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J. Phys. Chem. C 2009, 113, 3164–3167
Composition-Dependent Plasmon Shift in Au-Ag Alloy Nanotubes: Effect of Local Field Distribution Jian Zhu† School of Science, Xi’an Jiaotong UniVersity, Xi’an, 710049, China ReceiVed: NoVember 20, 2008; ReVised Manuscript ReceiVed: December 28, 2008
The composition-controlled shift of the transverse surface plasmon resonance (SPR) in Au-Ag alloy nanotubes was theoretically studied by using the Drude model and quasi-static approximation. Increasing the gold composition leads to the red shift of both low- and high-energy SPR. The antisymmetric plasmon mode is more sensitive to the change in gold composition. The physical origin based on local electric field distribution in the transverse section plane was investigated to illuminate the effect of gold composition on the shift of the SPR. The local field corresponding to antisymmetric coupling is polarized parallel to the incident polarization. Thus, the thin shell enhances the electron scattering and lowers the plasmon energy, which in turn results in an intense red shift of the SPR. 1. Introduction Noble metals such as Au and Ag nanoparticles have been studied in great detail in recent years.1-5 Especially, the effect of size,6 shape,7 structure,8 and surroundings9 on the unique plasmon absorption in the visible and infrared region has been of major interest. It is well-known that solid nanoparticles made of pure Ag and Au only exhibit one surface plasmon resonance (SPR) peak around 400 and 520 nm, respectively. However, the optical properties of bimetallic nanoparticles depend on the structure and composition of particles greatly. For core-shell structure Au-Ag bimetallic nanoparticles, they are characterized by two SPR peaks between 400 and 520 nm.10 In single-phase alloy Au-Ag bimetallic nanoparticles, there is only one surface plasmon band between the peaks corresponding to pure silver and pure gold, whose absorption maximum depends on the alloy composition.11 It is concluded that mixing of gold and silver leads to a homogeneous formation of alloy nanoparticles.12 A linear relationship is observed experimentally between surface plasmon absorption maxima value and the Au mole ratio in various alloy compositions.11,12 Theoretical calculation based on quasi-static limit and Mie theory further clearly indicates a red shift of the plasmon band with the increase in Au concentrations.13 The linear dependence provides a convenient way of tuning the optical absorption properties of bimetallic nanoparticles and also makes it possible to online monitor the formation of alloyed bimetallic nanoparticle by optical spectroscopy.14 Bimetallic alloy nanoparticles have received special attention due to the possibility of tuning their optical and electronic properties over a broad range by simply varying the alloy composition.11,15 However, the tuning range is within the visible region. In another demonstration, it has been shown that the SPR band of pure gold nanoshells supported on dielectric cores could be readily swept from 500 to 1200 nm by varying their shell thickness.16,17 Thus, we believe that the SPR band of Au-Ag alloy nanoshells or nanotubes may be tuned in the infrared region by varying the alloy composition. In recent years, Au-Ag alloyed nanoshell-like structures have been prepared † E-mail:
[email protected].
by Xia and co-workers,18,19 in which (their nanocage work) the shifts in SPR have been observed. However, in the experimental preparation of these structures, both wall thickness and alloy composition are altered, making it difficult to separate the two effects from the observed optical phenomena. In order to provide theoretical backing that distinguishes between both effects, we calculated the SPR-induced light absorption of bimetallic alloy nanotubes in this paper. For this dielectric wire coated by an Au-Ag alloy shell, the SPR red shift in the visible and infrared regions by increasing the gold composition. Furthermore, we discussed in detail how the local electric field influences the oscillation of the conduction free electrons and, consequently, leads to the shift of SPR. 2. Modeling In our studies, we chose a long nanotube as our model. This bimetallic alloy nanostructure consists of a dielectric wire core of radius r1 coated by an Au-Ag alloy shell (with a homogeneous distribution of these two metals) of thickness r2 - r1. The dielectric functions of the dielectric core, alloy shell, and embedding medium are ε1, ε2, and ε3, respectively. It is important to note that ε2 has real and imaginary frequency-dependent components and can be expressed as20
ωp2 ε2(ω) ) εr + iεi ) εb -
ω2 1+
1 ω2τ2
ωp2 +i
(
ω2
ωτ 1 +
1 ω2τ2
)
(1)
The parameters for the AuAg alloy are obtained through the following mixing rules (weighted linear combination of parameters for single particles).14,21 The dielectric function of bulk metal εb ) pεb(Au) + (1 - p)εb(Ag), the plasmon frequency of the bulk metal ωp ) pωp(Au) + (1 - p)ωp(Ag), and the relaxation time τ ) pτ(Au) + (1 - p)τ(Ag), where p is the molar composition of gold. In this analysis, the radius of alloy nanotube is 25 nm, which is much smaller than the incident light wavelength. So the incident field does not vary spatially over the diameter of the nanotube. Then the nanotube is subjected to an almost uniform field. In this case, the transverse
10.1021/jp810192f CCC: $40.75 2009 American Chemical Society Published on Web 01/28/2009
Plasmon Shift in Au-Ag Alloy Nanotubes
Figure 1. (a) Absorption spectra of Au-Ag alloy nanotube with different molar composition of gold, r1 ) 17.5 nm and r2 ) 25 nm. (b) Resonance wavelength of surface plasmon in Au-Ag alloy nanotube as a function of gold molar composition.
SPR and local electric field in the section plane of gold tube can be calculated based on the quasi-static theory,20,22 which may be derived from Laplace’s equation. The calculations of the local field factor and SPR absorption of Au-Ag alloy nanotube are an extension of our previous work on the basic equations of absorption cross section and electric field in the core-shell structure metallic nanowires.23 3. Results and Discussion The calculated absorption spectra that resulted from transverse SPR of Au-Ag alloy nanotube are shown in Figure 1a. In this calculation, r1 ) 17.5 nm and r2 ) 25 nm. Dielectric core and embedding medium have the same dielectric constant ε1 ) ε3 ) 2. The intrinsic feature of the SPR in a metallic nanoshell/ nanotube can be described by the plasmon hybridization model reported by Halas et al.24 Because of having two dielectricmetallic interfaces, there are two SPR peaks resulting from the hybridization between the two free plasmon modes, i.e., the wire plasmon which corresponded to outer surface and the well plasmon which corresponded to inner surface. In Figure 1a, the shorter wavelength peak (high-energy mode) corresponds to an antisymmetric coupling between the free surface plasmons, whereas the longer wavelength peak (low-energy mode) corresponds to a symmetric coupling between the free surface plasmons. Figure 1a also shows that the increase of gold molar composition leads to the red shift of both shorter and longer wavelength SPR. Furthermore, shorter wavelength SPR is more sensitive to the change of gold composition. The shift fashion of SPR in the alloy nanotube is also tunable by changing the shell thickness r2 - r1. The composition-
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3165
Figure 2. Contour plot of local electric field polarization direction for Au-Ag alloy nanotube (a) at low-energy resonance wavelength 939 nm; (b) at high-energy resonance wavelength 389 nm. p ) 0.2, r1 ) 22.5 nm, and r2 ) 25 nm.
dependent shift of SPR for different shell thicknesses are shown in Figure 1b. The effect of shell thickness on the shorter wavelength SPR is weak. However, the effect of shell thickness on the longer wavelength SPR is great. When shell thickness is 2.5 nm, the low-energy mode red-shifts from 928 to 974 nm, ∆λ ) 46 nm, whereas when shell thickness is broadened to 15 nm, the low-energy mode red-shifts from 461 to 583 nm, ∆λ ) 122 nm. As we know, the strength of the interaction between the wire (inner surface) and well (outer surface) plasmons is controlled by the thickness of the tube shell. Too thick shell of the gold tube will prevent the bare plasmon modes from coupling. However, with decreasing the shell thickness, the strength of the interaction gets intense and the energy difference of antisymmetric and symmetric plasmon increases. Therefore, the space between the two SPR peaks increases too, as shown in Figure 1b. In order to find the effect of local electric field distribution on the shift fashion of the composition dependent SPR in Au-Ag alloy nanotube, we also plot the patterns of polarization direction and local field factor in the transverse section plane of the alloy nanotube, as shown in Figures 2 and 3. Local field enhancement is an interesting phenomenon of metallic nanostructures. When the metal particle is much smaller than the incident wavelength, this particle is subjected to an almost uniform field and oscillates like a simple dipole with polarization proportional to the incident field. This polarized electronic field is called local field.25 This local field will be dramatically enhanced at frequencies close to the SPR, which is responsible for the amplification of their nonlinear properties, surface-enhanced Raman spectroscopy, improved fluorescence emission, and so on.26 The local field factor is the magnitude ratio of the local electric field and the incident field. In order to study the direction of the local electric field at different spatial
3166 J. Phys. Chem. C, Vol. 113, No. 8, 2009
Zhu
Figure 3. Contour plot of local electric field enhancement factor for Au-Ag alloy nanotube (a) at low energy resonance wavelength 939 nm with gold molar composition p ) 0.2; (b) at low-energy resonance wavelength 965 nm with gold molar composition p ) 0.8; (c) at high-energy resonance wavelength 389 nm with gold molar composition p ) 0.2; (d) at high-energy resonance wavelength 481 nm with gold molar composition p ) 0.8. r1 ) 22.5 nm and r2 ) 25 nm.
point, we calculated the included angle (denoted by the symbol θ) between the local electric field vector and polarization direction of the incident field. Figure 2a shows the distribution of polarization direction of local field corresponding to the symmetric mode for a thin nanotube; the scale bar shows the included angle θ of the local field. At the low-energy resonance wavelength λ ) 939 nm, same kind of charges (negative or positive) signed on both inner and outer surfaces of the nanotube along the incident polarization. So the local field polarized perpendicular to the incident polarization and then the field lines inside the metallic shell repel each other in the poles along the incident polarization.27 This weak coupling results in the weak local field (near the poles along the incident polarization) and plasmon resonance with low energy, as shown in Figure 3a. Because Au has shorter electron relaxation time than Ag, when gold composition increases to 0.8, the electron scattering gets intense and counteracts the collective motion of free electrons, consequently lowering the plasmon energy. Therefore, the local field becomes more weak, as shown in Figure 3b, and the SPR red-shifts to lower energy. Figure 2b shows the distribution of polarization direction corresponding to the antisymmetric mode for a thin nanotube. At the high-energy resonance wavelength λ ) 389 nm, different kind of charges (negative and positive) signed on inner and outer surfaces of the nanotube along the incident polarization. So the local field polarized parallel to the incident polarization and then the field lines inside the metallic shell concentrate in the poles along the incident polarization. This strong coupling results in the intense local field (near the poles along the incident polarization) and plasmon resonance with high energy, as shown in Figure 3c. When gold composition increases to 0.8, the SPR red-shifts to lower energy because of the decreasing local field, as shown in Figure 3d, which is similar to the symmetric mode in Figure 3a,b. However, the shift of this shorter wavelength SPR is more intense than that of the longer wavelength peak,
as shown in Figure 1b. The corresponding mechanism may be illuminated by the contour plot of local field polarization direction in Figure 2. In the antisymmetric mode, the local field is polarized parallel to the incident polarization. Thus, the free electrons also oscillate in the direction of the incident polarization. And then the thin shell will make the collisional frequency of electron scattering increase, consequently lowering the plasmon energy. The effect of shell thickness on the shift of SPR in Au-Ag alloy nanotube may also be illuminated by the distribution of local field. As we know, the strength of the interaction between the outer and inner plasmons is controlled by the thickness of alloy shell. So the plasmon coupling is weak for the thick shell. In the symmetric mode of thick shell (15 nm), weak coupling will decrease the repelling of field lines, and consequently, increases the local field and plasmon energy. When gold composition increases to 0.8, the SPR red-shifts to lower energy because of the decreasing local field, which is similar to the thin shell (2.5 nm) in Figure 3. However, the increased local field in this thick shell also enhances the electron scattering and consequently lowers the plasmon energy. Therefore, the shift of this symmetric mode SPR for this thick shell is more intense than that of the thin shell, as shown in Figure 1b. SPR is the collective motion of free electrons following the oscillation of the electromagnetic field in the incident polarization. Thus, the SPR energy is greatly dependent on the local field in the poles along the polarization direction of incident field. Figure 4 calculated the local electric field enhancement factor of the Au-Ag alloy nanotube with different gold molar compositions, when r ) r2 and φ ) 0 (here φ is the included angle that the incident field makes with the position vector). It is obvious that the local field from both symmetric and antisymmetric mode decreases with increasing molar composition of gold. Furthermore, the deceasing speeds of the local field corresponding to antisymmetric hybridization are faster than that
Plasmon Shift in Au-Ag Alloy Nanotubes
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3167 References and Notes
Figure 4. Local electric field enhancement factor of Au-Ag alloy nanotube with different molar compositions of gold, r ) r2 and φ ) 0.
of the symmetric mode. These decreasing local fields lead the red shift of SPR. 4. Conclusions In summary, theoretical calculations based on the Drude model and quasi-static approximation show that both symmetric and antisymmetric SPR in Au-Ag alloy nanotube can be tuned by changing the alloy composition and shell thickness. The symmetric SPR can red-shift in the infrared region by increasing the gold composition or decreasing the shell thickness, whereas the antisymmetric SPR can only red-shift in the visible region. Because the local electric field corresponding to antisymmetric coupling is polarized parallel to the incident polarization, the thin shell enhances the electron scattering and lowers the plasmon energy, which in turn results in an intense red shift of the SPR. Acknowledgment. This work was supported by the National Natural Science Foundation of China under grant No. 10804091.
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