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We demonstrate continuous-wave four-wave mixing to probe the acoustic vibrations of gold nanorods in aqueous solution. The nonlinear optical response of gold nanorods, resonantly enhanced by electrostriction coupling to the acoustic vibration modes, shows an extensional vibration which combines an expansion along the long axis with a contraction along the short axis. We also observed the extensional vibration of gold nanospheres as byproducts of the gold nanorod synthesis. Theoretical calculation of the nanoparticle size and distribution based on the vibrational frequency agrees well with the experimental results obtained from the scanning electron microscopic examination, indicating the four-wave mixing technique can provide in situ nanoparticle characterization.
© 2016 Optical Society of America
1. Introduction
Gold nanorods find broad applications in bioimaging, biosensing, cancer diagnostics and therapy, catalysis, optical storage, and nonlinear optics [1–8]. Accurate characterization of gold nanorods is important since the unique optical, electronic, and mechanical properties are strongly size and shape depend [9–11]. The common characterization methods include the extinction measurement and the direct imaging by scanning or transmission electron microscopy (SEM, TEM) [12–15]. Gold nanorods have two localized surface plasmon resonance (LSPR) bands, corresponding to the longitudinal LSPR (along the long axis) band and the transverse LSPR (along the short axis) band [16]. The longitudinal band, which can be tuned from visible to near-infrared region, exhibits linear dependence on the aspect ratio (length/width) while the transverse band is insensitive to the size [17]. Therefore, the extinction spectrum which shows the LSPR bands can provide information about the aspect ratio only. SEM or TEM characterization is still needed for further determination of the length, width, and size distribution.
The study of the acoustic vibrations of metal nanoparticles can provide insight into the mechanical properties of these nanostructures since the acoustic resonance is dependent on the size, shape and elastic properties of the material [18–20]. The acoustic vibrations of gold nanorods have been extensively studied by the time-resolved pump-probe spectroscopy [21–24]. In a typical pump-probe experiment, an ultrafast laser is required to provide the pump pulses to excite the acoustic vibrations of the sample. After a controlled delay, the optical response of these vibrational modes is measured by recording the extinction or transmission change of the probe pulses. Experimental results exhibit two distinct vibrational modes of gold nanorods: an extensional mode which combines an expansion along the long axis with a contraction along the short axis; a breathing mode which consists of radial expansion and contraction [25]. The resonant frequency of the extensional mode shows linear dependence on the reciprocal of the length while the resonant frequency of the breathing mode shows linear dependence on the reciprocal of the width for a given material [26]. Therefore, analysis of the vibrational modes can provide information about the size and distribution of gold nanorods. It is believed that high peak power of the pump laser is crucial for vibrational modes excitation and appreciable optical response detection.
Our recent report on the acoustic vibrations of individual dielectric nanoparticles and proteins in an optical trapping setup shows that large response can be obtained even using relatively weak continuous-wave (CW) lasers [27]. This suggests that the acoustic vibrations of metal nanoparticles could also be studied without ultrafast lasers. Therefore, here we investigate a four-wave mixing (FWM) setup using CW lasers to probe the acoustic vibrations of gold nanorods in aqueous solution. We perform measurements on gold nanorod samples of three different aspect ratios. We observe two different vibrational modes: one extensional mode from gold nanorods; the other extensional mode from gold nanospheres as byproducts of the gold nanorod synthesis. We calculate the size and distribution based on an established model and compare them with the SEM results. Good agreement between the theoretical and experimental results shows the FWM method can serve as a new technique for nanoparticle characterization.
2. Experiments
Figure 1 shows the CW FWM experimental setup. The sample placed in a quartz cuvette was illuminated by the counter-propagating optical beams composed of a CW tunable external-cavity laser (ECL) (DL100, Toptica Photonics) and a CW tunable distributed Bragg reflector laser (DBRL) (DBR852P, Thorlabs). The polarization of the DBRL beam was adjusted by a polarization controller and a polarizer to ensure co-polarized illumination. 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 4° to allow the full coverage of the cuvette thickness (1 mm) as the light-matter interaction region. The interference between the two counter-propagating beams (I2 at frequency ω2 and I3 at frequency ω3) imposes an electrostrictive force that stetches gold nanorods along the beam polarization. When the beat frequency (ω3 − ω2) matches the acoustic resonance, the acoustic vibrations of gold nanorods will be resonantly excited, resulting a travelling periodic variation in refractive index of the medium (similar to a moving Bragg grating). The FWM signal wave I4 at frequency ω4 (ω4 = ω2) is then created as the beam I1 at frequency ω1 (ω1 = ω3) diffracts from the Bragg grating. An optical chopper was used to modulate beam I2. The FWM signal was measured by an avalanche photodetector (APD120A, Thorlabs) connected to a lock-in amplifier (SR510, Stanford Research Systems). The power of the ECL was set to 67 mW and the wavelength was fixed at 853.4 nm. The power of the DBRL was set to 25 mW 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 CW FWM experimental setup. ECL: extermal cavity laser; BS: beam spliter; MR: mirror; IRS: iris; APD: avalanche photodetector; LA: lock-in amplifier; L1: lens1 (20 cm focal length); L2: lens2 (4 cm focal length); DBRL: distributed Bragg reflector laser; PC: polarization controller; FC: fiber coupler; OSA: optical spectrum analyzer; BLR: blocker; OC: optical chopper; POL: polarizer; FPC: fiber-port collimator.
The extinction spectra of gold nanorod samples of three different aspect ratios in aqueous solution (A12-10-780, A12-10-808, and A12-10-850, Nanopartz) were obtained by a SpectraMax M5 multi-mode microplate reader. The SEM images of gold nanorods were obtained by a Hitachi S-4800 field emission SEM at 2kV. Gold nanorods were drop-coated and dried on an aluminum stage for the SEM imaging.
3. Results
Figure 2 shows the extinction spectra of gold nanorods of three different aspect ratios in aqueous solution. The longitudinal LSPR peaks locate at 780, 800, and 830 nm while the transverse LSPR peaks locate at 512 nm. The longitudinal LSPR peak position has a linear correlation with the aspect ratio. According to the published results [17], gold nanorods with longitudinal LSPR peaks locating at 780, 800, and 830 nm have aspect ratios of 3.8, 4.0, and 4.3, respectively.
Fig. 2 Extinction spectra of gold nanorods of three different aspect ratios in aqueous solution. The longitudinal LSPR peaks locate at 780, 800, and 830 nm for aspect ratios of 3.8, 4.0, and 4.3, respectively. The transverse LSPR peaks locate at 512 nm.
Figure 3(a) shows the SEM image of gold nanorods of a 3.8 aspect ratio obtained at 2 kV and 700000 × magnification. The spherical byproducts can be clearly seen in the image. We manually measured 32 nanorods and 32 nanospheres from the SEM image to obtain the size distribution. Histograms were fitted by Gaussian distribution. Results show that the nanorods have an average length of 38.2 ± 3.0 nm and an average width of 10.0 ± 1.0 nm. The aspect ratio is 3.82, which matches the value obtained from the extinction spectrum. The coexisting nanospheres have an average diameter of 14.0 ± 2.1 nm. The errors represent the standard deviation. We performed the same characterization on the other two aspect-ratio nanorod samples. Table 1 summarizes the size information of the three different aspect-ratio samples based on SEM characterization.
Fig. 3 (a) SEM image of gold nanorods of a 3.8 aspect ratio obtained at 2 kV and 700000 × magnification. (b) Length distribution of gold nanorods. (c) Diameter distribution of gold nanospheres as the byproduct. (d) Width distribution of gold nanorods. Histograms were fitted by Gaussian distribution. The errors represent the standard deviation. The inset images are the SEM images of a single nanorod and nanosphere with a 25 nm scale bar.
Table 1. Size information of three different aspect-ratio nanorod samples.
Figure 4(a) shows the FWM signal of the 3.8 aspect-ratio nanorod sample collected by an APD 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. Two acoustic resonance peaks were found at 20.0 GHz with a full width at half maximum (FWHM) of 4.0 GHz and 74.0 GHz with a FWHM of 20.0 GHz. The 20.0 GHz resonance corresponds to the frequency of the extensional mode of gold nanorods. For a cylindrical rod of a length L and a width W, the extensional and breathing mode frequencies in free space can be estimated by the following equations [26]:
where the non-negative integer n is the extensional mode number (for the fundamental extensional mode, n = 0), E (42 GPa) is the Young’s modulus along the long axis [28], and ρ (19300 kg/cm3) is the density of gold [29]. It should be noted that the Young’s modulus for nanoparticles is different from the bulk material [30]. νl (3240 m/s) is the longitudinal sound velocity in gold [29], and φ (2.28 for the fundamental breathing mode) is an eigenvalue that depends on the transverse and longitudinal sound velosities in gold [31]. The calculated fundamental extensional mode frequency for a gold nanorod of a 38.2 nm length is 19.3 GHz, which is close to the experimental value 20.0 GHz. The size distribution of gold nanorods mainly contributes to the broadening of the resonance peak. The spectral linewidths of the lasers (DL100 Toptica Photonics and DBR852P Thorlabs) used are in the MHz range and so they contribute negligibly to the broadening. According to Eq. (1) and assuming a Gaussian size distribution, FWHM can be calculated by:where and σ is the standard deviation. The calculated FWHM is 3.6 GHz, which agrees well with the experimental FWHM of 4.0 GHz. The calculated fundamental breathing mode frequency for gold nanrods of 10.0 ± 1.0 nm width is 235.3 GHz with a FWHM of 55.4 GHz. However, we did not observe the breathing mode in that frequency range.Fig. 4 (a) FWM signal of the 3.8 aspect-ratio nanorod sample as a function of the beat frequency between the ECL and DBR lasers. The error bar stands for the standard deviation calculated by taking 148 data points at each beat frequency. The 20.0 and 74.0 GHz resonance peaks correspond to the frequencies of the extensional modes of gold nanorods and nanospheres, respectively. The dashed line indicates the calculated resonant frequencies of 19.3 and 72.6 GHz according to the SEM results. The grey area indicates the broadening (3.6 GHz for the nanorod extensional mode and 25.6 GHz for the nanosphere extensional mode) induced mainly by size distribution. The inset images are the SEM images of a single nanorod and nanosphere with a 25 nm scale bar. (b) Comparison of experimental data with theoretical predictions for different aspect-ratio gold nanorod samples.
The 74.0 GHz resonance corresponds to the frequency of the extensional mode of gold nanospheres. For a sphere with a diameter D, the extensional and breathing mode frequencies in free space can be estimated by Lamb’s theory [32]:
where νl (3240 m/s) is the longitudinal sound velocity in gold [29]. ξ (0.985 for the fundamental extensional mode) and η (2.945 for the fundamental breathing mode) are proportionality factors calculated by the equations derived in [33] under the free boundary condition. For gold nanospheres of 14.0 ± 2.1nm diameter, the calculated fundamental extensional mode frequency is 72.6 GHz with a 25.6 GHz FWHM, which agrees well with the experimental value of 74.0 GHz with a 20.0 GHz FWHM. We did not observe the breathing mode which should locate at 217.1 GHz with a 76.7 GHz FWHM based on Eq. (5).We performed FWM measurements on different aspect-ratio gold nanord samples. Figure 4(b) shows the experimental data matches well with the theoretical predictions based on Eqs. (1) and (4). Tables 2 and 3 summarize the acoustic vibrational mode information of diffenent nanorods and coexisting nanospheres, respectively. Calculations are based on the size information shown in Table 1. We also performed the FWM measurement on commercial gold nanoshperes (EM.GC20, BBI Solutions) with an average diameter of 20.0 ± 1.5 nm for further verifying the origin of the higher frequency mode. We observed a 49.4 GHz mode which fits well with Eq. (4), confirming that the higher frequency mode in Fig. 4 is the fundamental extensional mode of nanospheres.
Table 2. Fundamental acoustic vibrations of different aspect-ratio nanords.
Table 3. Fundamental acoustic vibrations of coexisting nanospheres.
4. Discussion
The assignments of the FWM peaks to the corresponding vibrational modes were made based on best matches in theoretical analysis, and confirmed with SEM images. For 3.8 aspect-ratio nanorod sample, according to the resonant frequency and linewidth information from the FWM curve, calculations based on Eqs. (1) and (4) show that the nanorods have an average length of 36.9 ± 3.1 nm and the nanospheres have an average diameter of 13.7 ± 1.6 nm. Using the aspect ratio of 3.8 obtained from the extinction spectrum, the calculated width of the nanorods is 9.7 ± 0.8 nm. These values agree well with the experimental results shown in Table 1.
Disregarding nanoparticles of irregular shape in the sample, the relative concentrations of nanorods and coexisting nanospheres are around 80% and 20% of the total number of nanoparticles, respectively. The concentration difference may induce the intensity difference between the nanorod and the nanosphere extensional modes shown in Fig. 4. Although the concentration ratio (nanorod/nanosphere) matches the FWM intensity ratio, we cannot exclude other factors that may cause the intensity difference, such as nanorod orientation in solution and LSPR difference. It should be noted that the laser wavelength is far away from the LSPR of nanospheres. The off-resonance excitation can still induce considerable FWM signal. Further studies are needed to quantitatively investigate the influence of the excitation wavelength on the FWM signal.
Despite the small differences from the SEM imaging results, the FWM measurement shows the potential to acquire the size and distribution information of gold nanoparticles accurately. The FWM technique has its unique advantages, such as the ability of characterizing nanoparticles in solution compared to SEM or TEM which is difficult to image liquid samples. It should be noted that the reliance of the extinction spectrum to obtain the aspect ratio could be avoided if the nanorod breathing mode could be observed since the breathing mode provides the width information of nanorods. However, we did not observe the breathing mode in nanorods or coexisting nanospheres. The absence of the breathing mode might be caused by the failure of exciting the mode under the current excitation condition. Higher laser power may be required to excite this breathing mode.
5. Conclusion
We used a FWM setup to investigate the acoustic vibrations of gold nanorods in aqueous solution. We obtained the size and distribution information based on the analysis of the vibrational modes. Good agreement was achieved between the calculated values and the experimental results obtained from the SEM imaging, showing potential of the FWM method as an accurate and convenient tool for nanoparticle characterization in situ.
Acknowledgment
The authors acknowledge financial support from the the Materials for Enhanced Energy Technologies NSERC CREATE program, the NSERC Discovery Grant program, and the Chinese Scholarship Council.
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