Transient Absorption Studies of Single Silver Nanocubes - American

There is only a weak correlation between the damping times and the periods. This implies that damping is affected by the particle's local environment ...
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2008, 112, 7535–7539 Published on Web 04/30/2008

Transient Absorption Studies of Single Silver Nanocubes Hristina Staleva and Gregory V. Hartland* Department of Chemistry and Biochemistry, 251 Niewland Science Hall, UniVersity of Notre, Notre Dame, Indiana 46556-5670 ReceiVed: February 21, 2008; ReVised Manuscript ReceiVed: April 14, 2008

Single silver nanocubes have been studied by transient absorption spectroscopy. The traces show clear modulations due to coherently excited vibrational modes. The average period measured in the experiments was 18.6 ( 1.7 ps, which is in excellent agreement with the calculated period for the breathing mode of the cubes. The distribution of the periods was also in a good agreement with that expected from the size distribution of the sample. The average damping time was 57.6 ( 7.4 ps, which is approximately 2 times longer than the damping time measured in ensemble studies. There is only a weak correlation between the damping times and the periods. This implies that damping is affected by the particle’s local environment and that there is significant heterogeneity in the environment. Introduction Ultrafast pump-probe spectroscopy has been used widely to study the dynamics of metal nanoparticles.1–4 These experiments provide information about processes that take place on time scales ranging from tens of femtoseconds to a few hundred picoseconds, such as electron-electron (e-e)5,6 and electronphonon (e-ph) scattering,7 the acoustic vibrational modes of the particle,2–4 and heat dissipation in the environment.8,9 To date, most of these studies have been carried out on ensembles of particles. In this case, the distribution of sizes and shapes in the sample hinders the accurate determination of the dynamic properties, not so much the internal e-ph coupling processes,7 but how the particles interact with their environment. For example, one quantity of interest is the time scale for the relaxation of the acoustic vibrational modes. In ensemble measurements the damping times are dominated by sample heterogeneity: different sized particles have different periods, which leads to a dephasing of a signal.3,4 Thus, the way energy flows out of these modes into the environment cannot be determined. Problems with sample heterogeneity can be overcome if the experiments can be performed at the single-particle level. Recent studies have shown that single-particle pump-probe experiments can be performed by either (i) using total-internal reflection and detecting scattered probe light10,11 or (ii) focusing the pump and the probe beams to a diffraction-limited spot at the sample, and using highly sensitive optical detection techniques.12–14 In this paper, the transient absorption scheme developed by Del Fatti and co-workers13 is employed to study the vibrational response of single silver nanocubes. An ultrafast 880-nm pump pulse was used to excite the particles, and the subsequent dynamics was monitored with a time-delayed 440nm probe pulse. Acoustic modulations were seen clearly in the transient absorption traces. Fourier transformation of the modulated portion of the data yields the vibrational frequencies. * Corresponding author. E-mail: [email protected]

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The relaxation times were obtained by fitting the transient absorption signal to a damped cosine function. The vibrational modulations were assigned to the breathing mode of the particles.3,4 The average period measured in the single-particle experiments was in good agreement with the period calculated from the average size of the particles, and was consistent with the period in the ensemble measurements.15 The distribution of the measured periods was also consistent with that expected from the ensemble size distribution. However, the damping times obtained in the single-particle experiments were roughly 2 times longer than those from the ensemble measurements. The damping times differ considerably from particle to particle, which is attributed to differences in how the particles interact with their environment.12 Reasonable agreement was found between the experimental damping times and those calculated using a model based on the acoustic impedance mismatch between the particle and its surroundings.16,17 Several traces showed a complex behavior, which could not be explained by a single frequency. This has been observed in previous single-particle experiments12 and also in ensemble measurements for silver nanocubes.15 Experimental Section The laser system used in this study was a femtosecond TiSapphire oscillator (Clark-MXR NJA 4, pumped by a Coherent Verdi V-5 DPSS laser) operating at 880 nm, with a repetition rate of 101 MHz. The output from the oscillator was split by a 70-30 beam-splitter. The 70% portion of the beam was frequency-doubled in a 0.4-mm-thick β-barium borate crystal to produce 440-nm probe pulses. The 30% portion provided the pump pulses. The pump was chopped at 60 kHz by an acousto-optical modulator (Crystal Technology, Model No. 5100-35) driven by the internal reference of a lock-in amplifier (Stanford Research Systems, SR830). The pump and the probe beams were made collinear and focused at the sample using a high numerical aperture (NA) oil-immersion objective (100x, 1.3 NA).12,13 Both beams were attenuated with waveplate/  2008 American Chemical Society

7536 J. Phys. Chem. C, Vol. 112, No. 20, 2008 polarizer combinations to avoid damaging the particles. The powers used were approximately 300 µW for the pump and 10–15 µW for the probe. Special care was taken to keep the probe power level low because it is in resonance with the plasmon band of the particles. After interacting with the sample, the pump and probe were recollimated by a second oil-immersion objective (100x, 1.35 NA), and the probe was monitored using a Hamamatsu C533101 avalanche photodiode (APD).12,13 A 440-nm interference filter (10 nm bandpass) was placed before the detector to block the pump, and the output of the APD was fed into the lock-in amplifier. Transient absorption traces were collected by scanning the delay between the pump and probe with a mechanical translation stage (Newport, UTM150PP.1). The step size used was 1 ps, and the traces were averaged for 10-15 min. The signal level in the experiments ∆I/I was determined by dividing the output from the lock-in with the intensity of the probe (measured directly by observing the signal from the APD with a Tektronix TDS 380 oscilloscope). The time-resolution of the instrument was estimated to be ca. 300 fs, based on the risetime of the signal in traces collected with small time steps. The silver nanocubes examined in the experiments were obtained from the Xia group at Washington University.18,19 The average edge length of the particles in the sample was measured by scanning electron microscopy (SEM) as 35.5 ( 3.4 nm (error equals standard deviation). A small volume of the nanocube sample was dispersed in a 1% PVA solution and then spin-cast on a microscope coverslip. The deposition conditions were varied and chosen to produce very dilute samples with a nanoparticle density low enough to study isolated single nanocubes. The thickness of the polymer film created was approximately 30 nm, as measured by ellipsometry (Gaertner Scientific Corp.). No effort was made to remove surfactants or stabilizing molecules from the surface of the particles before deposition. It is not clear what role these moieties play in the dynamics. The coverslip was mounted on an inverted optical microscope (Olympus IX-71), equipped with a piezoelectric scanning stage (Physik Instrumente, P-527.3CL). Single nanocubes appear as blue or green diffraction-limited spots under the microscope when illuminated with white light.20 Red spots are also seen, which are attributed to either aggregates, or particles with a very different size and/or shape.21 These particles are avoided in the time-resolved measurements. Rayleigh scattering spectra of single cubes were recorded with the apparatus described in ref 22. Transient absorption images were collected by raster-scanning the piezoelectric stage with a sampling time of 300 ms/point and a step size of 0.1 µm. Fourier transforms of the transient absorption traces were performed using Igor Pro (Version 6.02A, WaveMetrics, Inc.). Before Fourier transformation, the signal was symmetrized around zero time, zero filled to 512 data points, and multiplied by a Hanning window function. Results and Discussion Figure 1a shows a transient absorption image of single silver nanocubes. The image was taken at zero delay time between the pump and probe, to maximize the signal.12 The particles are well-spaced in the image, showing that individual particles can be addressed easily in these experiments. The differences observed in the signal levels from the different particles arise because the absorption spectra of metal particles are highly sensitive to size and shape.21,23 A histogram of the signal intensities at zero delay is presented in Figure 1b. The curve shows the distribution of intensities expected from the size

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Figure 1. (a) Transient absorption image of single silver nanocubes spin-coated onto a glass coverslip. The image was acquired by rasterscanning the piezo stage while recording the magnitude of the transient absorption signal at zero time delay between the pump and probe. (b) Histogram of the measured intensities at zero time. The curve shows the distribution expected from the known size distribution of the sample (signal proportional to volume). Particles with signal levels greater than the cutoff (2x the average signal) were not included in the analysis of the vibrational modulations.

distribution of the sample, assuming that the signal is simply proportional to the volume of the particles. Most of the particles have intensities consistent with the expected distribution. Particles that had signal amplitudes considerably larger than the average signal level (2x, indicated by the “cut-off” in Figure 1b) were not included in the data analysis below; large signal levels could correspond to dimers or aggregates of particles.12 Figure 2a shows the ensemble extinction spectrum of the nanocube sample used in our experiments, as well as a representative single-particle Rayleigh scattering spectrum. The single-particle spectra are red-shifted compared to the solutionphase spectra because of the interaction of the particles with the glass substrate.20 This shift means that we need probe pulses with wavelengths around 450 nm to interrogate the particles effectively in the single-particle transient absorption experiments. Figure 2b shows a comparison of the transient absorption traces from a single cube and the bulk sample.15 Coherently excited vibrational modes can be seen in both traces, but the modulations in the single-particle trace are more pronounced and show a much longer damping time than the ensemble measurements. Fitting the modulations to a damped cosine function yields a lifetime of 30 ( 3 ps for the bulk sample, compared to 58 ( 2 ps for the single-particle experiment. The faster damping rate in the ensemble studies is due to sample inhomogeneity: different sized particles have different periods, leading to a dephasing.3,4 In contrast, the damping in the singleparticle studies is due to mechanical interactions between the particle and its surroundings.12,17 The advantages of using singleparticle pump-probe experiments over ensemble measurements for studying vibrational dynamics are obvious.12

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Figure 3. Transient absorption traces from single silver nanocubes and the corresponding power spectra, obtained by Fourier-transforming the modulated portion of the data. The y axis gives the absolute signal level in the measurement (∆I/I).

Figure 2. (a) Ensemble extinction spectrum and representative singleparticle Rayleigh scattering spectrum of the nanocubes used in the timeresolved measurements. (b) Comparison of transient absorption traces from ensemble measurements (top trace) and from a single silver nanocube (lower trace). The two traces show very similar periods and phases (as shown by the vertical lines), but different damping times.

Figure 3 shows transient absorption traces from two single silver cubes and the corresponding power spectra (inserts), obtained by Fourier-transforming the modulated portion of the data. The traces show a small background, which is attributed to a thermal signal.24 The different sign of the signal in the two traces is due to differences in the plasmon resonances of the particles. Whether the transient signal is an absorption or bleach depends on whether the plasmon resonance of the particle is red- or blue-shifted from the probe wavelength.3,4 The power spectra show a single frequency at 51 GHz for the upper panel, and 66 GHz for the lower panel. These frequencies are close to the value expected for the breathing mode of a cube with an edge length equal to the average edge length of the sample, 55 GHz for 35.5-nm edge length.15 Thus, the observed beat signals are assigned to the breathing mode of the particles. The difference between the measured frequencies is attributed to differences in the size of the particles (vide infra). The majority of the particles examined (23 out of 25) showed a single modulation, with a frequency similar to that of the particles in Figure 3. However, several particles produced complex traces with more than one mode. Figure 4 presents one of these traces, along with the corresponding power spectrum. The power spectrum shows two well-defined frequencies at 54 and 16 GHz. The high-frequency 54 GHz peak is assigned to the breathing mode of the particle. The lowfrequency peak at 16 GHz could not be assigned to any of the calculated normal modes for a cube,15 which may indicate that this mode is perturbed significantly by interactions with the substate.12

Figure 4. Complex transient absorption trace from a single silver nanocube and the corresponding power spectra. The y axis gives the absolute signal level in the measurement (∆I/I).

We do not believe that the complex traces arise from laserinduced damage of the particles because the signals are relatively stable with time, and no visible color change was observed during the experiments. It is also unlikely that the complex traces arise from dimers or aggregates: (i) the signal levels for the complex traces are similar to those for the single-frequency traces (they are within the cutoff defined in Figure 1b), and (ii) the low-frequency modes have lower intensities, which is not consistent with this peak arising from a second larger particle. The particles that give the complex traces also must be close in size to the particles that yield a single frequency because they have essentially the same breathing-mode frequency. Transient absorption traces with multiple frequencies have also been observed in studies of single gold nanospheres by van Dijk and co-workers,12 with the lower-frequency mode being assigned to a nonspherically symmetric mode that is excited due to interactions with the substrate. This assignment was based on the observation that the ratio of frequencies is the same for all particles that display multiple frequencies, which is not consistent with changes in shape being the cause of the effect.12

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Figure 5. Transient absorption traces from single silver nanocubes. The symbols are experimental data, and the solid lines are fits to the data using a damped cosine function. The traces have been normalized and offset for clarity.

Multiple vibrational modes were also seen in the ensemble measurements for silver nanocubes.15 However, the particles were much larger (edge lengths > 50 nm), and the proposed excitation mechanism involved nonuniform heating. Both of these explanations are possible for the present experiments. In addition, it is also possible that the particles that give a complex response are not perfect cubes and that the change in symmetry allows the excitation of vibrational modes that are not seen for regular cubes. Figure 5 shows transient absorption traces for three different particles, along with the fits to a damped cosine function. In the fitting procedure, the frequency was fixed to the value determined in the Fourier analysis. The damping times are much longer than the damping times measured in the ensemble studies and are attributed to homogeneous dephasing of the vibrational modulations.12 The damping times of 23 single particles were measured. Particles that displayed complex transient absorption traces, like that in Figure 4, were not included in this analysis: fitting such traces is very difficult and leads to considerable error in the damping time. Statistical analysis of the single-particle transient data is presented in Figure 6. The top panel displays a histogram of the vibrational periods from all of the particles examined: 25 total, both single-frequency and complex traces. For the complex traces, only the breathing mode is included. The mean of the measured periods is 18.6 ps, with a standard deviation of 1.7 ps (9%). The average period is in good agreement with the period of 19.1 ( 1.0 ps measured in the ensemble experiments.15 The curve in the top panel shows the distribution of periods expected from the size distribution of the sample.15 In this calculation, the particles are assumed to have a Gaussian j ) 35.5 nm and σL ) 3.4 distribution of edge lengths with L nm (measured by SEM). The periods are calculated by T ) 2πL⁄θ√E⁄F , where E and F are the values of Young’s modulus and the density of the particle, respectively, and θ is the reduced frequency for the breathing mode. The value of θ was determined numerically by finite element calculations and depends on the values of Young’s modulus, the shear modulus, and Poisson’s ratio for the particle.15 The good match between the calculated distribution and the period histogram shows that the distribution of periods is due to the distribution of particle sizes. The middle panel in Figure 6 shows a histogram of the damping times, with only particles that showed a singlefrequency modulation included (23 total). The average damping time is 57.6 ps, with a standard deviation of 7.4 ps (13%). The slightly broader distribution for the damping times is attributed to the higher sensitivity of the relaxation process to the local

Figure 6. Statistical analysis of data from the single-particle transient absorption experiments. The top panel shows a histogram of the vibrational periods (all particles), the middle panel shows a histogram of the damping times (only single-frequency traces), and the bottom panel shows a plot of the damping times versus the periods.

environment of the particles.17 The bottom panel presents a plot of the measured damping times versus the corresponding periods. This figure shows that there is only a weak correlation between the damping time and the period (correlation coefficient ∼0.13). This is somewhat unexpected: a simple model for the damping of the acoustic vibrations of a sphere in a homogeneous medium predicts that both the period and damping time should be proportional to the size of the particle (this model is discussed in more detail below).17 The weak correlation between the periods and damping times in the single-particle measurements implies that damping is strongly affected by the particle’s microenvironment and that there is significant heterogeneity in the microenvironment.12 The particles in our experiments are embedded in a polymer film and, therefore, experience a solid environment. In this case, the damping of the acoustic vibrations is controlled by the difference in the acoustic impedances of the particle and the surroundings. The acoustic impedance is given by Z ) F × cl, where F is the density and cl is the longitudinal speed of sound.16,17 A large mismatch between the acoustic impedances gives long damping times, whereas for a small difference the acoustic energy in the particle flows rapidly into the environment. This problem has been solved for spherical particles in a homogeneous solid.16 The damping times of the radial breathing modes can be obtained by solving the eigenvalue equation

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ξ2n (1 + iξn ⁄ R) (1) ξncotξn ) 1 η [ξ2 - 4R2ε2(1 + iξ ⁄ R)(1 - 1 ⁄ ηβ2)]

calculated for silver particles in a glass or a polymer environment using a model developed for spherical particles.

where R ) β) ε) η ) Fm/Fp, and cil, cit and Fi are the longitudinal and transverse speeds of sound and the density, respectively, of the particle (i ) p) or medium (i ) m).17 The eigenvalues ξn are complex and generate complex eigenfrequencies

Acknowledgment. This work was supported by the National Science Foundation (Grant CHE06-47444) and the University of Notre Dame Faculty Research Program. We are very grateful to the Xia Group (Washington University) for supplying the silver nanocube sample, and to Prof. D. Gezelter for help with the quality factor calculations.

n

p cm l /cl ,

n

p cm t /ct ,

ω jn)

m cm t /cl ,

ξnclp ) ωn + iγn R

References and Notes

(2)

where Re[ξn] gives the frequency ωn of the vibrational mode and Im[ξn] gives the damping constant γn.17 Equation 2 shows that the damping constant and frequency scale with dimensions in the same way. In order to compare the predictions of this model to our experimental data, we calculate the quality factor for the resonance Q ) ωn/γn ) Re[ξn]/Im[ξn] for silver particles in glass (cl ) 5100 m/s, ct ) 2840 m/s, F ) 2240 kg/m3), and a polymer environment (cl ) 2400 m/s, ct ) 1100 m/s, F ) 1100 kg/m3).25 We find Q(glass) ) 9.9 and Q(polymer) ) 33.8. The average quality factor measured in our experiments is 19.7 ( 2.9 (error equals standard deviation), with values ranging from 14.7 to 25.0. Thus, the experimental damping times are in between the values expected for glass and polymer environments. We speculate that the distribution of damping times arises from how strongly the particles interact with the glass substrate: particles in close contact with the substrate have strongly damped acoustic modes (low-Q vibrational resonances), whereas particles that experience an essentially polymer environment display less damping (higher-Q vibrational resonances). Note that the range of quality factors measured in our experiments is almost identical to that reported for gold nanospheres in ref 12. In summary, single silver nanocubes have been studied by transient absorption spectroscopy using the technique described in ref 13. These measurements allow us to determine the period and damping time of the breathing mode of the particles. Both of these quantities vary significantly from particle to particle. The average values measured in the experiments are 18.6 ( 1.7 ps for the period and 57.6 ( 7.4 ps for the damping time, where the errors indicate the standard deviation. For the period, the average value and the width of the distribution are in good agreement with calculations using the known size distribution of the sample.15 The damping times show only a weak correlation with the period, which implies that damping is strongly influenced by the environment and that there is significant heterogeneity in the local environment of the particles.12 The damping times are in between the values

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