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Predicting the Surface Plasmon Resonance Wavelength of Gold-Silver Alloy Nanoparticles Sammy Walter Verbruggen, Maarten Keulemans, Johan A. Martens, and Silvia Katelijne Lenaerts J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4070856 • Publication Date (Web): 27 Aug 2013 Downloaded from http://pubs.acs.org on September 2, 2013

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The Journal of Physical Chemistry

Predicting the Surface Plasmon Resonance Wavelength of Gold-Silver Alloy Nanoparticles

Sammy W. Verbruggen †,‡,*, Maarten Keulemans †,‡, Johan A. Martens ‡ and Silvia Lenaerts †,*

† Sustainable Energy and Air Purification, Department of Bio-science Engineering, University of Antwerp, Groenenborgerlaan 171 , 2020 Antwerp, Belgium ‡ Center for Surface Chemistry and Catalysis, Department of Microbial and Molecular Systems, KU Leuven, KasteelparkArenberg, 3001 Heverlee (Leuven), Belgium

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ABSTRACT

Gold-silver alloy nanoparticles display surface plasmon resonance (SPR) over a broad range of the UV-VIS spectrum. In this paper we propose a model to predict the SPR wavelength of goldsilver alloy colloids based on the combined effect of alloy composition and particle size. The SPR wavelength is derived from extinction spectra simulated using available experimental dielectric constant data and accounting for particle size by applying Mie theory. Comparison of calculated values with experimental data evidences the accuracy of the model. The new SPR wavelength estimation tool will be of particular interest for developing dedicated bimetallic plasmonic nanostructures.

KEYWORDS bimetallic, Au-Ag, colloids, model, Mie theory, SPR


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INTRODUCTION Noble metal nanoparticles are of interest to many fields of biological and chemical science because of their remarkable optical properties. Colloidal solutions of noble metal nanoparticles exhibit a wide range of bright colors that are attributed to the oscillation of conduction band electrons in the alternating electric field of the incident light.1 For a given metal and dielectric environment, this Surface Plasmon Resonance (SPR) effect can be tuned by controlling nanoparticle size2,3 and shape4,5. Tuning the SPR of nanoparticles at specific wavelengths is needed for dedicated applications. For instance, in SPR mediated photocatalysis6 the overlap between the SPR band in the UV-VIS absorption spectrum and the emission spectrum of the light source determines the efficiency of visible light photocatalytic activity.7,8 Metal particle size and shape adaptation are means to adjust the SPR wavelength, but careful control over particle size and shape is not always easy and often requires very specific and demanding reaction conditions. Alloying of different noble metals is an alternative synthesis strategy for tuning the SPR wavelength. AuxAg(1-x) alloy nanoparticles display SPR over a broad range of the visible light spectrum.9,10 Spherical plasmonic AuxAg(1-x) alloy nanoparticles can be conveniently synthesized by co-reduction of dissolved HAuCl4 and AgNO3 with sodium citrate in aqueous solution11, similar to Turkevich synthesis of pure spherical gold nanoparticles.12 AuxAg(1-x) alloy nanoparticles display SPR at wavelengths ranging from ca. 390 nm for pure silver to ca. 530 nm for pure gold. For a fixed chemical composition, the SPR wavelength increases with particle size. In this paper we propose a semi-empirical model for predicting the SPR wavelength of water suspended AuxAg(1-x) alloy nanoparticles, based on their chemical composition and particle size. The model will assist the future design of dedicated bimetallic plasmonic nanostructures.


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THEORETICAL METHODS SPR wavelengths were derived from extinction spectra of monodisperse spherical nanoparticles simulated using Mie theory2,13 with the software package MiePlot (v4300)14. While accurate values of dielectric constants of the pure metals are available15, for alloys this information is scarce. Attempts to estimate dielectric constants of alloys have been made given the limited availability of experimental data.16 Link et al. estimated the dielectric constant, ε, of AuxAg(1-x) alloys from the pure compounds by linear combination (eq. 1): . 1 .

(1)

Extinction spectra simulated using these dielectric constants were in disagreement with experimental spectra.11 Likewise, we experienced that estimation of dielectric constants following an effective medium approach17 is not satisfactory either. A qualitatively better agreement was obtained using experimentally determined complex dielectric functions of Au-Ag alloy thin films of different compositions reported by Ripken.16 The complex dielectric function ε = ε1 + iε2 is correlated with the complex refractive index ñ = n + ik, through the relation ε = ñ2. Real and imaginary parts of the refractive index needed for application of the Mie theory in the MiePlot software were calculated from equations 2 and 3:

(2)

(3)


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The real and imaginary part of the complex refractive index for AuxAg(1-x) alloys with x equal to 0, 0.09, 0.21, 0.38, 0.69, 0.89 and 1.00 as determined from Ripkens's data by applying eq. 2 and eq. 3 are shown in Figure 1a and b, respectively. Figure 1c shows some of the resulting simulated extinction spectra for monodisperse 20 nm alloy spheres in water. Spherical alloy particles are known to have (i) a SPR wavelength between those of the pure metals and (ii) one single SPR signal in the extinction spectrum instead of two, which would be the case for segregated metals such as core-shell nanoparticles.18,19 The simulated extinction spectra in Figure 1c meet both criteria. Also the increasing contribution of interband transitions at smaller wavelengths becomes apparent with increasing gold content.10

Imaginary part refractive index, k

1.2

0.8

0.4

0.0

b)

c)

0

0.21 0.38 0.69 0.89

1

Absorbance (normalized) [a.u.]

3.0

a) 1.6 Real part refractive index, n

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2.5 2.0 1.5 1.0 0.5 0.0

2.0

2.5

3.0

3.5

Energy [eV]

4.0

4.5

2.0

2.5

3.0

3.5

4.0

4.5

300

Energy [eV]

350

400

450

500

Wavelength [nm]

Figure 1. Real (a) and complex (b) part of the refractive index of AuxAg(1-x) alloys. Gold fraction x = 0.0 (), 0.09 (), 0.21 (), 0.38 (), 0.69 (), 0.89 (), 1.0 (). (c) Simulated extinction spectra of 20 nm AuxAg(1-x) alloy nanoparticles in water based on the experimental dielectric constants by Ripken16. The gold fraction x is indicated in the graphs.

The simulated extinction spectra based on Ripken's dielectric constant values were observed to overestimate the SPR wavelength by ca. 9 nm. The origin of this discrepancy was investigated by simulating SPR of differently sized spherical silver nanoparticles using dielectric constants of


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Ripken vs. Johnson and Christy (Figure 2). In Figure 2 both data series run parallel with an offset of 9 nm. Ripken stated the shape of his plots of complex dielectric constant values versus energy for pure gold and silver corresponded well with literature data.16 However, especially for the complex part, which is mainly responsible for SPR, there is a significant discrepancy in the absolute values. The error margin of ε2 for pure gold in Ripken’s data is ± 0.4 compared to ± 0.08 for Johnson and Christy's data. For pure silver and gold Ripken’s refractive index values are 0.08 ± 0.04 lower compared to the values by Johnson and Christy. This systematic error can explain our overestimation of the SPR wavelength of alloys using Ripken’s data. Correcting the complex refractive index by 0.08 and simulating the resulting extinction spectrum leads to satisfactory agreement and elimination of the 9 nm higher values.

420 SPR Wavelength [nm]

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R2 = 0.999 410 400 R2 = 0.997 390 380 0

10

20

30

40

50

Particle Diameter [nm]

Figure 2. Size dependence of the SPR wavelength of spherical silver nanoparticles in water simulated using optical constants reported by Ripken16 (closed symbols) or Johnson and Christy15 (open symbols). The R2 values correspond to a second order polynomial fit.

RESULTS AND DISCUSSION


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The size dependence of the SPR wavelength in Figure 2 can be fitted with a second order polynomial with composition-dependent coefficients (eq. 4): .

! .

"

(4)

in which SPR, D and γ(x) are in nm, β(x) in nm-1 and α(x) in nm-2. The fitting of experimental data with eq.4 is illustrated in Figure 2 for pure silver nanoparticles based on two independent data sets.16,15 We limited our calculations of SPR wavelengths to particles smaller than 50 nm where the dipolar approximation of the Mie formalism is valid. The red-shift of SPR wavelength with increasing particle size in Figure 2 is mainly due to retardation effects becoming important for particles larger than 20-30 nm.2 The variation of SPR wavelength with composition for 20 nm gold-silver alloy nanoparticles is illustrated in Figure 3. In literature, linear variation of SPR wavelength with gold content of the gold-silver alloy has been reported11,20. In the middle range of compositions with gold fractions x from 0.2 to 0.8 the composition dependence can indeed satisfactorily be approached by a linear relation (inset in Figure 3). Deviations from linearity are significant for alloy compositions with small amounts of one of the metals. Especially for these compositional ranges the SPR wavelength can be better described by a general third order function of composition with size dependent coefficients (eq. 5): ′ . $ !′ . "′ . %′

(5)

with SPR, D and coefficients α'(D), β'(D), γ'(D) and δ'(D) in nm.


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550

R2 = 0.996

500

450 SPR [nm]

SPR Wavelength [nm]

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400

350 0.0

0.2

525 2 R = 0.994 500 475 450 425 0.0 0.2 0.4 0.6 0.8 1.0 Gold Fraction

0.4

0.6

0.8

1.0

Gold fraction

Figure 3. Composition dependence of the SPR wavelength for 20 nm spherical alloy nanoparticles with different compositions in water. The R2 value corresponds to a third order polynomial fit. The R2 value of the inset corresponds to a linear regression of the composition dependence of the SPR wavelength at intermediate gold fractions. The composition dependent coefficients in eq. 4 and the size dependent coefficients in eq. 5 are presented in Table 1. These coefficients were derived from a matrix of simulated extinction spectra of gold-silver alloy nanoparticles with 10 different particle sizes between 5 and 50 nm and 7 different compositions (x= 0.00, 0.09, 0.21, 0.38, 0.69, 0.89 and 1.00). SPR wavelengths calculated from eq. 4 and 5 using the coefficients of Table 1 satisfactorily matched the original simulated values using Mie theory, with deviations from 0.1 to 1.5% and 0 to 2.2%, respectively. The deviations were not systematic. The range of attainable SPR wavelengths for different sizes and compositions is illustrated in the mesh plot of Figure 4, based on calculated values from eq. 4. The plot shows how to tune the SPR wavelength by altering the AuxAg(1-x) alloy composition and particle size. Alloy composition is clearly the dominating


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effect. The particle size effect is most pronounced at high silver content but generally less important. Table 1. Composition dependent coefficients of eq. 4 and size dependent coefficients of eq. 5. Equation 4*

Equation 5**

α,α'

-0.0028.x + 0.0088

0.64.D + 231

β,β'

-0.151.x + 0.073

-0.64. D -342

γ,γ'

234.x3 - 342.x2 + 243.x + 395

-0.27. D +248

δ'

N.A.

0.0092.D2 + 0.0262.D + 393

*x = gold fraction, **D = particle diameter (nm)


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520 480 440 400 360 0.8 0.6 Go ld F 0.4 0.2 rac tion 0.0

50 40 30 nm] 20 er [ t e 10 iam le D c i t r Pa

Figure 4. Mesh plot of the SPR wavelength of AuxAg(1-x) alloy nanoparticles in function of gold content and particle diameter. Data obtained using the size dependent formula eq. 4 with the composition dependent coefficients from table 1. The agreement of experimental SPR wavelengths11,20 and estimates from eq. 4 is illustrated in Figure 5 for a broad range of compositions and particles sizes. It is again obvious that mainly the alloy composition determines the SPR wavelength, whereas particle size is of secondary


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importance. This is evidenced by the gray contours showing third order dependence on composition, while for a fixed composition the band width accounts for the size effect. Refining of the model by accounting for the particle size distribution21 instead of mean particle size is therefore not expected to add substantially.


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500 450 400 350 0.0

0.2

0.4 0.6 0.8 Gold fraction

1.0

Figure 5. Experimental SPR wavelengths (Mallin et al.: red20, Link et. al.: yellow11, own data: green) and predictions using eq. 4 (black bars). The grey contours indicate the third order theoretical bounds of the SPR wavelength for particle sizes from 5 to 50 nm. The particle sizes of the data bars are, from left to right: 17.2, 4.9, 48, 25, 40, 18, and 7.2 nm.

CONCLUSIONS Summarizing, we have simulated the SPR wavelength of colloidal AuxAg(1-x) alloy nanoparticles using Mie theory and dielectric data reported in literature. The SPR wavelength depends on particle size following a second order polynomial expression with composition dependent coefficients. Dependence of SPR wavelength on chemical composition is described by a third order polynomial with size dependent coefficients. We propose a semi-empirical model to


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estimate the SPR wavelength based on the combined effect of alloy composition and particle size. The accuracy of the model is demonstrated by comparison with experimental data. The proposed methodology can potentially be extrapolated towards other noble metal alloys, provided dielectric functions are known. AUTHOR INFORMATION Corresponding Authors * [email protected]; [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT S.W.V. kindly acknowledges the Research Foundation of Flanders (FWO) for the financial support. J.A.M. acknowledges the Flemish government for long-term structural funding (Methusalem).

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(3) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment. J. Phys. Chem. B 2003, 107, 668-677 (4) Grzelczak, M.; Perez-Juste, J.; Mulvaney, P.; Liz-Marzán, L. M. Shape Control in Gold Nanoparticle Synthesis. Chem. Soc. Rev. 2008, 37, 1783-1791 (5) Sanchez-Iglesias, A.; Grzelczak, M.; Perez-Juste, J.; Liz-Marzán, L. M. Binary SelfAssembly of Gold Nanowires with Nanospheres and Nanorods. Angew. Chem., Int. Ed. 2010, 49, 9985-9989 (6) Linic, S.; Christopher, P.; Ingram, D. B. Plasmonic-Metal Nanostructures for Efficient Conversion of Solar to Chemical Energy. Nat. Mater. 2011, 10, 911-921 (7) Liu, Z. W.; Hou, W. B.; Pavaskar, P.; Aykol, M.; Cronin, S. B. Plasmon Resonant Enhancement of Photocatalytic Water Splitting under Visible Illumination. Nano Lett. 2011, 11, 1111-1116 (8) Ingram, D. B.; Christopher, P.; Bauer, J. L.; Linic, S. Predictive Model for the Design of Plasmonic Metal/Semiconductor Composite Photocatalysts. ACS Cat. 2011, 1, 1441-1447 (9) Liz-Marzán, L. M. Tailoring Surface Plasmons through the Morphology and Assembly of Metal Nanoparticles. Langmuir 2006, 22, 32-41 (10) Rodriguez-Gonzalez, B.; Sanchez-Iglesias, A.; Giersig, M.; Liz-Marzán, L. M. AuAg Bimetallic Nanoparticles: Formation, Silica-Coating and Selective Etching. Faraday Discuss. 2004, 125, 133-144


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(11) Link, S.; Wang, Z. L.; El-Sayed, M. A. Alloy Formation of Gold-Silver Nanoparticles and the Dependence of the Plasmon Absorption on Their Composition. J. Phys. Chem. B 1999, 103, 3529-3533 (12) Turkevich, J.; Stevenson, P. C.; Hillier, A Study of the Nucleation and Growth Processes in the Synthesis of Colloidal Gold. J. Discuss. Faraday Soc. 1951, 11, 55-75 (13) Kozadaev, K. V. Diagnostics of Aqueous Colloids of Noble Metals by Extinction Modeling Based on Mie Theory. J. Appl. Spectrosc. 2011, 78, 692-697 (14) MiePlot. www.philiplaven.com/mieplot.htm 2013 (15) Johnson, P. B.; Christy, R. W. Optical Constants of Noble Metals. Phys. Rev. B 1972, 6, 4370-4379. (16) Ripken, K. N. U. T. Optical Constants of Au, Ag and Their Alloys in Energy Region from 2.4 to 4.4 Ev. Z. Phys. 1972, 250, 228-234 (17) Sachan, R.; Yadavali, S.; Shirato, N.; Krishna, H.; Ramos, V.; Duscher, G.; Pennycook, S. J.; Gangopadhyay, A. K.; Garcia, H.; Kalyanaraman, R. Self-Organized Bimetallic Ag-Co Nanoparticles with Tunable Localized Surface Plasmons Showing High Environmental Stability and Sensitivity. Nanotechnology 2012, 23, 275604-275612 (18) Moskovits, M.; Srnova-Sloufova, I.; Vlckova, B. Bimetallic Ag-Au Nanoparticles: Extracting Meaningful Optical Constants from the Surface-Plasmon Extinction Spectrum. J. Chem. Phys. 2002, 116, 10435-10446


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(19) Han, S. W.; Kim, Y.; Kim, K. Dodecanethiol-Derivatized Au/Ag Bimetallic Nanoparticles: TEM, UV/VIS, XPS, and FTIR Analysis. J. Colloid Interface Sci. 1998, 208, 272-278 (20) Mallin, M. P.; Murphy, C. J. Solution-Phase Synthesis of Sub-10 nm Au-Ag Alloy Nanoparticles. Nano Lett. 2002, 2, 1235-1237 (21) Doak, J.; Gupta, R. K.; Manivannan, K.; Ghosh, K.; Kahol, P. K. Effect of Particle Size Distributions on Absorbance Spectra of Gold Nanoparticles. Phys. E (Amsterdam, Neth.) 2010, 42, 1605-1609


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TABLE OF CONTENTS ARTWORK 560 SPR Wavelength [nm]

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520 480 440 400 360 0.8 0.6 Go ld F 0.4 0.2 ra c tion 0.0

50 40 30 m] 20 er [n t e 10 iam D ticle Par


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