Morphological Evolution of Fractal Dendritic Silver Induced by Ions

Sep 25, 2008 - found that walking of ions within the diffusion layer can affect the morphology of ... As the longitudinal velocity of silver ions walk...
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J. Phys. Chem. C 2008, 112, 16301–16305

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Morphological Evolution of Fractal Dendritic Silver Induced by Ions Walking within the Diffusion Layer Hongjun You, Jixiang Fang, Feng Chen, Miao Shi, Xiaoping Song, and Bingjun Ding* State Key Laboratory for Mechanical BehaVior of Materials, Materials Science and Engineering School, Xi’an Jiaotong UniVersity, Xi’an, Shaanxi 710049, People’s Republic of China ReceiVed: May 13, 2008; ReVised Manuscript ReceiVed: August 8, 2008

Fractal dendritic morphologies will be formed when metal materials are synthesized in nonequilibrium conditions. In the past, scientists mainly studied the effect of noise and anisotropy on morphology evolution. However, in this Article, fractal dendritic silver is synthesized through a simple wet-chemical method, spontaneous galvanic displacement between Ag ions and Zn plate, and through Monte Carlo simulation we found that walking of ions within the diffusion layer can affect the morphology of the whole shape, and anisotropy only affects the shape in local area. As the longitudinal velocity of silver ions walking within the diffusion layer increases, the ions are more easily distributed on the hollow part of fractal silver, and thus the fractal silver will transform from loose fractal (LF) to dense branch morphology (DBM), and shape densities and fractal dimensions of fractal morphologies also increase. 1. Introduction Nanostructure materials of noble metals have drawn considerable attention due to their unique magnetic, optical, electrical, and catalytic properties.1 Among various specific nanostructures, fractal and dendrite have attracted scientists’ most interests because of their attractive hyperbranched structures that not only provide a framework for the study of nonequilibrium conditions growth,2 but also have widespread application in surfaceenhanced Raman spectroscopy,3 chemical sensors,4 biosensors,5 and superhydrophobic films.6 Because these novel properties strongly depend on the size and shape of fractal dendritic structure, the studies of shape control in nonequilibrium conditions are crucial for fractal dendritic noble metals preparation. In the past 20 years, plenty of studies have been performed on the fractal shape transition in experiment and theory. In the wet-chemistry system, many factors can affect the fractal dendrite shape, such as convection,7 ion concentration,8 voltage in electro deposition,9 agent,10 crystalline anisotropy,11 competition between thermodynamic and kinetic,12 temperature,13 thickness of diffusion layer,14 et al. All of these factors can be classified into two categories, noise and anisotropy. The former spoils the regular growth of metal crystal and induces disordered pattern; conversely, the anisotropy can limit the growth in some certain directions to form symmetry and regular pattern. Many theoretical models considering both noise and anisotropy have been built to analyze morphology evolution15 and successfully depicted the evolution of fractal dendrite in local area, such as oscillatory nucleation.16 However, in our recent experiments of fractal dendritic silver growth in electrolyte, we found that noise and anisotropy can only affect the local area structure of silver dendrite; the whole shape morphology is affected by other factors. Using Monte Carlo (MC) simulation, we found that the walking of ions within the diffusion layer has a crucial effect on the whole shape transition. Anisotropy and noise are factors that influence morphology in local area. Two basic parameters of fractal shape, shape density (quality of fractal shape being * Corresponding author. E-mail: [email protected].

dense in space) and fractal dimension, are studied in the morphology evolution. 2. Experimental Methods A simple and straightforward strategy is developed to fabricate Ag fractal shape with complex hierarchical structures by a wet-chemical route based on spontaneous galvanic displacement between Ag ions and Zn plate. Through a redox mechanism, in which Zn substrate acts as reducing agent for Ag+ in the solution, Ag is deposited at the edge of the Zn plate in a typical two-dimensional quartz glass reaction cell (length and width are much larger than thickness; sizes are 80 mm × 60 mm × 1 mm). Zn plate (10 mm × 10 mm × 0.7 mm) is first treated by hydrochloric acid to remove surface contamination and rinsed by double-distilled deionized water. Next, the Zn plate is fixed at one bottom side of the cell. When AgNO3 aqueous solution is poured into the cell, fractal silver trees will grow at the linear edge of Zn plate. A CCD camera with ×200 lens is settled vertically on the cell to take the photo of fractal silver trees while the chemical reaction is taking place. To study the evolution of silver fractal shape in different AgNO3 concentration solutions, three concentrations were used: 20, 50, and 80 mM. Images of fractal dendritic silver in local area are recorded on a JEOL JEM-3010 transmission electron microscope (TEM) with an accelerating voltage of 300 kV. The samples for TEM are prepared by the following process: the fractal silver trees are put into double-distilled deionized water, shocked by ultrasonic, and then dropped onto a carbon-coated TEM grid. The thickness of the diffusion layer near the reaction surface is measured by a Michelson interferometer. The measurement device is shown in Figure 1. A half-reflect glass plate (denoted as “A”) is used to split the incoming monochromatic sodium light into two branches. Because of the optical path difference in the two branch lights, an interference fringe map can be formed and recorded by CCD camera (with ×10 lens). The refracting index varies in different concentration solutions, so the interference fringe will curve when the light penetrates the diffusion layer where the concentration is nonuniform. Thus,

10.1021/jp8042126 CCC: $40.75  2008 American Chemical Society Published on Web 09/25/2008

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Figure 1. Schematic sketch to illustrate the measurement of diffusion layer thickness. “A” denotes half-reflect glass plate; about one-half of incidence light can be reflected by one side of this glass. “B” denotes compensation glass plate, which is used to compensate optical path difference.

Figure 3. (a) Schematic diagram to illustrate Ag+ walking within the diffusion layer. (b) Thickness of the diffusion layer near Zn plate edge is measured by Michelson interferometer in different AgNO3 concentration solution. The inset is the interference fringe map of diffusion layer recorded by the Michelson interferometer.

Figure 2. Optical images of fractal dendritic silver synthesized in (a) 20 mM, (b) 50 mM, and (c) 80 mM AgNO3 solution, respectively. (d) Shape densities of the three images.

the thickness of diffusion layer can be measured from the interference map. 3. Results and Discussion Three images of fractal dendritic silver synthesized in different AgNO3 concentration solutions are shown in Figure 2a-c. To emphasize the whole morphology evolution, optical micrographs are shown here. In Figure 2a, the concentration is 20 mM and the reaction time is 120 s, and the fractal trees are separate without overlapping each other. In Figure 2b, the concentration increases to 50 mM and the reaction time is 80 s, and every fractal tree can be separated out although one meets with another. In Figure 2c, the concentration further increases to 80 mM and the reaction time is 40 s, and fractal trees connect together and joint into a whole shape in which single trees cannot be separated out. Comparing the three figures of silver fractal trees, it shows that with increasing concentration morphologies become denser and denser, from loose fractal shape (LF) to dense branch morphology (DBM). Shape densities are measured by software that scans every pixel of fractal image; the ratio between black and whole pixel amount is the shape density. Shape densities of these three fractal images are shown in Figure 2d. With increasing concentration, shape densities increase accordingly.

As shown in Figure 3a, when Ag+ locates in bulk solution, it moves freely and performs random Brownian motion. When Ag+ moves into the diffusion layer, it will be driven to move toward the reaction surface by gradient of concentration within the diffusion layer. With Michelson interferometer, thicknesses of diffusion layers in different concentrations are measured and shown in Figure 3b. With increasing concentration, the thickness of the diffusion layer decreases and the concentration difference between bilateral sides of diffusion layer increases, so that the concentration gradient within diffusion layer increases remarkably with increasing concentration. Within the diffusion layer, movement of Ag+ can be described by longitudinal velocity (Vy, perpendicular to the Zn plate edge) and transverse velocity (Vx, parallel to the Zn plate edge). The longitudinal velocity is driven by concentration gradient within the diffusion layer and the transverse velocity roots on the Brownian motion. Driven by increasing concentration gradient, longitudinal velocity of Ag+ within the diffusion layer will increase as concentration increases. In our experiment, Ag+ moves through the diffusion layer from bulk solution to the reaction surface. At the reaction surface, it gains an electron and is reduced to a silver atom. Next, the reduced silver atom deposits on the reaction surface. As previous analyses mentioned, with increasing concentration, longitudinal velocity of Ag+ within the diffusion layer increases remarkably. This situation will have a crucial effect on the morphology evolution of fractal silver in the whole area. Referring to the DLA Monte Carlo (MC) simulation method,17 the formation of silver fractal trees is simulated with the MC method. There are two common types of sticking conditions, which are “bond-DLA” and “site-DLA”.18 Because it is believed that the large-scale structure of DLA is not sensitive to the type

Morphological Evolution of Fractal Dendritic Silver

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Figure 5. Sketches of fractal shape evolution as velocity ratios (λ) approach to limit: (a) λ ) 0, (b) λf∞. Particles are emitted ordinally from left to right. Figure 4. MC simulation images simulated in conditions: (a) λ ) 0.25, (b) λ ) 1, and (c) λ ) 4, respectively. The image sizes are all 320 × 270 in (a), (b), and (c). Shape densities of the three images are shown in (d).

of sticking conditions,19 in this Article, “site-DLA” condition is used. To consist with our experimental case, two-dimensional (2D) cylindrical geometry20 is selected in our simulation. In our simulation, in 2D space, a particle denoted Ag+ in experiment is released at the random site on the top horizontal line. This particle performs a random walk until it reaches the bottom horizontal line, and then deposits on it. The next particle is then released, the third, and so on. These particles will aggregate on the bottom line and form clusters. When particles arrive at a site that is nearest neighbor to the cluster, it sticks and forms a part of the cluster. Periodic boundary condition is set on the left and right sides of the 2D space. Two velocities are introduced to describe the particles walking: longitudinal velocity (Vy, perpendicular to the bottom line) and transverse velocity (Vx, parallel to the bottom line). According to previous analyses on the experimental results, the longitudinal velocity of particle walking is changed to form a different fractal shape, which simulates Ag+ moving within the diffusion layer. The velocity ratio between Vy and Vx is denoted as λ (λ ) Vy/Vx). Simulation results with λ ) 0.25, λ ) 1, and λ ) 4 are shown in Figure 4. The simulation image sizes are denoted as particle number. The sizes of Figure 4 images are all 320 × 270 particles, so they have the same scale and can be comparable to each other on the morphology evolution. Like the morphology evolution of fractal dendritic silver in different AgNO3 concentration solutions, the patterns of simulation also change from LF to DBM as λ increases. The shape density changing of the three simulation images is shown in Figure 4d. In simulation, if λ decreases, the particle can move over more transverse lattices in every horizontal lattice layer before it drops into the next horizontal lattice layer. Particles are more easily captured by the tip of fractal trees. Conversely, if λ increases, more particles will not be shielded by the tip of fractal trees and can aggregate on the hollow of fractal shape. Morphologies will become compact, and shape densities increase accordingly. Figure 5a and b are the two cases in which λ approaches the minimum, λ ) 0, and maximum, λf∞, respectively. If λ ) 0, the transverse velocity will approach infinite, thus Vx . Vy, indicating that before the falling particle moves from one horizontal lattice layer to the next, it can reach any position in the current horizontal layer. Thus, every particle can be captured by the tip and shielded to aggregate on the hollow position.

Figure 6. TEM images of fractal dendritic silver synthesized in different AgNO3 concentration solutions: (a) 20 mM, (b) 80 mM.

Figure 5a is a case of this condition simplified by emitting particles ordinally from left to right at the top horizontal line. In this situation, only one particle can be contained in every horizontal lattice layer. When the lattice number in every horizontal layer is large enough, the shape density approaches zero (Ff0). If λf∞, Vy . Vx, the particle moves directly from top to bottom without transverse moving. Figure 5b is this case and simplified by emitting particles from left to right at the top horizontal line; the shape becomes most compact, and shape density reaches to maximum 0.5 (F ) 0.5). Through simulation, it shows that the walking of Ag+ within the diffusion layer has a crucial effect on the morphology evolution of silver fractal trees in the whole area. As concentration increases, the thickness of the diffusion layer decreases and the concentration gradient within the diffusion layer increases. Driven by the increased concentration gradient, the longitudinal velocity of Ag+ within the diffusion layer increases. Coincident with simulation, the changing of longitudinal velocity will modify the distribution of Ag+ deposited on tip or hollow site of fractal shape. When longitudinal velocity increases, as previous analyses mentioned, particles are more easily deposited at the hollow part, and when longitudinal velocity decreases, particles are more easily captured by the tip part. Thus, when longitudinal velocity increases, the distribution of Ag+ deposited on the hollow part of the fractal shape will increase, and the silver shape will change from LF to DBM. Walking of Ag+ within the diffusion layer determines the morphology of silver fractal trees in the whole area. Yet in the local area, morphology is mainly determined by noise and anisotropy. Figure 6 shows the fractal dendritic silver in local area: in lower concentration (20 mM), the morphology is fractal shape; in high concentration, the morphology is dendrite. When Ag+ moves through the diffusion layer and deposits on the reaction surface as atom, the atom will diffuse on the silver

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M(bl) ) bdfM(l)

(1)

Here, M denotes the quantity of fractal shape in space, b is the enlargement factor, and l is the original size. The expanding of Euclidean geometry space can be depicted as:

S(bl) ) bdS(l)

(2)

In this equation, S denotes the quantity of Euclidean space, and d is the dimension of Euclidean space. Thus, the density of fractal shape can be computed as:

F ) M(bl)/S(bl) ) bdfM(l)/bdS(l)

(3)

In our two-dimensional deposition system, aggregation starts from one line, l ) 1 (represents one layer lattices), and b is the height of the fractal shape. At the start, the density of the linear seed is 1, F0 ) 1, and b ) 1, so M(1) ) S(1). Depending on eq 3, as the shape grows, the fractal dimension will be:

df ) d + ln F/ln b

(4)

In our two-dimensional system, where d ) 2, the value of b can be calculated by:

b ) N/mF Figure 7. Density profiles along height direction. (a) The density profile of silver fractal shape in Figure 1c. (b) The density profiles of λ ) 1 simulation shapes with different height.

where m denotes the lattices amount of simulation space width, and we use m ) 1000 in all simulations. Introducing eq 5 into eq 4 to substitute b, one obtained:

df ) d + trees surface. Because of the difference in energy barriers in different diffusion orientations, the atoms diffuse more easily along a certain orientation, which induces the anisotropic growth.13b,21 In addition, the absorption energies of water molecule and [NO3-] are different on different crystalline planes, such as the absorption energy of the water molecule on (111) plane of fcc silver is maximum, and silver atoms have difficulty displacing the water molecule to deposit on (111) plane, so that silver deposition in the water system is mainly covered by (111) plane.22 Thus, the different absorption energy will limit growth on some certain planes and induce anisotropic growth. In addition, the other kinetics and thermodynamic factors can also affect the anisotropic or noise growth.7-14 Noise and anisotropy on materials growth in the wet-chemical system have been studied by many researchers, but are still not quite clear. Here, we mainly discuss the morphology evolution in the whole area affected by Ag+ walking within the diffusion layer; the effect of noise and anisotropy on morphology evolution in local area will not be discussed profoundly. Here, we only account that materials’ anisotropic growth has an effect on the morphology in local area and ions walking has an effect on morphology in the whole area. When the fractal shape transforms from LF to DBM induced by Ag+ walking within the diffusion layer, the shape characters change accordingly. The density profile of Figure 2c along height is shown in Figure 7a, and density profiles of different height simulation shapes (simulated with λ ) 1) are shown in Figure 7b. All of the density profiles decrease sharply at the beginning, then fluctuate around a constant in the middle, and at the end they rapidly decrease to zero. The difference between all of the curves is the length of the middle section. From these density curves, we can conclude that in the stable growth region of fractal shape, the shape density (F) remains constant. Depending on the definition of the Hausdorff fractal dimension,23 the fractal shape growth can be depicted as:

(5)

ln F ln N - ln mF

(6)

According to the former discussion, the shape density (F) remains constant in stable growth, so eq 6 describes the variation of df with increasing fractal shape height. In the case of λ ) 1, the shape density F is 0.14. The df values of simulation shapes with different particle numbers N are measured and are shown in Figure 8a. Depending on eq 6, the relation curves of df versus N of different F are calculated

Figure 8. (a) Fractal dimension (df) varying with particle number (N) increasing. (b) Fractal dimension (df) varying with shape density (F) increasing. The densities of most DLA shapes are between 0.08 and 0.18, so df changes between 1.65 and 1.77 usually (as the area of dashed lines shown).

Morphological Evolution of Fractal Dendritic Silver and shown in Figure 8a. By comparing the theory and measurement results, it shows that when N is larger than 5 × 104, they are well consistent. When N is less than 5 × 104, the whole growth is mainly dominated by the unstable stage (start section and end section), and the shape density (F) is variable, so df is inconsistent with theory. Curves also show that as N increases, df increases dramatically at the beginning, and then as the increasing speed slows, when N is larger than 1 × 105, df approximately approaches a constant. Similarly, according to eq 6, the curve of df versus F is calculated and shown in Figure 8b. The maximum F in simulation is 0.5, so F is chosen from 0 to 0.5. The curve shows that as F increases, df increases. In most simulation shapes, the density is about 0.08-0.18, so df changes between 1.65 and 1.77 usually, as the dashed line shows in Figure 8b. 4. Conclusion The silver fractal dendritic pattern obtained with the wetchemical method has a complex hierarchical structure, from macro structure to a micro structure, from whole to local. Walking of Ag+ within the diffusion layer has a crucial effect on the whole morphology. Changing of longitudinal velocity can affect the Ag+ distribution on different areas of the deposition surface. As the longitudinal velocity increases, Ag+ more easily deposits on the hollow part of fractal trees, and the fractal shape will transform from LF to DBM. The shape densities and fractal dimensions also increase accordingly. Acknowledgment. We are grateful for discussions with Prof. Zhimao Yang and Prof. Yaping Wang and grateful for help from Dr. Chao Zhu in simulation work. This work was supported by the National Science Foundation of China (No. 50871080). References and Notes (1) (a) Cox, A. J.; Louderback, J. G.; Bloomfield, L. A. Phys. ReV. Lett. 1993, 71, 923. (b) Alivisatos, A. P. Science 1996, 271, 933. (c) Heath, J. R. Science 1995, 270, 1315. (d) Hu, J. Q.; Chen, Q.; Xie, Z. X.; Han, G. B.; Wang, R. H.; Ren, B.; Zhang, Y.; Yang, Z. L.; Tian, Z. Q. AdV. Funct. Mater. 2004, 14, 183. (2) (a) Langer, J. S. Science 1989, 243, 1150. (b) Fleury, V.; Watters, W. A.; Allam, L.; Devers, T. Nature 2002, 416, 716. (c) Dick, K. A.;

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