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We probe the acoustic vibrations of silver nanoprisms and gold nano-octahedrons in aqueous solution with four-wave mixing. The nonlinear optical response shows two acoustic vibrational modes: an in-plane mode of nanoprisms with vertexial expansion and contraction; an extensional mode of nano-octahedrons with longitudinal expansion and transverse contraction. The particles were also analyzed with electron microscopy and the acoustic resonance frequencies were then calculated by the finite element analysis, showing good agreement with experimental observations. The experimental mode frequencies also fit with theoretical approximations, which show an inverse dependence of the mode frequency on the edge length, for both nanoprisms and nano-octahedrons. This technique is promising for in situ monitoring of colloidal growth.
© 2016 Optical Society of America
1. Introduction
Triangular and octahedral metallic nanoparticles have been used extensively in sensing, imaging, medicine, catalysis, photovoltaics, and non-linear optics [1–10]. The morphology of nanoparticles is of great importance in those applications. The study of the acoustic vibrations of metallic nanoparticles is crucial since it can provide information about nanoparticles’ size, shape, and elastic properties [11–13]. The pump-probe spectroscopy is the typical technique used in the study [14–16]. In a pump-probe experiment, a pump pulse thermally excites the nanoparticles’ vibrations and a probe pulse records the extinction change caused by the deformation of nanoparticles. High peak power of the pump laser is required for mode excitation and optical response detection. Nanoparticles of different shapes (e.g., spherical, rod-shaped, and cubic) and materials (gold and silver) have been studied using the pump-probe method [17–19].
Our recent reports on the acoustic vibrations of dielectric and metallic nanoparticles used four-wave mixing (FWM) to probe the acoustic vibrations and showed appreciable optical response and accuracy [20–22]. Hence, we use the FWM method to study triangular and octahedral nanoparticles’ acoustic vibrations in this work. We observe two acoustic vibrational modes: an in-plane mode of nanoprisms with vertexial expansion and contraction; an extensional mode of nano-octahedrons with longitudinal expansion and transverse contraction. Numerical simulation has been performed to illustrate the mode profiles using the finite element method (FEM). We also investigate simple theoretical approximations, showing the inverse dependence of the mode frequency on the inverse of the edge length, for both nanoprisms and nano-octahedrons.
2. Experiments
2.1 Silver nanoprisms synthesis
Silver nanoprisms were synthesized following the photo-induced conversion method of silver nanospheres to nanoprisms [23]. As a typical synthesis process, an aqueous solution of silver nitrate (0.1 mM, 100 ml), (204390, Aldrich Chemicals), and trisodium citrate (0.3 mM), (S2990, ACP Chemicals Inc.), was prepared in presence of air with a moderate stirring rate (~120 rpm). Next, sodium borohydride solution (50 mM, 100 ml), (7420-1, Caledon Laboratories Ltd.), was injected to the system. Following this, Bis (p-sulfonatophenyl) phenylphosphine dehydrate dipotassium salt (BSPP) (5 mM, 2 ml), (698539, Aldrich Chemicals), was dropped into the solution over 2 min. BSPP was used as a stabilizer agent. The system was irradiated with a 24 W halogen lamp (ser. 700, Sunnex Inc.) for 40 h. During the synthesis process, we could observe the solution’s color change as an indicator. The clear initial solution of silver salt and citrate turned to yellow after the injection of the sodium borohydride, indicating the formation of silver nanospheres. During the irradiation process, the solution’s color turned to green and finally blue. The reaction was terminated after 40 h irradiation.
2.2 Gold nano-octahedrons synthesis
Three different sizes of gold nano-octahedrons were synthesized. For gold nano-octahedrons with edge length larger than 50 nm, we used the method described in [24]. A volume of 10 mL of an aqueous solution containing 2.5 × 10−4 M hydrogen tetrachloroaurate trihydrate (HAuCl4⋅3H2O, 99.9%, Aldrich) and 0.10 M cetyltrimethyl-ammonium chloride (CTAC, 95%, TCI) was prepared. Concurrently, 10 mL of 0.02 M ice-cold sodium borohydride (NaBH4, 98%, Aldrich) solution was made. To the HAuCl4 solution was added 0.45 mL of the NaBH4 solution with stirring. The resulting solution turned brown immediately, indicating the formation of gold particles. The seed solution was aged for 1 h at 30 °C. Two vials were labeled A and B. A growth solution was prepared in each of the two vials. First, 0.32 g of CTAC surfactant was added. The concentration of CTAC in the final solution was equal to 0.10 M. 9.47 mL deionized water was added to each vial. The vials were then kept in a water bath set at 30 °C. To both vials were added 250 μL of 0.01 M HAuCl4 solution and 5 μL of 0.01 M KI. Finally, 220 μL of ascorbic acid was introduced for the synthesis of octahedrons. The total solution volume in each vial was 10 mL. The solution color turned colorless after the addition of ascorbic acid, indicating the reduction of Au3+ to Au+ species. Next, 55 μL of the seed solution was added to the solution in vial A with shaking until the solution color turned light pink (∼5 s). Then 55 μL of the solution in vial A was transferred to vial B with thorough mixing for ∼10 s. The solution in vial B was left undisturbed for 15 min for particle growth and centrifuged three times at 3000 rpm for 10 min. The particles were concentrated to a 1 mL solution.
For nano-octahedrons with edge length smaller than 50 nm, we used the hydrothermal synthesis method [25] for shape maintaining. Briefly, 92 mL of ultrahigh purity water, 7.545 mL of 0.2 M cetyltrimethylammonium bromide (CTAB, Aldrich), 50 µL of 0.5 M HAuCl4, and 0.1 M trisodium citrate (Na3C6H5O7·2H2O, Mallinckrodt) were added into a 350 ml glass container sealed with a cap. Then we added 630 and 690 µL of trisodium citrate to synthesize nano-octahedrons with side length of ∼45 and ∼35 nm, respectively. Solutions are incubated in oven at 110 °C for 24 hours and cooled naturally down to room temperature. The cooled solutions were then centrifuged at 6000 rpm for 20 min to remove excess CTAB.
2.3 Instrumentation
Figure 1 shows the FWM experimental setup. The sample placed in a quartz cuvette was illuminated by the counter-propagating laser beams composed of a continuous-wave (CW) tunable external-cavity laser (ECL) (DL100, Toptica Photonics) and a CW tunable distributed Bragg reflector laser (DBRL) (DBR852P, Thorlabs). Weak focusing lenses were used with focal lengths of 20 cm (Lens1) and 4 cm (Lens2), respectively. The angle between the two laser beams focused by the lens1 (I1 and I3) was adjusted around 4° to allow the full coverage of the cuvette thickness (1 mm) as the light-matter interaction region. The polarization of the DBRL beam was adjusted by a polarization controller and a polarizer to ensure co-polarized illumination. The interference between the two counter-propagating beams (I2 at frequency ω2 and I3 at frequency ω3) imposes an electrostrictive force that stretches nanoparticles along the beam polarization direction. When the beat frequency (ω3 − ω2) matches the acoustic resonance, the acoustic vibrations of nanoparticles will be resonantly excited, resulting a travelling periodic variation in the refractive index of the medium (similar to a moving Bragg grating). The FWM signal wave I4 at frequency ω4 (ω4 = ω2) is then generated as the beam I1 at frequency ω1 (ω1 = ω3) diffracts from the Bragg grating. Beam I2 was modulated by an optical chopper. The FWM signal was obtained by an avalanche photodetector (APD120A, Thorlabs) connected to a lock-in amplifier (SR510, Stanford Research Systems). The power of the ECL was set to the maximal output power of 67 mW and the wavelength was fixed at 853.4 nm. The power of the DBRL was maintained at 25 mW during the wavelength tuning and the wavelength (> 853.4 nm) was monitored by an optical spectrum analyzer (86142B, Agilent) during the wavelength tuning. The APD output voltage was recorded as a function of the frequency difference of the two lasers.
Fig. 1 FWM experimental setup. ECL: external cavity laser; BS: beam splitter; MR: mirror; IRS: iris; APD: avalanche photodetector; DBRL: distributed Bragg reflector laser; PC: polarization controller; FC: fiber coupler; OSA: optical spectrum analyzer; BR: blocker; OC: optical chopper; PR: polarizer; FPC: fiber-port collimator.
The extinction spectra of nanoprisms and nano-octahedrons were obtained by a SpectraMax M5 multi-mode microplate reader, respectively. The scanning electron microscopy (SEM) images of the nanoparticle samples were obtained by a Hitachi S-4800 field emission SEM at 2kV. Nanoparticles were drop-coated and dried on an aluminum stage for SEM imaging.
3. Results and discussion
Figure 2(a) shows the SEM image of silver nanoprisms obtained at 2 kV and 300k × magnification. We manually measured the edge length of 100 nanoprisms from the SEM image to obtain the size distribution. The histogram was fitted by Gaussian distribution. The result shows that nanoprisms have an average edge length of 72.9 ± 15.8 nm. Figure 2(b) shows the SEM image of the nanoprism stacks for thickness estimation (~10 nm). Figure 2(d) shows the extinction spectrum of silver nanoprisms in aqueous solution. The extinction spectrum shows two localized surface plasmon resonance (LSPR) peaks: a 650 nm peak corresponding to the in-plane dipole plasmon resonance; a 490 nm peak corresponding to the in-plane quadrupole resonance [26].
Fig. 2 (a) SEM image of silver nanoprisms obtained at 300k × magnification. (b) SEM image of the nanoprism stacks for thickness estimation (~10 nm). (c) Nanoprisms’ edge length distribution obtained by manually measuring 100 nanoprisms and fitted by Gaussian distribution. The error represents the standard deviation. (d) Extinction spectrum of silver nanoprisms in aqueous solution.
Figures 3(a)–3(c) show the edge length distribution of nano-octahedrons with different sizes. We manually measured the edge length of 100 nano-octahedrons for each size from the SEM image to obtain the size distribution. The histogram was fitted by Gaussian distribution. Figure 3(d) shows the extinction spectra of different size nano-octahedrons in aqueous solution. The extinction spectra show the major LSPR peaks at 551, 560, and 575 nm for 36.1, 43.2, and 53.4 nm nano-octahedrons, respectively. The LSPR corresponds to the in-plane (parallel to the symmetry plane that bisects the octahedron into two square pyramids) dipole resonance [27].
Fig. 3 Edge length distribution of different sizes: (a) 53.4 nm average edge length. The inset shows the SEM image obtained at 350k × magnification; (b) 43.2 nm average edge length. The inset shows the SEM image obtained at 300k × magnification; (c) 36.1 nm average edge length. The inset shows the SEM image obtained at 300k × magnification. The edge length distribution is obtained by manually measuring 100 nano-octahedrons for each size and fitted by Gaussian distribution. The error represents the standard deviation. (d) Extinction spectra of different size nano-octahedrons in aqueous solution.
Figure 4(a) shows the FWM signal of the silver nanoprism sample as a function of the beat frequency between the ECL and DBR lasers. The solid line through the data points is only for outlining the peak. It is not a theory curve. The background signal from Rayleigh scattering of the DBR laser was subtracted. The spectrum shows one major acoustic resonance peak at 29.7 GHz with a full width at half maximum (FWHM) of 19.6 GHz. The resonant frequency of in-plane vibrational mode can be approximated by the equation [28]:
where Vl,silver (3650 m/s) is the longitudinal speed of sound in silver and Lprism is the edge length of nanoprisms. The calculated mode frequency for a silver nanoprism with a 72.9 nm edge length is 28.9 GHz, which is close to the experimental value (29.7 GHz). The size distribution mainly contributes to the broadening of the resonance peak. According to Eq. (1) and assuming a Gaussian size distribution, FWHM can be calculated by:where ΔLprism = 2.355σprism and σprism is the standard deviation of the edge length. The calculated FWHM is 17.2 GHz, which agrees well with the experimental FWHM of 19.6 GHz.Fig. 4 (a) FWM signal of the silver nanoprism sample as a function of the beat frequency between the ECL and DBR lasers. The error bar represents the standard deviation calculated by 148 data points at each beat frequency. The 29.7 GHz resonance peak corresponds to the frequency of the in-plane vibrational mode. The dashed line indicates the theoretically calculated resonant frequency of 28.9 GHz according to the SEM result. The grey area indicates a 17.2 GHz broadening induced mainly by the size distribution. (b) Simulated mode profiles of maximal displacements with a mode frequency of 28.7 GHz within a vibrational cycle. The solid lines indicate the outlines of the undeformed nanoprisms.
To illustrate the mode profile, we use a commercial FEM solver (COMSOL) to simulate the acoustic vibrations of silver nanoprisms. Parameters used in the simulation are silver’s Young’s modulus of 83 GPa, Poisson’s ratio of 0.37, density of 10490 kg/m3, edge length of 72.9 nm, and thickness of 10 nm [28]. Figure 4(b) shows the simulated mode profiles of maximal displacements within a vibrational cycle. The simulated mode frequency is 28.7 GHz, which is close to the experimental result. The mode profiles show an in-plane vibration with vertexial expansion and contraction.
Figure 5(a) shows the FWM signal of 53.4 nm nano-octahedrons as a function of the beat frequency between the ECL and DBR lasers. The background signal from Rayleigh scattering of the DBR laser was subtracted. The spectrum shows an acoustic resonance peak at 13.8 GHz with a FWHM of 8.1 GHz. The resonant frequency of the vibrational mode can be approximated by the equation [29]:
where Vl,gold (3240 m/s) is the longitudinal speed of sound in gold and Loctahedron is the edge length of nano-octahedrons. The calculated mode frequency for a gold nano-octahedron with a 53.4 nm edge length is 14.4 GHz, which is close to the experimental value (13.8 GHz). Similar to Eq. (2), the calculated FWHM is 3.2 GHz, which is much smaller than the experimental FWHM of 8.1 GHz. We also note that there is asymmetry in the lineshape. We do not have a suitable explanation for the increased linewidth and asymmetric lineshape observed. The inset shows the simulated mode profiles of maximal displacements within a vibrational cycle. Parameters used in the simulation are gold’s Young’s modulus of 42 GPa, Poisson’s ratio of 0.43, density of 19300 kg/m3, and edge length of 53 nm [30]. The mode profiles show an extensional vibration of longitudinal expansion combined with transverse contraction and vice versa.Fig. 5 FWM signal of gold nano-octahedrons with different sizes: (a) 53.4 nm average edge length with a resonance at 13.8 GHz. The inset shows the simulated mode profiles of maximal displacements with a mode frequency of 13.3 GHz within a vibrational cycle. The solid lines indicate the outlines of the undeformed nano-octahedrons; (b) 43.2 nm average edge length with a resonance at 18.2 GHz; (c) 36.1 nm average edge length with a resonance at 21.9 GHz. The error bar represents the standard deviation calculated by 148 data points at each beat frequency. The dashed line indicates the theoretically calculated resonant frequency according to the SEM result. The grey area indicates the broadening induced by the size distribution. (d) Inverse dependency of the mode frequency on the edge length.
We also performed the FWM measurement on smaller nano-octahedrons as shown in Figs. 5(b) and 5(c). The dashed line indicates the theoretically calculated resonant frequency according to the SEM result. The grey area indicates the broadening induced by the size distribution. We note that the asymmetry in the lineshape disappeared as the mode frequency increases. Figure 5(d) compares the experimental data with the theoretical approximation and the simulation result, validating the inverse dependency of the mode frequency on the edge length. The acoustic mode information of nano-octahedrons with different sizes is summarized in Table 1.
Table 1. Acoustic mode information of nano-octahedrons with different sizes
The FWM technique has two advantages over the extinction spectroscopy: more sensitive about the nanoparticle size and capable of providing the size distribution information. For example, with a 48% size change (36.1–53.4 nm) for nano-octahedrons, the FWM spectra show a 47% peak shift (21.2–14.4 GHz) compared to only a 4% peak shift (551–575 nm) in extinction spectra. The FWM linewidth can provide the size distribution information while the extinction linewidth cannot since the extinction linewidth (affected by nanoparticle’s scattering and absorption) is mainly from homogeneous broadening. By contrast, the FWM linewidth is mainly from inhomogeneous broadening. Our previous FWM measurement on more homogeneous samples shows a much narrower linewidth [22]. Single nanoparticle acoustic vibrations have also been investigated using an optical tweezers setup and the result shows a very narrow linewidth as well [31]. These results imply that homogeneous broadening is negligible and the linewidth of the nanoparticle ensemble via FWM is from inhomogeneous broadening which is due to the size distribution.
4. Conclusion
We used a FWM setup to probe the acoustic vibrations of silver nanoprisms and gold nano-octahedrons in aqueous solution. We observed two acoustic vibrational modes: an in-plane mode of nanoprisms with vertexial expansion and contraction; an extensional mode of nano-octahedrons with longitudinal expansion and transverse contraction. FEM simulations were performed to illustrate the mode profiles. Theoretical approximations were investigated, showing the inverse dependence of the mode frequency on the inverse of the edge length, for both nanoprisms and nano-octahedrons.
Funding
Materials for Enhanced Energy Technologies NSERC CREATE program; NSERC Discovery Grant program; Chinese Scholarship Council.
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