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J. Phys. Chem. C 2008, 112, 3358-3361
Nonspherical Half-Shells by Ultrasonic Cleavage of the Hollow Polyhedral Particles in Water Shuhong Jiao,† Kai Jiang,*,‡ Yanhong Zhang,§ Ming Xiao,† Lifen Xu,† and Dongsheng Xu*,† Beijing National Laboratory for Molecular Science (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking UniVersity, Beijing 100871, China, College of Chemistry and EnVironmental Science, Henan Normal UniVersity, Xinxiang, Henan 453002, China, and China Institute of Water Resources and Hydropower Research, Beijing 100044, China ReceiVed: October 19, 2007; In Final Form: December 11, 2007
We present a facile route to preparing nonspherical half-shells of copper sulfide in which the octahedral mesocages of copper sulfide were grown on the substrate by a two-step electrochemical method first and then were cleaved into tetrahedral half-shells by ultrasonic vibration in water. The obtained half-shells are 1-3 µm in lengths, and the shell thickness is uniform in ∼100 nm. It is found that only centrosymmetric octahedral and six-pod shells can be equally split into two similar half-shells. Furthermore, a finite element analysis has been used to model the stress distribution in the octahedral CuS shell structure during ultrasonic vibration.
1. Introduction The ability to synthetically tune the structure, size, and shape of inorganic materials is an important goal in current material synthesis and device fabrication at the mesoscale. For example, much attention has been paid to the synthesis of micro- and nanostructures with hollow interiors, owing to their potential applications in photonic crystals, catalysis, drug delivery, artificial cells, and the protection of light sensitive components.1-6 It is noted that a variety of methods have been developed to generate hollow spherical and polyhedral structures of inorganic materials.7-19 Despite recent progress, it remains the case that hollow structures with closed shells will encounter many difficulties when they are used as carriers to transport functional materials. Nowadays there are few reports on the synthesis of hollow structures with open shells.20-24 Notably, Whitesides and co-workers have deposited metallic thin films onto arrays of spherical colloids, subsequently producing metallic half-shells through dissolution of the colloidal template.20 Xia and coworkers prepared spherical polymer shells with controllable holes in their surfaces by a solvent swollen process.21 However, there has been no report on the synthesis of the hollow polyhedral particles with half-shells until now. In this letter, we presented a facile route to preparing nonspherical half-shells of copper sulfide, in which the polyhedral mesocages of copper sulfide were grown on the substrate by a two-step electrochemical method first and then were cleaved into half-shells by ultrasonic vibration in water. High power ultrasound is commonly employed for cleaning, extraction, accelerating chemical reaction, etc.25 The potential use of ultrasound with the aim to reduce the adverse effects on the cut materials and to produce a controlled, high quality cut is being studied extensively.26,27 Herein, the use of power ultrasound in the cleavage of the polyhedral mesocages has been studied for the first time. * To whom correspondence should be addressed. E-mail: dsxu@ pku.edu.cn;
[email protected]. Fax: +86 10 62760360. Tel: +86 10 62753580. † Peking University. ‡ Henan Normal University. § China Institute of Water Resources and Hydropower Research.
Furthermore, a finite element analysis has been used to model the stress distribution in the octahedral CuS shell structure during ultrasonic vibration. 2. Experimental Section Scheme 1 outlines the procedure for fabricating hollow, tetrahedral half-shells of copper sulfide. First, octahedral Cu2O crystals were electrodeposited on indium-doped tin oxide (ITO) glass substrates. Second, the electrodeposited Cu2O octahedrons were immersed in Na2S aqueous solution to form octahedral Cu2O/CuS core/shell structures. Subsequently, the inner Cu2O cores of the core/shell structures were removed in ammonia solution, producing octahedral CuS mesocages. Finally, the octahedral CuS mesocages were cleaved into two tetrahedral half-shells by power ultrasound. All electrodepositions were carried out in a configured glass cell at 65 °C in which an ITO substrate with a sheet resistance of ∼20 Ω/cm2, a platinum plate, and a saturated calomel electrode (SCE) served as the working electrode, counter electrode, and reference electrode, respectively. A thin film of cubic Cu2O particles was electrodeposited in a 10% (V/V) ethanol aqueous solution, which contains 0.01 M CuSO4 and 0.075 M lactic acid, the pH value was adjusted to 9 by adding 1 M NaOH in the solution. To control the shapes of the deposits, different concentrations of HCl were added to the baths. As a result, octahedral and six-pod particles were obtained in the CuSO4 bath containing 0.3 and 0.6 M HCl, respectively. All depositions were done at a potential of -0.24 V versus SCE for 20 min. The obtained Cu2O thin films were then dipped in a 0.01 M Na2S solution at 0 °C in air atmosphere for 10-20 min and immersed in ammonia solution (12%) for 1-2 h to remove the inner Cu2O core, as illustrated in our previous work.19 Ultrasonic treatment of the products in water was carried out on an ultrasonic cleaner with a frequency of 40 kHz and a power of 100 W. The morphology and the phase indentification of the products was characterized by field-emission scanning electron microscopy (Strata DB235 FIB) and power X-ray diffractometry (D/ MAX-PC 2500 with Cu KR radiation and a normal θ-2θ scan),
10.1021/jp710145a CCC: $40.75 © 2008 American Chemical Society Published on Web 02/13/2008
Nonspherical Half-Shells by Ultrasonic Cleavage
J. Phys. Chem. C, Vol. 112, No. 9, 2008 3359
SCHEME 1: Schematic Illustration of the Procedure for Fabricating Tetrahedral Half-Shells of CuSa
a (a) Formation of octahedral Cu2O/CuS core/shell structures in Na2S aqueous solution; (b) dissolution of the inner Cu2O cores in ammonia solution; and (c) ultrasonic treatment.
Figure 2. XRD patterns of the octahedral Cu2O particles (a) and the tetrahedral CuS half-shells (b) on ITO substrates. The starred peaks are ITO substrates.
Figure 1. SEM images of (a) octahedral Cu2O particles, scale bar is 5 µm; (b) octahedral CuS mesocages, scale bar is 2 µm; and (c) tetrahedral CuS half-shells, scale bar is 2 µm. (d) EDS pattern of the CuS half-shells. For EDS analysis, the samples were deposited on thin amorphous carbon films supported by nickel grids.
respectively. Further structural analysis of CuS half-shells was carried out by transmission electron microscopy (TEM) (TEM, JEOL 200CX) and high-resolution TEM (HRTEM, FEI TECNAI F30). 3. Results and Discussion Figure 1a shows a typical scanning electron microscopy (SEM) image of the octahedral Cu2O films by electrodeposition in the copper-sulfate complex solutions. The sizes of the octahedrons typically range from 1 to 3 µm with an average edge length of 2 µm. By the reaction of these octahedrons with aqueous Na2S solution, followed by dissolution of the Cu2O cores in ammonia solutions, copper sulfide particles with uniform octahedral morphologies similar to those of the primary Cu2O templates were produced (Figure 1b). Ultrasonic treatment in water is employed to break these octahedrons. Surprisingly, the octahedrons on the substrates can be divided into two tetrahedrons with one open face along the symmetrical plane (Figure 1c). It can be seen that all the particles have a shape of half-shell with a smooth edge, and the inner surface of octahedron is smoother than the outer surface. The shell thickness is uniform in ∼100 nm. The X-ray energy dispersion spectrum (EDS) shown in Figure 1d indicates that the halfshells only consist of Cu and S, and the atomic composition of Cu and S is approximately 0.9: 1. Figure 2a presents the X-ray diffraction (XRD) patterns of the as-prepared Cu2O octahedrons on ITO substrate. The diffraction peaks at 2θ ) 29.74, 36.58, 42.46, and 62.10° are labeled and can be indexed to the (110), (111), (200), and (220)
Figure 3. Typical TEM (a) and HRTEM (b) images of a single halfshell. The inset in panel b is the corresponding Fourier transformation of the HRTEM image.
of the cubic phase of Cu2O (PDF file No. 05-0667), respectively. Figure 2b shows the XRD pattern of the hollow CuS octahedrons formed by reaction of the Cu2O cubes with Na2S solution and removing of the Cu2O core in ammonia solution. The pattern of the obtained CuS half-shells is consistent with the standard spectrum of hexagonal covellite CuS (PDF file No. 78-2121). The morphology and interior structure of the CuS half-shell are further investigated by TEM and HRTEM. Figure 3a shows the typical TEM image of a single CuS half-shell, clearly indicating the hollow structure of the half-shell. The HRTEM image of the half shell (Figure 3b) displays a hexagonal covellite of CuS. The corresponding Fourier transformation of this HRTEM image (the inset in Figure 3b) further reveals that the (102) plane is parallel to the edge of the tetrahedral half-shell. The above procedure has also been extended to other Cu2O crystal templates. By increasing the HCl concentration of the copper-sulfate complex solution to 0.6 M, six-pod Cu2O particles with four-symmetric morphologies were electrodeposited on ITO substrate. By the reaction of these six-pod Cu2O particles with aqueous Na2S solution and the removal of the Cu2O cores in ammonia solutions, six-pod copper sulfide particles were produced (Figure 4a). Figure 4b shows the SEM image of a pair of half-shells against a six-pod CuS hollow particle with a flower-shaped morphology, indicating that the six-pod CuS particle was also cleaved along the symmetrical plane by the ultrasonic treatment. For cubic Cu2O crystal template (Figure 4c), we found that the obtained cubic CuS shells were broken into irregular pieces by power ultrasound (Figure 4d). In addition, we found that the stick of the CuS shells on the substrates is another important factor for the formation of halfshells. Octahedral copper sulfur shells suspended in water cannot be cleaved into two pieces under power ultrasound.19
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Figure 4. SEM images of (a) six-pod CuS cages, scale bar is 2 µm; (b) half-shells of a six-pod CuS cage, scale bar is 2 µm; (c) cubic CuS cages, scale bar is 2 µm. (d) the broken cubic CuS cages.
Figure 5. Finite element mesh of a 3D octahedral CuS cages with an edge size of 2 µm and a shell thickness of 100 nm.
According to the above observations during breaking trials of the CuS shells by power ultrasound, we proposed that the cleavage is dependent on the mode of vibration of the shell. Cleaning and disintegration of the adhered surface films by power ultrasound is attributed to cavitation forming at a liquid/ solid interface. During the ultrasonication process, the formation of the collapsing cavities or the cumulative microjets produce high-pressure pulses, which transfers energy and loads to the octahedral shells that pass over it. This process would result in the vibration of the shells. Generally, the motion equation for a freely vibrating undamped system can be described as28
[M]{u¨(t)} + [K]{u(t)} ) {0}
(1)
where [M] is the mass matrix of the system, [K] is the stiffness matrix, {u¨(t)} is the acceleration vector of the node at time t, {u(t)} is the displacement vector, and {0} is the zero vector. By analogy with the behavior of SDOF systems, it will be assumed that the free-vibration motion is simple harmonic, which may be expressed for the system as
{u(t)} ) {uˆ }sin(ωt +θ)
(2)
where {uˆ } represents the shape of the system, ω is the vibration frequency, and θ is the phase angle. Combining eqs 1 and 2 yields the frequency equation of the system
||[K] - ω2[M]|| ) 0
(3)
From solution of the above expression (eq 3), the vibration frequencies of the system can be determined. The vibration modes can also be determined. For example, if the n-order vibration frequency, ωn, is known, the n-order vibration mode of the system, {uˆ n}, can be deduced from eq 4
([K] - ωn2[M]) {uˆ n} ) {0}
(4)
For a complex system, the vibration frequency values and the vibration modes can be determined by numerical method, for example, finite element method, which has a wide range of application in practical engineering structures.29 For ultrasonic cutting, the component under design is the vibrating system that transfers energy and loads to the friable material. In the present work, finite element analysis is used to model the stress distribution about the crack tip in an octahedral CuS shell structure, in which three-dimensional (3D) solid elements are
Figure 6. Finite element predicted modes of vibration for 3D octahedral CuS cages: (a) the first, (b) the second, (c) the third, and (d) the fourth vibration modes.
used to simulate the structure. The specimens were modeled using 27-noded brick elements and fixed on the substrate, as shown in Figure 5. By applying of the space iterative method,30 we calculated the vibration frequencies and the vibration displacements at different modes. Figure 6 gives four vibration modes predicted by finite element analysis. There are four outof-plane bending modes and four in-plane bending modes in each breath vibration mode. In the first vibration mode (Figure 6a), at the upside of the octahedral shell, two out-of-plane bending modes deviate from the paper plane, and meanwhile at the underside of the shell the bending modes point to the outsides. This result indicated that during ultrasonic cutting, the transverse stress that acted on the shell may be focused on the arrises at the middle of the shell. Analogical conclusions can also be made from the second (Figure 6b), the third (Figure 6c), and the fourth vibration modes (Figure 6d). Conclusions In conclusion, the synthesis of uniform nonspherical copper sulfide half-shells has been demonstrated by an ultrasonic cleavage of the corresponding copper sulfide mesocages on ITO substrates. It is found that only centrosymmetric octahedral and six-pod shells can be equally split into two similar half-shells. By means of the finite element analysis, we proposed that the
Nonspherical Half-Shells by Ultrasonic Cleavage crack is dependent on the mode of vibration of the cutting shell, in which the transverse stress that acted on the shell may be focused on the arrises at the middle of the shell under the ultrasonic vibration. Although the present work is focused on CuS, we believe that a similar approach is applicable to other inorganic materials as long as their mesocages with centrosymmetric morphologies can be grown or stoked on the substrates. It is expected that due to its bowl-shape this novel type of hollow, nonspherical half-shell particles would find potential uses as containers to hold nanoparticles as well as controlling release of drugs, cosmetics, pigments, or chemical reagents. On the other hand, as the ratio of the surface area to volume is approximately twice that of the core/shell particles and it presents a substantial linear, nanometer-scale edge, we believe that the thin, semiconducting edges of the half-shells will produce enhancements in chemical reaction and optical fields that will be useful in studies involving heterogeneous catalysts and nonlinear optical properties. Acknowledgment. This work is supported by NSFC and MSTC (MSBRDP, Grant 2006CB806102, 2007CB936201). Supporting Information Available: Information regarding finite element predicted modes of vibration for 3D cubic CuS cages. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Chang, S. Y.; L. Liu, S. A. Asher, J. Am. Chem. Soc. 1994, 116, 6745. (2) Caruso, F.; Caruso, R. A.; Mo¨hwald, H. Science 1998, 282, 1111. (3) Huang, H.; Remsen, E. E.; Kowalewski, T.; Wooley, K. L. J. Am. Chem. Soc. 1999, 121, 3850. (4) Bergbreiter, D. E. Angew. Chem., Int. Ed. 1999, 38, 2870. (5) Sun, Y.; Xia, Y. Science 2002, 298, 2176. (6) Yin, Y.; Rioux, R. M.; Erdonmez, C. K.; Hughes, S.; Somorjai, G. A.; Alivisatos, A. P. Science 2004, 304, 711. (7) Kim, S.-W.; Kim, M.; Lee, W. Y.; Hyeon, T. J. Am. Chem. Soc. 2002, 124, 7642.
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