Article pubs.acs.org/JPCC
Discerning the Origins of the Amplitude Fluctuations in Dynamic Raman Nanospectroscopy Jérémie Margueritat,†,§ Alexandre Bouhelier,† Laurent Markey,† Gérard Colas des Francs,† Alain Dereux,† Stéphanie Lau-Truong,‡ Johan Grand,‡ Georges Lévi,‡ Nordin Félidj,‡ Jean Aubard,‡ and Eric Finot*,† †
Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, Université de Bourgogne, 9 Avenue A. Savary, F-21078Dijon, France ‡ Interfaces, Traitements, Organisations et Dynamique des Systèmes, Université Paris7-Denis Diderot, UMR 7086 CNRS, Bâtiment Lavoisier, 15 rue Jean de Baïf, F-75205 Paris, France S Supporting Information *
ABSTRACT: We introduce a novel experimental and analytical method for discerning rare surface-enhanced Raman scattering (SERS) events observable at the nanoscale. We show that the kinetics of the Raman activity recorded on an isolated nanostructure is punctuated by intense and rare events of large amplitude and spectral variations. The fluctuations of thousands of SERS spectra were analyzed statistically in terms of power density functions, and the occurrence of the rare events was quantified by a wavenumber statistics. Our analysis enables one to extract valuable and unique spectroscopic signature of Raman variations usually hidden in time-average or space-average measurements. We illustrate our approach using molecular surface dynamics of gold adatoms on nanoparticles.
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INTRODUCTION Sensors based on surface-enhanced Raman spectroscopy (SERS) simultaneously provide ultimate sensitivity down to the single molecule level1,2 and an exceptional selectivity via the identification of molecular spectral fingerprints.3 This unique combination is attracting considerable interest for detecting chemical traces in a complex environment. In dynamic systems, a fast screening of the sensor output is generally required to follow chemical processes such as molecular docking. SERS signatures, however, fluctuate in time and amplitude even for simple probe molecules in static experimental conditions.4 Photoinduced processes and optical forces promoted by large electric field gradients near the surface can contribute to the instability.5,6 Changes in plasmon resonance due to high optical power cause spectral instability in SERS. Such rearrangement can change the electromagnetic (EM) field distribution in hotspots resulting in spectral fluctuations of EM enhancement factors.7 Molecular photodegradation and surface interactions can also have a strong impact on the Raman cross-section.8,9 Pioneer work in the mid-80's also suggests that the self diffusion of cluster can affect the stability of the SERS signal.10 These temporal and amplitude fluctuations can severely limit the identification of specific molecular vibrational signatures at the nanoscale. A stable and robust analytical procedure to analyze SERS dynamics could be an efficient way to generalize the use of SERS in these fluctuating conditions. Temporal fluctuations were recently formulated in terms of bright and dark occurrences that are well described by a power law.11−13 © 2012 American Chemical Society
The statistical amplitude variations of the SERS signal have, however, not yet been explored carefully. This aspect was essentially discussed in terms of spatial distribution of enhancement sites.14 We propose here a different statistical treatment based on the probability of occurrence of very intense SERS events. We found that the probability distribution of the events are wavenumber-dependent, enabling one to retrieve valuable dynamical spectroscopic information that is not contained in a single time-average measurement.
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EXPERIMENTAL SECTION SERS-active substrates were fabricated by depositing 25-nm diameter gold colloidal nanoparticles (GNPs) on functionalized predefined areas following the method described in ref 15. The random organization of the GNPs into a micrometer-size cluster is suitable for high SERS enhancement regardless of the incident polarization. The inset of Figure 1 shows the arrangement of GNP used in the present study. This GNP cluster is robust to chemical solvent and enables an analysis of a SERS response before and after the sequential deposition and immobilization of benzenethiol (BT) Raman probes. SERS signals from the GNP cluster were acquired in air with an inverted confocal optical microscope. A 633 nm laser line was focused on a diffraction-limited spot using a high numerical Received: September 20, 2012 Revised: November 21, 2012 Published: November 29, 2012 26919
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rate (see Supporting Information16). The PDs associated with the three colored-coded APD kinetics were calculated from histograms generated by plotting the number of events versus the corresponding measured count rate and are illustrated in Figure 1b−d. Five orders of magnitude in the PD plotted in the logarithmic scale mean that the brightest events occur with odds of 1:105, in other words, 10 microchance. Clearly, the PDs differ between the three kinetics with the presence of multiple shoulders forming heavy tails in the distributions. To understand the origin of these multimode distributions, we have simultaneously recorded SERS spectra during the three kinetics and conducted a statistical treatment on measured amplitude for each wavenumber. The PDs of the SERS amplitude for a set of 350 wavenumber histograms are displayed in Figure 2 for the three time periods. The amplitude
Figure 1. (a) APD rate showing temporal fluctuations in Raman amplitude. Black trace: citrate degradation; red trace: post degradation phases of the citrate; blue trace: after 3 h of BT deposition. (b−d) PD of the APD rate corresponding to citrate photodegradation, stabilization phase, and BT kinetics, respectively. The most probable rate is around 2 to 3 × 105 count/s. Inset: scanning electron micrograph of the SERS active cluster used in this study.
aperture objective (100×, NA = 1.49). The laser intensity was kept constant at 100 μW/μm2. Raman Stokes photons scattered in the 850−1800 cm−1 spectral window were detected every 1 ms using an avalanche photodiode (APD). Simultaneously, SERS spectra were acquired every second using a spectrometer equipped with a 633 nm Notch filter attached to a cooled charge-coupled device (CCD) camera. All simultaneous measurements (SERS spectra and APD signal) were recorded for 500 s, before and after BT deposition on the GNP cluster, providing an experimental set of 5 × 105 data points and 500 spectra.
Figure 2. (a−c) PDs of the amplitude fluctuations as a function of wavenumber for the kinetics corresponding to the black, red, and blue temporal regions (defined in Figure 1), respectively. The most probable events are in red whereas rare events are in deep blue.
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RESULTS AND DISCUSSION Figure 1a shows a reconstructed time trace of the APD signal acquired during the complete experiment. When the GNP cluster was first exposed to the laser beam (black trace), the APD photon rate shows a nonmonotonous decay with strong amplitude fluctuations with many superimposed intense shortlived bright events similar to a blinking behavior.12 This kinetics is followed by a much more stable baseline (red trace). Since the GNPs were used as prepared during this initial period, the detected APD SERS signal originates from citrate capping agent used for the colloidal synthesis and/or its photodecomposition product as discussed below. The substrate was then dip-coated for 3 hours in a BT solution at 10−4 M and rinsed carefully using ethanol before being dried under a nitrogen flow. One monolayer of BT is then expected with at least 106 molecules on the cluster.14 The blue trace in Figure 1a shows the APD kinetics for 500 s after BT deposition. The baseline is observed at the same count level as the red trace, indicating that the GNP cluster did not change during BT deposition. The APD signal for the blue trace is punctuated by intense bright events reaching up to 10 times the mean value. The occurrence of the bright events is evaluated by introducing the probability density (PD) of the APD count
of the most probable event at each wavenumber is colored in red, whereas infrequent rates are in deep blue. The fluctuating nature of the SERS amplitude emphasized by this analysis is either masked in ensemble average using long time acquisition or only partially analyzed by extracting the highest amplitude spectrum. This visual representation summarizes the systematic statistical spectral treatment enabling a PD assessment of both amplitude fluctuations and the heterogeneities among the line shapes. Superimposing all the rare events having the highest amplitude highlights the richness of a Raman spectrum enabling vibrational analysis and identification of molecular species involved in these amplitude fluctuations. The spectral histograms for the initial period (black trace) shown in Figure 2a are dominated mainly by eleven distinct lines: 950, 980, 1030, 1085, 1150, 1200, 1250, 1300, 1350, 1450, and 1580 cm−1. These lines can be assigned to adsorbed citrate and/or its decomposition products, i.e., the acetonedicarboxylic acid and acetoacetic acid17 (see Supporting Information16). The amplitude decay of this initial time period (black trace in Figure 1a) is thus explained by the photodecomposition products of excess citrates that accumulate in a 26920
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of spectral fluctuations with typical correlation times of milliseconds. The black spectrum (middle curve) in Figure 3b is a special case showing a rich Raman spectrum with 13 distinct lines corresponding to at least three different APD bursts (Figure 3a). Before and after the bright events in Figure 3, the SERS spectrum is stable. These temporal and amplitude fluctuations can be explained by considering surface diffusion of gold adatoms on the particle. Gold adatoms are estimated to cover ∼40% of the GNP surface leading to a strongly disordered structure.22,23 The hypothesis of simple molecular reorientation was first discarded; the characteristic time of the rotational diffusion at the ambient temperature cannot be inferred experimentally. A relatively high self-diffusion of gold adatoms (10−15 cm2/s) was measured by scanning tunneling microscopy,24 corresponding to a translational rate of about 3 nm/s. By comparison, the estimated diffusion coefficients of thiol on gold were generally reported around 10−17−10−18 cm2/s at elevated temperatures25 corresponding to a rate of lateral diffusion of approximately 10−2 nm/s. However, the gold adatom diffusion coefficient should be dependent on the local density of adsorbate, and certainly reduced with the adsorbate. The inhomogeneity in the adsorption of the BT can then disrupt the adatom diffusion. It was also shown recently that BT can be used as a marker of gold adatoms.9 The Raman cross section varies with the orientation of the phenol ring toward the gold surface. A Raman cross section of the BT lying perpendicular to a Au adatom was estimated theoretically as 10 times larger than for a BT ring lying parallel to the gold terrace.9 The amplitude ranges of both APD and Raman lines (Figures 1d and 2c) indicate a modest 10-fold enhancement factor in agreement with the chemical enhancement expected from BT anchored on an adatom.9 It may be also tempting to propose a causal relationship between the surface diffusion and the fluctuations of the SERS background observed by the most probable and less intense Raman events. In fact, since Otto demonstrated that the SERS background is explained by the Raman scattering by electron− hole pair excitations (exciton),26 the spectral shape of the background is then related to the electron scattering by the surface roughness, which is in turn controlled by the surface diffusion. In order to analyze the amplitude fluctuations, we introduce the Mandel parameter Q.27 This parameter, frequently used in photon counting statistics to measure the deviation from Poisson distribution,28,29 has not yet been explored to quantify SERS fluctuations. The Q parameter writes as follows:
few minutes.17 All these organic species that are not tightly attached to the GNPs diffuse through the cluster in the vicinity of enhanced local EM fields and give intense sporadic SERS signals, explaining the heavy oscillating tail in the PD distribution of Figure 1b. The spectral histograms associated with the red trace shown in Figure 2b exhibit weak lines, corresponding to citrate photodecomposition products (see above), which are superimposed on two broad bands peaking in the 1400 and 1600 cm−1 region. These bands are typical of amorphous carbon arising from the degradation of various organic species adsorbed onto the GNP cluster.18 Finally, a scenario of the events occurring during the first 500 s can be drawn: after laser irradiation, the GNP cluster is covered by amorphous carbon and acetonedicarboxylic acid coming from citrate decomposition. The amplitude fluctuations are then considerably reduced, leading to the quasi-normal distribution illustrated in Figure 1c. The fluctuations of both APD rate and spectral histograms after BT deposition are shown in Figure 1d and Figure 2c. These two PDs reveal particularly rich and strongly fluctuating spectra. Typical SERS lines of chemisorbed BT (under its BT form) are observed at ca. 992, 1020, 1095, 1485, and 1540 cm−1.19−21 Numerous other lines that do not correspond to any known vibrations of BT are also present (more than seven extra lines). BT is strongly attached to the GNPs and does not exhibit any photobleaching or photodegradation processes.19 The presence of other organic species, such as 3-aminopropyltriethoxysilane (APTES) used for GNPs immobilization15 or citrate capping agent, may be considered to explain the origin of these additional lines. Since we have not been able to record neither a spontaneous Raman nor a SERS spectrum of APTES in solution, additional lines in Figure 1d probably arise from citrates and/or their photodecomposition products (see ref 16), which were redeposited on the cluster during BT dipping and rinsing. The time fluctuations of bright events are revealed in a selected 5 s temporal window in Figure 3a. Each occurrence measured by the APD was correlated in time to its Raman spectrum. Observation of the APD time trace provides evidence
Q = −1 +
σν2 Aν
(1)
where σν and ⟨Aν⟩ are the standard deviation and the arithmetic mean of the Raman amplitude, respectively, evaluated at each wavenumber ν. A positive Q parameter concludes on a superPoissonian statistics.30,31 The spectral variations in Q are depicted in Figure 4 for spectra acquired after BT deposition. The Q spectrum corresponds roughly to the brightest events in Figure 2c. Note that the highest Q observed at 1540 cm−1 indicates a strongly fluctuating mode from the BT. Zayak et al. theoretically demonstrated that the Raman cross section of this particular line was sensitive to the presence of an adatom.9 This confirms our assumption of adatom/BT diffusion as the origin of the highly fluctuating signals.
Figure 3. (a) Selected 5 s time series of the APD photon counts correlated with (b) five successive SERS spectra recorded every second. The color of the spectra corresponds to the colored temporal regions in the APD kinetics (1 s integration). 26921
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Figure 4. Spectral evolution of the Mandel parameter Q. The peaks in the spectra are indicative of the fluctuating Raman lines.
The Q parameter is essentially a first indicator to quantify the fluctuating Raman lines but will depend on the acquisition time with respect to the characteristic time governing the temporal fluctuation. A more complete visualization is to determine the statistical law that governs the process responsible for the amplitude fluctuations. Figure 5 shows one example of experimental PDs (data point) for the fluctuating BT line at 1540 cm−1 . The log−logistic distribution was found to be the most appropriate law at all wavenumbers ν according to the Anderson−Darling test. The distribution combines a lognormal distribution with a power law to describe heavy tails. This distribution can be interpreted as a multiplicative product of random independent variables. Such interactions occur in the Au−BT system when the BT Raman cross sections vary and the adatom of the GNP diffuse on the surface. The twoparameter log−logistic distribution is described by the power density function pν: β−1
pν (A ν ) =
β (A ν / α ) α (1 + (A ν /α)β )2
(2)
where α is a scale parameter corresponding to the median of the distribution, and β is a shape parameter describing its tail. α and β depend both on ν. The fit of pν to the experimental distribution of the Raman amplitude fluctuations at 1540 cm−1, shown by the solid red line in Figure 5a, leads to α1540 = 161 count/s and β1540 = 5.11. Figure 5b,c shows the evolution of α and β as a function of ν. α closely follows the mean value ⟨Aν⟩ (most probable Raman spectrum) except for at least four peaks highlighted by the shaded areas. In these spectral bands, deviations indicate amplitude variation of the Raman signal. Figure 5c plots the wavenumber dependence of the shape parameter β. β determines the slope of the tails and hence the occurrence of rare events. An heavy tail corresponds to low values of β. The peaks present in this β spectrum are commun to the shaded areas in Figure 5b. Two main characteristic lines at 1095 cm−1 and 1540 cm−1 present in the β spectrum are associated with the orientation-dependence of the BT lines,9 thus supporting our assumption about adatom diffusion. The two others peaks are attributed to the fluctuating citrate species. From a spectroscopic point of view, Q is a readily accessible parameter without any fitting procedure, compared to β. However, Q is not sensitive to rare events; it only provides information about fluctuating Raman amplitudes. The parameter β, on the other hand, is extracted from a universal law and is a unique factor introduced to quantify fluctuations occurring at the microchance level.
Figure 5. (a) PD function of the Raman amplitude fluctuation of the 1540 cm−1 line (circle). The solid red curve is a fit with a log−logistic distribution with α1540 = 161 count/s and β1540 = 5.11. (b) Spectral variations of the scale parameter α (black curve) with respect to the mean of the distribution (red curve). (c) Spectral variation of the shape parameter β. The shaded spectral regions, associated with citrate and/or BT lines, are characteristic of an heavy-tail distribution typical of rare events.
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CONCLUSION In summary, we have developed a new statistical treatment of the amplitude fluctuations in SERS. Contrary to fluorescence fluctuations, the photon statistical distribution was found to be frequency-dependent. The PD of the fluctuating amplitude was then calculated for each wavenumber. We introduced a Mandel analysis to investigate the spectral dispersion associated with all the possible Raman active selection rules. Universal parameters, independent of the time binning, were obtained by a log− logistic statistical law sensitive to rare events. Monitoring the spectral dynamics offers new insight into possible causes of the fluctuations of the molecule−substrate system with lifetime of a few milliseconds. Our results applied to molecular adsorbate on 26922
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gold clusters indicate that the fluctuations observed in this time scale are due to a surface rearrangements with the self-diffusion of the gold adatoms. We address here the fundamental question of the ergodicity and the statistical treatment of the SERS signature. The amplitude of the SERS signal remains fluctuating even at a long time, thereby indicating a nonergodic behavior typically due to the aging process of the surface induced by surface rearrangement.A good SERS substrate should then be a good compromise between (i) a high enhancement obtained using colloids but unequaled by lithography and (ii) a clean or inert surface free of residual molecules issued from the preparation process. We are pushing the oxygen plasma cleaning process after the colloid immobilization onto the surface.
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(15) Margueritat, J.; Gehan, H.; Grand, J.; Lévi, G.; Aubard, J.; Félidj, N.; Bouhelier, A.; Colas-Des-Francs, G.; Markey, L.; Marco De Lucas, C.; Dereux, A.; Finot, E. ACS Nano 2011, 5, 1630−8. (16) See Supporting Information (http://pubs.acs.org). (17) Munro, C. H.; Smith, W. E.; Garner, M.; Clarkson, J.; White, P. C. Langmuir 1995, 11, 3712−3720. (18) Lévi, G.; Pantigny, J.; Marsault, J. P.; Aubard, J. J. Raman Spectrosc. 1993, 24, 745−752. (19) Joo, T. H.; Kim, M. S.; Kim, K. J. Raman Spectrosc. 1987, 18, 57−60. (20) Li, S.; Wu, D.; Xu, X.; Gu, R. J. Raman Spectrosc. 2007, 38, 1436−1443. (21) Szafranski, C. A.; Tanner, W.; Laibinis, P. E.; Garell, R. L. Langmuir 1998, 14, 3570−3579. (22) Kautz, N. A.; Kandel, S. A. J. Phys. Chem. C 2009, 113, 10286− 19291. (23) Mariscal, M. M.; Olmos-Asar, J.; Gutierrez-Wing, C.; Mayoral, A.; Yacaman, M. C. Phys. Chem. Chem. Phys. 2010, 12, 11785−11790. (24) Maksymovych, P.; Yates, J. T. J. Am. Chem. Soc. 2008, 130, 7518−9. (25) Bizzarri, A. R.; Cannistraro, S. Phys. Rev. Lett. 2005, 94, 1−4. (26) Otto, A.; Akemann, W.; Pucci, A. Isr. J. Chem. 2006, 46, 249− 346. (27) Kimble, H. J.; Dagenais, M.; Mandel, L. Phys. Rev. Lett. 1977, 39, 691−695. (28) Mandel, L. Opt. Lett. 1979, 4, 205−207. (29) Treussart, F.; Alléaume, R.; Le Floc’h, V.; Xiao, L. T.; Courty, J.M.; Roch, J.-F. Phys. Rev. Lett. 2002, 89, 093601. (30) Margolin, G.; Barkai, E. Phys. Rev. E 2005, 72, 1−4. (31) Margolin, G.; Protasenko, V.; Kuno, M.; Barkai, E. J. Phys. Chem. B 2006, 110, 19053−60.
ASSOCIATED CONTENT
S Supporting Information *
Assignment of Raman lines, the statistical treatment of spectra, and the log−logistic distribution. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: eric.fi
[email protected]. Present Address §
LPCML-UMR 5620 CNRS/UCBL, 10 rue Ada Byron F69622, Villeurbanne, France. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was funded by the national grants ANTARES 007NANO-006 and DGA REI 2007-34-026 and by the European project SPEDOC (FP7-ICT-2009-4) under Grant Agreement No. 248835. We acknowledge the assistance of the central mechanical Workshop, ICB-AMON for the realization of the microscope stages.
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