Article pubs.acs.org/JPCC
Crossover Phenomenon in Third-Order Nonlinear Optical Susceptibilities of Gold Nanoparticles from Plasmons to Discrete Electronic States Yasushi Hamanaka* Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
Noriyuki Okada, Koji Fukagawa, and Arao Nakamura Department of Applied Physics, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
Yutaka Tai Materials Research Institute for Sustainable Development, National Institute of Advanced Industrial Science and Technology, Nagoya 463-8560, Japan
Junichi Murakami Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8562, Japan S Supporting Information *
ABSTRACT: We report on the size-dependent behavior of third-order nonlinear optical susceptibilities, χ(3), of thiolate monolayer-protected Au clusters and Au nanoparticles embedded in SiO2 in the size range between 25 and 170 000 atoms. The imaginary part of χ(3) is negative and increases with increasing size above 135 Au atoms, while it is positive and increases with decreasing size below 66 Au atoms. These results reveal a crossover from the local-field effect due to surface plasmons in the metal electron system to the quantum size effect of a molecule-like electronic system. From the transient absorption spectra in the femtosecond time region, it is found that the optical nonlinearity in the quantum-size region reflects the characteristic electronic states due to geometric and electronic interactions between the core and ligand in the Au clusters.
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electrons generated by pulsed laser excitation.9−11 Materials with large values of χ(3) have attracted special attention for their potential application in all-optical switching devices because real and imaginary parts of χ(3) are related to the intensitydependent refractive index and absorption coefficient, respectively.12 Accordingly, a number of studies on third-order nonlinear optical properties of Au, Ag, and Cu NPs embedded in various matrices have been reported during the past two decades.6−11,13−17 On the other hand, in NPs with diameters less than 1 nm, which is close to the Fermi wavelength of an electron, quantum size effects appear, resulting in discrete electronic transitions. Pioneering work on thiolate monolayer-protected Au clusters (Au MPCs) has shown molecular-like features of optical spectra
INTRODUCTION There has been long-standing interest in the optical properties of metal nanoparticles (NPs) with controlled size and shape in a wide range of research area encompassing physics, chemistry, and materials science, not only because of fundamental interest in understanding the behavior of nanoscopic materials but also because of the large potential for nano-optical applications.1−5 In metal NPs with diameters larger than ∼3 nm, localized surface plasmons (SPs), which are collective oscillations of conduction electrons, play a major role in the optical response because of the confinement of electromagnetic fields to the metallic surface.1 Third-order optical susceptibilities χ(3) of noble-metal NPs embedded in a dielectric matrix are strongly enhanced around the SP resonance.6−8 This enhancement effect decreases with decreasing diameter of the NPs because the local electric field is reduced due to the limit of the electron mean free path to the NP size.8 A subpicosecond-order response time indicates cooling dynamics of nonequilibrium © 2012 American Chemical Society
Received: December 16, 2011 Revised: April 16, 2012 Published: April 25, 2012 10760
dx.doi.org/10.1021/jp2121388 | J. Phys. Chem. C 2012, 116, 10760−10765
The Journal of Physical Chemistry C
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details of the synthetic method and the precipitation technique are described in the Supporting Information. Further large Au NPs (>3 nm) embedded in SiO2 matrices were prepared by a sputtering and double-heat-treatment method. Details of the preparation method are described in ref 32. The average diameters of the Au NPs prepared by this method are 3.9, 4.9, 7.0, and 17.5 nm. The fcc crystal structure of these NPs were confirmed by X-ray diffraction measurement. The diameters of Au NPs embedded in SiO2 and Au NPs with thiolate surfactants except for DDT were determined using transmission electron microscopy (TEM) analysis. The corresponding numbers of Au atoms contained in the NPs (NAu) with diameters of 3.9, 4.9, 7.0, and 17.5 nm were estimated to be 1800, 3600, 10 600, and 170 000, respectively, assuming a spherical NP with an fcc structure. Similarly, the NAu values of the NPs protected with 2-NT, 4-mBT, and α-TT were determined to be 247, 376, and 835, respectively. The values of NAu for size-selected NPs with the DDT surfactant were measured using laser desorption time-of-flight (LD-TOF) mass spectrometry. Third-order nonlinear optical responses of Au NPs were investigated by pump and probe spectroscopy using an amplified femtosecond Ti:sapphire laser system operating at 1 kHz and a polychromator equipped with a Si photodiode array. The output pulse was frequency doubled in a 1 mm thick BBO crystal and used as a pump pulse of 3.12 eV. To generate pump pulses with other photon energies, an optical parametric amplifier was used. The pump pulses were focused onto a quartz cell containing Au NPs with thiolate surfactants or Au NPs embedded in SiO2 matrices to excite the sample. Differential absorption spectra of Au NPs after pump-pulse excitation were measured by a white-continuum probe pulse generated by self-phase modulation of the fundamental pulse from the laser system focused onto a H2O cell. The pulse duration of the pump pulses were typically 150 fs. Nondegenerate components of Im χ(3)(−ωprobe: −ωpump, ωpump, ωprobe) at the probe frequency of ωprobe were deduced from the change in the absorption coefficient Δα just after the pump− pulse excitation with frequency of ωpump. Im χ(3) values can be obtained from the equations33
and femtosecond dynamics of excited states, which differ from those of the localized SPs.18−23 In Au MPCs, a series of absorption bands due to transition between discrete energy levels appear in a wide energy range from the near-infrared to the ultraviolet, instead of a strong SP resonance band in large NPs.18 Femtosecond transient absorption studies of sizeselected Au MPCs indicate that electron relaxation dynamics reflect molecular-like electronic orbitals formed by Au atoms and ligand molecules and differ from plasmon-like behavior characteristic of continuous electronic states.21−24 However, the nonlinear optical properties of Au MPCs remain unexplored, though two-photon absorption has been reported in luminescent Au25 clusters in one study.25 This is because the geometry of Au MPCs (number of Au atoms in a cluster, atomic packing in a cluster, and arrangement of thiolate ligands) as well as the energy level structure of excitation states were unresolved. Recently, a breakthrough in Au MPCs research was reported on Au25(SR)18 (R = thiolate) cluster which is exceptionally stable among variable Au MPCs. Total structure determination based on X-ray diffraction data and molecular orbital calculation by density-functional theory revealed that the structure of Au25(SR)18 consists of a nearly icosahedral Au13 core surrounded by six −SR−Au−SR−Au−SR− motifs in an approximately octahedral arrangement.26−28 The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) was calculated to be 1.63 eV.29 These findings motivate us to investigate how nonlinear optical response evolves from plasmon-like to molecular-like with decreasing number of Au atoms. In this study, we report a systematic investigation of thirdorder nonlinear optical response of size-selected Au NPs including MPCs, with sizes ranging from 25 to 170 000 Au atoms per NP. The size dependence of the imaginary part of χ(3) (Im χ(3)) values and the Im χ(3) spectra showed that the transition from a plasmon-like to a molecular-like behavior takes place around 100 Au atoms. These results reveal a crossover from metallic electronic states in large NPs to discrete electronic states in small clusters consisting of an Au core and a surrounding shell. Considering the new crystal structure model for Au MPCs, we reexamine femtosecond transient absorption data and discuss relaxation dynamics of electrons in the small cluster region.
Im χ (3) =
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n 2c 2 β, 480π 2ωprobe
Δα = βI (1)
where n and c represent the refractive index of the sample and the velocity of light in vacuum, respectively, and I and β are the pump pulse intensity and the nonlinear absorption coefficient. Therefore, we can estimate Im χ(3) values from the dependence of Δα on I that is measured by changing the excitation fluence over wide range not exceeding 30 μJ/mm2. Measurements for Au NPs with thiolate surfactants were done on their toluene solution without circulation.
EXPERIMENTAL METHODS Au NPs capped with various thiol molecules were prepared by a liquid phase reduction method.30 NPs with diameters less than 3 nm were synthesized by the reduction of chlorauric acid (HAuCl4) with sodium borohydride (NaBH4) using 1dodecanethiol (DDT), 2-naphthalenethiol (2-NT), 4-methylbenzenethiol (4-mBT), or α-toluenethiol (α-TT) as surfactants. To obtain Au NPs with a narrow size distribution, we used a fractional precipitation (FP) technique.31 Precipitates obtained by adding acetonitrile (antisolvent) to a toluene solution of Au NPs were separated from soluble fractions by centrifugation. Then, acetonitrile was added to the soluble fraction again, and precipitates were removed. After this procedure is repeated for the Au NPs with a DDT surfactant, a series of extremely small ( 135). The dispersion curves of Im χ(3) (Im χ(3) spectra) for Au25−Au835 and Au1800 are shown in Figure 1e−h and Figure 2 by the closed circle symbols. The features of the dispersion curves for Au25, Au44, and Au66 essentially differ from those for Au135 and larger Au NPs. The Im χ(3) values of these clusters are positive, while the Im χ(3) value for the larger NPs changes from a positive to a negative value in the spectral region studied. The most noticeable feature of the dispersion curve in Au25 is that the spectrum shows a minimum at ∼1.85 eV, which is slightly higher than the absorption peak due to the HOMO−LUMO transition. On the other hand, the Im χ(3) values of NPs with sizes larger than Au247 are negative around the SP resonance (∼2.3 eV) and positive on both sides of the resonance peak. This spectral behavior is characteristic of the dispersion curve at the SP resonance and is ascribed to saturation and broadening of the SP band due to the creation of nonequilibrium electrons in metal NPs.9−11,13 We now discuss the size dependence of the third-order nonlinear susceptibilities. As the nonlinear susceptibility is dependent on the fraction of NPs contained in the solution or matrix, we use a figure of merit of Im χ(3) which is defined as Im χ(3)max/α, where Im χ(3)max is the maximum Im χ(3) value in the dispersion curve and α is the linear absorption coefficient. Shown in Figure 3 is Im χ(3)max/α as a function of the number of Au atoms in a single NP. For the Au135−Au170000 NPs, we consider the value at the SP resonance (∼2.4 eV) and for Au25 to Au66 at 1.6 eV. This energy approximately corresponds to 10762
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in Figure 3. One of possible reasons for such size-dependent behavior is the different size dependences of the local field effect and the quantum size effect. The sign of Im χ(3) is opposite, and thus a competition between the two components around the crossover region may result in a jump of the data points. Another reason for the abrupt change in Im χ(3)max/α is the difference in media surrounding the NPs; matrix materials for Au1800 and larger NPs are SiO2, whereas Au835 and smaller NPs are capped by thiolate and dispersed in toluene. The local electric field inside the NPs around the SP resonance frequency is strongly dependent on a dielectric constant of surrounding medium as well as an NP size, and thus the difference in the local electric fields may lead to a jump in Im χ(3)max/α values.6−8 We next investigated the mechanisms of the nonlinear absorption and the origin of the characteristic features of the Im χ(3) spectra for Au25−Au66 clusters. In our previous report,22 we reported the differential absorption spectra measured by pump−probe spectroscopy for small Au clusters and discussed spectral behavior and electron dynamics. As shown in Figure 2 of ref 22, the differential absorption spectra measured at delay times between the pump and probe pulses td of 0.3−2.0 ps with a pump photon energy of 1.93 eV corresponding to the HOMO−LUMO transition exhibit an absorption increase (Δα > 0) at the low-energy side of the absorption peaks, suggesting a red-shift of the absorption peaks. When the pump photon energy was changed to 2.53 eV corresponding to the transition energy of HOMO−LUMO+1, we observed similar behavior of differential absorption spectra. Figure 4 shows the linear absorption spectrum for Au25 (a) and differential absorption spectra measured at delay times of 0.3 ps (b) and 2.0 ps (c) with a pump photon energy of 2.53 eV. This result suggests that the spectral feature does not depend on the electronic state in the Au core excited by the pump pulse. Other groups have also observed differential absorption spectra in Au MPCs, Au28(SG)16 (SG = tripeptide glutathione) clusters21 and Au25(SCH2CH2Ph)18− (Ph = phenyl) cluster anions.23 The differential spectra reported by Miller et al. for the anion Au25(SCH2CH2Ph)18− show the similar behavior to our results, though the spectral range is limited to 1.55−2.25 eV23 compared to our experiments (up to 3 eV). In their report, Au MPCs reach the quasi-equilibrium states localized on the −SR−Au−SR−Au−SR− semirings surrounding the Au13 core within 1.2 ps after the excitation and relax to the ground state with a time constant greater than 4 ps (up to 100 ps). This result supports the superatom model of electronic structure of the Au25(SCH2CH2Ph)18− anion cluster. Considering geometric and electronic interactions between core and ligand in the Au clusters, we analyze and discuss the differential absorption spectra in Figure 4. The differential absorption spectrum measured at td = 2.0 ps is fitted well to the differential spectrum calculated by assuming a red-shift of the observed absorption spectrum by 140 meV, shown as a dashed curve in Figure 4c. For shorter td, however, the observed differential spectra could not be well reproduced by the redshift component. On the other hand, we could successfully reproduce the differential spectra for td < 2.0 ps by taking into account the absorption saturation and the induced absorption being linearly dependent on the photon energy, in addition to the red-shift component (140 meV). These spectral components obtained for the spectrum at td = 0.3 ps are shown in Figure 4b as the dotted, dot-dashed, and dashed plots, respectively. We can see that the observed spectrum is well reproduced by the sum of these three spectral components
Figure 3. Dependence of Im χ(3)max/α values on the number of Au atoms in a single Au NP/MPC. Closed circle, triangle, and open circle symbols represent Im χ(3)max/α values for clusters passivated by DDT molecules, NPs passivated by 2-NT, 4-mBT, and α-TT molecules, and NPs embedded in SiO2, respectively.
the maximum value of the dispersion curve due to the red-shift component as discussed later in Figure 4b. The sign of Im
Figure 4. Absorption spectrum (a) and differential absorption spectra measured after 0.3 ps (b) and 2.0 ps (c) at a pump photon energy of 2.53 eV in Au25 clusters. The dotted (green), dashed (red), and dotdashed (orange) lines indicate spectral components of the bleaching, red-shift, and absorption increase, respectively. The solid line (blue) in (b) is the total differential absorption spectrum fitted to the measured spectrum.
χ(3)max/α is negative for Au135−Au170000 and is positive for Au25−Au66. With further decreasing NP size, Im χ(3)max/α exhibits a change in sign and subsequently its value increases. The decrease in χ(3)/α at the SP resonance with decreasing NP size was reported for Cu and Ag NPs with diameters larger than 4 nm (∼2000 atoms) and is ascribed to the suppression of local field enhancement due to size-dependent changes in dielectric functions of metal NPs.8 Hence, the size-dependent behavior of Im χ(3)max/α observed in this study indicates that the local field effect on third-order optical nonlinearities plays a role even in Au135 (∼1.6 nm). The positive values of Im χ(3)max/α and the opposite dependence on NP size observed for Au25 to Au66 are characteristic of the presence of discrete electronic states. Therefore, we found that the transition of third-order nonlinearities from the local field effect in the metal electron system to the quantum size effect in the molecule-like system takes place around 100 Au atoms in a cluster. We note that the values of Im χ(3)max/α exhibit an abrupt change between the data points for Au835 and Au1800 as shown 10763
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dynamics reported by Miller et al. for the Au25(SCH2CH2Ph)18− anion cluster, where the electron relaxation from the LUMO+1 to the LUMO sates occurs within 0.2 ps.23 We compare our results with the results observed in semiconductor NPs. The absorption saturation effect is predominant in semiconductor NPs, and Coulomb and exchange interactions that give rise to the spectral shift are negligible.38 The red-shift of 140 meV for Au25 and Au44 clusters is extremely large compared to the shift of the exciton band observed in semiconductor NPs (∼8 meV in In0.5Ga0.5As quantum dots) due to the band renormalization effect by photoexcited carriers.40 Finally, we discuss the physical meaning of the sizedependent change in the sign of Im χ(3)max/α values shown in Figure 3. The positive values of Im χ(3)max/α for smaller clusters with NAu < 100 mainly originate from the red-shift of the absorption bands and are characteristic of the small metal MPCs. In contrast, larger nanoparticles characterized by the SP resonance exhibit the negative Im χ(3)max/α. The many studies on the nonlinear absorption mechanisms of noble metal nanoparticles have shown the broadening effect of the SP resonance band due to the generation of hot electrons with the pump pulse, which leads to suppression of absorption at the resonance peak energy.9−11,13,17 This spectral broadening gives rise to the negative value of Im χ(3)max/α at the SP resonance energy. Therefore, the nonlinear absorption mechanisms of gold NPs are essentially different whether their electronic states are classified as discrete or continuous character, and hence, the sign of Im χ(3)max/α is as well.
(solid curve). The differential absorption spectra measured with the pump photon energy of 1.93 eV were also successfully analyzed by the same procedure (shown in ref 22). Similar experiments and analysis were done for Au44 clusters. In Figure 5a,b, absorption and differential absorption spectra of Au44
Figure 5. (a). Absorption spectrum of Au44 clusters. (b) Differential absorption spectrum of Au44 clusters measured after 0.3 ps at a pump photon energy of 1.93 eV. The dotted (green), dashed (red), and dotdashed (orange) lines indicate spectral components of the bleaching, red-shift, and absorption increase, respectively. The solid line (blue) in (b) is the total differential absorption spectrum fitted to the measured spectrum.
clusters are shown. The differential absorption spectrum of Au44 at td = 0.3 ps could be also well decomposed into red-shift, saturation, and induced absorption components, assuming the red-shift of 140 meV. We interpret the absorption saturation component as the blocking of the transition into the occupied level due to the Pauli exclusion principle.38 The decay of the absorption saturation within 1 ps indicates the fast relaxation of excited electrons in the Au13 core to the surrounding shell. For Au25(SR)18, the time-dependent density functional theory reveals that the absorption spectrum is not separable into core and ligand contributions, and a complex absorption spectrum arises from geometric and electronic interactions between two fragments.29 Considering this absorption origin, we ascribe the large red-shift induced by the pump pulse to charge transfer between the Au core and surrounding shell which leads to rearrangement of the electronic states in the Au25−DDT system. The rearrangement of the electronic state accompanied by the geometric rearrangement may last even after electronic relaxation in the Au core is completed, which is consistent with our observations (∼5 ps). According to the theoretical study by Aikens, characteristic features of the absorption spectrum of Au25 MPCs, such as a position and height of the absorption peaks, are dominantly affected by the geometric and electronic structures of the core, and the ligand size is less responsible for the spectral features.39 Our interpretation of the origin of the red-shift is consistent with these theoretical expectations. The induced absorption component with a featureless spectral shape might be ascribed to the red-shift of the absorption band tail of the ligand molecules whose peak is located in the high-energy region beyond the spectral range measured in this study. The fact that the same spectral behavior is observed for both the pump− photon energies of 1.93 eV (HOMO−LUMO) and 2.53 eV (HOMO−LUMO+1) indicates the very fast relaxation from the LUMO+1 to the LUMO sates (
