SUPPORTING INFORMATION. Plasmon Spectroscopy and Chemical Structure of Small Bimetallic Cu (1-x) Ag x clusters.

Transcription

1 SUPPORTING INFORMATION Plasmon Spectroscopy and Chemical Structure of Small Bimetallic (1-x) x clusters. Michel Pellarin a*, Inas Issa a, Cyril Langlois b, Marie-Ange Lebeault a, Julien Ramade a, Jean Lermé a, Michel Broyer a, and Emmanuel Cottancin a a Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 696 Villeurbanne Cedex,France b MATEIS, UMR 5510, INSA-Université Lyon 1-CNRS, INSA de Lyon, 6961 Villeurbanne Cedex, France * To whom correspondence should be addressed. michel.pellarin@univ-lyon1.fr 1

2 1 HRTEM image of clusters deposited at high temperature Figure SI1. HRTEM image of a cluster deposited on this carbon film (copper TEM grid) heated to 300 C. The oscillating intensity pattern in the center of the nanoparticle can be interpreted as a Moiré due to the epitaxial arrangement of both metals. In the Fourier transform pattern (upper left) of the Moiré, two radially aligned spots can be distinguished (epitaxy). The distances correspond to the (00) planes of copper and silver

3 Geometrical and chemical structures of model clusters. In core-shell geometries discussed in the body of the manuscript, a spherical silver shell (radius R) surrounds a spherical copper core that can be arbitrarily off-centered. Copper oxidation ( O) will result in the formation of an outermost third shell of constant thickness (Figure 1a). The Janus structure will consist in a sphere (radius R) made of two juxtaposed spherical caps having the same curvature radius (R). The size of their disk shaped common face depends on the relative atomic (or volumic) ratio of both elements. In Janus oxidized clusters of type I, the copper oxide forms a shell only at the surface of the copper metal spherical cap. In Janus oxidized clusters of type II, the metal oxide consists of an outer spherical shell. Figure SI. Modelling of basic bimetallic cluster structures used for most of optical response calculations. (a) Core-shell structure. The spherical core is assumed to be made of copper (yellow) and is surrounded by a silver shell (spherical outer envelope). The copper oxide shell (dark orange) is chosen to be at the outer cluster surface. (b) Janus structures for two possible locations of the copper oxide layer. The separation between the two spherical caps is indicated by the dashed circle. 3

4 In the main text, the oxidation rate (R ox. = N b N b +N nb ) is defined as the ratio between b the number of copper atoms linked to oxygen N and the initial number of copper atoms N = N b nb +N (superscripts b for bound and nb for not bound). Knowing the cuprite and copper volume densities (6.11g/cm 3 and 8.96 g/cm 3 respectively) and the copper and oxygen atomic masses, R ox. can be directly related to the volume fraction of copper oxide C ox. = V b V b +V nb. The relation is not exactly linear as illustrated in figure SI3. Figure SI3. Relation between the oxidation rate (as defined and used in the main text) and the relative volume of copper oxide. The important point here is that, for the same number of involved copper atoms, pure copper and cuprite have different volumes (the latter is larger). Since calculations are chosen to be performed at a fixed size of 5 nm (outer sphere diameter) whatever the structure and oxidation state, the size of the oxidized clusters is properly scaled to compensate this dilatation. 4

5 3 Plasmon damping by electron-surface collisions: modelling of size ects. a) General considerations on the choice of the dielectric function If the bulk dielectric function () is chosen to describe the optical response of small clusters, the absorption cross-section of a spherical particle with radius R (R<<c/) embedded in a medium of dielectric function m () writes abs 9 ( ) c 3 / m ( ) 4 ( R 3 3 ( ) ) ( ( ) ( )) 1 m ( ) (1) where ( ) and ( ) are the real and imaginary parts of () respectively. 1 C Considering coinage metals, () can be expressed as ( ) 1 ( ) ( ). The dielectric susceptibility C () describes the polarization/absorption properties of the conduction electron gas in relation to optical transitions internal to the conduction band. The interband transition contribution ( ) ( ) 1 describes the polarization/absorption properties of the ionic background (bounded core electrons and d valence band). The gap between the top of the valence band and the Fermi level defines the threshold above which interband transitions are allowed ( 3.9eV for silver and 1.9eV for copper). In the absence of a general theory for describing the modifications of the dielectric screening by bound core electrons, the rough approximation of retaining a bulk value for the interband susceptibility ( ( ) ) is commonly accepted and justified on the basis of the general agreement between experimental observations and numerical simulations in various systems, even for very small ones (D<10nm). C () can be approximated by the Drude-Sommerfeld relation C p p ( ) ( i ( )) ( i ) that is all the more valid that the conduction electrons can be considered as free electrons or, in other terms, if hybridization between the nd valence and the (n+1)s np conduction bands is not too important. () is the frequency dependent optical collision rate that is assumed (), 5

6 almost constant in the studied range ( ( ) ), P e is the plasma frequency m e o where is the bulk electron density, m e the electron ective mass and e the electron charge. The LSPR condition is obtained from (1) by minimizing the denominator according to the general condition ( ) ( ) and is fulfilled in the near UV-visible range for 1 LSPR m LSPR coinage metals. Light absorption involving transitions from filled core-electron bands to empty states in the conduction band may compete with the surface plasmon excitation. This is all the more sensitive as is close to as in the case of copper. In such cases, () and LSPR ( ) both contribute to a strong LSPR damping (see eq.1). b) Introduction of a size dependent dielectric function For very small clusters as we are concerned in, retardation ects and the possible excitation of plasmon modes beyond the dipolar mode are negligible. In the quasistatic approximation and according to (1), size ects in the absorption cross section reduce to a mere scaling factor proportional to the particle volume, the profile of the LSPR being size independent. The permittivity of small clusters will essentially deviate from the bulk because of intrinsic size ects induced by the confinement of the conduction electron gas. From a classical point of view, scattering of electrons by the cluster surface actually reduces their mean free path and consequently increases their overall collision rate. 1- contribution scales as v F where This additional v F is the Fermi velocity and a limited mean free path for the electron motion. For a spherical particle of radius R, the collision rate can be written as vf (, R) ( ) g where g is a coicient close to unity. R 1, 3-4 According to a previously published procedure 5, we introduce a size dependent dielectric function (, R) on the basis of an approximate but easy to handle parameterization. The first exp step is to decompose the bulk dielectric function ( ) in the approximate form C ( ) 1 ( ) ( ) with C () in the form of (). 6

7 The interband dielectric susceptibility ( ) ( ) 1 is then evaluated from tabulated exp data of ( ) by extracting ( ) and a threshold such as ( ) 0 for<. ( ) is afterwards obtained from ( ) 1 by a Kramers-Kronig analysis. The difference ( ) ( ) is then assumed to consist of a Drude-Sommerfeld contribution in the form D p (, R) 1 as it would be in the case of a perfect free conduction electron metal. ( i ) The collision rate is treated here as an adjustable parameter so as to fulfill at best two exp criterions: (i) the proximity between the real and imaginary parts of ( ) and C 1 ( ) ( ) and (ii) the better resemblance between the LSPR profiles calculated with both functions using the Mie theory in the dipolar approximation (eq. 1). Drude- Sommerfeld collision rates for copper and silver have thus been estimated to be 0.15eV and 0.15eV respectively. The difference between experimental and parameterized dielectric functions is not very sensitive to the exact value of in the case of copper because of the importance of the interband term (see Figure SI4). In the case of silver, the same remark holds for the real part of the dielectric function. Only the imaginary part is significantly sensitive to the choice of below ev. The value 0.07eV is the best with respect to criterion (i) but does not correctly reproduce the width of the plasmon resonance as it can be obtained by the direct use of experimental tables. This is illustrated in figure SI4. The electron densities, Fermi velocities and ective electron masses for copper 3 3 and silver are cm, cm, v m s, v m s, F / F / 1.4a. u. and m 1.03a. u. They provide the volume plasmon energies 8.98eV m and 9.97eV. P P 7

8 Figure SI4. Comparison between experimental (Palik tables) 6 and parameterized dielectric functions for silver and copper assuming energies 8.98eV and 9.97eV and selected values of P the ective electron collision rates (, ). In the case of silver, the curves giving the real P part of the dielectric function (dotted blue lines) are superimposed for the three ev, 0.11 ev, and 0.07 ev) values (0.15 C Once this decomposition is made ( ( ) 1 ( ) ( ) ), intrinsic size ects can be straightforwardly introduced by defining a size dependent dielectric function in the form: (, R) p ( ). As an illustration, Figure SI5 show a comparison ( i ( R)) between Mie calculations of the optical response of (1-x) x clusters assuming core shell geometry. Since conduction electrons are assumed to be delocalized over the whole structure, scattering by the copper-silver interface is neglected. Size ects are then disregarded in the dielectric function of the copper core. It will be taken as the bulk one 6 since its parameterized form does not give significantly different results as noted before. On the contrary, the dielectric function of the silver shell will be corrected from size ects as explained above (R is taken as the external cluster radius). 8

9 Figure SI5. Calculations of the optical absorption cross-section for 5 nm diameter core-shell (1-x) x clusters embedded in an ective dielectric medium of refractive index n=1.64 in the absence of size damping ects (black curves) or assuming electron-surface scattering at the outer interface between the silver shell and the embedding medium (red curves). c) Dielectric function of alloys. The knowledge of the dielectric function of (1-x) x alloys is a prerequisite for calculations of their cluster optical response. If it was not previously determined experimentally, an ective dielectric function () has to be defined from those of both 9

10 constituents, () and (). The simple weighted average ( ) (1 x) ( ) x ( ) does not account for the delocalized character of conduction (Drude) electrons that experience a homogeneous ionic background that differs from those of pure elements. The basic idea is to write () as C ( ) 1 ( ) ( ), the sum of an ective Drude-like and an ective interband contribution. The Drude susceptibility will be defined as C p ( ) ( i ) where and are the weighted average values of the volume plasmon and the P electron collision rate of both metals. The central point is to determine () from the knowledge of () and (). () is related to the alloy electronic band structure which is expected to be intermediate between the band structure of pure metals, displaying a single threshold. This one can be reasonably defined as the weighted average of both thresholds ( ( 1 x) x ). As for pure metals, the imaginary part of () will have a step-like profile at the threshold ( ) and will be intermediate between the profiles of the imaginary parts of () and () : Im( ( ) (1 x)im( ( ) xim( ( ) The real part of () is finally obtained from the imaginary part by a Kramers-Kronig analysis. This procedure introduced in previous works on silver-gold nanoalloys 5 has proven to correctly describe the dielectric function of bulk alloys measured by Nillson et al. for instance. 7 10

11 4 Effects of core off-centering on the optical absorption spectra coreshell clusters. Figure SI6. Calculations of the optical absorption cross-section for 5nm diameter clusters embedded in an ective dielectric medium of refractive index n=1.64 (Mie theory) for a centered core (blue curves), a maximum off-centered core tangent to the cluster surface (gray curves) and an intermediate position (red curve). Dielectric functions of copper and silver are taken from Ref [ 6 ]. The position of the copper core hardly influences the optical response of the core-shell system. 11

12 5 Effects of the choice of the dielectric functions on the evolution coreshell cluster absorption spectra with the composition. Mie calculations of the optical absorption core-shell clusters can use and dielectric functions, either taken from Palik s tables 6 or parameterized in the form explained above. Figure SI7 compares the results of such calculations when only the silver ective electron collision rate is varied ( 8.98eV, 9.97eV, and 0.15eV ). P The corresponding dielectric functions are displayed in figure SI4. The main ect of increasing the value is to broaden the plasmon bands. It is all the more obvious that the relative amount of silver is large. The choice P 0.15eV gives a good qualitative agreement with calculations performed from Palik s tables. The copper plasmon band is more damped when using parameterized dielectric functions. This is not dependent on the choice of but rather a consequence of a less sharply defined plasmon resonance condition (see eq. 1) owing to the specific spectral dependence of ( ) form (choice of p and values). and ( ) 1 in their parameterized In the case of mixed clusters, spectra obtained with parameterized dielectric functions disclose the same and clear overall blue-shift of the LSPR band when decreasing the relative amount of silver. This shift is more pronounced than in calculations using tabulated values of the dielectric functions (upper spectrum). This discrepancy obviously originates from the small deviations between tabulated and ective dielectric functions (see Figure SI4). 1

13 Figure SI7. Calculations of the optical absorption cross-section for 5nm diameter clusters embedded in an ective dielectric medium of refractive index n=1.64 (Mie theory). Calculations are performed with tabulated values of the metal dielectric functions (upper spectrum) or with their parameterized form (lower spectra). Here, the only varying parameter is the size- independent silver ective electron collision rate. 13

14 6 Effects of exchanging the metal composition of the optical absorption spectra of / core shell clusters. Figure SI8. Calculations of the optical absorption cross-section for 5nm diameter (blue curves) clusters (red curves) embedded in an ective dielectric medium of refractive index n=1.64 (Mie theory). Dielectric functions of copper and silver are taken from Ref [ 6 ]. 14

15 7 Effects of the location of the copper oxide layer on the optical absorption spectra core-shell clusters Figure SI9. Mie calculations of the optical absorption cross-section of 5nm in core shell clusters with a relative compositions 50%-50% and for increasing rates of copper oxidation. A 0 shell is assumed to be formed between the core and the shell (a) or at the outer cluster surface, on top of the shell (b). The oxidation rates range from 0% (blue curves) to 50%. The red curves give are arbitrarily drawn for a 30% oxidation. 15

16 8 Effects of the nature of the oxide on the optical absorption spectra core-shell clusters. Figure SI10. Comparison between the optical spectra of 5 nm core shell clusters as a function of the relative proportion x of silver (non-oxidized cluster taken as a reference) and the chemical nature of the outer oxide shell ( O-top spectra or O-bottom spectra). The oxidation rate R ox. ranges from 0% to 40 % with 10% steps for progressively red-shifted spectra. Spectra of nonoxidized clusters are drawn in blue. The dielectric function of silver oxide was taken from Refs.[ 8, 9 ] and those of copper, silver, and copper oxide from Ref [ 6 ]. 16

17 9 Effects of the location of the copper oxide layer on the optical absorption spectra of Janus / clusters Figure SI11. Comparison between optical spectra of 5 nm oxidized / Janus clusters as a function of the relative proportion x of silver (non oxidized cluster taken as a reference). Left spectra: hypothesis of the formation of a O outer layer in contact with metallic copper only. Right spectra: hypothesis of the formation of a O outer layer forming a shell around the whole cluster. The copper oxidation rate R ox. ranges from 0% to 40 % with 10% steps for progressively red-shifted spectra. The morphology of these clusters as input of numerical calculations by finite element method is shown in figure SI1. Spectra of non-oxidized clusters are drawn in blue. The dielectric function of copper, silver, and copper oxide are taken from Ref [ 6 ]. 17

18 10 Effects of the copper oxide shell reduction into metallic copper Assuming that oxidized clusters have core-shell structure and that about 30% of copper is oxidized so as to form a 0 cuprite outer shell (see Figure 6 of the main text), a possible consequence of annealing under hydrogen exposure is the reduction of the cuprite shell and its substitution by a copper shell. Simple calculations with the Mie theory displayed in figure SI9 show that there is almost no significant difference between absorption clusters. If they exist, these structures cannot be distinguished by optical experiments only. Figure SI1. Calculations of optical absorption cross-sections for 5nm diameter (blue 0 (dashed gray curves) clusters (red curves) embedded in an ective dielectric medium of refractive index n=1.64 (Mie theory). The amount of in the outer shell (oxide or metal) is 30% of the copper initially present in the core..dielectric functions of copper and silver are taken from Ref [ 6 ]. 18

19 References (1) Kreibig, U.; Fragstein, C. v. The Limitation of Electron Mean Free Path in Small Silver Particles. Zeitschrift für Physik 1969, 4, () Kawabata, A.; Kubo, R. Electronic Properties of Fine Metallic Particles. Journal of the Physical Society of Japan 1966, 1, (3) Kreibig, U.; Vollmer, M., Optical properties of Metal Clusters. Springer: Berlin, (4) Baida, H.; Billaud, P.; Marhaba, S.; Christofilos, D.; Cottancin, E.; Crut, A.; Lermé, J.; Maioli, P.; Pellarin, M.; Broyer, M.; Del Fatti, N.; Vallée, F.; Sanchez-Iglesias, A.; Pastoriza-Santos, I.; Liz-Marzan, L. M. Quantitative Determination of the Size Dependence of Surface Plasmon Resonance Damping in Nanoparticles. Nano Lett. 009, 9, (5) Gaudry, M.; Lermé, J.; Cottancin, E.; Pellarin, M.; Vialle, J. L.; Broyer, M.; Prével, B.; Treilleux, M.; Mélinon, P. Optical properties of (Au x 1-x ) n clusters embedded in alumina: Evolution with size and stoichiometry. Physical Review B 001, 64, (6) Palik, E. D., Handbook of optical constants of solids. Academic Press: New York, (7) Nilsson, P. O. Electronic structure of disordered alloys: optical and photoemission measurements on -Au and -Au alloys. Phys. Kondens. Materie 1970, 11, (8) Qiu, J. H.; Zhou, P.; Gao, X. Y.; Yu, J. N.; Wang, S. Y.; Li, J.; Zheng, Y. X.; Yang, Y. M.; Song, Q. H.; Chen, L. Y. Ellipsometric study of the optical properties of silver oxide prepared by reactive magnetron sputtering. Journal of the Korean Physical Society 005, 46, S69-S75. (9) Grillet, N.; Manchon, D.; Cottancin, E.; Bertorelle, F.; Bonnet, C.; Broyer, M.; Lermé, J.; Pellarin, M. Photo-Oxidation of Individual Silver Nanoparticles: A Real-Time Tracking of Optical and Morphological Changes. Journal of Physical Chemistry C 013, 117,