Shalaev‘s hot EM spots and single molecule SERS This lecture is based on A.Otto, On the significance of “hot spots” in ensemble and single molecule SERS by adsorbates on metallic films at the percolation threshold, J.Raman Spectr., accepted
Colloidal aggregates Motivation: Single molecule surface enhanced Raman scattering may become an important analytical method (e.g. K.Kneipp). Often, the enhancing samples are aggregated silver colloids, modelled as fractals at the percolation limit, though SM-SERS has also been reported for small colloidal clusters and single colloidal particles.
C. McLaughlin, D. Graham, and W. E. Smith, J. Phys. Chem. B 2002, 106, 5408-5412
The use of Shalaev‘s theory to fractals Fractal means an approximate self similarity at all scales above the scale of the monomer, which is the single nano particle. The aggregates have in general a linear extension of about 3 orders with respect to the monomer , but that will not make the assignment to a fractal useless. My oppinion: The application of Shalaev‘s theory to SERS from fractals has not left the stade of a qualitative discussion. However, quantitative application to metal island films is possible
Theory of giant Raman scattering from semicontinuous metal films, F. Brouers et al, Phys.Rev B55(1997)13234. Silver at the percolation threshold
E (r )
106
2
E (r )
note, that at most points |E(r)|2 1
and
2
E (r , ω Stokes )
E incident (ω Laser , Ω Laser )
2
E incident (ω Laser , Ω Laser )
2 2
E (r , ω Stokes )
E incident (ω Stokes , Ω Laser ) 2
E incident (ω Stokes , Ω Laser )
2
>> 1
2
I=
E-E 0 E0
follows
Gretro (r , ω Laser , ω Stokes , Ω Laser ) ≅ I (r , ω L , Ω Laser ) I (r , ω Stokes , Ω Laser ) Because these two intensities at r are uncorrelated, the log-normal function yields
I (ω Laser ) =
+∞
∫
−∞
I
P( I ) log( I ) d (log I ) = 10 10 d (log I )
Gretro (r , ω Laser , ω Stokes , Ω Laser ) = 10
ln10 ∆ 2 2
( log( I Laser ) + log( I Stokes ) )
10
ln10 ( ∆ 2Laser +∆ 2Stokes ) 2
The first factor is the result for ∆=0, therefore the second factor is the contribution of hot sites in ensemble SERS spectra
2
Numerical values, Ag films at percolation threshold Shalaev et al used the relaxation frequency for silver ωτ = 0.021eV according to Johnson and Christy
λ(Laser)=514.5nm
ωτ = 0.021eV
ca.142 contribution 13.4 of hot spots ca 4 H 104 ca 2.85×105
„The very intense fields that exist at hot spots would dominate this average [V.M.Shalaev, personal communication to M. Moskovits]“
Assuming, that the relaxation frequency in the island films produced in UHV at the percolation threshold is a factor of 3.4 higher than measured with the continuous films evaporated at 4×10-6 Torr by Johnson and Christy, yields 300, in agreement with experiment in UHV
Mapping single-molecule SERRS from Langmuir-Blodgett monolayers on nanostructured silver island films, R.F. Aroca and collaborators, JRS 2005, 36, 574
Laser wavelength 514nm resonance Raman scattering
Langmuir-Blodgett film of Arachidic acid (AA) C19H39COOH
Dye diluted in a Langmuir-Blodgett monolayer, pixels of 1µm2 contain 400 silver islands. 3.64 × 105 dye molecule/µm2
about one dye molecule/ µm2
Single molecule signal from 0.3% of pixels of 1 µm2
The measured surface concentration of hot spots Nhot spot/ Nspot does not depend on the spot area N hot spot `n dye number of dyes observed 2 ×À (µm )× = hot spot 2 2 µm µm pixel N hot spot ×À hot spot (µm2 )×1=0.003 2 µm N hot spot 0.003 = µm 2 À hot spot (µm 2 ) N hot spot Nspot 0.003 1 / = / =0.003 for A spot (µm 2 )=A hotspot (µm 2 ) 2 2 2 2 µm µm À hot spot (µm ) Aspot (µm )
Given the experimental value P(I(ωL)) x P(I(ωS)) = 5 x 10-3 and the log-normal distribution, the highest single molecule enhancement occurs at P(I(ωL)) = P(I(ωS)), yielding log I2max = 2 H 3.4 and I2max = 6.33 x 106
(5 x10-3)1/2
I2 = 6.33 x 106
Raman spectra of 3.64 × 105 dye molecule/µm2 luminescence resonance Raman scattering
on glass
on silver island film experimental ensemble enhancement by silver island film: 103 - 104 (a) Resonance Raman spectrum of a single 10:1 AA-salPTCD monolayer deposited on glass. (b) Surface enhanced resonant Raman scattering spectrum of a single 10: 1 AA-salPTCD monolayer deposited on evaporated 6nm Ag nanoparticle film, from Goulet PJG, Pieczonka NPW,Aroca RF, Journal of Raman Spectroscopy 2005; 36: 574
Shalaev-theory: is ca 4 H 104
Raman spectra from single dye molecules observed
Estimation of single molecule enhancement 1) 3.64 ×105 salPTCD molecules/pixel deliver the resonant Raman signal both on a glass substrate and enhanced by 103 – 104 on an island film. 2) A Raman spectra from a single molecule/pixel of salPTCD was observed. 3) Intensity and exposure time when monitoring the ensemble spectra in have been 10 times more than in the case of single molecule spectra [24]. 4) Assuming that Raman intensity is proportional to enhancement times number of molecules one needs an enhancement of 3.64 × 107 to observe a signal from a single molecule. Aroca has remarked: “We have not actually tested to see what the limit of resonance Raman (on glass, without surface-enhancement) detection is. They are certainly below 3.64 × 105 molecules for this perylene system, however. This would bring the necessary hot spot enhancement below 3.64 ×107”.
Comparison of experiment and theory Single molecule EM enhancement in hot spots of island films: < 3.64 × 107 enhancement in Shalaev type hot spots of island films ca 6.33 × 106 Shalaev hot spots do dominate the theoretical ensemble enhancement of 4 × 104: Enhancement × probability = (6.33 × 106) × (5 × 10-3) = 3.16 × 104 Shalaev‘s theory, when properly used, is indeed a very good theory
The quoted quantitative enhancement depends on the quoted dilution Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS), Katrin Kneipp, Yang Wang, Harald Kneipp, Lev T. Perelman, Irving Itzkan, Ramachandra R. Dasari, and Michael S. Feld, Phys.Rev. Letters 78,(1997) 1667
Samples were prepared by adding 5 H 10-13 M crystal violet solution in methanol to this colloidal solution in a volume ratio of 1:15, resulting in a final sample concentration of 3.3 H 10-14M, which means an average of 0.6 molecules in the probed 30 pl volume. Mapping single-molecule SERRS from Langmuir– Blodgett monolayers on nanostructured silver island films, Paul J. G. Goulet, Nicholas P. W. Pieczonka and Ricardo F. Aroca, J.Raman Spectroscopy 2005; 36: 574–580
One arachidic acid molecules occupies about 25 Angstroms squared within the monolayer. In fig 8, each micron squared should contain approximately 4 × 106 molecules. Of these, about 3.64 × 106 will be arachidic acid molecules and about 3.64 × 105 will be salPTCD molecules (R.Aroca, private communication). The single molecule spectra were obtained with 1 salPTCD molecule per micron squared . This corresponds to a dilution of about 2 × 10-6 For comparison: one individual person in the chinese society corresponds to a dilution of about 10-9, a dilution of 2 × 10-6 corresponds to a village of 2000 people. But what about an individual in a society, ten thousand times as big as the chinese society?
Submonolayer enhancement G of the peak Raman intensity of the CC-breathing mode of benzene on various silver substrates I.Mrozek, A. Otto, Quantitative separation of the "classical" electromagnetic and the "chemical" contribution to SERS. J. Electron Spectrosc. Relat. Phenomena 54/55 (1990) 895-911
silver island film on sapphire, thickness varied
GEM= ca. 300 at percolation threshold
Scattering configurations 1 or 2, evaluated by comparison to the case of thick condensed benzene layers on silver-free reference samples. (The normalized signal from the condensates at constant spectrometer setting are indicated in the second column, hut have not been used in the comparison of G of the different silver substrates.) Upper values: Clean silver substrates; lower values: oxygen-passivated silver substrates (arrows: signal below detection threshold). Numbers give average film thickness of island films. GSC: graphite single crystal, c: coal, EG: exfoliated graphite. Horizontal bars give the electronic („chemical“) enhancement.
