Article pubs.acs.org/Langmuir
Self-Assembly of Doublets from Flattened Polymer Colloids Laura Mely Ramírez,† Adrian S. Smith,† Deniz B. Unal,† Ralph H. Colby,*,‡ and Darrell Velegol*,† †
Department of Chemical Engineering, ‡Materials Science and Engineering Department , The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *
ABSTRACT: Bottom-up fabrication methods are used to assemble strong yet flexible colloidal doublets. Part of a spherical particle is flattened, increasing the effective interaction area with another particle having a flat region. In the presence of a moderate ionic strength, the flat region on one particle will preferentially “bond” to a flat region on another particle in a deep (≥10 kT) secondary energy minimum. No external field is applied during the assembly process. Under the right conditions, the flat−flat bonding strength is ≥10× that of a sphere−sphere interaction. Not only can flat−flat bonds be quite strong, but they are expected to remain freely rotatable and flexible, with negligible energy barriers for rotation because particles reside in a deep secondary energy minimum with a ∼20−30 nm layer of fluid between the ∼1 μm radius particles. We present a controlled technique to flatten the particles at room temperature, the modeling of the interparticle forces for flattened spheres, and the experimental data for the self-assembly of flat−flat doublets.
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INTRODUCTION Anisotropic colloidal particles provide numerous possibilities for controlled self-assembly.1 Patchy particles with heterogeneous chemistries have been fabricated numerous times in the literature.2−6 However, fabricating patchy particles consisting of a small physical deformation is much less common.7−9 We have developed a bottom-up, controlled technique to create localized flat regions on spherical polymer colloids, which are then able to self-assemble into colloidal doublets. When two spherical colloidal particles interact, they do so through electrostatic forces and van der Waals forces (i.e., the usual “DLVO forces”), as well as other forces such as depletion forces.10,11 For the DLVO forces, particles often reside in either a shallow secondary energy minimum or a much deeper primary energy minimum. Typical energy wells for sphere− sphere interactions in the secondary energy minimum are on the order of the thermal energy (kT, where k is Boltzmann’s constant and T is absolute temperature). However, if particles are flattened over some region on their surfaces, the effective interaction area in the contact region between two particles greatly increases when the two flat regions meet (i.e., “flat−flat” configuration), analogous to having two circular flat plates interacting. We have found that under proper conditions the local interaction forces become ≥10× stronger with the flat− flat configuration compared to sphere−sphere or even flat− sphere interactions, leading to long-lasting assemblies. These strong particle assemblies are also expected to be flexible (i.e., be freely rotating). Full DLVO calculations reveal that there is ∼20−30 nm of water in the contact region between the two flats, for our systems (i.e., 10 mM KCl, micrometer-sized particles).12,13 In this paper we describe how we self-assemble doublets from flattened spheres, and explain the equations and © 2012 American Chemical Society
experiments that enable us to tune system parameters for a successful assembly. In previous work14 we flattened polymer colloids (polystyrene particles) at one region of their surfaces by depositing them on a flat substrate and heating above their glass transition temperature (Tg). We examined the spreading of the particle onto a flat surface, and established an accurate model for the flat size as a function of time, based on Hertzian concepts.14 In the present work, we have developed a better-controlled particle-flattening technique, in which we lowered the Tg of the polystyrene below room temperature (20−25 °C) by adding toluene, rather than heating the system above the original Tg of polystyrene. Our new system enables us to avoid the chemical degradation of the charge groups on the particles, which causes them to become unstable. The new method also enables uniform control of the flattened regions. Numerous groups have produced doublets previously.15−19 However, the techniques used have been limited in scalability or in the purity of doublets (as opposed to other assemblies) that are readily obtained.16−19 Several of the previous studies have involved producing chemical patches on the particles to produce doublets.15,16 In one recent report,20 the researchers used a physical deformation to assemble particles with depletion forces. It is not clear from that work how strongly held the aggregates are nor how long the assemblies endure. In our work we also use physical deformations to induce selfassembly. The key results from this work are (1) a simple method to flatten polymer colloids on one spot at ambient Received: November 21, 2011 Revised: January 27, 2012 Published: February 1, 2012 4086
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temperature, with a model to predict the change in Tg as a function of time (see Appendix for the model), (2) a DLVO model for flattened spheres to predict the interparticle forces in which the proper conditions to assemble flat−flat doublets are identified, and (3) the doublet formation data of strong yet flexible flat−flat doublets. The long-term aim of this research is to produce flexible colloidal polymers (i.e., “polloids”) consisting of many colloidal particles. This energetically favored flat−flat state might arise if each particle has two flat regions. In order to better understand the energetic interactions of polloidal chains, the simplest structure to build and study is a doublet. In this paper we explore the experimental conditions for fabrication of doublets consisting of two flattened polymer colloids.
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Figure 1. Local separation distance h(r, δ)/a between particles with radius a and flat radius s. The distance of closest approach between two particles is denoted by δ (shown in the inset schematic). For this plot, δ/a = 0.02 was chosen (i.e., a δ = 20 nm gap for particles of radius a = 1 μm). The geometry of the pairwise interaction, cylindrically symmetrical, is shown by the h(r, δ)/a function for a particle with a sphere−sphere (blue, sph-sph), flat−sphere with s = 0.25a (magenta, f l0.25-sph), flat−flat with s = 0.25a (purple, f l0.25-f l0.25), flat-sphere with s = 0.75a (brown, f l0.75-sph), and flat−flat with s = 0.75a (green, f l0.75-f l0.75) interaction. The curves are calculated for each configuration from eq 2 and Table 1, respectively.
DLVO MODELING OF PARTICLE−PARTICLE INTERACTIONS At ionic strengths of 0.1 mM salt or less, our flattened particles remain stable and do not aggregate, similar to the original unflattened particles. The Debye length11 (κ−1), where ⎛ 2z 2n e 2 ⎞1/2 ∞ ⎟ κ = ⎜⎜ ⎟ ε kT ⎝ ⎠
(the valence z = 1 for KCl, n∞ is the bulk ionic strength, e is the proton electric charge, and ε is the permittivity of the water), is κ−1 = 30 nm at 0.1 mM KCl. To induce flocculation, the ionic strength of the solution is therefore increased. The higher ionic strength screens electrostatic repulsions between the particles and enables aggregation by van der Waals attractive forces. The Derjaguin−Landau−Verwey−Overbeek (DLVO) theory10,11,21−23 is used as a guide to predict colloidal stability and identify conditions (salt concentration) where flat−flat interactions are strong, while sphere−sphere and flat−sphere interactions are weak. To do this, we evaluate the depth of the secondary energy minimum as a function of ionic strength for sphere−sphere, flat−sphere, and flat−flat interactions. From this plot, we are able to find a feasible regime to achieve weak sphere−sphere and flat−sphere interactions (25 kT) flat−flat interaction energy, so that we make almost exclusively flat−flat doublets that are very stable in a secondary energy minimum. DLVO theory accounts for the total interparticle energy (ΦDLVO), which includes electrostatic (ΦES in our case strictly repulsive) and van der Waals (ΦVDW attractive) contributions11
parabolic approximation since the results turn out nearly identical.10 For a sphere−sphere (sph−sph) interaction hsph − sph(r , δ) = δ +
Table 1. Local Separation Distance h(r, δ) between Two Particles with Radius a and Flat Radius s for Flat−Sphere and Flat−Flat Configurations, Using the Parabolic Approximation Shown in Eq 2 for a Sphere−Sphere Interaction if: r≤s
2π
a
V [h(r , δ)]r dr dθ
flat−sphere ( f l−sph)
hfl − sph(r , δ) = δ +
r2 2a
hfl − sph(r , δ) = δ +
r2 s2 − a 2a
r>s
If the energy per area is given by V, then we can approximate the energy between two spheres or flattened spheres using the Derjaguin approximation, assuming cylindrical symmetry, in terms of the radial distance r from the central z-axis and the distance of closest approach between two particles δ
∫0 ∫0
(2)
The result of similar calculations for flat−sphere and flat−flat are summarized in Table 1, with the flats always perpendicular to the central z-axis that goes through the two particle centers.
ΦDLVO = ΦES + Φ VDW
Φ(δ) =
r2 a
flat−flat ( f l−f l)
hfl − fl(r , δ) = δ
hfl − fl(r , δ) = δ +
r 2 − s2 a
Equation 1 uses the electrostatic and van der Waals energies with the proper V functions. A simple expression for electrostatic energies is ΦES = 2πεaζ2e−κδ, but we use the Ohshima model (eqs 43−45 for VES between two parallel flat plates)24 because it is suitable for moderate surface potentials (≥|50 mV|). Lifshitz theory25,26 has been used for the van der Waals energy (VVDW =−AHamaker[h(r, δ), κ−1]/(12πh(r, δ)2) where AHamaker is the Hamaker constant between two parallel flat plates). The Hamaker constant AHamaker was calculated as a function of the local separation distance between two particles h(r, δ) and the Debye length κ−1 in order to consider retardation effects in all configurations27,28 (see Table 5 of ref 27 for a polystyrene-water-polystyrene system and the fitted function, Case 1, in p 237 from Appendix 1 of ref 28). A DLVO plot was numerically integrated (Figure 2) for sphere−sphere,
(1)
where θ is the angular direction, a is the particle radius, and h(r, δ) is the local separation distance function that is different for a sphere−sphere (sph−sph), flat−sphere (f l−sph), and flat−flat (f l−f l) interaction (see Figure 1). The flat radius of each particle is s. We could use the actual geometric equations for a sphere to obtain the separations numerically, but here we use the usual 4087
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Figure 3. Finding the feasible region (labeled as “f l-f l”) for flat−flat doublets. The plot shows the secondary energy minima (|2ndΦmin/kT|) for sphere−sphere (blue), flat−sphere (brown), and flat−flat (olive) configurations of 2.5 μm particles (a = 1.25 μm) with s = 0.55a as a function of Debye length (κ−1). A constant surface charge density (ρs) of ρs ≈ −1 μC/cm2 was assumed to determine the zeta potential (ζ) value for each Debye length, using the Gouy−Chapman result for a sphere:10ρs ≈ εκ(kT/ze)[2 sinh(zeζ/2kT) + (4/κa) tanh(zeζ/4kT)]. The Debye lengths correspond to salt concentrations ranging from 1 to 50 mM KCl. The black horizontal lines mark the cutoff between a strong interaction (≥10 kT) and a very weak interaction (≤5 kT). The light purple vertical bars mark the different regimes where singlets, flat−flat doublets (“f l-f l”), flat−flat and flat−sphere aggregates (“fl-sph + f l-f l”), and clusters are expected.
Figure 2. Pairwise interaction energies (Φ/kT) for sphere−sphere (blue), flat−sphere (brown), and flat−flat (olive) configurations as a function of the separation distance (δ in nm) for 2.5 μm particles (a = 1.25 μm) with a flat radius s = 0.55a and zeta potential ζ = −35 mV at 10 mM KCl (κ−1 = 3.0 nm). The maximum energy and descent into the primary energy minimum are not shown in the plot. Note that the secondary energy minimum for the flat−flat configuration is much deeper (∼27 kT) than flat−sphere (∼3.5 kT) or sphere−sphere (∼2.0 kT) configurations.
flat-sphere, and flat−flat configurations as a function of the separation distance between two particles (δ). The plot zooms in on the secondary energy minimum of each configuration. It can be observed that the sphere−sphere configuration has the weakest secondary energy minimum when compared to the other two particle−particle interactions. In this system, the flat−flat configuration has a secondary energy minimum depth of ∼27 kT. The formation of a doublet is much more favorable if two flattened regions interact, as opposed to two spherical regions. The secondary energy minima as functions of salt concentration are shown in Figure 3. The plot shows where we can expect to find singlets, flat−flat doublets, and a mixture of higher order aggregates. We operate in the region where mostly flat−flat doublets form (i.e., 10 mM monovalent salt with κ−1 = 3.0 nm). From Figure 3, we can deduce that at low ionic strengths (i.e., 1 mM KCl) sphere−sphere, flat−sphere, and flat−flat interactions have secondary energy minima less than 1 kT, where no aggregation would occur. In this low-salt limit, electrostatic repulsion dominates. Conversely, at very high ionic strengths (i.e., 50 mM KCl) all configurations have strong interactions, greater than 10 kT, resulting in strong nonselective aggregation and precipitation from solution. Large, irreversible clusters form. An intermediate regime is needed, where flat−flat doublets can be selectively assembled. At 10 mM KCl, there is a weak secondary energy minimum ( Tg. Previously we raised T above the usual Tg of polystyrene. Here, we decided to use the ambient T, but lower the Tg of the polymer with a plasticizer and cause particle deformation at ambient conditions. In this new technique, we flatten particles at room temperature (20−25 °C) by adding toluene and then rinsing enough toluene off with water to return the Tg of the particles close to the original value. Our current technique consists of four main steps: (1) electrostatically adhering particles in water to a flat surface; (2) allowing a plasticizer (i.e., toluene) to diffuse through the water phase and be absorbed by the polystyrene microspheres to lower the glass transition temperature (Tg) of the system within a controlled time, thus leading to particle flattening at ambient conditions; (3) raising the Tg of the particles to above room temperature by removing sufficient toluene; and (4) detaching the particles from the substrate to obtain spherical polymer colloids with a well-defined flat patch. 4089
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Figure 4. continued to not deforming appropriately on a Si wafer in the autoclave, the exposure to heat decreases the particles’ zeta potential to an unstable value, ζ = −11 ± 5 mV. clusters form. In order to induce the particles to aggregate, we used a moderate ionic strength. We added a solution of potassium chloride (KCl, Sigma-Aldrich) with known conductivity to reach a target concentration of interest (1−50 mM KCl). The test tube (1.5 mL Microcentrifuge Eppendorf tubes, VWR International) with the particles was then mixed well with a vortexer for several seconds to allow the salt solution to be homogeneous. Our DLVO modeling plot (Figure 3) for particle stability as a function of ionic strength guided us to experimentally determine the feasible conditions for the flat−flat doublet assembly. After examining a range of ionic strengths using both our experiments and our modeling, a feasible salt concentration for our experiments was found to be roughly 10 mM KCl (κ−1 = 3.0 nm), where we observed the highest yield of strong doublets and no higher order aggregates. All doublet formation experiments were run at room temperature (20−25 °C).
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RESULTS AND DISCUSSION The flattened particles in water are induced to form dimers by adding salt to increase the ionic strength of the solution. As the electrostatic repulsions between the particles are diminished, they start aggregating due to the attractive van der Waals forces. Guided by our DLVO modeling, we experimentally determined feasible salt concentrations to obtain the highest number of flat−flat doublets. Figure 5 shows how two flattened particles are undergoing rotational Brownian motion. Being in a secondary energy
Figure 4. Issues and solutions on obtaining single flattened polymer particles. Shown is an optical microscopy image (40× air objective) of (a) 2.5 μm amidine-functionalized PSL particles adhered onto a flat glass substrate. Note that local impurities on glass cause the particle deposition to be nonuniform, and thus, (b) particles formed fused clusters after flattening for 6 h at 20 °C using the toluene particleflattening technique. (c) SEM image of 2.5 μm A-PSL particles strongly adhered to a flat RCA-I cleaned Si wafer. The particles space themselves more evenly over the surface compared to glass. (d) SEM image of flattened 2.5 μm A-PSL particles using the toluene particle flattening technique at 20 °C for 3.25 h. These particles have a consistent flat patch size, s = 0.75a ± 30 nm. (e) A-PSL particles adhered to a Si wafer using a standard pressure pressure vessel at 150 °C. The particles locally etch the substrate and create nanowells.40 Sonication was performed to observe the resulting nanowells and the particles with “teeth”, as shown in the SEM image above. In addition
Figure 5. Time-lapse sequence of two particles locking into a flat−flat configuration. The particles start in a flat−sphere configuration, where the particle on the left has its flat region facing the particle on the right. The flat patch on the right-hand side particle is slightly darker, denoted by the arrow. Microscopy images (60× air objective) of 2.5 μm amidine-functionalized PSL flattened particles (s = 0.75a, ζ = −35 ± 5 mV, pH = 5.6 ± 0.4) at 10 mM KCl are shown at (a) 0 s, (b) 5 s, (c) 10 s, (d) 15 s, (e) 30 s, and (f) 2 min. Note that by image (e) the darker region disappears, thus implying that both flat patches have locked. After several minutes, the particles stay in this flat−flat configuration because it has the strongest energetic interaction (∼48 kT compared to 25 kT deep for a ∼1 μm particles with s > 0.50a in 10 mM KCl, the secondary energy minimum disappears at sufficiently low ionic strength. When particles are assembled at a primary energy minimum, they do not break apart with dilution of ionic strength. In fact, that is how doublets are fabricated with the Stimulus-Quench-Fuse technique (ref 18).
Figure 6. Assembling strong and flexible flat−flat doublets. (a) Optical microscopy image (40× air objective) of flattened 2.5 μm amidinefunctionalized PSL particles dispersed in DI water using the toluene particle-flattening technique. (b) A sample from image (a) was taken to the SEM in order to determine the actual size of the flat patch. Measurements were taken for at least 50 particles for each experiment. Shown is an SEM image of 2.5 μm A-PSL particles with s = 0.55a ± 30 nm flat radius. (c) Optical microscopy image (60× air objective) of flat−flat doublets formed at 10 mM KCl (ζ = −35 ± 5 mV at 10 mM KCl, pH = 5.6 ± 0.4). This image shows a 60% doublet yield (number of doublets over number of doublets plus singlets and any higher order aggregates times 100%). (d) Doublets from image (c) become singlets after diluting the ionic strength to 0.1 mM KCl, thus showing that the particles lie in a secondary energy minimum. The optical microscopy image (60× air objective) was taken after several days of dilution. 4091
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It is important to note that there are inevitable factors that limit the doublet yield. The doublet formation process is governed by diffusion-limited aggregation. As more singlets interact to become doublets, the singlet concentration decreases and it subsequently increases the flocculation time. In addition to the significant increase in aggregation time, the probability of two particles finding each other through the flat patch is still the lowest relative to having two particles meeting in a flat−sphere or sphere−sphere state. This is due to the small surface area of the flat region (A) compared to the spherical part of the particle (Afl/Asph < 0.2). Thus, this system does not closely approach a 100% doublet yield in 24 or even 48 h. Also, when imaging takes place in an optical microscope the singlets closest to the glass substrate adhere to the plate quickly if the flat region is facing the flat surface. This is why the particles were allowed to interact for very long times before imaging, in an effort to diminish these limitations. Nevertheless, some of the individual spheres will remain. The formation of colloidal polymers (i.e., “polloids”) with particles that have two flat regions (see Figure 7 of ref 14) is the next step in our research. A polymerization probability p > 0.9 is needed to create significant polloid lengths of flat−flat bonds. For our large bond strengths (>25 kT in the secondary energy minimum), we expect p to be close to 1. Theory indicates that Nn = 1/(1 − p) is the number-average degree of polymerization and Nw = (1 + p)/(1 − p) is the weight-average degree of polymerization for condensation polymerization of linear chains.29 And yet, we see a p for doublets of approximately 0.65. One possibility is to allow our system to flocculate for longer periods of time (several days), which would give a higher Nn and Nw. However, practical issues such as incubation of bacterial growth and decay of the particles’ zeta potential with time at ambient conditions make this difficult. A potential way to increase p from 0.65 (as seen in flat−flat doublets) to 0.99 or higher, on a practical laboratory time scale, will be to significantly increase the concentration of flattened particles.
Different sizes of flat regions on particles were created to study this effect on the doublet formation. The doublet yield was defined as number of doublets over number of doublets plus singlets and any higher order aggregates. Figure 7 shows
Figure 7. Statistics on average yields of singlets and doublet fractions for different flat patch sizes at 10 mM KCl. 2.5 μm amidinefunctionalized PSL particles (ζ = −35 ± 5 mV at 10 mM KCl, pH = 5.6 ± 0.4) were flattened using the toluene particle-flattening technique. Over 2000 particles were counted per each experiment, leading to a 95% confidence interval of ±1 particle. Each experiment was performed at least 3 times. As the flat patch increases, the average doublet yield increases as well. No higher order aggregates (e.g., trimers) were observed.
the statistics at 10 mM KCl on four different sets of data, 2.5 μm particles with an s of 0.00a, 0.25a, 0.55a, and 0.75a. At s = 0.25a, there was a 30% average doublet yield. This is expected since the flat−flat configuration has a relatively weak energetic interaction of ∼7 kT. Thus, the dissociation time for a doublet to break apart with an association energy of ∼7 kT is on the order of minutes and the predicted flocculation time (τfl−f l) for particles with an s of 0.25a is on the order of days. However, for particles with an s of 0.55a and 0.75a, the flat−flat energetic interaction is greater than ∼25 kT. In this case, the dissociation time for a doublet to break apart is predicted to be extremely long, as discussed above. Thus, the number of experimentally observed doublets increased with increasing flat radius. The largest observed average doublet yield percentage for our flattened spheres was ∼65%. In contrast, spherical particles of similar zeta potential (ζ = +30 ± 5 mV, pH = 5.6 ± 0.4) at 10 mM KCl do not form doublets at all. In addition to this significant yield increase from the control experiments, our readily obtained doublet yield greatly exceeds that of existing doublet fabrication methods with diffusion-limited kinetics, whose doublet yield is only ∼20−40%.16−19 Hence, localized flat spots on spherical particles can enhance the doublet yield obtained from full spheres from nonexistent at 10 mM KCl to ∼65%. We tried one further control experiment, to test the hypothesis that at high ionic strength (>50 mM KCl) doublets would form in a primary minimum for all three cases: sphere− sphere, flat−sphere, and flat−flat interactions. The experiments showed higher order aggregates of micrometer-sized amidinefunctionalized PSL flattened particles for all three cases. At such high salt concentrations, all three configurations yield large clusters and appear to fall in a primary energy minimum, giving no preferential orientation.
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CONCLUSIONS We have developed a method for producing micrometer-sized polymer particles with localized circular flat spots. By introducing a slight physical asymmetry to spherical colloids with the toluene particle-flattening technique, we are able to significantly strengthen typical energetic particle−particle interactions. The DLVO modeling for flattened particles provided guidance for finding a feasible regime to exclusively assemble doublets with a preferential energetic interaction of flat face to flat face. Our experiments showed that at 10 mM KCl a 65% average doublet yield is obtained, where micrometer-sized particles with an s > 0.50a flat patch have a strong flat−flat interaction (>25 kT) and a weak flat−sphere and sphere−sphere interaction (
