Gold-silver nanostructures: Plasmon-plasmon interaction

Accepted Manuscript Gold-silver nanostructures: Plasmon-plasmon interaction Atrayee Hazra, Syed Minhaz Hossain, Ashit Kumar Pramanick, Mallar Ray PII:

S0042-207X(16)30957-5

DOI:

10.1016/j.vacuum.2017.05.016

Reference:

VAC 7416

To appear in:

Vacuum

Received Date: 6 December 2016 Revised Date:

9 May 2017

Accepted Date: 11 May 2017

Please cite this article as: Hazra A, Hossain SM, Pramanick AK, Ray M, Gold-silver nanostructures: Plasmon-plasmon interaction, Vacuum (2017), doi: 10.1016/j.vacuum.2017.05.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Gold-Silver Nanostructures: Plasmon-Plasmon Interaction Atrayee Hazraa1, Syed Minhaz Hossainb, Ashit Kumar Pramanickc and Mallar Raya2 a

Dr. M. N. Dastur School of Materials Science and Engineering, Indian Institute of Engineering

[email protected]

Department of Physics, Indian Institute of Engineering Science and Technology, Shibpur, West

Bengal, India. [email protected] c

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b

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Science and Technology, Shibpur, West Bengal, India. 1 [email protected], 2

Materials Science & Technology (MST) Division, CSIR - National Metallurgical Laboratory

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Jamshedpur - 831 007, India. [email protected]

Abstract: Gold and silver coupled nanostructure system presents immense possibilities for understanding plasmon-plasmon interaction in colloidal suspension. The origin of surface

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plasmon resonance (SPR) in noble metal nanostructures and the dependence of SPR on various factors have been widely investigated and the interactions of plasmons have also been studied. However, the plasmon-plasmon coupling in interchangeable core and shell

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plasmonic materials is not clearly understood. In this work we present synthesis of Au-Ag and Ag-Au core-shell nanostructures i.e. the materials of the core and the shell can be

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interchanged. For such interchangeable core-shell noble metal nanostructures, we see that the plasmon-plasmon interaction is not only dependent on the size, shape, polarities etc. but also on the position of a particular metal in the composite structure. Experimentally, the plasmon resonance interaction is studied by simple absorption spectroscopy and the structure is investigated by electron microscopy. Classical model of simple, forced vibration of damped, coupled oscillators with Coulombic couplings is utilized to understand the

ACCEPTED MANUSCRIPT plasmon-plasmon interaction in these systems. Such core shell nanostructures with interchangeable core and shell materials offer huge potential for various applications. Keywords: Nanostructure; core-shell nanoparticles; hetero-nanosystem; plasmon;

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resonance. This research did not receive any specific grant from funding agencies in the public,

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commercial, or not-for-profit sectors.

Introduction

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Noble metal nanostructures have been widely investigated, primarily because of the surface plasmon resonance (SPR) observed in such nanosystems, which render them amenable for a variety of applications. At resonance, the induced oscillations of nearly free electrons in the nanoparticles (NPs) – the surface plasmons, drastically perturb the near-field, resulting in

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strong light scattering and absorption, in addition to huge local field enhancement [1]. The dependence of SPR on size, shape, composition, local environment and surface characteristics of the NPs is well documented [2,3,4,5]. In a typical wet chemical synthesis

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process, all these parameters can be reasonably controlled through appropriate selection of

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metal salt, reducing and capping agent, background solvent, concentration, temperature, pH, etc. [2]. Therefore, it is possible to obtain a variety of Au/Ag NP systems with varying sizes, shapes and surface configuration. In fact, the advances in this field has enabled applications of plasmonic materials in sensing [6,7], catalysis [8], photovoltaic [9], biological applications [10], etc. These noble metal NPs when embedded in different matrix or when used in conjunction with other materials have also been used in medical diagnostics[11],

ACCEPTED MANUSCRIPT light induced switching [12], optical sensor [13], molecule detection [14], SERS based detection [15], etc. Bimetallic, core-shell nanostructures of Au and Ag are of even greater significance since the

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optical, catalytic, electronic and other properties of the hetero-nanosystems are considerably different and more sensitive compared to their individual counterparts. Even minor

fluctuations in the size, shape and/or composition of bimetallic NPs can influence their

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physicochemical properties [16,21,18]. By integrating Au and Ag NPs in a single

nanostructure it is possible to couple and tune their exotic properties for wider and more

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useful applications. For example, Au NPs have low scattering efficiency but a broad spectral response. On the other hand, the scattering efficiency of Ag NPs is much higher than Au NPs, although the SPR region in this case is limited to a shorter band, roughly 400-500 nm [19]. To design custom plasmonic metal NPs with a high scattering efficiency as well as

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broad SPR region, core-shell nanostructures of Au and Ag are much preferred. Many preparation techniques have been used previously to produce core-shell Au-Ag NPs

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[20,21]. Atomic level phase separation between Au and Ag makes it favourable for development of Au-Ag core-shell structures rather than alloy NPs [22,23]. However, nearly

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all studies so far have focussed either on Au-Ag or Ag-Au core shell structures. We are yet to come across a report, where core-shell nanostructures of Au and Ag with interchangeable core and shell materials have been systematically studied to understand the plasmonplasmon coupling. This is important as the outer shell layer is expected to dominate the interaction with light, since electromagnetic fields decay exponentially inside metals [24]. In this study, we report the formation of core-shell nanostructures of Au and Ag with readily interchangeable core and shell materials. As expected, we see that the interaction between

ACCEPTED MANUSCRIPT Au and Ag plasmons not only depend on the size, shape and surrounding environment, but also on the relative position of the metal in the core-shell structure. To understand the fundamental plasmon-plasmon interaction in Au and Ag core-shell nanostructures we also present a simple 1D (one dimensional) model, where plasmon modes are represented by the

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modes of damped harmonic oscillators coupled with each other through simple Coulombic interaction.

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Experimental:

The Au and Ag NPs and the core-shell structures were synthesized via wet chemical

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technique. Synthesis of Au and Ag NPs by citrate reduction is a good model system, which has been widely studied and a substantial amount of information regarding this method is already available in literature [25,26,27]. It is rather straight forward to control size by changing the concentration ratios of the salt and the reducing agent and by controlling the

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pH [4]. In our case, for synthesis of Au NPs, auric acid (HAuCl4) was heated to 900C and then citrate was added under vigorous stirring. The molar ratio of HAuCl4 (0.25mM) and

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citrate was set to 1:3.5, as this ratio reportedly produces Au NPs with minimum diameter [28]. For synthesis of Ag NPs, AgNO3 was added dropwise in the reducing agent — sodium

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borohydride, placed in an ice bath under magnetic stirring. Just after addition of AgNO3 noticeable colour change was observed and immediately citrate was added to prevent agglomeration. In this case the primary role of the citrate is to stabilize the Ag NPs. For obtaining small Ag NPs with good size distribution, the molar ratio of AgNO3, citrate and borohydride was set to 1:5:10 [28]. Shell growth on pre-synthesized NP cores were performed following earlier report for synthesizing similar structures, with minor modifications. For development of Ag shell on

ACCEPTED MANUSCRIPT Au NPs, 0.06 ml of 100 mM ascorbic acid, 0.015 ml of 100 mM AgNO3, and finally, 0.075 ml of 100 mM NaOH was added to 10 ml aqueous solution of pre-synthesized Au NPs [29]. The reaction allowed to proceed at room temperature, under vigorous stirring. The typical redwine colour of the Au NP solution gradually turned orange. After 30 min, exactly the same

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amounts of ascorbic acid, AgNO3 and NaOH (0.06 ml, 0.015 ml and 0.075 ml, respectively) were again injected to the orange solution. This step was repeated five times till the solution

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colour changed to bright straw yellow. Such stepwise addition of the reactants is supposed to initiate Ag shell growth on the Au NPs, with the shell thickness increasing with time,

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after each injection. A small amount of the solution was taken out and stored for analyses after the third injection, with the expectation that the Ag shell thickness will be greater for the sample stored after the fifth injection compared to the one stored after the third injection. A similar process was followed for development of Au shell on Ag NPs. First, the Ag NP

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solution was heated to 700C. Then, an aliquot of 0.342 ml of 5 mM HAuCl4 was added to 10 ml of pre-synthesized Ag NPs and was further heated at 900C [28]. Subsequently, 0.085 ml of

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100 mM citrate in 1.57 ml DI water was added to the solution. The molar ratio of Ag and Au in the solvent was changed from 1:0.3 to 1:0.43 to obtain two different shell thicknesses. All

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the chemicals used were of analytical grade purchased either from Sigma Aldrich or Merck, India. 18.2 MΩ-cm, Millipore water was used for synthesis. The samples were characterized by powder x-ray diffraction (XRD), high resolution transmission electron microscope (HR-TEM) with energy dispersive (EDX) x-ray spectroscopy, dynamic light scattering (DLS) and UV-visible spectroscopy. XRD patterns were recorded by PW1380 with Philips diffractometer with 35KV operating voltage and 25mA current. Colloidal samples coated on glass were analyzed using Co Kα1 (λ= 1.78897 Å)

ACCEPTED MANUSCRIPT in the range of 2θ = 20–80°. For HR-TEM analyses, approximately 2µl of sample solutions were pipetted out and deposited on carbon coated copper grids. Bright field images and selected area electron diffraction patterns (SAEDPs) were recorded by a JEOL JEM 3010

path length by taking samples in two sided quartz cuvettes. Results and Discussion:

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operated at 200KV. UV-vis spectra were recorded using Hitachi U-2900 with having 1cm

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It is non-trivial to obtain x-ray diffraction (XRD) patterns of metal NP colloids. Most of the studies on single component or bi-metallic Au/Ag NPs have remained silent on their XRD

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characteristics. Yet, XRD is undoubtedly a very important tool to understand the overall crystalline features of any system. We obtained the XRD profile of Au, Ag and the bimetallic core-shell NPs by investigating the spin-coated films formed after careful and multistage deposition of the colloids on a glass substrate. Figures 1 (a)-(d) show the typical XRD

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patterns of the Au NPs, Ag NPs, Au-Ag and Ag-Au bimetallic NPs, respectively. Since both Au and Ag have similar lattice constants, the characteristic XRD peaks for Au and Ag

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are nearly coincident and with the given apparatus it is impossible to distinguish them individually. The diffraction profiles for single component Au, Ag and the bimetallic Au-Ag

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or Ag-Au are therefore, identical, as evidenced from Figure 1. The patterns clearly indicate that XRD is dominated by a noisy background hump due to amorphous SiO2 present in the glass substrate, with interspersed crystalline peaks that can be attributed to Au and/or Ag and their crystalline complexes with Na. The observed peaks at 2θ ≈ 44.60 and 52.30 correspond to the (111) and (200) Bragg reflections from Au/Ag [JCPDS No. 02-1095 for Au and No: 03-0921for Ag]. While the atomic planes corresponding to the peak positions confirm the face-cantered-cubic (fcc) structure of the resultant bimetallic NPs, the broadened

ACCEPTED MANUSCRIPT nature of the peaks indicate the nanocrystalline nature of the samples. We see from Figure 1 that in addition to the Bragg peaks of Au and/or Ag, there are distinct peaks for crystalline Na complexes of Au and Ag. These peaks become more prominent for the core-shell structures. The origin of these peaks is due the excess addition of the reducing agent which

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is purposefully added in excess in an attempt to inhibit galvanic replacement. Such peaks are usually found along with Au and Ag when crystalline Na compounds are used as

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reducing agents. Importantly, we do not notice any Au-Ag alloy peak, which allows us to

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infer that alloy formation, if any, is restricted below the detection limit of the XRD.

Figure 1: XRD profiles of (a) Au NPs, (b) Ag NPs, (c) Ag-Au and (d) Au-Ag core-shell nanostructures. The background amorphous hump present in all the profiles is due to the glass substrate. In an attempt to understand the structural details of the synthesized structures, HR-TEM along with EDX analyses were performed on the four types of samples — bare Au NPs, bare

ACCEPTED MANUSCRIPT Ag NPs and the Au-Ag and Ag-Au core-shell nanostructures. Citrate protected spherical Au and Ag NPs and their approximate size distributions calculated from TEM images as well as from DLS measurements are shown in Figures 2 (a) and (b). The histograms obtained from TEM images and shown as insets of Figure 2 (c) and (d), indicate that the average sizes of the

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Au NPs and Ag NPs are ~19 nm and 22 nm, respectively. However, the size distribution estimated from the DLS measurements of the same sample suggest larger particle sizes.

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Such minor discrepancies in size estimation of NPs are not unexpected. In fact we would like to emphasize here that nearly all methods utilized for determination of size distribution

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of colloidal NPs are prone to substantial error. TEM micrographs can never be representative of a sample in the absence of a statistically large dataset. On the other, methods like DLS or XRD peak broadening allows rough estimation of the average sizes based on certain assumptions which are not always very accurate, particularly while dealing

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with nanomaterials. We purposely include both TEM and DLS results to show that that size estimation of the same sample is dependent on the method adopted to calculate size. There is yet another issue – NPs are generally unstable and tend to aggregate when left without

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proper surface protection. The rate at which they tend to agglomerate depends on their size,

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ambient conditions, surface conditions and storage conditions. It is therefore imperative to do all measurements exactly after the same time interval and after storing samples under identical conditions. This condition is hardly satisfied in the laboratory. Hence, strict resemblance between estimated sizes of colloidal NPs are more often coincidental, rather than being suggestive. For our samples, the TEM was performed very soon after preparation, while DLS was done weeks later. Hence it is expected that DLS will show larger particle sizes compared to TEM. We also see that the size distribution for Ag NPs

ACCEPTED MANUSCRIPT shows a bimodal character with peaks at 23 nm and 36 nm, suggesting that Ag NPs

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aggregate more that Au NPs, when stored under similar conditions.

Figure 2: HR-TEM images of citrate protected (a) Au NPs and (b) Ag NPs. The size distributions of Au NPs and Ag NPs, calculated from TEM micrographs and DLS study are

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shown in (c) and (d), respectively. It is to be noted that DLS measurements were performed few weeks later and hence reveal larger sizes due to time dependent agglomeration.

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The core-shell NPs of Au and Ag with interchangeable core and shell are shown in Figure 3. The bright field images shown in Figure 3 (a) and (b) clearly show cores surrounded by

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shells. The difference in contrast of the core and the shell is governed by the formation of Moiré fringes upon superposition of two crystalline lattices [30]. In general, the core appears darker than the shell. However, we see that for our case the shell is relatively darker than the core. This is possibly due to de-focus setting of the TEM – a phenomenon that needs to be further investigated in details. Galvanic replacement of Ag in case of Ag-Au core-shell nanostructures can lead to formation of a hollow sphere, thereby accounting for a lighter contrast of the core. However, since, galvanic replacement involves the oxidation of one

ACCEPTED MANUSCRIPT (sacrificial) metal by the ions of another metal having a higher reduction potential, such a process is unlikely to occur in the Au-Ag core-shell structures. Hence, we should not see lighter core contrast for Au-Ag core-shell nanostructures. But that is not the case. We see from the TEM images in Figure 3 (a) and (b) that the cores of both the nanostructures appear

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to be lighter. We are therefore inclined to believe that the apparent reversal in the relative contrast of the core and the shell is due to defocus setting of the TEM. Nevertheless, for the

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higher magnification images of the Au-Ag, as well as for the Ag-Au core-shell

nanostructures, shown as insets of Figure 1 (a) and (b), respectively, the contrast of the core

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is more than the shell. The dashed circles demarcating the core and the shell are for guiding the eye. Both the images capture nearly spherical nanostructures with a thin layer of shell,

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which is further confirmed by the high magnification images shown as insets.

Figure 3: High-resolution TEM images of (a) Au core surrounded by Ag shell, and (b) Ag core surrounded by Au shell. High magnification images showing single core-shell NPs of

ACCEPTED MANUSCRIPT each type are shown as insets of (a) and (b). The SAED pattern of a typical Au-Ag as well as Ag-Au core shell system is shown in (c); (d) is the histogram of the particle size distribution for Au-Ag NPs calculated from several TEM images; and (e) is the EDX spectrum showing

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the presence of both Au and Ag in a core-shell system. The electron diffraction pattern, size distribution and the EDX spectrum corresponding to the bright field image of a typical Au-Ag core-shell system is shown in Figure 3 (c), (d) and

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(e), respectively. Due to closeness of the d-values of Au and Ag, the electron diffraction

patterns of both the noble metals are nearly identical. Nevertheless, the formation of rings

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along with a bright halo re-establishes the nanocrystalline nature of the sample. However, it is impossible to assign the SAED rings exclusively to Au or to Ag in the diffraction pattern of the core-shell system as the positions of these rings are nearly coincidental. The size distribution of Au-Ag core-shell system is exhibited in (d). We see that the average size of

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the composite NPs is around 23 nm, as estimated from TEM images. Finally, the presence of both Au and Ag in the core-shell system is confirmed by the EDX which clearly captures

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peaks that are attributed to Au and Ag. The large Cu peak is due to Cu grid on which the sample was deposited. The SAEDP and EDX of the Ag-Au core-shell system are very similar

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and hence not presented separately. Therefore, from the TEM analyses, we infer that coreshell NPs involving Au and Ag have been successfully formed. We do not further investigate the variation of size of the core and the shell through TEM, instead we focus on the plasmon interaction through UV-vis study. Absorption features of noble metal NPs are dominated by plasmon interaction with external electromagnetic perturbation. In agreement with previous reports, the SPR peak for the citrate protected Au NPs appears at around 525nm, as shown by the black curve in Figure 4

ACCEPTED MANUSCRIPT (a) and the SPR peak for bare Ag NP colloid is centred on 394nm [black curve in Figure 4 (b)]. Such plasmonic behaviour of Au and Ag NPs is quite well known. Upon growth of Ag shell on Au NPs, we note that the absorption profile changes significantly — the absorption peak blue shifts to 400 nm and a shoulder like feature appears around 500 nm as seen from

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the red curve in Figure 4 (a). This particular spectrum is for the Au-Ag core-shell NPs

formed after 3rd injection and consequently expected to have lower shell thickness. With

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increase in the thickness of the Ag shell, the absorption profile is found to change further. The shoulder appearing at 500 nm disappears and the absorption maximum shows a red

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shift from 400 nm to 423 nm, as evident from Figure 4 (a). Following Au shell growth on Ag NPs, the absorption peak shifts from 394 nm to 415 nm, as can be seen in Figure 4 (b).With increase in shell thickness the peak tend to get flattened and a hump like feature appears, as

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seen in the blue curve if Figure 4 (b).

Figure 4: UV-vis absorption spectra of (a) Au and Au-Ag core-shell NPs, and (b) Ag and AgAu core-shell NPs. The black curves represent the absorption profile for the citrate protected core NPs, the red curves are the spectra when there is a thin shell growth, and the blue curves represent the feature when the shell thicknesses are increased. The actual

ACCEPTED MANUSCRIPT photographs of the bare (citrate protected NPs and the core-shell NP colloids after 3rd and 5th injections are shown as insets. In addition to the dominant features observed in the respective absorption curves, there are

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some additional features which should not go unnoticed. A reasonably sharp dip at ~321 nm in the absorption spectrum is observed for both Au-Ag and Ag-Au core-shell NPs. This

absorption minimum is also present in the spectrum of bare Ag NPs, but has been rarely

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discussed in literature. In fact this sharp fall in absorption is due of interband transition of Ag and is a size independent implicit property of Ag [31]. We see that this size independent,

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interband transition remains unaffected for all variants of core-shell nanostructures involving Ag NPs. Both types of core-shell structures involve interaction of Au and Ag plasmons, but the absorption features are remarkably different when core and shell are altered. We also see that with shell thickness the band feature changes and there is a red

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shift of the absorption peak under the combined effect of shell growth and overall increase in size. Importantly, there is no straight forward explanation of such absorption feature

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modification.

In an attempt to understand the above plasmon-plasmon interaction, we consider a very

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simple classical oscillatory model. Localized surface plasmon oscillation of bare metallic NPs have been assumed to be represented as single classical oscillator with natural frequency of oscillation corresponding to the plasmon absorption peaks of the bare NPs as illustrated in the schematic shown in Figure 5. Here oscillator ‘a’ and oscillator ‘b’ are assigned to oscillate with natural frequencies of oscillation of bare Au and Ag NPs, respectively, separated by a distance ‘d’ with their centres at ‘X0'’. Upon external perturbation they will start to oscillate

ACCEPTED MANUSCRIPT in the direction as shown by the arrows in the Figure 5. At any certain time their positions

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are at Xi and Xj, respectively.

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Figure 5: Schematic sketch of the transverse vibration of the coupled plasmons on the surfaces of bimetallic NPs through Coulombic interaction

When these two oscillators are far apart, they do not interact with each other and hence, oscillates with their natural frequencies. But when these two are close enough one will affect

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another and thus will modify their oscillations in response to external perturbation. This interaction is quite well-known. In our case the two oscillators are nothing but two different

interaction.

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clusters of charges and it is, therefore, expected that they will interact through Columbic

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The oscillation of the composite system can be described as forced vibration of a set of coupled oscillators under electromagnetic excitation governed by the equation: ⁄

cos

…………… 1

Where, ωis are the natural frequencies of the ith oscillator estimated from the peak of the absorption spectrum of the bare NPs.

are the damping factors corresponding to

individual oscillators and have been estimated from the FWHM of the individual plasmon

ACCEPTED MANUSCRIPT absorption peaks. Here, we have solved a set of two coupled equations (1), simultaneously to get the Coulombic coupling effect. The subscripts i and j interchangeably represent Au and Ag. The Coulombic interaction strength is accounted by the term gij given as, '4#$ $ & %

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!!

0 corresponds to no interaction between the oscillators, where, qi, qj are effective

charges of ith and jth oscillator and mij is the effective mass of the coupled oscillators. The

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distance by which two oscillators are separated is denoted by d. Here ε0 and εr are free space

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permittivity and effective permittivity of the medium, respectively. Right hand side of (1) represents the oscillatory electromagnetic excitation with incident frequency .

)

is the

amplitude of incident electromagnetic wave.

Equations (1) have been solved by using standard 4th order Runge-Kutta method with 1st approximation to obtain the absorption spectra of the composite system for different values and the gap

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of the interaction strength

between the individual oscillators.

With increase in the strength of the Coulombic interaction the plasmon absorption peaks

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have been found to shift toward each other for a fixed value of the gap as shown in Figure 6

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(a). Here, peaks denoted by ‘a’ and ‘b’ in figure 6 and 7, corresponds to oscillators ‘a’ and ‘b’ respectively. This effect is similar to what we have discussed in the experimental results section. At a certain value of the interaction strength, both the peaks overlap. For a fixed value of the interaction strength if we increase the gap between the oscillators, as evident in Figure 6 (b), the peaks shift apart and beyond a certain value of gap the peak positions of these oscillators merge with that of bare core NPs. This is expected as with increase in distance the Coulombic interaction fades out.

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Figure 6: Resonance peak shifts of oscillators ‘a’ and ‘b’ with variation of (a) “g” and (b) “d”. When two classical oscillators are coupled with each other they modify each other’s natural

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frequency of oscillation. This is an expected feature but the most fascinating fact is that their interaction pattern matches with the feature of modification for core-shell structure as observed experimentally. For Au-Ag 3rd injection, peak positions for these oscillators, match with deconvoluted experimental peaks of this complex structure as shown in Figure 7. But there are mismatches in the FWHM for both the calculated curves as we have not considered the shape effect of shell and other details of the system. However, this simple model qualitatively explains the observed peak shifts in the absorption peaks due to shell growth.

ACCEPTED MANUSCRIPT Further calculations involving the shape of the NPs are necessary to explain the quantitative

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details of the experimental observations.

Figure 7: Comparison between deconvoluted spectra of Au-Ag core-shell and simulated intensity of oscillator ‘a’ and ‘b’.

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Conclusions:

In summary, we have prepared Au-Ag and Ag-Au core-shell nanostructures with interchangeable materials of the core and the shell. Structural investigations reveal

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formation of spherical core-shell NPs with fairly uniform size distribution. These core-shell

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nanostructures exhibit interesting plasmon-plasmon interaction. The plasmon peaks appearing in the absorption spectra of the individual Au and Ag NPs shift after the formation of the core-shell composite and this shift increases with increase in the shell thickness. A simple 1D model assuming the plasmons to behave like classical harmonic oscillators explains qualitatively the shift in plasmon peak due to Coulombic interaction. Such core-shell NPs of noble metals with tunable plasmon resonance are extremely important candidates for various applications. --

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ACCEPTED MANUSCRIPT Highlights of the paper titled: Gold-Silver Nanostructures: Plasmon-Plasmon Interaction We have synthesized Au and Ag core-shell nanostructures with interchangeable core and shell. Plasmon-plasmon interaction between Au and Ag is found to be dependent on the relative position of Au or Ag in the core-shell structure.

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Simple 1D classical model of a forced simple harmonic oscillator with damping effectively explains qualitatively the plasmon-plasmon interaction.