Computational Matching of Surface Plasmon Resonance: Interactions

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Computational Matching of Surface Plasmon Resonance: Interactions Between Silver Nanoparticles and Ligands Julien Clément Romann, Jingjing Wei, and Marie-Paule Pileni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511859p • Publication Date (Web): 15 Jan 2015 Downloaded from http://pubs.acs.org on January 21, 2015

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The Journal of Physical Chemistry

Computational Matching of Surface Plasmon Resonance: Interactions Between Silver Nanoparticles and Ligands Julien Romann a,b, Jingjing Wei a,b, Marie-Paule Pileni a,b,c * a Sorbonne Universités, UPMC Univ Paris 06, UMR 8233, MONARIS, F-75005, Paris, France b CNRS, UMR 8233, MONARIS, F-75005, Paris, France c CEA/IRAMIS, CEA Saclay, 91191, Gif-sur-Yvette, France * Corresponding author

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Abstract A multilayer model of a single coated nanoparticle has been refined through Finite Elements Method based simulations and resulted in a successful matching of the experimental UV-visible spectra of ligand-coated silver nanoparticles. The computational matching of the Surface Plasmon Resonance (SPR) band reveals both a ligand type dependence of the effective plasma frequency and a size dependence of the SPR damping effect within the modeled nanoparticle. The observed differences of effective plasma frequency between thiol and amine-coated nanoparticles are consistent with the already known stronger bonding of thiols on silver compared to amines. The significant increase of the damping effect at the surface of the nanoparticle when increasing their size suggests an inverse relation between the ligand packing density and the nanoparticle size, which is supported by the expected influence of the surface curvature radius on the ligand packing. Keywords: nanoparticles; surface plasmon resonance; ligands; interactions; simulation; Finite Elements Method.


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Introduction The study of noble metal nanoparticles (NPs) for their particular optical properties has been subject to widespread interest over the past few decades.0-6 This interest is primarily motivated by the surface plasmon resonance (SPR) phenomenon, the strong localized resonant optical absorption shown by a variety of nanostructures. The possibility to fine-tune the SPR by controlling several parameters such as the geometry or chemical environment of these nanostructures is still giving birth to new materials with flexible optical properties. Many potential applications are expected to largely benefit from such new optical materials, including sensors7, light emitting devices8, photovoltaics9, optoelectronics10,11 and optical absorbers12-16. For many years now, the fundamental understanding of how the SPR in NPs is affected by various parameters has been significantly extended, both through experimental and computational studies.17-25 In particular, the respective influences of the NP size, shape and near environment on the SPR has been studied quite extensively for several metals, especially silver (Ag) and gold (Au).3,17-23,26,27 When the NPs are synthesized in solution, the main contribution of the environment is from the molecular ligands used to avoid coalescence by counterbalancing the Van-der-Waals attractive forces. Two key parameters arise from the presence of ligands around metal NPs: the effective optical index at the near field of the NPs, influencing the interface damping effect on the SPR, and ligands-metal chemical interactions affecting the coherent oscillations of conduction electrons within the NPs. Several studies have shown that both parameters significantly affect the optical response of noble metal NPs through shifting and broadening effects on the SPR absorption band.3,28,29 Conversely, the profile of the SPR absorption band must contain detailed information about the way molecular ligands affect the optical properties of noble metal NPs. A notable work carried out by Peng et al. on silver NPs could link the size-dependence of the SPR band position to a size-dependent competition between the core and the outermost atomic layer of the NPs, assuming that such a “skin” would be affected differently by the ligands from the NPs core.29 Their multilayer model successfully explained the SPR band blueshift to redshift turnover observed when decreasing the NP size below 10 nm. However, remaining mismatches between experimentally observed and calculated SPR bands call for further investigations in this field, taking not only the SPR band position, but the whole SPR band profile as a matching criterion. In this work, we elaborate an improved multilayer model for ligand-coated spherical NPs and implement it in a computational study based on the Finite Elements Method. This allows us to extract physical information from the detailed profile of the SPR absorption band observed in experimentally acquired absorption spectra of ligand-coated silver NPs in solution. As we mostly focus here on NPs below 10 nm, for which plasmonic properties remain poorly understood30, we strongly expect such information to provide a clearer view of how the NP size and the nature of the ligands can affect both the ligands-metal interactions and the resulting SPR phenomenon.

Experimental methods Sample preparation Several ligands – amine (NH) or thiol (SH) ligands – have been used to stabilize Ag NPs of different sizes: dodecylamine (NH-C12), oleylamine (NH-C18), dodecanethiol (SH-C12) and hexadecanethiol (SH-C16). The synthesis of the NPs coated with these ligands (cf. SI text) is taken from Wei et al.31 and lead to multiply twinned particles with icosahedral geometry (cf. Fig. S1, S2, S3 and S4). The amount of ligand solution has been determined so that we can assume the NPs to be fully covered by these ligands. A drop of


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the colloidal solution is deposited on a transmission electron microscopy (TEM) grid and the size distribution is determined through the observation of nearly 500 NPs (cf. Table 1). UV-visible absorption measurements were performed on colloidal solutions of NPs dispersed in toluene by using a Varian Carry 5000 spectrophotometer and 1 mm quartz cuvettes. For convenience, samples are named by identifying the type of ligand first, such as NH-C12/Ag, which refers to NPs coated with NH-C12. Similarly, NH- and SHcoated Ag NPs will be identified respectively as NH/NPs and SH/NPs. Sample

NH-C12/Ag

NH-C18/Ag

SH-C12/Ag

SH-C16/Ag

d (nm) 2.9 4.1 5.0 6.3 2.2 4.1 5.9 8.7 12.9 2.2 2.9 4.0 5.3 6.0 2.9 4.0 5.0 6.0 7.8 σ (%)

9

9

8

8

9

8

8

8

8

13

10

9

9

9

10

9

9

9

9

Table 1. Size distributions (σ) determined for each NP size (d) synthesized with each ligand.

Simulation study The geometry of the system used for the computational study is inspired from the multilayer Mie theory based model described by Peng et al.29. As the NPs size distribution is low (below 10 %), the simulation geometry is based on a single NP coated with a layer of molecules. In order to average all the possible orientations of the icosahedral NPs to the incident light, the modeled NP is designed as a sphere. This single NP with diameter d features a skin made of a single atomic layer of Ag with a thickness, t, set to 0.25 nm and an underlying core of diameter d-2t. A layer of ligands with a thickness, s, isolates the NP from the surrounding medium, which is here toluene to match the experimental conditions. We here assume full and uniform ligand coverage of the NPs as the prepared samples do not show any coalescence.32 The modeled system is limited by virtual walls defined as perfect absorbers (or zero reflection) as a boundary condition. These virtual walls form a virtual limit square box with a dimension of 40 nm, the single coated NP being exactly as the center of it. The incident light is modelled by a linearly polarized electromagnetic plane wave with wavelength λ varying from 300 to 600 nm and travelling from one virtual wall to the opposite virtual wall of the limit box. A visualization of the system is provided in Figure 1.

r r Figure 1. Schematic design of the computational study. The wave ( k ) and polarization ( p ) vectors of the incident light are indicated by arrows. The system boundaries and the light wave are pictured by grey walls and translucent surfaces respectively.


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All domains used for the simulation model (core, skin, ligands and toluene) are defined by their dielectric constant εr. The dielectric constants for toluene (2.38) and for the ligands (cf. Table 2) are taken as wavelength-independent values. The thickness s of the ligands layer is evaluated as the length of the considered molecule taken in its trans conformation, assuming that a single layer of molecules constitutes the ligands layer. The s values for each used molecule are also indicated in Table 2. Ligand NH-C12 NH-C18 SH-C12 SH-C16 εr

2.069

2.132

2.129

2.140

s (nm)

1.6

2.3

1.7

2.2

Table 2. Dielectric constants (εr) and ligands layer thickness (s) for NH-C12, NH-C18, SH-C12 and SH-C16.

The dielectric constants for the core and skin are defined as functions of the incident radiation frequency ω. These functions are derived from the Drude model and allow expressing the effective dielectric function of a NP as a correction of the bulk dielectric function28: εNP ( ω, r ) = εbulk ( ω) +

ωp2 2 ω + iωγ0

−

ωp2 2 ω + iω ⋅ γ

,

(1)

(r )

with r the NP radius, εbulk the bulk dielectric function33, ωp the bulk plasma frequency, γ0 the bulk damping constant and γ(r) the size-dependent damping function expressed as: v γ ( r ) = γ0 + A⋅ F , r

(2)

with vF being the Fermi velocity and A a damping correction factor (generally taken as a constant close to 1) describing the electron scattering process within the NP and the electron-surface interactions, the latter depending on the surrounding medium28. We take ħωp = 8.78 eV and ħγ0 = 0.02 eV as the bulk plasma frequency and bulk damping constant for Ag.29 In our model, we define different dielectric functions for the skin (which only contains Ag atoms in direct interaction with ligands) and the core. As we expect the ligands to impact the electron density within the NPs, we replace the plasma frequency in the size-dependent Drude term of Eq. (1) by the effective plasma frequency ωNP, which will be different for the core and for the skin of the NPs. Regarding the damping phenomenon, it is quite well known that it is very dependent on temporary charge transfers between the NPs and the surrounding medium. Such phenomenon, called chemical interface damping, has been shown to feature a cluster size dependence and to induce a possibly widespread range of A values.28 To take these previously reported observations into account, we assume a size-dependent damping effect induced by the surrounding medium and affecting the skin and core differently. Therefore this damping correction is applied with a factor ANP, which will also be different for the core and the skin of the NP. These hypotheses give rise to the following expression of the dielectric function within the modeled NP: εNP ( ω, r ) = εbulk ( ω) +

ωp2 ωNP2 − ω2 + iωγ0 ω2 + iω ⋅  γ + A  0  

NP ⋅

(3) vF r

   

To evaluate the respective influences of the ligand type and the NP size on the effective plasma frequency and on the medium-related damping, we take ωNP and ANP as refinement parameters for the calculated ACS Paragon Plus Environment

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absorption spectra to match the experimental UV-visible absorption spectra. Because we assume the effective plasma frequency to only depend on the ligand type, the ωNP values for the core and skin are taken as constants for all samples coated with a given ligand. On the other hand, the assumed size dependence of the damping effect imposes refining ANP for all NPs sizes. The parameter refinement method consists of several computations with incrementing parameter before choosing the parameter value giving the best match between the calculated and the experimental UV-visible spectrum. Estimations of the ligand layer thickness (s) have been achieved using the Spartan 10 software. The computational study leading to the calculated optical absorption of the NPs has been carried out using the COMSOL Multiphysics® 4.3 software as an implementation of the Finite Elements Method. The software was run on a 2.40 GHz - 2.53 GHz (2 processors) Intel® Xeon® CPU with 32 Gb RAM.

Results and Discussion The investigated parameters are refined in order for the calculated spectra to match both the position and profile of the experimental UV-visible absorption spectra for all the investigated ligands and NP sizes. A comparison between the experimental data and the calculated spectra are presented for four different samples in Figure 2. Such a comparison for all investigated samples is available in the SI text (cf. Fig. S5). For all investigated samples, the position of the calculated plasmon band matches the position of the experimentally observed one. In spite of some differences, the calculated plasmon band profiles, full width at half maximum (FWHM) and band asymmetry, show a relatively good match with the experimental spectra. The differences in profile (mostly at the band far wings) could be induced by the approximation of perfectly spherical and single-sized NPs samples, as the NPs shape and size distribution should necessarily influence the aspect of the size-dependent SPR band17. It is interesting to note that, for similar NP sizes, SH ligands induce a significant redshift and broadening of the plasmon band compared to NH ligands.

Figure 2. Experimental (black line) and calculated (dotted red line) absorption spectra of coated NPs with given diameters. The refined parameters are given. A spectrum calculated without considering the NP skin is given for comparison (thin blue line).


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The calculated spectrum arising from a similar model which does not consider any NP skin clearly shows increased discrepancy with the experimental spectrum, especially for wavelengths below 400 nm. The refined values of the effective plasma frequency ħωNP are graphically presented in Figure 3 for the core and the skin of the modeled NP. This representation has been chosen to highlight the difference of effective plasma frequency both depending on the ligand type and between the core and the skin. As already shown elsewhere29, a modification of ωp to an effective plasma frequency is justified by the incidence of the ligands on the electron density within the NPs. Therefore, the refined values of ωNP provide some information about the electron density respectively within the NPs core and skin. For convenience, ħωp and ħωNP will be referred to as ωp and ωNP respectively.

Figure 3. Effective plasma frequency within the core and the skin of NPs coated with different ligands. The error bars show the uncertainty due to the NP size distribution. The dotted line indicates the Ag bulk plasma frequency (ωp).

These data show a significant difference of plasma frequency between the core and the skin of the modeled NP. Such a difference supports the interest of modelling the core and the skin as two distinct domains in order to achieve a satisfying match of the experimental UV-visible spectra. For all investigated samples, a lower ωNP value is found for the skin compared to the core. This confirms the need to lower the plasma frequency within the skin to describe the lack of electrons contributing to the SPR phenomenon due to their involvement in the NP-ligand interaction.29 Concerning the ligand-type dependence of the effective plasma frequency, it is clear that the ωNP values are significantly lower in the case of SH/NPs than in the case of NH/NPs. This feature is consistent with the stronger affinity of SH molecules for Ag compared to NH molecules. For the NP core, the same ωNP values are found respectively for both NH ligands and for both SH ligands. This suggests that the ligand aliphatic chain length has no incidence on ωNP within the NP core (core ωNP). In the case of the NH/NPs, the core ωNP is almost equal to the Ag bulk plasma frequency ωp. Although the obtained value of core ωNP (8.95 eV) is slightly higher than the chosen value of ωp (8.78 eV) in our model, it is still in the range of the commonly proposed values for ωp. This slight difference is therefore difficult to definitely attribute to any physical phenomenon. However, such high value for ωNP implies a very poor or even no effect of the NH ligands on the NP core. In the case of the SH/NPs, the core ωNP value (8.42 eV) is significantly lower than both the core ωNP value found for NH/NPs and the typical values given for ωp. This result indicates an effect of the NP-ligand interaction from the NP surface to its core, disturbing the contribution to the SPR of some electrons within the core. Such effect being again consistent with the known strong interactions between Ag and SH molecules, it is also an indication of charge transfers from the surface to the core of the NPs. ACS Paragon Plus Environment

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For the NP skin, the refined ωNP (skin ωNP) values are similar for the same type of ligand (NH or SH type), but nonetheless slightly dependent on the ligand aliphatic chain length. Because the NP skin is defined as the layer of Ag “surface” atoms, which are able to directly interact with the ligands, the refined skin ωNP values in this domain are likely to be more descriptive of the subtle differences regarding the ligand layer and the NP-ligand interaction. Similarly to the core, the skin ωNP are much lower for SH/NPs than for the NH/NPs, still in accordance with the stronger Ag–S bond than the Ag–N bond.

Figure 4. Illustrative representation of the possible conformations taken by the ligands at the surface of the Ag NPs.

Concerning the skin ωNP of NH/NPs, we observe that the value obtained for NH-C12/Ag (7.11 eV) is lower and further away from ωp than for NH-C18/Ag (7.28 eV). This difference suggests a stronger effect of the NH-C12 ligands on the NPs than of the NH-C18 ligands. Both ligands having the same amine group interacting with Ag, this observation is attributed to the difference in steric volume between the two ligands (cf. Fig. 4). Indeed, the linear conformation of NH-C12 in toluene allows a significantly denser packing of ligands than the angled conformation of NH-C18. The skin ωNP values obtained for SH-C12/Ag and SHC16/Ag are very close (6.49 eV and 6.41 eV respectively), suggesting a negligible effect of the aliphatic chain length difference on the Ag-ligand interactions for these two ligands. It is interesting to note that both SH ligands have a linear conformation (cf. Fig. 4), which might explain such close skin ωNP values. The refined values of the damping correction parameter ANP for the NPs core (core ANP) and skin (skin ANP) of all samples are shown in Figure 5. Describing the electron scattering process within the NP, this parameter has been shown to be significantly influenced by the NP surrounding medium through the contribution of the chemical interface damping phenomenon.28 Thus, it should provide some information about how the NP size may affect the coating ligands, which contribute with toluene to the NP surrounding environment. A notable feature in these results is the marked gap between the refined core ANP values and skin ANP values. The core ANP values are found in range going from 0.00 to 0.16 whereas the skin ANP values are found in a range going from 0.20 to 0.85. In spite of being poorly significant (below 0.1) in most cases, the refined core ANP values are difficult to understand. The SPR damping within the core of the NPs is likely to be influenced by intrinsic (NPs material determined) effects. The synthesized NPs being multiply twinned particles, it seems reasonable to


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assume that internal electron-scattering centers like twin boundaries contribute to the core ANP values. However, the observed differences of core ANP for the same NP size but with different ligands suggest that the Ag-medium interface also influences the damping phenomenon within the NP core (below the single layer of Ag surface atoms). Indeed, this is clearly the case for the smallest NPs for which the core ANP values are quite close to the skin ANP values, especially in the case of the 2.9 nm sized NH-C12/Ag NPs. It is interesting to note that the increase of core ANP when decreasing the NP size below 4 nm is only observed with NH-C12 and SH-C12. These two ligands having shorter alkyl chains than the two others, this might indicate an influence of the ligand alkyl chain length on the damping phenomenon at these small sizes. Nevertheless, refined values obtained for NPs smaller than 4 nm have to be considered with great caution as the optical properties generated by such small NPs are significantly influenced by quantum effects30, which cannot be taken into account using our computational approach.

Figure 5. Damping parameter ANP within the core (plain circles) and the skin (hollow circles) of coated NPs depending on their diameter. The circles sizes represent the estimated NP size distribution and the resulting error for the calculated damping parameter. Dotted lines are purely illustrative to provide better data visualization.

Within the NPs skin, we observe a monotonous increase of ANP with an increasing NP size for all the studied samples. Since the synthesized NPs feature the same geometry, it is probable that the atoms and molecules surrounding the NPs largely contribute to the size dependency of the skin ANP values. Several observations suggest that such a size-dependent change in the Ag-medium interface is a sign of a decreasing ligand density around the NPs as their size increases. Although it is difficult to accurately quantify the ligand density around NPs, both simple geometric considerations and computational models could correlate the conical packing of ligands and the curvature radius of NPs to explain observed signs of


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a size-dependent ligand density.34 Even in the case of perfectly facetted icosahedral NPs, recent studies suggest a denser ligand packing on NPs vertices and corners than on facets.35 Since the surface density of vertices and corners increases with a decreasing NP size, such a packing density difference produces a very similar size-dependent ligand density to the case of spherical NPs. A varying ligand density is also related to a varying optical index of the coating layer. Indeed, the relative change of the ANP value is consistent with that of the surrounding medium optical index.26,27 Here, the ligands and toluene form an effective medium which contributes to the damping of the SPR. Toluene having the highest optical index compared to all the investigated ligands, a decrease of ligand density would increase the effective optical index surrounding the NPs, therefore inducing an increased SPR damping effect. In such a case, the SPR damping effect could be seen as a possible probe to follow variations of the molecular density within a layer of ligands coating plasmonic NPs. The size-dependence of the SPR damping within the NPs skin appears different for NH/NPs and SH/NPs. Although following the same trend, the skin ANP values for NH/NPs are lower and seem less affected by the NP size than for SH/NPs. Several parallel contributions can be suggested to explain this difference. First, the slightly lower optical index of NH ligands compared to SH ligands may partly account for this difference, according to the previously discussed influence of the surrounding medium optical index on the SPR damping. Then, the different packing density of the ligands between the samples (cf. Fig. 4) is an important aspect, as previous studies suggest that SH ligands favor bridge-type binding sites rather than ontop-type binding sites36, the latter being more frequently adopted by NH ligands37. This may provide NH ligands the possibility for a higher packing density on curved metal surfaces, where the steric repulsion from the alkyl chains becomes less significant. Finally, the higher bonding energy of Ag–S compared to Ag–N could possibly generate increased electron scattering at the ligand-metal interface for SH-coated NPs, leading to both increased interface damping of the SPR and a larger size-dependence of the ligand density at the surface of the NPs.

Conclusions By using an improved multilayer model for the optical simulation of a single coated NP, this work resulted in a successful computational matching of the experimentally acquired SPR bands generated by narrowly sized ligand-coated NPs. The refined parameters extracted from this computational matching point out ligand-type dependence of the effective plasma frequency within the NPs and both ligand-type and NP sizedependence of the SPR damping process. Our results suggest a decreasing ligand density with an increasing NP size, which is consistent with an expected influence of the NP surface curvature radius and vertices surface density on the ligand conical packing principle. We also report clear differences related to the ligand-metal interactions between SH/ and NH/NPs. These differences seem consistent with the stronger bonding of Ag with SH ligands compared to NH ligands. This work illustrates an example of how detailed information about the chemical and physical interactions between noble metal NPs and their near-field environment can be extracted from the profile of the resulting SPR band.

Acknowledgements The authors are thankful to Dr. Nicolas Schaeffer for the helpful discussions on the surface chemistry of silver nanoparticles. This research was supported by the Advanced Research Grant of the European Research Council (ERC 267129).


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Supporting Information Paragraph Supporting Information available: contains the full description of the synthesis method, the detailed size distributions of the synthesized silver nanoparticles and a comparison between the measured and the calculated optical absorption for all samples investigated in this study. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 1. Schematic design of the computational study. The wave ( ) and polarization ( ) vectors of the incident light are indicated by arrows. The system boundaries and the light wave are pictured by grey walls and translucent surfaces respectively. 80x78mm (300 x 300 DPI)



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Figure 2. Experimental (black line) and calculated (dotted red line) absorption spectra of coated NPs with given diameters. The refined parameters are given. A spectrum calculated without considering the NP skin is given for comparison (thin blue line). 113x94mm (300 x 300 DPI)


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Figure 3. Effective plasma frequency within the core and the skin of NPs coated with different ligands. The error bars show the uncertainty due to the NP size distribution. The dotted line indicates the Ag bulk plasma frequency (ωp). 58x42mm (300 x 300 DPI)



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Figure 4. Illustrative representation of the possible conformations taken by the ligands at the surface of the Ag NPs. 80x70mm (300 x 300 DPI)


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Figure 5. Damping parameter ANP within the core (plain circles) and the skin (hollow circles) of coated NPs depending on their diameter. The circles sizes represent the estimated NP size distribution and the resulting error for the calculated damping parameter. Dotted lines are purely illustrative to provide better data visualization. 113x89mm (600 x 600 DPI)


he Journal of Physical Page 18Chemist of 18

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Computational Matching of Surface Plasmon Resonance: Interactions

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