Langmuir 1995,11, 2975-2978
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Size-Dependent Separation of Colloidal Particles In Two-Dimensional Convective Self-Assembly Mariko Yamaki," Junichi Higo, and Kuniaki Nagayama Nagayama Protein Array Project, ERATO, JRDC, 5-9-1 Tokodai, Tsukuba, 300-26Japan Received November 30, 1994. In Final Form: May 17, 1995@ We report a new phenomenon, size-dependent separation of colloidal particles in two-dimensional (2D) convective self-assembly that takes place in a wetting liquid film on a mercury surface [TLuo-dimensional (20)convectiveassembly (Nagayama,K. Phase Transition 1993,45,185)].Duringthe drying of suspensions of colloidal particles in wetting films, homogeneously mixed particles in the suspensions separated and assembled according to their size. In this size-dependentseparation of particles, large particles gathered in the center and were surrounded by small particles. To obtain a better understanding of this new phenomenon, we performed experiments on the convective assembly of particles on a mercury surface using binary mixtures of particles that ranged in size from 144 to 12 nm in diameter. To study the mechanism of this size-dependentseparation, we also did computer simulations in which we accounted for two types of assembly forces, lateral capillary force and convective flow, that we have been extensively studyingin actual assembly systems. The simulationssuccessfully reproduced a size-dependent separation of particles that was identical to that for the actual assembly systems. From the results of our experiments and simulations, we found that the mechanism that was concluded for the convective assembly also governs the size-dependent separation of particles in the actual assembly systems.
Introduction Our method for forming two-dimensional (2D)arrays of colloidal particles from suspensions on deformable surfaces, such as mercury,l and on solid surfaces, such as a glass late,^*^ relies mainly on two types of forces that occur specifically in a wetting liquid film: lateral capillary force4and convectivef l o ~ . Lateral ~ , ~ capillary force arises from an imbalance of the surface force arising from differences in curvature of the liquid surface due to the roles particles play in p a ~ k i n g .Convective ~ flow in the wetting film that is driven by the evaporation of the liquid that occurs predominantly at clusters of the particles carries the particles to the cluster^.^^^ Because ofits nature of self-assembly, we call this formation of 2D arrays of particles convective self-assembly.5 We have extensively studiedldnvective self-assembly by using many types of colloidal particles, such as proteins,1*6-8v i r u ~ e s ,and ~ polystyrene p a r t i ~ l e s . ~ , ~While J ~ - ~studying ~ the assembly of polystyrene particles on a mercury surface for particles with a 250-nm nominal diameter and a large standard deviation of f3.4nm, we accidentally discoveredthat these particles separated in the 2D assembly due to differences in their size. In the resulting arrays, the larger particles formed an array and were surrounded by the smaller particles, as seen in the electron microscope image in Abstract published in Advance ACS Abstracts, July 15, 1995. (1)Yoshimura, H.; Matsumoto, M.; Endo, S.; Nagayama, K. UZtramicroscopy 1990,32,265. (2)Denkov, N. D.; Velev, 0. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Langmuir 1992,8,3183. (3)Denkov, N. D.; Velev, 0. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature 1993,361,26. (4)Kralchevsky, P.A.;Nagayama, K. Langmuir 1994,IO,23. ( 5 )Nagayama, K.Phase Transition 1993,45,185. (6)Akiba, T.;Yoshimura, H.; Namba, N. Science 1991,252,1544. (7)Ishii, N.; Yoshimura, H.; Nagayama, K.; Kagawa, Y.; Yoshida, M. J. Biochem. 1993,113,245. (8)Yamaki, M.; Matsubara, K.; Nagayama, K. Langmuir 1993,9, 3154. (9)Nagayama, K.Mater. Sci. Eng. 1994,CI,87. (10)Dushkin, C.D.; Yoshimura, H.; Nagayama, K. Chem.Phys.Lett. 1993,204,455. (11)Dimitrov, A.; Dushkin, D.; Yoshimura, H.; Nagayama, K. Langhuir 1994,10,432. (12)Lazarov, G.S.;Velev, 0. D.; Denkov, N. D.; Kralchevsky, P. A.; Nagayama, K.J. Chem. Soc. Faraday Trans. 1994,90,2077. (13)Higo, J.; Nagayama, K. J. Chem. Phys. 1993,99,9156. @
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Figure 1. A transmission electron microscope image of twodimensional arrays of 55-nm polystyrene particles with a size dispersion of f3.4nm produced on a mercury surface by twodimensional convective assembly. Figure 1. This phenomenon may be hrther developed into a method for fractionating particles on the basis of their size. To obtain a better understanding of this new phenomenon, size-dependent separation, we performed systematic experiments using mixtures of colloidal particles of different sizes, namely, ferritin, polio virus, and polystyrene particles. Each mixture was a binary mixture containing two different particle sizes, large and small. We also did computer simulations to reproduce the separation seen in these experiments by assuming that the two forces described above were the major forces governing the assembly of the particles.
Experiments Materials. For the colloidal particles, we used different sizes of ferritin (an iron storage protein), polio virus, and polystyrene particles. Purified ferritin (12 nm in diameter, from horse spleen,
0743-7463/95/24 11-2975$09.00/0 0 1995 American Chemical Society
Yamaki et al.
2976 Langmuir, Vol. 11, No. 8,1995
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Figure 2. Transmission electron microscope images of two-dimensional arrays obtained from sample solutions containing various combinations of particle sizes. (A) polystyrene particles, 55 f 3.4 nm and 144 f 2.0 nm in diameter; (B) polystyrene particles, 95 f 2.0 nm and 144 f 2.0 nm in diameter; (C) horse spleen ferritin, 12 nm in diameter, and polystyrene particles, 22 f 3.3 nm in diameter; (D) ferritin, 12 nm in diameter, and polio virus, 30 nm in diameter.
from Boeringer Mannheim) was kindly supplied by Ms. K. Matsubara of this (the Nagayama Protein Array) project.8 Polio virus (30 nm in diameter) was a generous gift from Mr. S. Mori and Professor S. Shigeta at Fukushima Medical College. Polystyrene particles of 22 f 3.3 and 38 f 5 nm diameter were purchased from Interfacial Dynamics Co., those of 55 f 3.4,61 f 3.8, 79 f 2.3, 95 f 2.0, 117 f 3.0, 136 f 3.8, and 144 f 2.0 nm diameters were obtained from Japan Synthetic Rubber Co. Preparation of 2D Arrays. Sample solutions of these colloidalparticles were prepared by mixing suspensions of large particles 11% (w/v)lwith suspensions of small particles (1%[w/vl) at a volume ratio of 1:3. For the mixtures of the polystyrene particles, we always used 144nm particles as the large particles. We loaded 5pL of each sample solution (containing 10%glucose) on a 260-cm2mercury surface to provide an initial thickness of 190nm of the solution on the mercury surface, as detailed in our previous report.8 Transmission electronmicroscope observations of the arrays of these particles thus obtained were made as previously rep0rted.l9~-~ Order Parameter. To better understand size-dependent separation, we defined an order parameter for the 2D arrays of polystyrene particles as follows. This parameter represents the degree of separation and is defined as the ratio of the number of large particles surrounding a large particle to the maximum number of large particles that can surround the particle in a close-pack configuration, which is six. (For simplicity, we only used the results of the polystyrene particles for this analysis, because there was strong adsorption of the ferritin to the
polystyrene particles in their combination mixtures.) First, we looked at a large particle and counted the number of the nearestneighbor large particles. If a large particle was surrounded by six large particles (whichis called close-packing),then the order parameter was 1 (6/6). If a large particle was surrounded by four large particles, then the order parameter was 4/6 (0.67). Thus, a high-order parameter indicated distinct separation and a low-order parameter indicated poor separation. We surveyed 100 particles at random for each experiment. We then plotted the order parameter against a radii ratio, RJR1, where R, and RIare the radii of the small particles and large particles, respectively. The radii ratio ranged from 0.15 (22 nm/ 144 nm) to 0.94 (136 n d 1 4 4 nm). We determined order parameters and radii ratio for both the experiments involving actual particle systems and for the simulations. Simulations. A programthat was developed in-houseto study the aggregation process of model particles13was applied to the simulations here, namely, 2D assembly of particles in a wetting film. The Monte Carlo method by Metropolis14was used to simulate the behavior of the particles in a mixture of 37 large particles and 84 small particles in the presence of two types of forces, lateral capillary force and convective flow (detailed later in this paper). We did not account, however, for a rupture of the wetting film during its thinning process. We represented the particles by disks in a 2D space, and to simplifythe simulations, (14)Metropolis, N.; Rosenbluth,A. W.; Rosenbluth,M. N.; Teller,A. H.; Teller, E. J. C h m . Phys. 1963,21,1087.
Langmuir, Vol. 11, No. 8, 1995 2977
Size-Dependent Separation of Colloidal Particles we used a two-body expression. Thus, the interaction energy for the two forces is given by
E = 0.5 log r (1) where r is the distance between the centers of the particles, and the energy E is nondimensional. We note that this equation is a good approximation to experimentally obtained values for lateral capillary force.12 We discriminatedthe lateral capillaryforce from the convective flow by differentiating the way that particles interacted with their nearest neighbors and with other particles (the details will be described later). At each step in the simulations, random forces with a standard deviation (Le., 5.0 divided by particle radius) were applied to all particles. The Boltzmann contant and temperature were set to 1and 0.1, respectively. We rejected configurationsthat involved the overlappingof particles. In the initial configurations, the particles were randomly distributed within a square region (50 x 50, nondimensional)and the radius of a large particle was set to 1. Because we applied no boundary conditions, the particles could escape from the square region unless eq 1was applied. The initial thickness of the solution was set to the diameter of a large particle in the mixture. To model the evaporation of water in the wetting liquid film, we set the thickness to decrease at a constant rate, with the simulation finishing when the thickness reached zero. We considered the role of water in the medium in the assembly only as the origin of surfacetension that is responsiblefor both the lateral capillary force and the convective f l o ~ . ~ - ~ In these simulations,we discriminatedtwo stages,called stages 1and 2, in the thinning process of the wetting film. In stage 1, where the thickness was between R1 and R, (Le., where large particles protrude from the wetting film surface and small particles are suspended in the wetting film),only large particles were allowed to interact as follows. Each largeparticle interacted with the twelve nearest large particles by lateral capillary force and with the large particles other than the particle of interest by convective flow. In this stage, small particles only fluctuated by random force. In stage 2, where the thickness was smaller than R,(Le., where both large and smal particles protrude from the wetting film surface),all particles interacted with the twelve nearest neighbors by lateral capillaryforce and with the particles other than the particle of interest by convective flow. To quantitativelyidenti$ the effect of a size differencebetween the particlesin a mixture, wevariedR, while& was kept constant for a range of RJR1 from 0.300to 0.975. For each R,, we made 10 simulations, each starting with a different random configuration. In addition, we tested two evaporation rates, 4 x and 1x step-l. To analyzethe final configurationsobtained from these simulations,we defined order parameters as described above but with the following modificationsto normalizethe scale of the order parameter required. We first determinedthe number of contacting pairs in a final configuration,where we defined a contacting pair as two large neighboring particles within a distance 2R1+ 0.1 of each other. To obtain the order parameter, we then normalized these numbers by 4.86, which was then average number of contacting pairs for the 37 large particles when all these particles were assembled in a hexagonal closepacking structure (Note: because the large particles at the boundary of this group of 37 particles did not have six nearest neighbors,the averagenumber of nearest neighbors for the entire group that corresponded to close-packingwas less than six).
Results
As describedabove,we always used 144-nmpolystyrene particles as the large particle in the binary mixtures of polystyrene particles. The polystyrene particles of 55and 61-nm diameterswere clearly separated from the 144nm particles; the electron microscope image in Figure 2A shows round arrays of the 144-nm particles surrounded by the 55-nm particles. On the contrary, when 144-nm particles were combined with 95-nm particles, particles of both sizes appeared mixed in the center of the array, with this mixed groupingbeing enclosed by 95-nmparticles (Figure 2B). In a mixture with ferritin (12 nm in 'diameter),each 22-nm particle was surroundedby ferritin
Figure 3. The final configuration from a simulation, where step-l. R$Rl= 0.5 and the evaporation rate was 4 x
+
1
% e
0
0
03
0.4
0.6
0.8
1
ratio of radius (R,JRl) Figure 4. Order parameter as a function of radii ratio for a system containing two particle sizes, for the experiments (e) and simulations at evaporation rates of (0)4 x stepd1and (0)1 x step-l.
molecules. These ferritin-covered polystyrene particles associated to form round arrays and were separated from the rest of the ferritin molecules, as shown in Figure 2C. Ferritin was separated from polio virus, which appeared as a small cluster in the center (Figure 2D). Thus, mixed particles with large size differenceswere clearly separated from each other, resulting in round arrays of larger particles in the center (Figure2A,C,D). On the other hand, particles of similar size remained as a homogeneous mixture (Figure 2B). We then did simulations for various binary mixtures assuming an evaporation rate of 4 x low4step-l. Figure 3 shows the final configurationof the simulation for R$Rl = 0.5. This simulated image reproduced the electron microscope images of the actual assembly systems on a mercury surface (Figure 2). Figure 4 shows profiles of the order parameter as a function of R$Rl obtained both for the actual assembly systems and for the simulated systems (Figure 4). The two profiles agree well with each other, with both indicating discernible separation when R$Rl is smaller than 0.5. We also tested another evaporation rate, 1 x step-l, for the simulations. The results indicated
2978 Langmuir, Vol. 11, No. 8, 1995 that slow-speed evaporation produces better separation (closed circles in Figure 4) than high-speed evaporation step-l, open circles in Figure 4). (4 x To understand the role of the convective flow, we also did simulations that did not account for this force. The simulations that accounted for the convectiveflow of small particles in stage 1 indicated no discernible separation for any particle size combination. These simulations indicated three types of small aggregates: large particles, small particles, and a mixture of both particles (data not shown).
Discussion By using particles of various sizes in experiments involving actual assembly systems and in simulations, we illustrated that the ratio of the particle sizes (Le., radii ratio) is critical in separating these particles when two particle sizes are present. The profiles of the order parameter as a function of the radii ratio of the particle sizes for the actual assembly systems, that is, 2D assembly on a mercury surface (Figure 4) show that the degree of the separation between the particle groups becomes discernible when the radii ratio approaches a value of 2. More importantly, this profile of the actual systems is identical to that for the simulated systems (Figure 4) that assumed two major forces, lateral capillary force and convective flow. In spite of this agreement, in the actual assembly systems there are also other processes involved, such as spreading of a sample solution on a mercury surface1and adsorption of particles on a mercury surface (Dimitrov et al., in preparation). Thus, we can conclude first that two forces, namely, the lateral capillary force and convective flow, which govern the 2D assembly also govern the size-dependent separation. In the simulations, when we assumed that the convective flow acted on both small and large particles in the early stages of the assembly, however, we reproduced no discernible separation. Consequently, we further conclude that the convec-
Yamaki et al. tive flow is effective mainly for large particles in the early stage of the assembly in the actual systems. We must discuss this different effect of the convective flow on large particles and on small particles in the early stage of the assembly in the actual systems, because we believe that the convective flow might also drive small particles during that early stage. We suspect one possibility is that the random force strongly drives small particles in the actual systems and, consequently, dominates the convective flow, essentially canceling it out. Another possibility is the role of a rupture in a wetting film because a wettingfilm is not stable when it is thinned to the size of particles smaller than 100 nm.l0J1 In this respect, we speculate that wetting films are stabilized by colloidal particles and t h a t this stabilization differs according to the difference in the particle sizes. In this article, we have demonstrated a new phenomenon, size-dependent separation of colloidal particles in a wetting film by convective self-assembly. The details of the mechanism in this phenomenon, however, need further clarification. Many currently available techniques for fractionating particles, such as centrifugation, sedimentation, sieving and field-flow fractionation, and its variants are generating interest as effective methods for fractionating particles the sizes of which span the submicrometer range (Le., 10-1000 nm).15 For all of these techniques, however, improvement in the degree of fractionation is strongly needed. In this study, we gained a better understanding of the mechanism of size-dependent separation, which should help to improve these particle separation techniques.
Acknowledgment. We thank Dr. S. Ebina (this project) for critiquing this manuscript. LA9409485 (15) Janca, J.;Field-Flow Fractionation; Marcel Dekker: New York,
1988.
