secondary energy minimum.16 On the other hand, the effective interaction area in the contact region between two particles is greatly increased if both flat regions face each other. This is analogous to having two parallel, flat, circular plates interacting. The energies, both the attractive energy in the secondary minimum and the repulsive energy between the particles, often increase by 1 or 2 orders of magnitude, enabling the particles to fall into a deep secondary minimum, sometimes as deep as 50kT, with a large barrier preventing particle contact. In previous work8 we showed that the flattened particles form the simplest of chainsdoubletsconsistently and selectively. These doublets were fabricated at 10 mM KCl, where the flat− flat state is strongly favored according to our full colloidal energy calculations. From our interparticle force model, we also determined that for particles with radius a ≈ 1 μm, a flat radius of s > 0.50a was necessary to obtain strong and selective interactions in a moderate ionic strength.8 We began by studying flat−sphere bonds between particles and discovered that the flat region from one particle can preferentially bond with the spherical part of another particle in a >15kT deep secondary energy minimum, while sphere− sphere interactions remain relatively weaker ( 0.50a) are in a secondary energy minimum >15kT, bonds are predicted to be stable for longer than 1 day, while at 15kT and the sphere−sphere to be 15kT), we expect a long residence time in that configuration. Also, for particles to go from a flat−sphere to a flat−flat configuration often requires that particles go through a “flat−corner” configuration, which gives a significant energy barrier that inhibits its formation.
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EXPERIMENTAL RESULTS AND DISCUSSION. POLLOIDAL CHAINS WITH 30 PARTICLES
Upon self-assembling our chains, we observed several features. First, the chains follow classical polymer theory for condensation polymerization (Figure 2), where every particle (“monomer”) has the same probability of bonding with another particle17 (i.e., physically bonding for our polloids, forming a flat−sphere bond). Despite the fact that some hyperbranched structures are present in our system, inevitable factors like steric hindrance to bond rotation and hydrodynamic resistance limit the degree of hyperbranching. The functionality f, defined as the number of bonds per monomer,17 is found from analyzing our experimental images. No branching was observed at 20 mM KCl. At 25 and 30 mM KCl, we saw limited branching, and the functionality value was f = 2.001 ± 0.001 and 2.01 ± 0.01, respectively, thus supporting our observation. Therefore, we find that the mostprobable distribution for our polloids resembles a linear condensation polymerization system ( f ≡ 2) closely. Our distribution for the number of monomers per chain follows classical polymer theory. For linear condensation polymers, the mostprobable distribution of molecules is expressed as the number fraction distribution nN = pN−1(1 − p) and the weight fraction distribution wN = NpN−1(1 − p)2, where N is the number of monomers in the chain.17 The polymerization probability p is defined as the fraction of flats in flat−sphere bonds.17 Figure 2 shows experimental data for the number fraction of polloids (particles with a = 1.1 μm and s = 0.65a) assembled at three different salt concentrations (20, 25, and 30 mM KCl). To obtain the theoretical p value for each sample, the number fraction distribution with the corresponding N values was put into the classical equations described above. The most-probable distribution nN(N,p) was then plotted with this fitted p for each data set where the uncertainty is calculated as the 95% confidence interval. As observed in Figure 2, the theoretical prediction shows the same trend as the experimental data. At 20 mM KCl, the fitted p was 0.59 ± 0.04, yielding chains with N ranging from 2 to 15. A low polymerization probability is expected under these conditions, since the flat−sphere bond is ≈10.1kT, where bond dissociation is on the order of 40 min. By comparison, the corresponding sphere−sphere secondary minimum is only ≈4.7kT. When the ionic strength is slightly increased to 25 mM KCl, the flat− sphere bond becomes ≈15.1kT with a resulting p = 0.74 ± 0.04 and chains as long as N ≈ 20. At 30 mM KCl, the flat−sphere bond is ≈18.1kT, thus giving longer chains up to N ≈ 35, corresponding to p = 0.86 ± 0.02. The inset plot of Figure 2 shows the experimental weight fraction data for polloids at 30 mM KCl, showing the maximum at the number-average degree of polymerization Nn = 7 ± 1 expected for the
Figure 2. Polloids following classical polycondensation synthesis. (a) A scanning electron microscope (SEM) image of 2.2 μm flattened amidine-functionalized polystyrene latex particles with a = 1.1 μm and s = 0.65a. The uncertainty of the particle and flat radius measurement from the SEM is ±30 nm. The confocal microscope images show particles from part a assembled at (b) 20 mM KCl, (c) 25 mM KCl, and (d) 30 mM KCl. The average chain length increases with ionic strength in this range. Above 30 mM KCl, particles are found to aggregate into random particle clusters, as predicted by our model. (e) Most-probable number fraction distribution nN(N,p) determined with a fitted p (on a log-scale) and the experimental data for polloids (a = 1.1 μm and s = 0.65a) assembled at 20 mM KCl (green squares) with p = 0.59 ± 0.04, 25 mM KCl (red triangles) with p = 0.74 ± 0.04, and 30 mM KCl (blue circles) with p = 0.86 ± 0.02. All uncertainties are calculated as the 95% confidence interval. Over 2000 particles were counted per data set. The inset plot shows the most-probable weight fraction distribution wN(N, p) for polloids assembled at 30 mM KCl compared to the experimental data (light blue diamonds). Experimentally, counting large particle chains (N > 20) accurately is challenging due to particles lying on different planes, thus introducing some error to the observations. Scale bars = 5 μm. most-probable weight fraction distribution wN(N,p) function in linear condensation polymerization with p = 0.86. This consistency reveals that our polloidal chains, even though composed of micrometer-size colloidal particles, mimic the behavior of molecular polymer systems. When suspended in solution, polloidal chains take on a threedimensional (3-D) conformation. Using confocal microscopy we are able to examine the structure of these chains by assembling z-stacks of images. The optical slices of z-sequences are then stacked to reproduce a 3-D image. Thus, we can visualize the conformation of the chains and observe chain flexibility and movement with time (see Figure 3a). Ideally, we would prefer to measure the end-to-end distance of the chains; however, the 3-D imaging is not sufficient to accomplish this presently. An alternative way to study chain flexibility is to observe the chains settling onto the imaging substrate. In solution, polloids have a 3-D 10342
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Figure 3. Flexible bonds of self-assembled polloidal chains. Images a and b were taken with confocal microscopy to capture polloids from 2.2 μm flattened A-PSL at 30 mM KCl. (a) 3-D polloid (N ≈ 15) in solution changing configuration over time (10 s between images). (b) Polloids settling onto the imaging substrate changing from a 3-D (first image) to a 2-D configuration (≈1 min interval per image). (c) Functional chains: 2.8 μm Dynabeads C-PSL mixed with 2.2 μm flattened A-PSL at 25 mM KCl moving as the magnetic field is applied in a circular motion and turned off by the last image (≈30 s interval per image). Snapshots of this movie were taken with optical microscopy (60× air objective). Scale bars = 5 μm.
Figure 4. Mimicking complex polymer systems with polloids. 3-D images a−c were taken with confocal microscopy to capture polloids from 2.2 μm flattened A-PSL particles at 30 mM KCl. (a) Polloidal chains suspended in solution, (b) complex, randomly hyperbranched chain (N ≈ 25), and (c) cyclic ring. 2-D images taken with optical microscopy (60× air objective) at 30 mM KCl: (d) H-star polymer from 2.2 μm flattened A-PSL particles; (e) copolymer “star” (N ≈ 40) composed of 2.2 μm flattened A-PSL particles and a 8.7 μm sulfatefunctionalized PSL particle acting as the “hub”; (f) complex, randomly branched copolymer (N ≈ 25) composed of 2.2 μm flattened A-PSL and 1 μm flattened A-PSL particles; and (g) complex, randomly branched terpolymer (N ≈ 20) composed of a 8.7 μm sulfatefunctionalized PSL particle as the “hub”, 2.2 μm flattened A-PSL, and 1 μm flattened A-PSL particles. Scale bars = 5 μm.
conformation (see Figure 4a). However, as polloids approach the flat substrate, they settle into a 2-D conformation. A time-lapse sequence was captured with confocal microscopy to observe this phenomenon, displayed in Figure 3b. The first snapshot of the chains into the bulk solution is taken in 3-D (extracted from an image stack) to show the conformation when suspended in real space. Then, we focus on one plane to observe how the polloidal chains accommodate themselves to lie “flat” on the 2-D substrate. Once the chains have reached the imaging substrate through gravitational settling, they come into focus and their movement is restricted by gravity and the colloidal forces acting between the plate and the polloids. Aside from assembling a variety of polymer-like structures, as shown in Figure 3b, we can functionalize our polloids with magnetic particles and study chain flexibility as well. A sample containing a 30:70 mixture by volume of 2.8 μm carboxyl-functionalized polystyrene latex (CPSL) Dynabeads and flattened 2.2 μm amidine-functionalized polystyrene latex (A-PSL) particles, respectively, was prepared at 25 mM KCl to study chain flexibility as a magnetic field is switched on and off (Figure 3c). When the magnetic field is turned on, the magnetic-functionalized polloids change configuration as the dipoles of the magnetic monomers align with the direction of the magnetic field, but the flattened monomer particles do not. Snapshots from a movie of magnetic-functionalized polloids under a magnetic field are shown in Figure 3c. The last sequential image shows how two mixed particle
chains became one due to the directed motion of the magnetic particles leading flattened particles on the ends to meet in a flat− sphere configuration and create one chain. Using our technique, it might be possible to fabricate chains of functional particles that in recent theoretical papers have proven to have interesting selfassembling properties.18−20 Even though we mostly observed a linear polycondensation system, hyperbranching occurred along with the linear chains due to the intrinsic nature of the geometrical binding with flattened particles. Multiple flats can bind to the spherical part of one particle into strong 10343
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flat−sphere bonds. The extent of hyperbranching was still small because steric hindrance and free volume limit bond rotation. Nonetheless, with our assembly method and characterization techniques, we were able to reproduce a polymer system with complex chain designs in three dimensions as well (at 30 mM KCl, Figure 4a). Although we have seen polloids in the form of hyperbranched chains, H-polymers, and cyclic rings (see Figure 4a− d), as well as in the form of randomly branched stars, copolymers, and terpolymers with N > 20 (see Figure 4e−g), we do not yet have solid control over this process. An important characteristic from all of our polloidal-like structures is their reversible bonds. Polloids revert back to singlets when the ionic strength is lowered to below 5 mM KCl, as our model for colloidal forces predicts, proving that the bonds are in the secondary energy minimum.
Confocal Microscope Sample Preparation (Figures 2b−d, 3a,b, and 4a−c). A sample of polloids was mixed with 1 mM Rhodamine B to be placed in a capillary tube 0.20 × 2.0 mm (VitroCom) sealed with wax, and the chains were allowed to settle for 10 min. Confocal images of settling polloids at different z-positions were taken with a Leica Microsystems TCS SP5 confocal laser scanning microscope (60× oil objective). Polloids were also imaged with a Nikon Eclipse TE2000-U inverted optical microscope (60× air objective, Figures 3c and 4d−g). SEM Sample Preparation (Figure 2a). A 5.0 μL aliquot of flattened particles in solution (
