Theoretical Analysis of Plasmon Modes of Au–Ag Nanocages - The

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Theoretical Analysis of Plasmon Modes of Au−Ag Nanocages Jiunn-Woei Liaw,*,†,‡ Jui-Ching Cheng,§ Cuiman Ma,∥ and Ruifeng Zhang∥ †

Department of Mechanical Engineering and ‡Center for Biomedical Engineering, Chang Gung University, 259 Wen-Hwa first Road, Kwei-Shan, Tao-Yuan, 333, Taiwan § Department of Electronic Engineering, National Taipei University of Technology, 1 Sec. 3, Chunghsiao E. Road, Taipei, 10643, Taiwan ∥ School of Electronic Information Engineering, Tianjin University, 92 Weijin Road, Nankai District, Tianjin, 300072, China S Supporting Information *

ABSTRACT: The plasmonic properties of porous Au−Ag alloy nanocages are studied theoretically. The finite element method is used to investigate numerically the scattering and absorption spectra of two kinds of nanocages: corner-truncated and face-holed nanocages. Our results indicate that the plasmon modes of the two porous nanocages are nearly equivalent and tunable, which are redshifted from that of nanobox. The larger the surface porosity, the more redshifted the plasmon band is. However, the dependence of the plasmon band (dipole mode) on the surface porosity of the corner-truncated nanocage is higher than that of the face-holed one. The absorption efficiency of the former is higher than those of the latter at the same plasmon mode, whereas the scattering efficiency of the former is weaker. In addition, the bandwidth of the former is narrower than that of the latter. Our results also show that the scattering and absorption efficiencies of a corner-truncated nanocage illuminated by a plane wave normal to the {111} facet are stronger than those to the {100} facet at the same plasmon mode.

I. INTRODUCTION Recently, Au nanoparticles (NPs) have become attractive theranostic (diagnostic and therapeutic) agents in biomedicine researches due to their strong scattering and absorption properties at surface plasmon resonance (SPR), a collective oscillation of free electrons in the entire metallic nanoparticle.1 In the past decade, a variety of Au or Ag NPs have been developed, for example, nanorod,2 nanoshell,3 nanocube,4 nanobox,5 nanocage, nanoframe6−8 and so forth. Because of the strong scattering property, Au NPs can be used as a contrast agent to enhance optical imaging, for example, darkfield microscopy,9 two-photon microscopy,10,11 optical coherence tomography (OCT),12 surface-enhanced Raman spectroscopy (SERS),13−15 surface-enhanced fluorescence (SEF),16 and so on. On the other hand, the absorption property of Au NPs can be utilized for the photothermal therapy17 and photoacoustic imaging.18 Moreover, because of their biocompatibility and low-cytotoxicity, the application of Au NPs in drug delivery is also being studied now.19 Each type of Au or Ag NPs possesses unique SPR properties. For example, the SPR bands of nanoboxes, which are hollowed nanocubes, are tunable by adjusting the metallic wall thickness. Moreover, the SPR bands of porous Au−Ag nanocages, fabricated by using the galvanic replacement reaction between aqueous HAuCl4 and Ag nanocubes,20 are within the near-infrared (NIR) regime, redshifted from that of Ag nanobox. Because of the replacement of Ag with Au, bimetallic Au−Ag nanocages are formed. In addition, the Au−Ag nanocages are wall-porous and interior© 2013 American Chemical Society

hollowed structures, which are good candidates for drug delivery and release system.19 On the basis of these multifunctional advantages, porous nanocages have lots of potential for biomedical applications.21,22 Although the SPR of porous Au−Ag nanocages were proven to be redshifted from that of Ag nanoboxes experimentally, the pore effect on the SPR is still unclear. In the previous studies,23,24 the aspect ratio of the edge length to the thickness of nanobox is the key factor to determine the SPR band. Of course, SPR band is also dependent on the composition of Au−Ag alloy.6−8 Recently, two types of Au−Ag nanocages with the sharp corners or truncated corners have been synthesized by controlling the molar ratio of the etchant (HAuCl4) properly.6−8 In this paper, we are motivated to study theoretically the relationship between the plasmonic properties and the surface porosity for the two different morphologies of nanocages. The discrete dipole approximation (DDA) has been used recently for the numerical simulation of nanocube, nanobox, nanocage, and nanoframe with sharp corners.23−26 In addition, the finite difference time domain (FDTD) method27 and finite element method (FEM)28,29 have also been used for the numerical simulation of nanocubes. In this paper, FEM is adopted for the numerical analysis of the corner-truncated and Received: March 29, 2013 Revised: August 22, 2013 Published: August 26, 2013 19586

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face-holed nanocages due to its flexibility for geometric modeling.

Ps =

1 Re{ 2

∫S (Es × H̅ s)·da}

(2)

where H̅ s is the conjugate of the scattered magnetic field, and Re is the real part. Here the integral surface S can be any closed surface enclosing the nanocage. The absorption (dissipation) power in the nanocage is expressed by the integration of the volume loss density ρv,

II. THEORY The geometric relationships of nanobox and nanocages are depicted in Figure 1, according to the chemical synthesis

Pa =

∫V ρv dv

(3)

where V is the total volume of nanocage. The volume loss density ρv in the metal can be expressed as ρv =

1 Re(E· J̅ ) 2

(4)

where J ̅ is the conjugate of the equivalent current density in a lossy material; J = ωε″E. Therefore, the absorption (dissipation) power is written as ω ε″|E|2 dv Pa = (5) 2 V

∫

Here the electric and magnetic fields in the metal are denoted by (E, H), and the surrounding medium is assumed lossless. The scattering cross section (SCS, σs) and absorption cross section (ACS, σa) of a nanocage are defined as

Figure 1. Configurations of (a) nanobox, (b) corner-truncated, (c) fully corner-truncated, (d) face-holed, and (e) fully corner-truncated and face-holed nanocages.

20

process, where Figure 1a is the nanobox. The configurations of two types of porous nanocages are depicted in Figure 1b,d, respectively; one is the corner-truncated nanocage and the other the face-holed one. Here, a is the edge length of nanocage, t is the thickness of the wall, b is the truncation length of the former (b ≤ a/2), and l is the square-hole size of the latter. For a fully corner-truncated nanocage as shown in Figure 1c, the truncation length of each edge reaches the half of the edge length, b = a/2. There are two kinds of facets: {100} and {111} for the corner-truncated nanocage, as shown in Figure 1c. Finally, Figure 1e is a special case of the combination of the two cases. A commercial FEM code (HFSS, ANSOFT) is adopted to simulate the electromagnetic fields induced by a plane wave illuminating a single nanocage. Throughout the paper, the time harmonic factor for Maxwell’s equations is exp(iωt), where ω is the angular frequency. The permittivity of Au−Ag alloy is expressed by ε = (1 − β)εAg + βεAu

σs =

Ps Pi

(6)

σa =

Pa Pi

(7)

where the time-average energy flux density of the incident plane wave is Pi = 1/2 Re{Ei × H̅ i·ek}. Here, ek is the unit vector of the wavenumber vector k of the incident plane wave. The extinction cross section (ECS, σe) of a nanocage or nanobox is defined as the sum of SCS and ACS, σe = σs +σa. The SCS, ACS, and ECS efficiencies of a single nanocage or nanobox are further defined as the dimensionless values of SCS, ACS, and ECS normalized by the cross-section area of a nanocage or nanobox, that is, Qs = σs/A, Qa = σa/A, and Qe = σe/A, where A = a2 and a is the edge length of nanobox and nanocage.

III. RESULTS AND DISCUSSION To verify the correctness of the FEM, our results were compared with those of the DDA method in ref 9 for Au−Ag (2:1) nanobox with an edge length of 58 nm and wall thickness of 8 nm in oil (refractive index 1.516), as shown in Figure S1 of Supporting Information. They are in agreement. We also have made compassions of our numerical data with experiment data (Figure S2 of Supporting Information) for validation.5 The peaks of the plasmon modes of numerical data agree with those of experiment. However, the bandwidth of the experimental data is broader than the numerical one, particularly in air. In addition, the second plasmon mode predicted by numerical result (in water) was not found in the experimental data. The discrepancies between the numerical and experimental data could be due to that the experimental measurement of the scattering spectrum of a nanocage is on an ITO substrate with high refractive index. Moreover, a dark-field spectroscopy with a condenser was used for the measurement of Rayleigh scattering, where the light source is an annular ring illumination, rather than a plane wave.5 In addition, the NA

(1)

where β is the atomic fraction of Au; ε = ε′ − iε″. Here εAg and εAu are the wavelength-dependent permittivity of Au and Ag, which are complex values.34 Equation 1 is based on Newton’s formulation.35 Reference 31 has proven that the numerical results by using Newton’s formulation are in agreement with their experimental measurement for the Au/ Ag nanorod. This linear equation is only an approximation, particularly valid in the red to NIR regime. However, it could be not correct in the blue to UV regime due to the interband transition of Ag/Au alloy. The imaginary part of permittivity of a lossy material is positive, ε″ > 0. In the surrounding medium, the total electromagnetic fields are the sum of the incident field and scattered field; E = Ei + Es, H = Hi + Hs. The superscripts “i” and “s” denote the incident and scattered parts, respectively. The scattered powers of the electromagnetic wave by the nanocage, in terms of the Poynting vector, is defined as 30−33

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(numerical aperture) of the objective lens for detecting scattered light is around 0.4; it means there is only a certain solid angle for collecting the scattered light from nanocage. In contrast, our FEM numerical calculations neglect the effect of substrate and only consider the total scattering of a nanocage illuminated by a normal incident polarized plane wave. In the following simulation, the edge length of nanobox and nanocage is a = 80 nm, and the thickness of Au−Ag alloy wall is t = 8 nm. The composition of Au/Ag is 1:2, that is, β = 1/3. The optical responses of nanocages in two different surrounding media, air and water, are discussed. The scattering and absorption properties of two types of porous nanocages, the corner-truncated and the face-holed nanocages, are analyzed and compared in the following. The SCS, ACS, and ECS efficiencies of a fully corner-truncated nanocage (b = a/2) in air are shown in Figure 2a, where the incident plane wave is

Figure 3. SCS, ACS, and ECS efficiencies of (a) fully corner-truncated nanocage (b = 40 nm) and (b) face-holed nanocage (l = 26 nm) in water. Dashed lines are for nanobox. [a, t] = [80, 8] nm.

regime, redshifted from the first mode of a nanobox, at 733 nm. The second plasmon modes of the corner-truncated nanocage, face-holed nanocage, and nanobox are at 596, 697, and 588 nm, respectively. Comparing Figure 2 panel a with panel b and Figure 3 panel a with panel b, we can draw a conclusion that the plasmon bands of the corner-truncated and face-holed nanocages can be nearly equivalent by adjusting properly the surface-hole sizes for both cases although their morphologies are different. However, the absorption efficiency of the cornertruncated nanocage is stronger than that of the face-holed one at the same plasmon modes, no matter in air or water. In contrast, the scattering efficiency of the corner-truncated nanocage is weaker than that of the face-holed one. In addition, the surface hole area of the latter is larger than that of the former; the total hole area on the eight faces of the cornertruncated nanocage is 1773 nm2, while the total hole area on the six faces of the face-holed one is 4056 nm2. Moreover, the bandwidth of the plasmon mode of a corner-truncated nanocage is narrower than that of a face-holed one. This is to say that the wavelength-selectivity of the former is superior to the latter. Of interest is that the second modes of the two kinds of nanocages and nanobox appear when the surrounding medium is water; the second plasmon mode is at 606 (cornertruncated nanocage), 683 (face-holed nanocage), and 588 nm (nanobox), as shown in Figure 3. Furthermore, the far-field scattering pattern of normalized |r2Es × H̅ s·er| as r →∞ and |E|/ |Ei| distribution on the surface of a fully corner-truncated nanocage in water at the first and second plasmon modes are shown in Figure 4a,b, respectively. The results of a face-holed

Figure 2. SCS, ACS, and ECS efficiencies of (a) fully corner-truncated nanocage (b = 40 nm) and (b) face-holed nanocage (l = 26 nm) in air. Dashed lines are for nanobox. [a, t] = [80, 8] nm.

normal to the {100} facet. The results of a face-holed nanocage are shown in Figure 2b, where the square-hole size on the six faces is l = 26 nm. In Figure 2, the dashed lines are the results of a nanobox. The first plasmon mode of the former nanocage in air is at 667 nm and that of the latter at 664 nm. For both nanocages, their plasmon modes in air are nearly the same, redshifted from that of a nanobox, at 588 nm. The second plasmon mode is at 505 nm for the former and at 557 nm for the latter. In addition, the results of these two nanocages in water are also depicted in Figure 3a,b, respectively, where the wavelength is the value in vacuum. The first plasmon mode of the former nanocage in water is at 848 nm and that of the latter at 845 nm. Again, both are also nearly the same in the NIR 19588

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Figure 4. Far-field scattering patterns and surface electric field distributions of corner-truncated nanocage in water at the (a) first mode (λ = 848 nm) and (b) second mode (λ = 606 nm). [a, t, b] = [80, 8, 40] nm.

Figure 5. Far-field scattering patterns and surface electric field distributions of face-holed nanocage in water at the (a) first mode (λ = 845 nm) and (b) second mode (λ = 683 nm). [a, t, l] = [80, 8, 26] nm.

nanocage in water at the first and second modes are shown in Figure 5a,b, where l = 26 nm. Figures 4a and 5a indicate that their first modes are the dipole mode according to the shape of far-field pattern. Additionally, the second mode of the faceholed nanocage is also easily confirmed as a quadrupole mode based on the four-lobe shape of the far-field patterns as shown in Figure 5b.36 However, the far-field pattern, as shown in Figure 4b, of the second mode of the corner-truncated one is more like the pattern of a dipole mode, rather than a quadrupole mode. This unique feature of corner-truncated nanocage is notable. Subsequently, the surface-porosity effect on the plasmon mode of nanocage is analyzed. Figure 6a shows the first and second plasmon modes of a corner-truncated nanocage in air or

water versus the surface porosity, which is the ratio of the surface pore area to the whole surface area. The results demonstrate that the larger the surface porosity, the more redshifted the plasmon band is. The corresponding curves in terms of corner truncation length b are shown in Supporting Information (Figure S3). However, the second mode, distributed from 591 to 606 nm, is nearly independent of the surface porosity. The results of a face-holed nanocage versus the surface porosity are shown in Figure 6b. Roughly speaking, the larger the surface holes, the more redshifted the plasmon bands are. The redshift of the plasmon band as the surface porosity of the face-holed nanocage increases is in agreement with the results of ref 14. Comparing Figure 6 panel a with panel b, we found that the corner-truncated nanocage is 19589

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nanocage in water illuminated by a plane wave normal to the {111} facet, the truncated plane as shown in Figure 1c. In fact, ref 5 has measured the scattering properties of a cornertruncated nanocage on ITO substrate with different orientations, {100} or {111}, using dark-field microscopy. However, the quantitative values of SCS and ACS are lacked. Comparing Figure 7 with Figure 3a, we find that the absorption efficiency of facet {111} is almost twice larger than that of facet {100} at the first plasmon mode. Additionally, the scattering efficiency of facet {111} is larger than that of facet {100}. Therefore the extinction efficiency of facet {111} is larger than that of facet {100}. This amplification could be attributed to that the ratio of the projected area of a nanocage from facet {111} (a hexagon) to that of a nanocage from facet {100} (a square) is the square root of 3. However, the plasmon modes of both cases are nearly the same at 848 nm (first mode) and 606 nm (second mode). Finally, the scattering and absorption spectra of a special porous nanocage with both the corner truncations and the face holes are analyzed. The first, second, and third modes of this porous nanocage in air are at 746, 617, and 541 nm, respectively, as shown Figure 8a, where [a, t, b, l] = [80, 8, 40, 26] nm. Figure 8b shows that the first, second, and third modes in water are at 959, 773, and 658 nm, respectively. These plasmon modes of this special nanocage are more redshifted from those of the corner-truncated nanocage and the face-holed one, because it has more surface porosity compared to those cases of Figures 2 and 3. This phenomenon again

Figure 6. First and second plasmon modes of (a) corner-truncated nanocage versus surface porosity and of (b) face-holed nanocage versus surface porosity in air or water. [a, t] = [80, 8] nm.

superior to the face-holed one, because that the dependence of the plasmon band (dipole mode) on the surface porosity of the former is higher than that of the latter. This is to say that a smaller surface porosity of the corner-truncated nanocage, compared to the face-holed one, causes the specified redshift of the plasmon band of the dipole mode. This finding could be useful to tailor the optical properties of nanocages on demand. Moreover, we analyze the optical responses of nanocage illuminated from different incident angles. Figure 7 shows that the ACS and SCS efficiencies of a fully corner-truncated

Figure 7. SCS, ACS, and ECS efficiencies of a fully corner-truncated nanocage illuminated by a plane wave normal to the {111} facet in water. [a, t, b] = [80, 8, 40] nm.

Figure 8. SCS, ACS, and ECS efficiencies of a nanocage with both the corner truncations and face holes in (a) air and (b) water. [a, t, b, l] = [80, 8, 40, 26] nm. 19590

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(5) Hu, M.; Chen, J.; Marquez, M.; Xia, Y.; Hartland, G. V. Correlated Rayleigh Scattering Spectroscopy and Scanning Electron Microscopy Studies of Au−Ag Bimetallic Nanoboxes and Nanocages. J. Phys. Chem. C 2007, 111, 12558−12565. (6) Skrabalak, S. E.; Chen, J.; Sun, Y.; Lu, X.; Au, L.; Cobley, C. M.; Xia, Y. Gold nanocages: synthesis, properties, and applications. Acc. Chem. Res. 2008, 41 (12), 1587−1595. (7) Chen, J.; McLellan, J. M.; Siekkinen, A.; Xiong, Y.; Li, Z.-Y.; Xia, Y. Facile Synthesis of Gold−Silver Nanocages with Controllable Pores on the Surface. J. Am. Chem. Soc. 2006, 128, 14776−14777. (8) Xia, Y.; Li, W.; Cobley, C. M.; Chen, J.; Xia, X.; Zhang, Q.; Yang, M.; Cho, E. C.; Brown, P. K. Gold nanocages: from synthesis to theranostic applications. Acc. Chem. Res. 2011, 44 (10), 914−924. (9) Hu, M.; Petrova, H.; Sekkinen, A. R.; Chen, J.; McLellan, J. M.; Li, Z.-Y.; Marquez, M.; Li, X.; Xia, Y.; Hartland, G. V. Optical Properties of Au−Ag Nanoboxes Studied by Single Nanoparticle Spectroscopy. J. Phys. Chem. B 2006, 110, 19923−19928. (10) Liaw, J.-W.; Tsai, S.-W.; Chen, K.-L.; Hsu, F.-Y. Single-photon and two-photon cellular imagings of gold nanorods and dyes. J. Nanosci. Nanotechnol. 2010, 10 (1), 467−473. (11) Tsai, S.-W.; Chen, Y.-Y.; Liaw, J.-W. Compound cellular imaging of laser scanning confocal microscopy by using gold nanoparticles and dyes. Sensors 2008, 8, 2306−2316. (12) Cang, H.; Sun, T.; Chen, J.; Wiley, B. J.; Xia, Y.; Li, X. Gold nanocages as potential contrast agents for spectroscopic and conventional optical coherence tomography. Opt. Lett. 2005, 30, 3048−3050. (13) Rycenga, M.; Wang, Z.; Gordon, E.; Cobley, C. M.; Schwartz, A. G.; Lo, C. S.; Xia, Y. Probing the photothermal effect of Au-based nanocages with surface-enhanced Raman scattering (SERS). Angew. Chem., Int. Ed. 2009, 48 (52), 9924−9927. (14) Mahmoud, M. A.; Snyder, B.; El-Sayed, M. A. Surface Plasmon Fields and Coupling in the Hollow Gold Nanoparticles and SurfaceEnhanced Raman Spectroscopy. Theory and Experiment. J. Phys. Chem. C 2010, 114 (16), 7436−7443. (15) Rycenga, M.; Hou, K. K.; Cobley, C. M.; Schwartz, A. G.; Camargo, P. H. C.; Xia, Y. Probing the surface-enhanced Raman scattering properties of Au−Ag nanocages at two different excitation wavelengths. Phys. Chem. Chem. Phys. 2009, 11, 5903−5908. (16) Bardhan, R.; Grady, N. K.; Cole, J. R.; Joshi, A.; Halas, N. J. Fluorescence Enhancement by Au Nanostructures: Nanoshells and Nanorods. ACS Nano 2009, 3 (3), 744−752. (17) Chen, J.; Wang, D.; Xi, J.; Au, L.; Siekkinen, A.; Warsen, A.; Li, Z.-Y.; Zhang, H.; Xia, Y.; Li, X. Immuno Gold Nanocages with Tailored Optical Properties for Targeted Photothermal Destruction of Cancer Cells. Nano Lett. 2007, 7 (5), 1318−1322. (18) Yang, X.; Skrabalak, S. E.; Li, Z.-Y.; Xia, Y.; Wang, L. V. Photoacoustic Tomography of a Rat Cerebral Cortex in Vivo with Au Nanocages As an Optical Contrast Agent. Nano Lett. 2007, 7, 3798− 3802. (19) Au, L.; Zhang, Q.; Cobley, C. M.; Gidding, M.; Schwartz, A. G.; Chen, J.; Xia, Y. Quantifying the Cellular Uptake of AntibodyConjugated Au Nanocages by Two-Photon Microscopy and Inductively Coupled Plasma Mass Spectrometry. ACS Nano 2010, 4 (1), 35−42. (20) Rycenga, M.; Cobley, C. M.; Zeng, J.; Li, W.; Moran, C. H.; Zhang, Q.; Qin, D.; Xia, Y. Controlling the Synthesis and Assembly of Silver Nanostructures for Plasmonic Applications. Chem. Rev. 2011, 111, 3669−3712. (21) Zhang, Q.; Cobley, C. M.; Zeng, J.; Wen, L.-P.; Chen, J.; Xia, Y. Dissolving Ag from Au−Ag Alloy Nanoboxes with H2O2: A Method for Both Tailoring the Optical Properties and Measuring the H2O2 Concentration. J. Phys. Chem. C 2010, 114, 6396−6400. (22) Cho, E. C.; Xie, J.; Wurm, P. A.; Xia, Y. Understanding the Role of Surface Charges in Cellular Adsorption versus Internalization by Selectively Removing Gold Nanoparticles on the Cell Surface with a I2/KI Etchant. Nano Lett. 2009, 9 (3), 1080−1084. (23) Ringe, E.; McMahon, J. M.; Sohn, K.; Cobley, C.; Xia, Y.; Huang, J.; Schatz, G. C.; Marks, L. D.; Van Duyne, R. P. Unraveling

demonstrates that the larger the pore area on the surface of a porous nanocage the more redshifted the plasmon mode. Moreover, our results also indicate that the substrate and surrounding medium with high refractive indexes can also redshift these plasmon modes.37 In addition, more higher-order modes appear for a highly porous nanocage.

IV. CONCLUSION Our results indicated that the SPR properties (scattering and absorption) of a corner-truncated nanocage are almost equivalent to that of a face-holed nanocage with sharp corners. For comparison, the wall thicknesses and the edge length of these two types of nanocages and their Au−Ag composition are assumed the same. The surface porosity of nanocage causes the redshift of the plasmon modes of a nanocage, compared to nanobox. The bandwidth of plasmon mode of a fully cornertruncated nanocage is narrower than that of a face-holed one. The absorption efficiency of a corner-truncated nanocage is stronger than that of a face-holed one at the plasmon modes. In contrast, the scattering efficiency of corner-truncated nanocage is weaker than that of face-holed one. These plasmon modes depend on the surface hole area for both cases; the larger the surface porosity, the more redshifted the plasmon bands. However, to obtain the same plasmon band of the dipole mode, a smaller surface porosity of the corner-truncated nanocage is required than the face-holed one. Moreover, our results indicate that the scattering and absorption efficiencies of a cornertruncated nanocage illuminated by a plane wave normal to the {111} facet are stronger than those to the {100} facet at the same plasmon mode. In addition, more higher-order modes appear for a highly porous nanocage. On the basis of these properties, porous nanocages have multimodalities for theranostic applications in NIR regime.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was supported by Chang Gung University (BMRP892).

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