pubs.acs.org/Langmuir © 2010 American Chemical Society
Directed Self-Assembly of Spheres into a Two-Dimensional Colloidal Crystal by Viscoelastic Stresses Rossana Pasquino,*,† Frank Snijkers,‡ Nino Grizzuti,† and Jan Vermant‡ †
Department of Chemical Engineering, University Federico II, Naples, Italy, and ‡ Department of Chemical Engineering, K.U. Leuven, Leuven, Belgium Received December 18, 2009. Revised Manuscript Received January 28, 2010
Ordering induced by shear flow can be used to direct the assembly of particles in suspensions. Flow-induced ordering is determined by the balance between a range of forces, such as direct interparticle, Brownian, and hydrodynamic forces. The latter are modified when dealing with viscoelastic rather than Newtonian matrices. In particular, 1D stringlike structures of spherical particles have been observed to form along the flow direction in shear thinning viscoelastic fluids, a phenomenon not observed in Newtonian fluids at similar particle volume fractions. Here we report on the formation of freestanding crystalline patches in planes parallel to the shearing surfaces. The novel microstructure is formed when particles are suspended in viscoelastic, wormlike micellar solutions and only when the applied shear rate exceeds a critical value. In spite of the very low volume fraction (less than 0.01), particles arrange themselves in 2D crystalline patches along the flow direction. This is a bulk phenomenon because 2D crystals form throughout the whole gap between plates, with the gap thickness being much larger than the particle size. Shear flow may hence be an easy method to drive particles into crystalline order in suspensions with viscoelastic properties. The crystalline structure reported here could be used to design new materials with special mechanical, optical, thermal, or electric properties.
Introduction The flow behavior of particle suspensions in viscoelastic matrices is an active research field because of its relevance in many different technological areas, which range from consumer care products to biological materials to nanocomposites. In recent years, rheological, scattering, and computer simulation techniques have been used to study the occurrence of ordered microstructures induced by the application of a simple shear flow, mainly focusing on concentrated suspensions in Newtonian matrices.1-6 In dilute and semidilute suspensions, spheres are expected to form strings in the flow direction7-10 yet only in the presence of both shear thinning and elasticity of the suspending fluids. The alignment of spheres in the flow direction has never been detected in Newtonian suspending media or Boger fluids,9 even after long shearing times. Along with alignment, the complex rheological behavior of the suspending medium influences other microstructural phenomena, such as migration.11 In the concentrated regime, with no imposed flow and when the particle volume fraction φ exceeds 0.5, monodisperse hard spheres begin to order into a macrocrystalline structure of centered cubic cells (FCC) or hexagonal close packing (HCP). When ordered phases are forced to flow, these 3D crystals give way to 2D layered structures, parallel to the shearing direction.12 *Corresponding author. E-mail:
[email protected].
(1) McMullan, J. M.; Wagner, N. J. Rheol. 2009, 53, 575–588. (2) Vermant, J.; Solomon, M. J. Phys.: Condens. Matter 2005, 17, R187–R216. (3) So, J. H.; Yang, S. M.; Hyun, J. C. Chem. Eng. Sci. 2001, 56, 2967–2977. (4) Krieger, I. M.; Dougherty, T. J. Trans. Soc. Rheol. 1959, 3, 137–152. (5) Bossis, G.; Brady, J. F. J. Chem. Phys. 1989, 91, 1866–1874. (6) Bender, J. W.; Wagner, N. J. J. Colloid Interface Sci. 1995, 172, 171–184. (7) Michele, J.; Patzold, R.; Donis, R. Rheol. Acta 1977, 16, 317–321. (8) Lyon, M. K.; Mead, D. W.; Elliot, R. E.; Leal, L. G. J. Rheol. 2001, 45, 881– 890. (9) Scirocco, R.; Vermant, J.; Mewis, J. J. Non-Newtonian Fluid Mech. 2004, 117, 183–192. (10) Won, D.; Kim, C. J. Non-Newtonian Fluid Mech. 2004, 117, 141–146. (11) Highgate, D. Nature 1966, 211, 1390–1391. (12) Ackerson, B. J. J. Rheol. 1990, 34, 553–590.
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In this work, the formation of shear-induced microstructures in dilute (0.004 < φ < 0.01) suspensions of hard spheres in a wormlike micellar solution is studied experimentally. Wormlike micellar liquids have received considerable attention as convenient model systems for rheological research.13,14 Micelles are elongated semiflexible aggregates created by the self-assembly of surfactant molecules in water. Under the proper conditions, micelles can grow and entangle, exactly like polymers, thus imparting viscoelasticity to the fluid. First, the induced microstructure is studied as a function of the imposed shear rate. The dynamics of a particle inside the induced string is probed. The direct self assembly of spheres induced by the nonlinear behavior of the suspending medium is observed when the shear rate exceeds a specific value. Particles arrange themselves into 2D crystalline patches aligned in the flow direction; this is a completely new phenomenon for such dilute suspensions and could be used to design new innovative materials.
Experimental Results and Discussion The suspensions were prepared by dispersing spheres in a wormlike micellar solution. Particles were self-synthesized monodisperse polystyrene spheres (PS, diameter 1.2-2.8 μm),15 nearly monodisperse poly(methyl methacrylate) spheres (PMMA, diameter 15 μm, Spheromers CA15, microbeads), and polydisperse glass beads (160-190 μm diameter, Flex-o-Lite). Our suspending medium is a solution of 100 mM cetyl pyridinium chloride (CPyCl, Merck), 60 mM sodium salicylate (NaSal, Fluka), and 100 mM sodium chloride (NaCl, Fisher scientific) in demineralized, doubly distilled water.16,17 The linear viscoelastic properties (Figure 1b), the steady-state viscosity η, and the first normal difference N1 (Figure 1a) were measured using an ARES strain-controlled
(13) (14) (15) (16) (17)
Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869–6892. Yang, J. Curr. Opin. Colloid Interface Sci. 2002, 7, 276–281. Reich, S.; Almog, Y.; Levy, M. Br. Polym. J. 1982, 14, 131–136. Miller, E.; Rothstein, J. P. J. Non-Newtonian Fluid Mech. 2007, 143, 22–37. Rehage, H.; Hoffmann, H. J. Phys. Chem. 1988, 92, 4712–4719.
Published on Web 02/04/2010
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Figure 1. Rheology of surfactant solution at 23 °C. (a) Steadystate viscosity η, shear stress σ, and first normal stress difference N1 as function of shear rate. (b) Elastic (G0 ) and loss (G00 ) moduli as a function of angular frequency (applied strain 20%). rheometer (TA Instruments, Newcastle DE) equipped with a sensitive 100 g/(g 3 cm) transducer. Measurements were performed using cone and plate (plate diameter 50 mm and cone angle 0.1 rad) and parallel plate (plate diameter 50 mm) geometries. The results clearly show that the fluid is strongly shear-thinning (power law index of about 0.3), and its viscoelasticity is well described by a Maxwell model with a single relaxation time of about 1 s. The fluid displays shear banding for shear rates higher than 3 s-1,16 as evidenced by the stress plateau in Figure 1. The development of the microstructure was followed by means of a rheo-optical parallel plate transparent flow cell (CSS 450, Linkam) equipped for both optical microscopy (Leitz, Laborlux 12 POL-S) and small-angle light scattering (SALS). Some experiments were also performed with a custom-made counterrotating rheometer.18 Shear flow start-up experiments were performed within a wide range of shear rates (0.5-100 s-1). It was always verified using microscopy that before start-up a random particle distribution was present. At shear rates below 1 s-1, the particles stayed randomly distributed. When the suspension was sheared at slightly higher shear rates, between 1 and 10 s-1, elongated 1D stringlike structures developed, regardless of particle size. One example of such strings is shown in Figure 2a. Experiments in the counterrotating device were performed in order to follow the rotation of the particles and test their stability in the induced string. In this case, larger glass particles (160190 μm diameter, Flex-o-Lite) were used with a volume fraction of 0.004 in a parallel plate geometry with a gap of 1 mm. In particular, the period of rotation of a single particle was measured by tracking the motion of either an optical imperfection present on the surface or air inclusions inside the particle. It was then (18) Snijkers, F.; D’Avino, G.; Maffettone, P. L.; Greco, F.; Hulsen, M. A.; Vermant, J J. Rheol. 2009, 53, 459–480.
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Letter possible to monitor the rotational behavior of a particle during the formation of a string. The particle angular velocity, scaled to the macroscopic shear rate, is plotted in Figure 2b as function of the experimental time (left axis). The mean distance between the traced particle and its two nearest neighbors, normalized for the particle diameter, is shown on the right axis. The rotation of the traced particle slows down more and more as the particle becomes part of the string, and it is always lower than for the case of an isolated particle.18 Furthermore, the traced particle seems to “fluctuate” in the string while the distance between the particles becomes gradually smaller. Figure 2b confirms that, as the particle becomes embedded in the ordered microstructure, string stabilization is accompanied by the suppression of particle rotation. Different explanations have been put forward to explain string formation. Giesekus argued that particles are being brought together under the effect of normal stress differences.19 However, it has been shown experimentally9 that elasticity is not a sufficient condition for string formation but substantial shear thinning is also required. The role of shear thinning is not yet settled; it has been suggested that shear thinning affects the hydrodynamic lubrication forces,9 whereas for the case of aligning spheres in sedimentation experiments, the effects of viscoelasicity have been suggested to create “evanescent corridors of reduced viscosity”20,21 with viscoelastic memory effects playing an important role. When the shear rate is increased, in spite of the very low volume fraction, particles start to arrange themselves in patches lying in the shear planes, aligned in the flow direction (Figure 3a). Optical microscopy showed that the structure is a 2D layered crystal. Such a structure, which is not formed in purely viscous fluids, is from directed self-assembly induced by the viscoelastic nature of the suspending medium and has never before been observed. For the particular case of the 2.8 μm beads shown in Figure 3a, patches of particles had an elongated shape with an average length (along the flow direction) of ca. 150 μm and a width of ca. 30 μm. Twodimensional crystal dimensions obviously depend on many factors, such as particle size, particle concentration, flow geometry, and intensity. The 2D crystal microstructure has been observed for the other PS particles with different sizes and for larger PMMA particles. For the smaller particles, the crystalline character of the 2D structure is confirmed by SALS measurements, showing the presence of a hexagonally close packed layer (Figure 3b). For the case of PS spheres, crystals begin to form at a critical shear rate of about 10 s-1 and they become more pronounced at higher shear rates. The distance d between the spheres can be calculated from the local maximum in the scattering intensity, I, in the θ direction (Figure 3b) according to the equation d = 2π/q = (λ/2)(1/sin(R/2)), with R being a polar angle. For the case shown in Figure 3, the characteristic length corresponds to about one particle diameter, indicating that particles touch each other or that very thin layers of fluid are wedged between them. Even if no definitive explanation can be given for the crystal formation, we can suggest at least two mechanisms, possibly strictly correlated, that could give rise to this particular phenomenon. As outlined before, the fluid is shear-banding; this means that layers of fluid sheared at different rates may form through the gap thickness, leading to preferential particle migration toward layers with lower shear rates. In addition, the formation of patches may be determined by the concurrent action of both a first (positive) and a second (negative) normal stress difference, giving rise to a sort of biaxial flow. In fact, nonnegligible N2 values have been measured in wormlike micellar solutions.22,23 As a final note, (19) Giesekus, H. Z. Angew. Math. Mech. 1978, 58, T26–T37. (20) Joseph, D. D.; Liu, Y. J.; Poletto, M.; Feng, J. J. Non-Newtonian Fluid Mech. 1994, 54, 45–86. (21) Joseph, D. D.; Liu, Y. J. J. Rheol. 1993, 37, 961–983. (22) Lee, J.-Y.; Magda, J. J.; Hu, H.; Larson, R. G. J. Rheol. 2002, 46, 195–208. (23) Kadoma, I. A.; Van Egmond, J. W. Phys. Rev. Lett. 1998, 80, 5679–5682.
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Figure 2. Stringlike microstructure. (a) Flow alignment in a micellar solution filled with PMMA particles (bead diameter d = 15 μm, volume fraction φ = 0.008) after one hour of shearing at 3 s-1. The gap between parallel plates is 500 μm. (b) Scaled particle angular velocity (left axis) and the mean distance between the traced particle and its neighbors (right axis), normalized for the particle diameter, as function of the relative experimental time (between two consecutive frames). The shear rate is 2 s-1.
Figure 3. Crystal formation. (a) Optical microscopy image of the 2D crystal formed by PS particles (bead diameter d = 2.8 μm, volume
fraction φ = 0.008) after 1 h of shearing at 30 s-1. The gap between the parallel plates is 100 μm. (b) Small-angle light scattering pattern after 1 h at 15 s-1. (c) Intensity of the scattered light as a function of the scattering vector in the q direction for different values of the shear rate.
it should be remarked that wormlike micelles may alter the colloidal interaction forces24 and whereas these attractive force are expected to be isotropic in nature and do not lead to the formation of sheets they may help to stabilize the structures. Several methods have been presented for the assembly of spheres in 2D sheets, for example, using specific chemistries with directional colloidal interactions, templating, or using capillary interactions between particles at interfaces. (See, for example, Srivastava and Kotov for a recent review.25) Other groups have exploited electric fields.26 The present work exploits the properties of the fluid (i.e., the viscoelasticity and shear banding) to direct (24) Jodar-Reyes, A. B.; Leermakers, F. A. M. J. Phys. Chem. B 2009, 113, 11186–11193. (25) Srivastava, S.; Kotov, N. A. Soft Matter 2009, 5, 1146–1156. (26) Singh, J. P.; Lele, P. P.; Nettesheim, F.; Wagner, N. J.; Furst, E. M. Phys. Rev. E 2009, 79, 050401.1–050401.4.
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the assembly of spheres into 2D structures. In contrast to other methods of flow processing of colloidal dispersions,27 the present method works at low concentrations. It has the potential of being used under different conditions and for different products, for example, to induce free-standing crystalline patches inside a bulk material.
Conclusions The experimental results shown in this letter demonstrate that relevant structural organizations of spherical particles in viscoelastic fluids can be obtained by the application of simple shear flow. In particular, the peculiar viscoelastic behavior of the (27) Shereda, L. T.; Larson, R. G.; Solomon, M. J. Phys. Rev. Lett. 2008, 101, 038301.1–038301.4.
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wormlike micellar solution used in this work is responsible for the onset of microstructure formation. Such a peculiar rheological response determines the formation of stringlike structures at low shear rate and 2D planar crystals at high shear rate. The latter microstructure, to our knowledge, has never before been generated under shear flow in dilute systems. This result gives the possibility of easily built up layered, well-ordered 2D crystalline structures in viscoelastic fluids.
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This technique bears the potential for innovative applications in several different fields, from the design of materials with special anisotropic physical barrier properties to the fabrication of highly selective membranes to the development of microfluidic-based selective separation processes. Acknowledgment. F.S. thanks FWO-Vlaanderen for a graduate fellowship. J.V. acknowledges support of the EU through FP7, project Nanodirect NMP4-SL-2008-213948.
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