J. Phys. Chem. B 2000, 104, 5681-5685
5681
Fractal and Dendritic Growth of Metallic Ag Aggregated from Different Kinds of γ-Irradiated Solutions Shizhong Wang*,†,‡ and Houwen Xin‡ Department of Scientific History and Archaeometry and Department of Chemical Physics, UniVersity of Science and Technology of China, Hefei 230026, People’s Republic of China ReceiVed: January 18, 2000; In Final Form: March 28, 2000
With γ-irradiation on AgNO3 dissolved in deionized water, ethanol, and 0.01 M C12H25NaSO4, metallic Ag with different dispersed states and particle sizes was obtained. In the former two solvents, metallic Ag particles precipitated from the solutions and the Ag particle size was about 100 and 20 nm, respectively. In the latter solvent, Ag colloid was produced. The morphology of structures formed during two-dimensional aggregation of Ag particles in three different solvents was studied by transmission electron microsocopy (TEM). The patterns were dendrite, fractal (with center), and fractal (no center) with the fractal dimension of 1.81, 1.73, and 1.70 corresponding to the aggregating structure from deionized water, ethanol, and 0.01 M C12H25NaSO4 solutions, respectively. The formation mechanism of different patterns was illustrated from different aspects.
1. Introduction Many physical, chemical, technological, and biological processes exhibit noninteger (or fractal) dimensionality as was recognized by Mandelbrot in his studies on complex geometrical shapes.1 Fractals are generally observed in far-from-equilibrium growth phenomena; hence they provide a natural framework for the study of disordered systems. There are many reports on the study of fractal structure and their formation in both theoretical and experimental aspects in the past decade. Electrochemical metallic deposition,2-4 fluid and air displacement in other media,5,6 and dielectric breakdown7 are a few experimental examples which are important for understanding general aggregation processes and establishing model simulation. The diffusion limited aggregation (DLA) model8,9 and clustercluster aggregation (CCA) model10,11 are widely used to explain and analyze these phenomena. The aggregating process of particles in a Laplacian field can be described by the DLA model, which involves cluster formation by the adhesion of a particle with random walk to a selected seed on contact. The resulting structure of DLA model has a fractal dimension D ∼ 1.7. Aggregation of small particles in a fluid medium, for example, metal colloids, can be depicted by the CCA model. Two limiting regimes of CCA aggregation have been accepted: 12 fast diffusion-limited cluster aggregation (DLCA) and slow reaction-limited cluster aggregation. In DLCA regime, the fractal dimension D of the grown structures is about 1.45 in two dimension (d ) 2) and may increase to 1.75 ( 0.07 in a system of high initial particle density as the system approaches the solgel transition.13 The nanostructured materials are now being studied intensively, as their physical properties are quite different from those of the bulk.14,15 Until now, many methods have been used to prepare the nanostructured materials. In the preparation of nanostructured materials from liquid phase, the solvent plays an important role in the process of reaction. Kimura et al.16 prepared metal ultrafine particles in pure organic solvents and † ‡
Department of Scientific History and Archaeometry. Department of Chemical Physics.
indicated that the dispersibility depends strongly on the kind of solvent; the larger the dielectric constant of the solvent, the more metals that can be dispersed. Qian et al.17 prepared many ultrafine particles in organic solvent using a solvent-thermal method. γ-Irradiation on aqueous solutions presented a new method for preparing nanocrystalline, many nanoscaled metals, and metallic oxides have been prepared by this method.18,19 In the present article, we report on the preparation of metallic Ag particles in the three solvents deionized water, ethanol, and 0.01 M C12H25NaSO4; the observation of two-dimensional aggregation patterns of metallic Ag in different systems; and the explanation for these phenomena. 2. Experimental Section Three portions of different AgNO3 solutions were prepared. The procedure was as follows: three portions of AgNO3 were prepared by dissolving 1 g of AgNO3 in 1 mL of deionized water, then these AgNO3 solutions were dripped into deionized water, ethanol, and 0.01 M C12H25NaSO4 aqueous solution, respectively, and the final volume of these solutions was made up to 100 mL. The above-mentioned solutions were named as solution A, B, and C, respectively. These solutions were γ-irradiated in the field of a 70 000 Ci 60Co γ-ray source with a dose of 5.3 kGy. Solutions A and B produced gray and black precipitates while solution C turned into a brownish red colloid. γ-Irradiated solutions A and B were dispersed by ultrasound for 30 min and then dripped together with γ-irradiated solution C onto a C-coated Cu grid, respectively, and observed in a Hitachi Model H-800 transmission electron microscope (TEM) using an accelerating voltage of 200 kV. X-ray powder diffraction (XRD) patterns were recorded at a scanning rate of 0.05 deg s-1 using a Rigaku Dmax γA X-ray diffractometer with high-intensity Cu KR radiation (λ ) 1.541 78 Å). For measuring the dimensions of Ag fractals, TEM images were digitized by the use of an OPTON image analyzer at 512 × 512 pixels. A threshold criterion was then applied to separate pixels in the fractal regions from the background. The fractal dimension (D) was obtained by using the box-counting algorithm.20 In this method, the digitized images were covered with a grid of squares
10.1021/jp000225w CCC: $19.00 © 2000 American Chemical Society Published on Web 05/27/2000
5682 J. Phys. Chem. B, Vol. 104, No. 24, 2000
Wang and Xin
Figure 1. X-ray diffraction pattern of Ag prepared by γ-irradition in (a) aqueous solution and (b) ethanol.
Figure 3. (a) TEM images of aggregated Ag particles prepared in ethanol. (b) log N(r) vs log r for (a).
Figure 2. (a) TEM images of aggregated Ag particles prepared in aqueous solution. (b) log N(r) vs log r for (a).
of size r. The total number N(r) of nonvacant boxes follows
N(r) ∼ r-D for a statistically self-similar structure. The value of D can be calculated from the slope of plot log N(r) vs log r. 3. Results The particle size of metallic Ag obtained from solution A is about 100 nm as determined by the width of half-peaks in XRD (Figure 1a). The microphotos of sample A are shown in Figure 2. The aggregating morphology is regular dendritic patterns. The nucleation of Ag particles was on the edge of the C-filmcoated Cu grid, and the aggregation was mainly along three different directions and formed three branches; each branch split into three subbranches, and so on. The crystal tips in the backbone or side branches are very sharp and have a very large radius of curvature. The patterns show self-similarity in different
scales. Because each branch is not along a definite direction, strictly speaking, the pattern is approximate to dentrite. Figure 2b shows the double logarithmic plots of N(r) versus r. The data points are well fitted by a straight line and the fractal dimension found is 1.81. Solution B produced a black turbid fluid. Calculated from Figure 1b, the particle size of metallic Ag found is 20 nm, much smaller than that obtained from solution A. In this system, Ag particles aggregated into typical fractal patterns. The nucleation of Ag particles was in the middle area of the C-coated Cu grid and the growth of Ag particles was random, which is quite different from that of sample A. The fractal dimension calculated from Figure 3b is 1.73, which is in agreement with the twodimensional DLA simulation (1.70). Solution C turned into a brownish red colloid after γ-irradiation. The micrograph shows that the colloidal Ag particles are about 10 nm. At the initial stage of aggregation (Figure 4b), the Ag particles formed very small clusters; the majority of Ag particles were single particles and did not aggregate into clusters. In Figure 4c, the aggregating level was a little higher than in Figure 4b. In Figure 4e, the aggregation finished, and no single Ag particle was found near the clusters. These patterns are ramified tortuous structures with no center, and the fractal dimension (Figure 4e) found is 1.70. The general conclusions are the following: 1. As a result of γ-irradiation on AgNO3 dissolved in three different solvents (deionized water, ethanol, and 0.01 M C12H25NaSO4 aqueous solution), different particle sizes of metallic Ag were obtained. The ethanol and surfactant can restrain the growth of Ag particles. 2. The aggregation patterns of large particles in deionized water were dendritic structure with the fractal dimension of 1.81. The aggregation of small Ag particles in the ethanol formed fractal patterns with the fractal dimension of 1.73. The coagula-
Fractal and Dendritic Growth of Metallic Ag
J. Phys. Chem. B, Vol. 104, No. 24, 2000 5683 of 2-propanol, the mechanism of the occurrence of metallic Ag is as follows. At first, some reactive radicals such as eaq(hydrated electron), H radicals, and other organic radicals formed. These radicals reduced Ag+ ions to Ag atoms, then the Ag atoms aggregated into clusters, and these clusters can serve as the core for nucleation. The whole process can be expressed as follows:
Ag+ + eaq- f Ag0 Ag+ + Ag0 f Ag2+ 2Ag22+ f Ag42+ nucleation
Ag clusters 98 colloid Ag
Figure 4. (a) TEM images of Ag colloid; (b)-(e) patterns in different stages of aggregation; (f) log N(r) vs log r for (e).
tion of Ag colloid results in ramified tortuous structures with the fractal dimension of 1.70. 4. Discussion By γ-irradiation on AgNO3 aqueous solution in the presence
When two particles of different sizes bumped into each other, the transmission of an electron would take place. There will be a tendency for ions to dissolve from the surface of smaller particles and precipitate on the surface of larger ones as discussed by Satoh et al.21 To reduce the possibility of bumps between particles and to prevent the particles from aggregating, surfactant or organic solvent should be used. Many reports indicated that the organic solvents can restrain the growth of metallic particles, and many kinds of metallic colloids can be prepared in organic solvents.16,21 In the present report, Ag particles prepared in ethanol were much smaller than those in deionized water, though the experimental conditions such as the doses of γ-irradiation and the concentration of AgNO3 were kept the same. This may be the reason that the solvent effect in the surface of metallic Ag enhances the stability and prevents Ag particles from aggregating effectively. In solution C, the formation of Ag colloid was due to the adsorption of surfactants onto the surface of metallic particles. The aggregation of Ag particles on the C-coated Cu grid was mainly caused by van der Waals attraction between metallic Ag particles. By γ-irradiation on AgNO3 aqueous solution (solution A), the Ag particles obtained were relatively large and these Ag particles were single crystals as determined from XRD patterns. When the turbid liquid was dripped onto the C-film of the Cu grid, the Ag particles crystallized on the edge of the tiny irregular edge of the Cu grid and involved low-angle grain boundaries. The other Ag particles, once absorbed on the surface of the aggregate from the turbid fluid, diffused with a random walk until they irreversibly stuck to the perimeter of the growing aggregate. According to the former reports, the dendritic patterns are formed only when the anisotropy dominates noise.22 Anisotropy, which is essential for the formation of dendritic pattern, can come from the interaction between the background and aggregating particles23 or the anisotropy of the growing crystalline itself.24 In the present experimental system, the aggregation of Ag particles took place in a two-dimensional C-film-coated Cu grid. The substrate of C-film was amorphous and the medium was also isotropic; no noise was induced into the growth system. The anisotropy, which causes dendrite patterns of the aggregate, comes from the Ag particles themselves. Because the single crystals of Ag particles intrinsically contain a strong crystalline anisotropy, the aggregation of Ag particles was mainly along the preferred growth direction and, accordingly, brought about a dendrite pattern. On the other hand, the large Ag particles have lower mobility; they cannot change their position or growth direction freely under the agent of anisotropy and grow strictly along the preferred growth direc-
5684 J. Phys. Chem. B, Vol. 104, No. 24, 2000 tion. Consequently, the final aggregation pattern was not very regular shaped branches, or oriented on definite directions. The metallic Ag prepared in ethanol has a smaller particle size and formed fractal patterns as aggregation took place. This can be assumed for the following reasons: first, nanoscale Ag grains contain a significantly higher percentage of their atoms at the grain boundary and the distortion of lattice in the surface layer. These characteristics of nanocrystalline decreased the crystalline anisotropy of Ag particles. Second, solvation occurred on the surface of Ag particles. The interaction of metallic surfaces with the solvent makes the surfaces become homogeneous; thus, Ag particles lost the anisotropy. When these Ag particles were absorbed on the C-film from the solution, they walked and stuck to the surface of aggregate randomly, and formed typically fractal patterns. The aggregation patterns of Ag particles from both solution A and solution B share common characteristics with DLA such as the ramified structure starting from a unique seed. The fractal dimension D of the aggregates from solution B (1.73) is close to the one in DLA simulation (1.70), while that from solution A (1.81) is larger. This deviation may be the reason that the aggregation experiment does not meet the conditions for ideal DLA processes. One difference between the DLA model and the actual physical aggregation process is that the concentration of particles tends to zero in the DLA model, while in any physical system there is a finite concentration of particles. Another difference is the “screening effect” in the DLA model. According to the DLA model, a particle diffuses with a random walk and irreversibly sticks to a growing aggregate once absorbed on the surface. There are very few possibilities for a random particle to enter the interior of the aggregates and this is called the “screening effect”. In the systems of both γ-irradiated solutions A and B, there is a finite concentration of Ag particles, and some Ag particles exist originally in the interior of the aggregate. Consequently, the aggregation of Ag particles resulted in a more compact structure, which has a larger fractal dimension than D ∼ 1.7 in the two-dimensional DLA simulations. The fractal dimension (D ) 1.81) in the present experiment (from solution A) is very close to that in silicate mineral textures (1.80) reported by Fowler et al.25 The occurrence of Ag colloid by γ-irradiation on solution C was due to C12H25NaSO4, which was absorbed on the surface of the Ag particles and prevented the Ag particles from aggregating. Following the standard theory of colloids, the stability of colloid is governed by the balance between van der Waals attraction and Coulombic repulsion of charged particles.26 Enhancing the van der Waals attraction force or weakening the Coulombic repulsion force induces rapid coagulation of colloids. When this Ag colloid was dripped onto the C-coated Cu grid, the evaporation of solvent resulted in the break of the balance and the aggregation took place. The final aggregates were random, tortuous structures and have no center; i.e., there were no seeds for the aggregation of Ag particles. This process is analogous to the two-dimensional DLCA simulation. However, the fractal dimension D ) 1.70 in the present experiment deviates from D ∼ 1.45 in two-dimensional DLCA simulation10 largely. The fractal dimension, often the sole structural parameter used in aggregation study, is related to the aggregation process. The cluster-cluster simulations involve a growth process in which all particles are of unique size and aggregation is irreversible. However, most of the real aggregation processes are certainly more complicated than what have been modeled in the theoretical treatments. In two-dimensional systems, fractal dimensions ranging from 1.2 to 1.74 have been obtained under
Wang and Xin different experimental conditions.27-29 The reasons for present fractal dimension value (1.70), which is larger than the one by DLCA simulation, can be assumed (1) the sol-gel transition, (2) restructuring, and (3) the varying size of clusters and particles in the system: First, from Figure 4d, one can see that in the left-bottom corner the structure looks homogeneous. This may be why the cluster-cluster aggregation leads to a gellike structure. The theoretical predictions and computer simulations indicate that the sol-gel transition can result in an increase in D, which can be up to 1.75 for DLCA in two-dimensional aggregation of colloids after the sol-gel transition. The fractal dimension found in the present experiment is close to the one (1.69) found in the compact, gelled structure aggregating from colloid particles trapped at a liquid surface.30 Second, in the DLCA regime, aggregation is irreversible when two clusters are contact. In the present case, however, aggregation may be not fully irreversible, because the aggregate was held together only by van der Waals attractive forces. Thermal or external force fluctuations can disrupt these relatively weak interactions and produce rearrangement of particles leading to more compact structures. Third, the CCA model involves a growth process in which all particles are of unique size and the aggregation proceeds synchronously at any area or time in the whole system. In the present experiment, however, Ag particles are not the same size in the colloid, the aggregation is not synchronal, and clusters with different particle size exist in different area (Figure 4b,c). It is presumably due to the possibility of the penetration of the larger clusters by smaller ones that D ) 1.7 in the present experiment is larger than the one obtained by computer simulation. 5. Conclusions 1. From γ-irradiation on AgNO3 dissolved in deionized water, metallic Ag with a particle size about 100 nm has been obtained. Such Ag particles formed dendritic patterns in the C-film of the Cu grid as the aggregation took place. The anisotropy of the Ag particle itself played an important role in the formation of dendritic patterns. 2. As an organic solvent, ethanol can restrain the growth of Ag particles effectively. Metallic Ag particles prepared in ethanol have a size about 20 nm and are obviously smaller than those prepared in deionized water. Imperfect arrangement of atoms in the surface layer of nanoscale Ag and solvation by ethanol resulted in the decrease in anisotropy of Ag particles. Consequently, Ag particles prepared in ethanol formed typical fractal structures as aggregation took place. 3. Ag colloid was prepared by γ-irradiation on AgNO3 aqueous solution in the presence of C12H25NaSO4. Ag particles in the colloid formed ramified tortuous structure with no center, which was quite similar to that formed by the DLCA model. The larger fractal dimension (D ∼ 1.7) obtained in the present experiment than in two-dimensional simulation may be due to the simultaneous effect of the sol-gel transition, the “restructuring”, and the different sizes of particles and clusters in the experimental system. References and Notes (1) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: New York, 1982. (2) Matsushita, M.; Sano, M.; Hayakawa, Y.; Honjo, H.; Sawada, Y. Phys. ReV. Lett. 1984, 53, 286. (3) Argoul, F.; Arneodo, A.; Grasseau, G.; Swinney, H. L. Phys. ReV. Lett. 1988, 61, 2558.
Fractal and Dendritic Growth of Metallic Ag (4) Fleury, V. J. Mater. Res. 1991, 6, 1169. (5) Nittmann, J.; Daccord, G.; Stanley, H. E. Nature 1984, 314, 141. (6) Daccord, G.; Nittmann, J.; Stanley, H. E. In On Growth and Form: Fractal and Non-Fractal Patterns in Physics; Stanley, H. E., Ostrowsky, N., Martinus Nijhoff: Dordrecht, 1986. (7) Niemeyer, L.; Pietronero, L.; Wiesmann, H. J. Phys. ReV. Lett. 1984, 52, 1033. (8) Witten, T. A.; Sander, L. M. Phys. ReV. Lett. 1981, 47, 1400. (9) Forrest, S. R.; Witten, T. A. J. Phys. A 1979, 12, L109. (10) Meakin, P. Phys. ReV. Lett. 1983, 51, 1119. (11) Kolb, M.; Botet, R.; Jullien, R. Phys. ReV. Lett. 1983, 51, 1123. (12) Lin, M. Y.; Lindesay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360. (13) Herrmann, H. J.; Kolb, M. J. Phys. A 1986, 19, L1027. (14) Ozin, G. A. AdV. Mater. 1992, 4, 612. (15) Gleiter, H. AdV. Mater. 1992, 4, 474. (16) Kimura, K.; Bandow, S. Bull. Chem. Soc. Jpn. 1983, 56, 3578. (17) Qian, X. F.; Zhang X. M.; Wang, C.; Wang, W. Z.; Qian, Y. T. Mater. Res. Bull. 1998, 33, 669.
J. Phys. Chem. B, Vol. 104, No. 24, 2000 5685 (18) Zhu, Y.; Qian, Y.; Zhang, M.; Chen, Z. Mater. Lett. 1993, 17, 314. (19) Wang, S.; Xin, H.; Qian, Y. Mater. Lett. 1997, 33, 113. (20) Russel, D. A.; Hanson, J. D.; et al. Phys. ReV. Lett. 1980, 45, 1175. (21) Satoh, N.; Hasegawa, H.; Tsujii, K.; Kimura, K. J. Phys. Chem. 1994, 98, 2143. (22) Ben-Jacob, E.; Godbey, R.; Goldenfeld, N.; Koplik, J.; Levine, H.; Mueller, T.; Sander, L. M. Phys. ReV. Lett. 1985, 55, 1315. (23) Brune, H.; Romainczyk, C.; Roder H.; Kern, K. Nature 1994, 369, 469. (24) Honjo, H.; Ohat, S. Phys. ReV. A 1987, 9, 4555. (25) Fowler, A. D.; Stanley, H. E.; Daccordd, G. Nature 1989, 341, 134. (26) Everett, D. H. Basic Principles of Colloid Science; Royal Society of Chemistry: London, 1988; p 130. (27) Richetti, P.; Prost, J.; Burois, P. J. Phys. Lett. 1984, 45, 1137. (28) Skjeltorp, T. Phys. ReV. Lett. 1987, 58, 1444. (29) Hurd, A. J.; Schaefer, D. W. Phys. ReV. Lett. 1985, 54, 1043. (30) Armstrong, A. J.; Mocklet, R. C.; O’Sullivan, W. J. J. Phys. A: Math. Gen. 1986, 19, L123-129.
