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Langmuir 1996, 12, 788-800
Surface Plasmon Spectroscopy of Nanosized Metal Particles Paul Mulvaney Advanced Mineral Products Research Centre, School of Chemistry, University of Melbourne, Parkville, Victoria, 3052, Australia Received April 4, 1995. In Final Form: July 7, 1995X The use of optical measurements to monitor electrochemical changes on the surface of nanosized metal particles is discussed within the Drude model. The absorption spectrum of a metal sol in water is shown to be strongly affected by cathodic or anodic polarization, chemisorption, metal adatom deposition, and alloying. Anion adsorption leads to strong damping of the free electron absorption. Cathodic polarization leads to anion desorption. Underpotential deposition (upd) of electropositive metal layers results in dramatic blue-shifts of the surface plasmon band of the substrate. The deposition of just 0.1 monolayer can be readily detected by eye. In some cases alloying occurs spontaneously during upd. Alloy formation can be ascertained from the optical absorption spectrum in the case of gold deposition onto silver sols. The underpotential deposition of silver adatoms onto palladium leads to the formation of a homogeneous silver shell, but the mean free path is less than predicted, due to lattice strain in the shell.
Introduction Interest in the optical properties of colloidal metals dates back to Roman times. Nanosized gold particles were often used as colorants in glasses, and quite complex optical effects were created using metal particles.1 In the seventeenth century, “Purple of Cassius”, a colloid of heterocoagulated tin dioxide and gold particles, became a popular colorant in glasses.2 These early manifestations of the unusual colors displayed by metal particles prompted Faraday’s investigations into the colors of colloidal gold in the middle of the last century. Today his studies are generally considered to mark the foundations of modern colloid science.3 The formation of color centers and small colloidal metal particles in ionic matrices and glasses has remained an area of very active research,4-6 driven, in part, by the technical importance of the photographic process.7 However, colloid chemists have tended to neglect the study of metal particles in aqueous solution because of their complicated double layer structure, which is more amenable to direct electrochemical investigation. The more recent discovery that the surface plasmon absorption band can also provide information on the development of the band structure in metals8-11 has led to a plethora of studies on the size dependent optical properties of metal particles, particularly those of silver and gold,12-17 while advances in molecular beam techniques now enable X Abstract published in Advance ACS Abstracts, December 15, 1995.
(1) See, for example: Savage, G. Glass and Glassware; Octopus Books: London, 1975. One of the most famous examples is the Lycurgus Cup which is ruby red in transmitted light but appears green in reflected light. The color is due to colloidal gold. It was manufactured in the 4th century AD. (2) See: Thiessen, P. A. Kolloid Z. 1942, 101, 241, for micrographs of this composite. (3) Faraday, M. Philos. Trans. R. Soc. 1857, 147, 145. (4) Siedentopf, H. Z. Phys. 1905, 6, 855. (5) Mott, N. F.; Gurney, R. W. Electronic Processes in Ionic Crystals; Oxford University Press: Oxford, 1948. (6) Hughes, A. E.; Jain, S. C. Adv Phys. 1979, 28, 717. (7) The Theory of the Photographic Process, 4th ed.; James, T. H., Ed.; MacMillan Press: New York, 1977. (8) Scott, A. B.; Smith, W. A.; Thompson, M. A. J. Phys. Chem. 1953, 57, 757. (9) Doremus, R. H. J. Chem. Phys. 1965, 42, 414. (10) Doyle, W. T. Phys. Rev. 1958, 111, 1067. (11) Ro¨mer, H.; von Fragstein, C. Z. Phys. 1961, 163, 27. (12) Perenboom, J. A. A.; Wyder, P.; Meier, F. Phys. Rep. 1981, 78, 173. (13) Papavassiliou, G. C. Prog. Solid State Chem. 1980, 12, 185. (14) Kreibig, U. J. Phys. F: Met. Phys. 1974, 4, 999.
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spectroscopic analysis of metal clusters to be carried out in vacuum.18,19 Although many of the optical effects associated with nanosized metal particles are now reasonably well understood, there are large discrepancies between the optical properties of metal sols prepared in water, particularly those of silver, and sols prepared in other matrices.6,20-27 In a recent review Kreibig noted that while much work has been done to isolate matrix effects and to determine the roles of defects, grain boundaries, crystallinity, and polydispersity on the optical properties of sols, little is known about the way specific surface chemical interactions may influence the absorption of light by small metal particles.28 These differences are attributed to unique double layer effects present at the metal-water interface. This review focuses on some of these surface chemical effects, and attempts to show how changes to the surface plasmon absorption band of aqueous metal colloids can be related to electrochemical processes occurring at metal particle surfaces. Simple models are proposed to explain some of these chemical changes within the Drude framework for surface plasmon absorption. 1. Light Absorption by Colloids In the presence of a dilute colloidal solution containing N particles per unit volume, the measured attenuation of light of intensity Io, over a pathlength d cm is given by (15) von Fragstein, C.; Schoenes, F. J. Z. Phys. 1967, 198, 477. (16) Kreibig, U. Z. Phys. B: Condens. Matter Quanta 1978, 31, 39; J. Phys. (Paris) 1977, 38, C2-97. (17) Yanase, A.; Komiyama, H. Surf. Sci. 1991, 248, 11, 20. (18) Fallgren, H.; Martin T. P.; Chem. Phys. Lett. 1990, 168, 233. (19) (a) Tiggesbau¨mker, J.; Ko¨ller, L.; Meiwes-Broer, K.-H.; Liebsch, A. Phys. Rev. A 1993, 48, R1749. (b) Huffman, D. R. Adv. Phys. 1977, 26, 129. (20) Frens, G.; Overbeek, J. Th. G. Kolloid Z. Z. Polym. 1969, 233, 922. (21) Berry, C. R.; Skillman, D. C. J. Appl. Phys. 1971, 42, 2818. (22) Miller, W. J.; Herz, A. H. In Colloid and Interface Science; Academic Press: New York, 1976; Vol. 4. (23) Heard, S. M.; Grieser, F.; Barraclough, C. G.; Sanders, J. V. J. Colloid Interface Sci. 1983, 93, 545. (24) Henglein, A. J. Phys. Chem. 1979, 83, 2209. (25) Lee, P. C.; Meisel, D. J. Phys. Chem. 1982, 86, 3391. (26) Creighton, J. A.; Blatchford, C. G.; Albrecht, M. G. J. Chem. Soc., Faraday Trans. 2 1979, 75, 790. (27) Linnert, T.; Mulvaney, P.; Henglein, A. J. Phys. Chem. 1993, 97, 679. (28) Kreibig, U.; Genzel, U. Surf. Sci. 1985, 156, 678.
© 1996 American Chemical Society
Optical Properties of Metal Particles
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(1)
′ ) ∞ - ωp2/(ω2 + ωd2)
(7)
where Cext is the extinction cross section of a single particle. For spherical particles with a frequency dependent dielectric function ) ′ + i′′, embedded in a medium of dielectric function m, Cext is given by29-33
′′ ) ωp2ωd/ω(ω2 + ωd2)
(8)
A ) log10 Io/Id ) NCextd/2.303
∑(2n + 1) Re (an + bn)
Cext ) 2π/k2
(2)
where k ) 2π xm/λ and an and bn are the scattering coefficients, which are functions of the radius R and the wavelength λ in terms of Ricatti-Bessel functions. The extinction cross section of a particle is often normalized to give the extinction cross section per unit area:
Qext ) Cext/πR2
(3)
where ∞ is the high frequency dielectric constant due to interband and core transitions and ωp is the bulk plasma frequency
ωp2 ) Ne2/mo
(9)
in terms of N, the concentration of free electrons in the metal, and m, the effective mass of the electron. ωd is the relaxation or damping frequency, which is related to the mean free path of the conduction electrons, Rbulk, and the velocity of electrons at the Fermi energy, vf, by
ωd ) vf /Rbulk
(10)
Conventionally, chemists measure the extinction coefficient of a solution in units of M-1 cm-1, where the colloid concentration is the molar metal atom concentration. This quantity is related to Qext by
When the particle radius, R, is smaller than the mean free path in the bulk metal, conduction electrons are additionally scattered by the surface, and the mean free path, Reff, becomes size dependent with
(M-1 cm-1) ) (3 × 10-3)VmQext/4(2.303)R
1/Reff ) 1/R + 1/Rbulk
(4)
where Vm (cm3 mol-1) is the molar volume of the metal. For very small particles where kR , 1, only the first, electric dipole term in eq 2 is significant, and
Cext )
24π2R3m3/2 ′′ λ (′ + 2 )2 + ′′2
(5)
m
This equation can be also obtained by purely electrostatic arguments, and a clear derivation is given by Genzel and Martin.34 In many cases to be described here, it will be necessary to consider the perturbation introduced by a thin surface layer. The extinction cross section of a small, concentric sphere is given by32 Cext ) 4πR2k* ×
{
Im
(shell - m)(core - 2shell) + (1 - g)(core - shell)(m + 2shell)
}
(shell + 2m)(core + 2shell) + (1 - g)(2shell - 2m)(core - shell)
(6)
where core is the complex dielectric function of the core material, shell is that of the shell, m is the real dielectric function of the surrounding medium, g is the volume fraction of the shell layer, and R is the radius of the coated particle. When g ) 0, eq 6 reduces to eq 5 for an uncoated sphere, and for g ) 1, eq 6 yields the extinction cross section for a sphere of the shell material. In the case of many metals, the region of absorption up to the bulk plasma frequency (in the UV) is dominated by the free electron behavior, and the dielectric response is well described by the simple Drude model. According to this theory,35 the real and imaginary parts of the dielectric function may be written (29) Toon, O. B.; Ackerman, T. P. Appl. Opt. 1981, 20, 3657. (30) van der Hulst, H. C. Light Scattering by Small Particles; John Wiley and Sons: New York, 1957. (31) Kurtz, V.; Salib, S. J. Imaging Sci. Technol. 1993, 37, 43. (32) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (33) Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969. (34) Genzel, L.; Martin, T. P. Phys. Status Solidi B 1972, 51, 91. (35) Kittel, C. Introduction to Solid State Physics, 2nd ed.; Wiley: New York, 1956.
(11)
Equation 11 has been experimentally verified by the extensive work of Kreibig for both silver and gold particles right down to a size of 2 nm.14,16,28 The advantage of the Drude model is that it allows changes in the absorption spectrum to be interpreted directly in terms of the material properties of the metal. The origin of the strong color changes displayed by small particles lies in the denominator of eq 5, which predicts the existence of an absorption peak when
′ ) -2m
(if ′′ small)
(12)
From eq 7 it can be seen that over the whole frequency regime below the bulk plasma frequency of a metal, ′ is negative which is due to the fact that the electrons oscillate out of phase with the electric field vector of the light wave. This is why metal particles display absorption spectra which are strong functions of the size parameter, kR. In a small metal particle the dipole created by the electric field of the light wave sets up a surface polarization charge, which effectively acts as a restoring force for the “free electrons”. The net result is that, when condition 12 is fulfilled, the long wavelength absorption by the bulk metal is condensed into a single, surface plasmon band. In the case of semiconductor crystallites, the free electron concentration is orders of magnitude smaller, even in degenerately doped materials (i.e., ωp is smaller), and as a result surface plasmon absorption occurs in the IR, rather than in the visible part of the spectrum. Semiconductor crystallites therefore do not change color significantly when the particle size is decreased below the wavelength of visible light, although the IR spectrum may be affected. It should be noted that the strong color changes observed when semiconductor crystallites are in the quantum size regime (R < ∼50 Å), are due to the changing electronic band structure of the crystal, which causes the dielectric function of the material itself to change. In Figure 1, a “typical” surface plasmon band is shown calculated using eq 5 with parameters typical of silver for several values of the damping parameter ωd. The most important parameter affecting ωd is the particle size. From eqs 10 and 11 it can be seen that decreases in the particle size lead to an increase in ωd, causing the band to broaden and the maximum intensity to decrease. The position of the peak is virtually unaffected by small changes to ωd
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Mulvaney
Figure 1. Calculated surface plasmon absorption band of a typical free electron metal particle for several values of the damping parameter, ωd, within the dipole approximation, eq 6. Parameters, ∞ ) 5.0, ωp ) 10 eV, R ) 5.0 nm. m ) 1.77. Damping frequencies in eV: (1) 0.4, (2) 0.6, (3) 0.8, (4) 1.2, (5), 2.4, (6) 3.6.
Figure 2. Plots of the square of the observed position of the surface plasmon bands of colloidal lead and silver as a function of twice the medium dielectric function. Data from Hughes and Jain.6
but for large damping a slow shift to lower energies occurs. In an inert matrix, the only cause of peak shifts is a change in the dielectric properties of the metal particles themselves, due to this surface scattering or for exceedingly small particle sizes (
