Coherent Acoustic Phonon Dynamics of Gold Nanorods and

Dec 30, 2013 - The ultrafast dynamics of photoexcited gold nanorods (Au NRs) and gold nanospheres (Au NSs) dispersed in poly(vinyl alcohol) (PVA) film...
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Coherent Acoustic Phonon Dynamics of Gold Nanorods and Nanospheres in a Poly(vinyl alcohol) Matrix and Their Temperature Dependence by Transient Absorption Spectroscopy Li Wang,*,† Shohei Takeda,† Changchun Liu,‡ and Naoto Tamai*,† †

Department of Chemistry, School of Science and Technology, Kwansei Gakuin University, Sanda 669-1337, Japan Department of Mathematics, Jilin University, Changchun 130012, China

‡

S Supporting Information *

ABSTRACT: The ultrafast dynamics of photoexcited gold nanorods (Au NRs) and gold nanospheres (Au NSs) dispersed in poly(vinyl alcohol) (PVA) films were investigated at various temperatures. The extensional mode of the coherent acoustic phonon vibration for Au NRs and breathing mode for Au NSs were both observed. For Au NRs, the vibrational periods in PVA decreased, and those in aqueous solution increased compared to the estimated periods in vacuum. These phenomena were not observed for Au NSs. When the temperature decreased from 296 to 10 K, the vibrational period of Au NRs (9 nm diameter, 46 nm length) decreased by 15%, but the decrease was only 3% for that of Au NSs (108 nm diameter). The environmental effects on coherent acoustic phonon vibrations for Au NRs were discussed in terms of mechanical interaction with the polymer matrix and liquid−solid coupling with the solution. A simplified model for the coupling of a vibrating rod to a viscoelastic environment, called a pile−soil interaction, was introduced for Au NRs in a PVA matrix, and the calculated periods were in good agreement with the experimental data. Our results indicate that viscous effects dominate for nanorods in water, whereas elastic effects dominate in PVA, resulting in frequency shifts with opposite signs. Moreover, because of the different interaction for extensional and breathing modes, the environmental sensitivity of Au NRs is obviously higher than that of Au NSs, and this difference can provide guidelines for mechanical applications of metal−polymer nanocomposites.

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coupling to the environment.9 In the dynamics, coherent acoustic phonon vibrations provide high-frequency oscillations, and metal nanoparticles become available for the applications of G/THz nanoresonators, such as ultrasensitive mass sensors.10,11 The acoustic vibration includes two factors: how fast (period) and how long (damping). In previous reports, the damping of the acoustic vibrations of metal nanoparticles was attributed to inhomogeneous damping of the polydispered ensembles, acoustic energy transfer from the metal nanoparticles to the environment, viscous damping from surrounding fluids, and intrinsic damping of the nanoparticles.12−14 The vibrational period has been discussed in terms of size, shape, elastic property (with a different crystalline structure), and components of the metal nanoparticles.15−19 Analytical expressions of the breathing and extensional modes derived for the bulk are still available for metal nanospheres and nanorods. These expressions are generally obtained for vacuum conditions, and the environmental effects on the vibrational periods were recently discussed. For the breathing mode of

INTRODUCTION Metal nanoparticles have attracted interest because of tunable optical properties and surface-enhanced electromagnetic fields. Their applications include such fields as biosensing and bioimaging, photothermal therapy, waveguiding below the diffraction limit, and surface-enhanced spectroscopies.1,2 With the help of time-resolved spectroscopies, the dynamics of metal nanoparticles can be understood, and the feasibility and availability of their applications can be improved. Time-resolved spectroscopies of various metal nanoparticles have been reported, and the dynamic properties of electrons, phonons, and thermal dissipation have been discussed.3−5 After laser excitation, conduction electrons of metal nanoparticles perform a collective oscillation, that is, localized surface plasmon resonance (LSPR), and then dephasing occurs with a time constant of ∼10 fs due to pure dephasing, radiative decay, and nonradiative decay by intrinsic damping and electron-surface scattering.6,7 If it is a nonradiative decay, the hot electrons are generated by ∼100 fs electron−electron scattering and relaxed by ∼1 ps electron−phonon coupling.8 The following process of ∼10 ps coherent acoustic phonon vibration is induced by hot electron pressure and lattice heating and then damped, which combines with ∼100 ps thermal © 2013 American Chemical Society

Received: October 10, 2013 Revised: December 27, 2013 Published: December 30, 2013 1674

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NR to 4000 PVA. This Au NR solution was spin-casted on a precleaned glass slide and dried in open air for 24 h. Four types of commercially available Au NSs with various diameters were purchased from Aldrich. Au NSs in PVA matrices were prepared with the similar methods for Au NRs. Experimental Apparatus. Au NRs and Au NSs were characterized by using transmission electron microscopy (TEM, FEI TECNAI 20, 200 kV) and/or scanning electron microscopy (SEM, ZEISS SUPRA40, 3 kV). Steady-state extinction spectra were measured by a U4100 spectrophotometer (Hitachi). Transient absorption (TA) spectroscopy was performed for all of the Au NR/NS samples with a conventional pump−probe method previously described.18 The pump beam was the second harmonic (400 nm) generated by a BBO crystal, and the visible or near-IR probe beam was the supercontinuum generated by D2O or a sapphire plate from an 800 nm femtosecond laser (Spitfire, Spectra-Physics, 1 kHz). The transient absorption spectrum of a sample at a certain delay time was obtained by using a 500 Hz chopper on the pump light path that alternately switched to “pump-on” and “pump-off” modes. The relative delay between the pump and probe beams was adjusted by a translation stage. Pump fluence was ∼25.5 μJ cm−2 unless otherwise stated. A closed-cycle He cryogenic system (Daikin Cryotec, V202C5LR) was used for the temperature-dependent measurements down to 10 K.

nanospheres, a weak effect only holds for a homogeneous environment.20 Larger deviations have been observed and predicted in the case of metal nanospheres embedded in a dielectric shell, which provides them with an inhomogeneous environment.21−23 For the breathing mode of nanowires, Major et al. performed ultrafast pump−probe microscopy and continuum mechanics calculations to study the viscosity effect of water on the acoustic vibrations.13 For the extensional mode of nanorods in aqueous solution, the coupling between the deformation of gold nanorods (Au NRs) and the fluid viscous effect should be considered for the acoustic vibration of Au NRs.14,22 In low-viscosity fluids such as water and methanol, the viscous effect on the longitudinal vibration of Au bipyramids was determined experimentally and theoretically, and the resonance frequency was reduced compared to vacuum conditions.14,24 For a solid environment with single Au NRs, Zijlstra et al. reported the oscillation periods (extensional mode) of a large portion of the single NRs deviated from the analytical calculation in vacuum because of the mechanical interactions with the glass substrate.25 However, systematic experimental research of the environmental effects on vibrational frequencies has not often been reported, especially for the extensional mode of metal nanorods embedded in a viscoelastic environment, and the corresponding theoretical explanation still remains an open question. Moreover, there are no reports on the coherent acoustic phonon vibrations of metal−polymer nanocomposites at low temperatures. In this paper, we present the ultrafast dynamics of Au NRs and gold nanospheres (Au NSs) dispersed in polymer films and aqueous solutions. At room temperature, the periods of the coherent acoustic phonon vibrations for Au NRs are significantly affected by the surrounding environments. However, the breathing mode of Au NSs is not affected by the surrounding media. These phenomena were discussed in terms of the environmental effects on the vibrational modes, such as mechanical interactions and liquid−solid couplings. The mechanical interaction for Au NRs and poly(vinyl alchohol) (PVA) films was explained with a coupling model of a vibrating rod in a viscoelastic environment, called a pile− soil interaction. The experimental data and simulation results were in good agreement. Moreover, we first report the ultrafast dynamics of metal nanoparticles at low temperatures. With decreasing temperature, the mechanical interaction of PVA films induced a large variance for the vibrational periods of Au NRs compared to that for Au NSs and the bulk. Additionally, the time constants of the electron−phonon coupling of Au NRs decreased with decreasing temperature. Our approach indicates that Au NRs are more sensitive to the surrounding environments compared to Au NSs and more suitable for mechanical applications of metal−polymer nanocomposites as nanotransducers.

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RESULTS AND DISCUSSION Characterization of Au NRs and Au NSs in PVA Matrices and Aqueous Solutions. A representative TEM image of Au NRs is shown in Figure 1a. The diameter and

Figure 1. TEM image of Au NRs with 9 nm diameter and 46 nm length (a) and normalized extinction spectra of the Au NRs embedded in a PVA matrix and dispersed in aqueous solution (b).

length of Au NRs are around 9 and 46 nm based on the fitting of histograms for over 100 nanorods using log-normal distribution functions. The TEM images for other samples and the corresponding histograms are shown in Figure S1 (Supporting Information). The average length, diameter, and aspect ratio of five Au NRs with standard deviations are listed in Table 1. In addition, the diameters of four types of Au NSs are estimated to be 20 ± 2, 44 ± 5, 65 ± 7, and 108 ± 11 nm from SEM measurements. The extinction spectra of Au NRs with 46 nm length in a PVA matrix and aqueous solution are shown in Figure 1(b). Both transverse- (T-) and longitudinal- (L-) surface plasmon modes for Au NRs in the PVA matrix are red-shifted compared to the Au NR aqueous solution. The peak wavelength of the Lmode shifts from 922 to 978 nm, and the full width at halfmaximum (fwhm) broadens from 282 to 342 meV. The difference in the refractive index between the PVA matrix (n =

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EXPERIMENTAL SECTION Sample Preparation. Five types of Au NRs with various aspect ratios and lengths were synthesized by the combination of chemical reduction and photochemical reactions (a joint research project between Mitsubishi Materials Corp. and DaiNippon-Toryo Co., Ltd.).26 A 1 mL Au NR solution was transferred to a 1.5 mL Eppendorf tube and purified by centrifugation at 12 000 rpm for 15 min to remove any excess hexadecyltrimethylammonium bromide (CTAB) surfactant. This was repeated three times. The pellet was dispersed in a 2 wt% PVA aqueous solution, resulting in a molar ratio of 1 Au 1675

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both Au NRs and Au NSs is observed. However, the bleaching peak wavelengths for Au NRs are red-shifted with the increase of delay time while blue-shifted for Au NSs. For Au NRs, the LSPR band is considerably affected by lattice heating, and the extended length of the Au NR results in red-shifted spectra. For Au NSs, it might be more sensitive to hot electron pressure, and the expanded LSPR band gives blue-shifted TA spectra (Figure S4, Supporting Information). Second, the oscillation of the bleaching peaks corresponds to the extensional mode of the coherent acoustic phonon vibration for Au NRs and the breathing mode for Au NSs. The oscillation periods for Au NRs in a PVA matrix and in aqueous solution are rather different, whereas those for both Au NS systems are very similar. To analyze the time dependence of the bleaching peaks, the data were fitted to the following function, and the fitting results are listed in Table 230

Table 1. Dimensions and Corresponding Standard Deviations for Five Samples of Au NRs length (nm) Au Au Au Au Au

NR NR NR NR NR

1 2 3 4 5

12 40 46 55 66

± ± ± ± ±

3 6 6 8 14

diameter (nm) 5 9 9 9 8

± ± ± ± ±

1 1 1 2 2

aspect ratio 3 4 5 6 8

± ± ± ± ±

1 1 1 1 2

1.53) and aqueous solution (n = 1.33) is one of the reasons for the red-shift of the L-mode because the LSPR band is sensitive to the dielectric constant of the surrounding medium.3 The formation of a percolated network with end-by-end arrangement of Au NRs in a polymer matrix may be a possible reason for the broadening and also for the red shift.27,28 The extinction spectra of other Au NRs and Au NSs in PVA matrices and in aqueous solutions showed similar tendencies and are illustrated in Figure S2 (Supporting Information). Transient Absorption Measurements for Au NRs and Au NSs in PVA Matrices and Aqueous Solutions. Near-IR TA spectra of Au NRs in a PVA matrix (46 nm length) at various delay times are shown in Figure 2a. TA spectra for Au NRs in solution and both Au NS (65 nm diameter) systems are shown in Figure S3 (Supporting Information). The bleaching peaks are a little shifted from the plasmon peaks of the corresponding L-modes, and the absorption bands are observed at both sides of the bleaching peaks. These TA spectral features are induced by the broadening and red-shift of the L-mode plasmon band originating from hot-electron pressure and thermal expansion of Au lattices.29 Time dependences of the bleaching peak wavelengths were obtained by fitting some of the Gaussian functions to TA spectra. As in our previous analysis for Au−Ag core−shell NRs,18 the evolution of the bleaching peak shift was used as a representative to avoid a wavelength dependence of the vibrational period for polydispersed Au NRs. The fitting results for Au NRs and Au NSs dispersed in PVA matrices and in aqueous solutions are shown in Figures 2b−2e. The time scale for Au NRs is 1−200 ps and 0.5−100 ps for Au NSs. The damping and periodical oscillation of the bleaching peak wavelengths can be easily observed. First, the amplitude damping of the bleaching peak wavelengths for

R(t ) = Ae − p exp( −t /τe − p) + Acool exp(−t /τcool) + A v exp[−(t /τv)2 ]cos(2πt /T + φ) + Baseline (1)

Table 2. Time Constant of Thermal Cooling Processes, Amplitudes, and Periods of Oscillation of Bleaching Peaks and Quality Factors for Au NRs (9 nm Diameter, 46 nm Length) and Au NSs (65 nm Diameter) in PVA Matrices and Aqueous Solutions τcool (ps) NRs NSs

PVA water PVA water

42.9 ± 1.5 64.6 ± 2.5 − −

Aν (nm) 11 20 2.4 2.6

± ± ± ±

1 2 0.3 0.3

T (ps) 40.5 65.2 21.5 21.3

± ± ± ±

0.5 0.7 0.1 0.1

Q 9.0 5.4 6.1 6.1

± ± ± ±

0.8 0.5 0.5 0.4

where Ax is the amplitude; τx is the time constant; T is the period of the coherent acoustic phonon vibration; φ is the phase of the vibration; and Baseline is the central bleaching peak wavelength of the oscillation. The first term (subscript e− p) is assigned to the electron−phonon coupling process. The fitted coupling time constants are not discussed here.31 The second term (subscript cool) is related with the cooling process of thermal transfer from metal nanoparticles to the environ-

Figure 2. Transient absorption spectra of Au NRs (9 nm diameter, 46 nm length) dispersed in a PVA matrix at different delay times (a) and oscillations of bleaching peaks for Au NRs and Au NSs (65 nm diameter) dispersed in PVA matrices (b and d) and dispersed in aqueous solutions (c and e). 1676

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Figure 3. Experimental periods of coherent phonon vibration were plotted as a function of Au NR length (a) and Au NS diameter (b) by filled and empty symbols, respectively. The samples were embedded in PVA matrices (squares) and in aqueous solutions (circles). The periods were calculated by using Young’s modulus of bulk Au with [100] growth direction E[100] = 42 GPa (filled triangles in (a)) and longitudinal sound velocity of bulk Au cl = 3240 m·s−1 (empty triangles in (b)). The simulated periods based on a coupling model of a vibrating rod to a viscoelastic environment (a pile− soil interaction) are plotted with the solid lines from top−down corresponding to Au NR diameter of 20, 10, and 7 nm (a).

detectable oscillations, can be discussed for different systems. Q = πτν/T, where τν is the damping constant and T is the oscillation period. For both Au NRs and Au NSs, Q values are not significantly affected by the environment, as listed in Table 2 and shown in Figure S7b (Supporting Information). In our ensemble experiments, the inhomogeneous broadening of the size polydispersity may have a large contribution and obscure the environmental effect on Q.34 As shown in Table 2, the oscillation period for Au NRs in a PVA matrix (40.5 ps) is 38% smaller than the period for the Au NR solution (65.2 ps). However, the oscillation periods are similar for both Au NS systems, 21.5 and 21.3 ps, respectively. The relationship between the experimental periods and sizes of the Au NRs or Au NSs is plotted in Figure 3a or 3b, respectively.35 The oscillation periods of the breathing mode for Au NSs in a PVA matrix with various diameters are similar to those in solution and are in good agreement with the analytical estimation (empty triangles in Figure 3b)36

ment. For Au NRs in a PVA matrix, the cooling time constant (43 ps) is much faster than in solution (65 ps). The thermal cooling process is dependent on heat transfer across the interface between the particle and its surroundings and on heat diffusion in the surroundings. Interface thermal resistance is dependent on the acoustic impedance of the surroundings, which is similar for PVA (∼2.5 MPa·m·s−1) and water (∼1.5 MPa·m·s−1).32 However, thermal diffusivity for PVA (3.95 mm2·s−1) is much higher than that for water (0.14 mm2·s−1),33 which might be the reason for the faster thermal cooling process of Au NRs in a PVA matrix. However, the second term can be neglected in the fitting for both Au NS systems. The cooling process of Au NSs may be vaguely reflected by the dynamics of bleaching peaks because their LSPR wavelengths are not as sensitive to the size variation induced by lattice heating as those of Au NRs. Moreover, the cooling time scale is usually several hundred picoseconds, but the time window discussed here is much shorter and does not completely include the cooling process. The third term (subscript ν) is assigned to the process of the coherent acoustic phonon vibration, and T is the period. As listed in Table 2, the oscillation amplitude of bleaching peaks (Aν) for the Au NRs is about 11 nm in a PVA matrix and 20 nm in aqueous solution. However, similar amplitudes are observed for Au NSs in a PVA matrix (2.4 nm) and in aqueous solution (2.6 nm). The dynamics of bleaching peaks for other Au NRs and Au NSs are illustrated in Figures S5 and S6 (Supporting Information), and the fitting results of the oscillation amplitudes (Aν) are summarized in Figure S7a (Supporting Information). Similar results are obtained for other Au nanoparticles. The surrounding environment has an obvious effect on the oscillation amplitudes of Au NRs but not on Au NSs. The oscillation amplitude of the bleaching peaks is due to the shift of the LSPR bands during the process of coherent phonon vibration and corresponds to the structural deformation of metal nanostructures induced by lattice heating. As shown in Figure S8 (Supporting Information), Aν and Baseline increase with the increase in excitation intensity and hence the lattice temperature of Au NRs. Moreover, as discussed above, the cooling process is much faster for Au NRs in a PVA matrix, and the lattice temperature could be much lower than those for the solution samples. Therefore, the oscillation amplitudes of Au NRs may be related to the lattice temperature and hence the variation of the surrounding environment. For environments with different phases, it is difficult to compare the damping constant (τν) directly. The quality factor (Q), the number of

T = πD/(χ0 c l)

(2)

where D is the particle diameter; cl is the longitudinal sound velocity of bulk Au; and χ0 is an eigenvalue of a vibrational mode (Table S1, Supporting Information). For metal nanospheres embedded in a solid matrix, it was proven that the effect of the embedding matrix on the oscillation period of the breathing mode is less, both experimentally and theoretically.20,37−39 Interestingly, the weak environmental dependence of the nanosphere breathing frequencies only holds for a homogeneous environment. Larger deviations have been observed and predicted in the case of metal nanoparticles embedded in a dielectric shell, which thus provides them with an inhomogeneous environment.22,40 We also obtained weak environmental effects using a numerical calculation of the oscillation period of the breathing mode for Au NSs in free surroundings, a PVA-, and a glass-matrix as shown in Figure S10 (Supporting Information). Here, the crystallinity of Au NSs is a negligible factor because it has almost no effect on the period of the fundamental breathing mode.41,42 Au NRs were synthesized as previously described and confirmed to be single crystals with [100] growth direction.18 The period of the extensional mode for Au NRs can be estimated by the analytical expression (filled triangles in Figure 3a)15

Text = 2L / E /ρ 1677

(3)

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where L is the length of the nanorod; E is the Young’s modulus of a Au single crystal with [100] growth direction (42 GPa); and ρ is the density (19.7 g·cm−3). The vibrational periods of Au NRs in PVA matrices are smaller than the calculations, whereas those of Au NRs in aqueous solution have larger values, as illustrated in Figure 3a. It is very clear that the vibrational periods of Au NRs deviate from the analytical calculations depending on the surrounding environments. Note that the dipole coupling does not affect the period of the coherent acoustic phonon vibration. In previous research on periodic Au pair nanocuboids, we found that the vibrational period of the fundamental breathing mode was not influenced when the nanogap and the separation were varied.43,44 The experiments were also done with different concentrations of Au NRs in PVA films, as shown in Figure S9 (Supporting Information). For the highly concentrated Au NRs, the LSPR band was slightly red-shifted and significantly broadened, and hence the bleaching peak wavelength red-shifted correspondingly. Even though the LSPR band was affected by the dipole coupling between Au NRs in PVA films, the vibrational period was not changed. Therefore, in our experimental data, the simple aggregation of Au NRs does not impact the vibrational period. We think the effect of the surrounding environment such as aqueous solutions, glass substrate, and PVA polymer should be considered as a reason for the variance in the extensional period of Au NRs. In aqueous solutions, the liquid− solid coupling between the viscous fluid dynamics and the deformation of Au NRs has been reported.14,24 The vibrational frequency for nanorods in a fluid was reduced compared to that in vacuum. This tendency is in good agreement with the experimental results of Au NRs in aqueous solutions. For a solid environment, the mechanical interaction for a single Au nanorod with the glass substrate has been mentioned but not theoretically explained.25 For metal nanostructures with particle sizes larger than a few hundred atoms, the standard theory of the elastic properties of bulk materials is still applicable.15,45 The discussion for the extensional mode of a vibrating rod (a pile) in a viscoelastic environment (a soil) can be applied to Au NRs in a PVA matrix as shown in Scheme 1.46 The displacement, u(x,t), of the free

interaction with a PVA polymer can be represented by a simple equivalent model of a parallel connection of a linear spring (the second term in the right side of eq 4) and a linear damping (the third term), corresponding to its elastic (K1 = 2.75Gs) and viscous (K2 = πd(ρsGs)1/2) properties.47 The interaction was only considered at the side of the rod and neglected at its ends because of the assumption of D ≪ L. Gs and ρs are the shear modulus (1.97 GPa) and density (1.003 g/cm3) of PVA, and d is the diameter of the Au NR.48 Therefore, the solution for a rod free at both ends is given by (see Supporting Information) ∞

un(x , t ) =

2

n=1

cos

(2n + 1)πx L

(5)

where ωn is the vibrational frequency and is given by ωn =

2 ⎛ K ⎞2 K E ⎛ (2n + 1)π ⎞ ×⎜ ⎟ + 1 −⎜ 2 ⎟ ⎠ ρ ⎝ ρA ⎝ 2ρA ⎠ L

(6)

where n = 0, 1, 2, ... and Cn and Dn are constants determined by the boundary condition. Therefore, the fundamental frequency ω0 is expressed by ω0 =

(ω0,vaccum)2 +

Gs × (2.75ρ − πρs ) ρ2 A

(7)

We simulated the values for the Au NR with diameters of 20, 10, and 7 nm as shown in Figure 3a. The elastic effect of the PVA matrix becomes obvious with a decrease in the diameter, and the calculated periods for 7 nm diameter Au NRs agree with the experimental results for diameters from 5 to 9 nm for Au NRs. The analytical results based on a 1D model show a tendency similar to the experimental data, i.e., that the vibrational periods of Au NRs in a PVA matrix are smaller than those in vacuum. As shown in eq 6, the elastic properties (the second factor) of the matrix increase the vibrational frequency, while the viscous properties (the third factor) decrease the frequency. For Au NRs in a PVA matrix, the elastic properties of PVA have a large contribution to the mechanical interaction, and the vibrational periods become smaller. However, in this model the diameter of the rod is assumed to be much smaller than the length, and the mechanical interaction at the rod tips is not considered. Then it is suitable for a rod with a large aspect ratio but may produce deviations for a rod with a small aspect ratio. However, for a nanorod with a small length, such as Au NR1 (aspect ratio 3), the frequency in vacuum is inversely proportional to the length and hence becomes a large value. Thus, the environmental effect on the frequency becomes small, and the deviation is not obvious for Au NR1. In summary, the vibrational frequency of the extensional mode is influenced by the mechanical interaction of the matrix and related to the elastic and viscous properties of the matrix in which the metal nanorod is embedded. Moreover, as shown in eq 4, the displacement of every small element on the rod for the extensional mode is directly related to the interaction of the surroundings by the second and third terms. For the sphere, the contribution of the surroundings (elastic and viscous properties) is not directly incorporated, but it is reflected in the boundary condition, where the continuity of the displacement and stress at the interface between the sphere and matrix are considered.20,37 Therefore, the different

Scheme 1. Coupling Model of a Vibrating Au NR with Extensional Mode in a Viscoelastic Environment (a Pile− Soil Interaction)a

a The displacement u of a Au NR is affected by elastic force (linear spring K1) and viscous force (linear damping K2).

extensional vibration of an elastic rod (D ≪ L) along the axis X can be expressed by using Newton’s second law of motion as ρAdx

∑ e−K t /2ρA(Cn cos ωnt + Dn sin ωnt )

∂ 2u(x , t ) ∂u(x , t ) ∂σ dx = A dx − K1u(x , t )dx − K 2 ∂t ∂x ∂t 2 (4)

where A is the cross-sectional area; σ is the axial stress; and σA is the tension applied on one end of the hatched element. Here, σ = E·ε = E·∂u/∂x, and ε is the strain. The mechanical 1678

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from eq 7 and is shown in Figure S11 (Supporting Information), which is in good agreement with the general elastic properties of polymers.51,52 Therefore, the mechanical interaction with a PVA polymer might contribute to the large variance of the vibrational periods for Au NRs because of the increased stiffness of PVA with decreasing temperature. Figure 5a illustrates the decay profiles of 46 nm length Au NRs in a PVA matrix at 10 K with a pump fluence of 12.8 and

interactions for the extensional and breathing modes may be the reason for the different environmental effects on nanorods and nanospheres. Temperature Dependence of Elastic Properties and Electron−Phonon Coupling for Au NRs (46 nm Length) and Au NSs (108 nm Diameter) in PVA Matrices. Lowtemperature transient measurements on metal nanoparticles have not been reported as far as we know. Figures 4a and 4c

Figure 5. Decay profiles at the bleaching peak wavelength of Au NRs in a PVA matrix with pump fluences of 12.8 (empty squares) and 50.9 μJ cm−2 (empty circles) at 10 K (a) and pump fluence dependence of ΔOD at bleaching peak wavelength in the inset (empty triangles). Pump fluence dependence of electron−phonon coupling lifetime at 296 K (filled squares) and 10 K (filled circles) (b) and temperature dependence of the lifetime at 25.5 μJ·cm−2 in the inset (filled triangles).

50.9 μJ·cm−2. The intensity of transient absorption (ΔOD) at the bleaching peak wavelength (940 nm) shows a linear relationship with the pump fluence as indicated in the inset of Figure 5a, suggesting that the measurements were performed within the low excitation regime. The lifetimes of electron− phonon coupling for Au NRs in a PVA matrix were obtained from the single exponential fitting of the decay profiles and plotted in Figure 5b. The time constants of e−p coupling were determined from the extrapolation of the lifetimes with the pump fluences and were found to be 1.13 and 0.89 ps at 296 and 10 K, respectively. These time constants are similar to the reported values for large Au NSs and the bulk value of Au.8 Moreover, the temperature dependence of the e−p coupling lifetime is shown in the inset of Figure 5b and is in agreement with the report for Au films.53 When the temperature decreases from 296 to 10 K, the lifetime of the e−p coupling has a nearly linear decrease due to the decrease of the electronic specific heat if the e−p coupling constant g is considered to be a constant.

Figure 4. Time dependence of bleaching peaks (scatters) with fitting curves (solid lines) (a and c) and the vibrational period (filled squares) (b and d) for Au NRs and NSs in PVA matrices at different temperatures. The calculated periods from Young’s modulus of the Au single crystal with [100] growth direction and of Au polycrystal are also shown in b and d (empty circles). The solid lines are only for visual guides (b and d).

show the oscillation behaviors of the bleaching peaks for Au NRs and Au NSs embedded in PVA matrices at various temperatures. The vibrational period was 15% less, from 40.5 to 34.3 ps, for Au NRs and 3% less, from 35.6 to 34.6 ps, for Au NSs, with decreasing temperature. For bulk Au, E[100] was calculated using the elastic constants49 and increased from 42.7 to 46.5 GPa as the temperature decreased from 296 to 10 K. Thus, the period of an extensional mode for a 46 nm rod was estimated to decrease by 4%, from 62.6 to 59.9 ps (the size variation can be neglected within the investigated temperature range).50 The longitudinal sound velocity was estimated to be increased, from 3040 to 3162 m·s−1, when the calculated E[polycrystalline] stiffened from 80.2 to 86.8 GPa as the temperature decreased from 296 to 10 K.49 Thus, the period of breathing mode for a 108 nm sphere is calculated to decrease by 4%, from 38.0 to 36.5 ps, accordingly. The experimental and calculated periods are plotted in Figures 4b and 4d for the rods and spheres, respectively. The temperature dependence of the vibrational period for Au NRs is much pronounced in contrast to the calculated period of bulk Au, but for Au NSs, it is comparable to the dependence of polycrystalline Au. This might be due to the increased stiffness of PVA with decreasing temperature. The temperature dependence of Gs was calculated

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CONCLUSIONS We measured the coherent acoustic phonon vibrations of Au NRs and NSs with variations in the surrounding environments and temperatures. We observed that the vibrational periods of the extensional modes of Au NRs are affected by the environment. Different physical (elastic and viscous) properties of the embedded environment should be considered in the coupling interaction with the vibrating Au NRs. Because of the liquid−solid coupling, the periods for Au NRs in aqueous solutions become larger than the calculated values in vacuum, where the viscous property of water is mainly considered. For the case of Au NR−PVA nanocomposites, the vibrational 1679

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periods become smaller, and the elastic property of PVA is the main influence factor. The mechanical interaction between Au NRs and PVA polymer was explained by the coupling of the vibrating rod to a viscoelastic environment, called a pile−soil interaction. When the temperature was decreased from 296 to 10 K, the large decrease in the periods of Au NRs is also caused by the mechanical interaction with the stiffened PVA matrix. Moreover, the electron−phonon coupling time constant of Au NRs becomes smaller with decreasing temperature. However, for Au NSs, the periods of the breathing modes were not much influenced by the surrounding environments, and the temperature dependence was similar to that of bulk Au, which may be related to the different interaction of the surroundings for the breathing mode. Therefore, the coherent acoustic phonon vibrations of Au NRs are obviously more sensitive to the environments compared to those of Au NSs. The mechanical applications of metal NRs in devices such as nanotransducers and THz resonance generators are particularly interesting with regard to environmental sensitivity, in contrast to those of metal NSs.

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ASSOCIATED CONTENT

S Supporting Information *

TEM images of four types of Au NRs and their histograms, steady-state extinction spectra of Au NRs and Au NSs and their transient absorption spectra, oscillation dynamics of the bleaching peaks and fitting results, pump fluence dependence and concentration dependence of Au NRs, numerical simulations of the periods of the breathing mode of Au NSs, and temperature dependence of shear modulus of PVA. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is partially supported by a Grant-in-Aids for Scientific Research from the Japan Society for the Promotion of Science (KAKENHI), Grant No. 22350012, Japan.

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REFERENCES

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