Spontaneous versus Stimulated Surface-Enhanced Raman Scattering of Liquid Water

We have observed for the first time the surface-enhanced (SE) signal of water in an aqueous dispersion of silver nanoparticles in spontaneous (SERS) and femtosecond stimulated Raman (SE-FSRS) processes with different wavelengths of the Raman pump (515, 715, and 755 nm). By estimating the fraction of water molecules that interact with the metal surface, we have calculated enhancement factors (EF): 4.8 × 106 for SERS and (3.6–3.7) × 106 for SE-FSRS. Furthermore, we have tested the role of simultaneous plasmon resonance and Raman resonance conditions for the aν1 + bν3 overtone mode of water (755 nm) in SE-FSRS signal amplification. When the wavelength of the Raman pump is within the plasmon resonance of the metal nanoparticles, the Raman resonance has a negligible effect on the EF. However, the Raman resonance with the aν1 + bν3 mode strongly enhances the signal of the fundamental OH stretching mode of water.


Data processing for losses correction
Correction for reabsorption was made due to the relatively high absorption of AgNPs blue sample at excitation wavelength (514.5 nm) used in Raman measurements. The optical path between the cuvette surface and cuvette centre where the laser beam was focused and from which original scattering signal was from, was assumed to be 5 mm. Laser power and other experimental parameters used in the Raman measurements were the same for water and AgNPs samples. For calculation of reabsorption correction, transmittance values in visible spectral region for dispersions of silver nanoparticles and pure water were needed. Absorption measurements were carried out in QX cuvettes with an optical path 1 mm for AgNPs samples (water as a reference) and in with a 1 cm optical path for water (empty cuvette as a reference  Figure S2. transmittance of the sample for 5 mm optical path at excitation wavelength (514.5 nm); ( )transmittance of the sample for 5 mm of optical path in spectral range of νOH (590 -648 nm); ( ) -intensity of scattered Raman signal; ( ) -intensity of scattered Raman signal corrected by transmittance of the sample: This procedure can be justified with following derivation. The intensity of the Raman pump in the cuvette can be represented by: where 0 is the intensity at the cuvette interface, is the absorption coefficient for the pump, is the distance from the interface and the depletion due to Raman scattering has been neglected. The intensity of the signal is diminished by absorption ( ) on its way through half of the cuvette width ( 2 ⁄ ) to the side interface: where 0 is the intensity of scattered light in the centre of the cuvette: and is the Raman gain. The average intensity measured by the detector is: The right-hand most factor can be expanded into Taylor series to the second order: For ≪ 1 (which is the case as the total absorption of the pump in the cuvette is 0.61 for AgNPs blue and much less for AgNPs yellow and pure water) this is equal to the expansion of: therefore, we conclude with approximation: water AgNPs yellow AgNPs blue Figure S3 -Spontaneous Raman spectra of pure water, AgNPs blue and AgNPs yellow after losses correction. Figure S4 -Spontaneous Raman spectra of pure water, AgNPS blue and AgNPs yellow after losses correction and background subtraction.

Processing of stimulated Raman spectra
The surface enhancement of the water signal in AgNPs blue was already observed in the raw SRS data (see comparison in Figure S5). To compare the "absolute" magnitude of surface enhancement the data were compared as Raman gain factor g (shown in Figure 3b in the Manuscript, for theoretical description see part SI3 of this SI). An alternative method for scaling the data was to normalize them to the reference peak (here: fused silica peak at 490 cm -1 ) after background subtraction.  S8 SRS spectra measured with 515 nm Raman pump normalized to the silica peak at 490 cm -1 . Figure S7 -stimulated Raman spectra obtained with 515 nm pump after baseline subtraction, normalized to fused silica peak at 490 cm -1 ; pure water (black lines), AgNPs blue (blue lines) and AgNPs yellow (red lines) in the spectral range from 100 to 4200 cm -1 .

SI2 Influence of losses in Raman signal in stimulated Raman experiment
The evolution of the intensity of the Raman pump ( ) and the signal ( ) are described by following equations S1,2 : where, ∈ [0, ] is the position within the sample of thickness , is the stimulated Raman gain and / describe linear losses of pump and signal, respectively. The '+' and '-' signs correspond to Stokes and anti-Stokes scattering, respectively. It can be safely assumed that changes in the intensity of the pump due to scattering are small: ≪ 1, in such a case Eq. S9 becomes: and has a solution: After insertion of Eq. S12 into Eq. S10: which can be solved to obtain an expression for calculation of Raman gain with knowledge of losses input intensities and output intensity of the signal: For the experimental scheme where intensity of the signal is measured, also in the absence of pump, the dependence of gain on the input signal intensity and signal losses can be removed. In the absence of Raman pump, the evolution of the signal beam intensity due to absorption is governed by equation: with solution: in such a case: For the = 0 case the Eq. S17 can be simplified to: This can be obtained by either solving Eq. S18 with constant or by finding a → 0 limit of Eq. S17. S10 Figure S8 -Stimulated Raman spectra presented as Raman g factor, before background subtraction, of pure water (black lines),

AgNPs surface
As all measurements were performed under the same conditions, all calculations, for simplicity, were done for 1 dm 3 of the samples (water as well as AgNPs blue dispersion). The maximal number of water molecules interacting directly with AgNPs surface was estimated on the basis of size and shape of AgNPs, which was determined by TEM, and Ag concentration in the dispersion (17.96 µg/ml), which was determined by Flame Atomic Absorption Spectrometry. Based on TEM results, the shape of nanoparticles in AgNPs blue sample was assumed to be a prism with an average size of 34 nm in a sense of radial diameter (d=2R) of a circumscribed circle of a model S12 prism. It was also assumed that the water molecules are densely packed on the AgNPs surface in a hexagonal system. However, this assumption is out of physical sense, it allowed to calculate the maximal number of water molecules able to contact Ag surface directly. Considering the real system, obtained herein values are overestimated. The size of a single water molecule was assumed to be equal two van der Waals radii r of water molecule -0.17 nm. S3 The following procedure was applied to estimate number of water molecules interacting directly with AgNPs surface for AgNPs blue:  where NA is Avogadro number.
Therefore, only 1 water molecule per almost 10 million is able to interact with the AgNPs surface.
The above calculated number of water molecules that can cover all AgNPs in a 1 dm 3 dispersion was estimated based off the average size of AgNPs (34 nm). Taking into account the size distribution in this sample (34 ± 14 nm), analogous calculations were performed for systems where all AgNPs have the smallest (20 nm) or the largest possible size (48 nm). Results of calculations in both cases give values in the same order of magnitude as the one obtained for averaged size.