Surface-enhanced Raman scattering from functionalized self-assembled monolayers

ANALYTICA

CHIMICA

ACTA EL-SEWER

Analytica

Chimica Acta 307 (1995) 333-340

Surface-enhanced Raman scattering from functionalized self-assembled monolayers Part 1. Distance dependence of enhanced Raman scattering from a terminal phenyl group Maoee Tsen, Li Sun

*

Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA

Received 11 August 1994; revised 1 November 1994; accepted 2 November 1994

Abstract The enhancement factor for surface-enhanced Raman scattering (SERS) is measured as a function of distance using a self-assembled monolayer as the spacer and a terminal phenyl group as the Raman label. The Raman label is covalently linked to the spacer layer by an amide bond. The measured enhancement factor decays approximately exponentially as a function of distance. The decay rate, expressed as the distance at which the enhancement factor decreases to half of its initial value, is about 0.35 nm. Analysis of the decay curve by two similar theories of electromagnetic enhancement shows that roughness dimensions on the order of 10 nm are responsible for the observed SERS signals under the 647.1 nm laser excitation. Keywords:

Monolayers,

self-assembled;

Raman spectrometry;

Surface enhanced

1. Introduction Self-assembled monolayers (SAMs) of functionalized n-alkanethiols have been increasingly studied in a variety of fundamental as well as applied research areas [l-3]. Present research interests include nonlinear optical properties, electron transfer, intermolecular interactions, lithography, biological cell adhesion, crystal growth, and chemical sensors [4211. SAMs have been shown to exhibit a higher degree of structural ordering than other types of

* Corresponding

author.

0003-2670/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0003-2670(94)00594-X

Raman spectrometry;

Surface techniques

ultrathin organic films. Consequently, modification of surface properties and surface structures can be achieved through SAMs in a more predictable manner. In order to understand the correlation between a SAM structure and its physical, chemical, or biological properties, many sensitive surface analytical techniques have been utilized, which include contact angle measurements, surface acoustic wave measurements, interfacial force measurements, electrochemistry, ellipsometry, X-ray photoelectron spectroscopy, Auger electron spectroscopy, UV-visible absorption spectroscopy, fluorescence spectroscopy, infrared spectroscopy, Raman spectroscopy, scanning probe microscopies, and mass spectrometry [4-

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311. Although these techniques have been very informative in revealing SAM structures at the molecular level, future development of SAM-based fundamental investigations or practical technologies depends on the invention and application of new analytical techniques and on the refinement of the existing techniques. We are interested in applying surface-enhanced Raman spectroscopy (or scattering) (SERS) to the structural analysis of SAMs for three main reasons. First, SERS offers submonolayer sensitivity because of the six-orders-of-magnitude enhancement of the Raman scattering cross-section for surface-confined molecules [32,33]. Second, being a vibrational spectroscopy, SERS is very sensitive to the conformations of individual self-assembling molecules and their molecular environments. Finally, compared to surface infrared spectroscopy, SERS exhibits two unique attributes: (1) SERS provides vibrational information complementary to that provided by surface infrared spectroscopy and (2) SERS can be used to study structures in biologically important aqueous media with negligible spectral interference from water [34]. Several other research groups are also actively combining the unique features of SERS and SAMs for various applications [29,34-361. For example, Bryant and Pemberton [29] have shown that SERS can provide information concerning the conformations of n-alkanethiol SAMs on Ag surfaces. In this paper, we report the distance dependence of enhanced Raman scattering from a terminal phenyl group covalently attached to a SAM through a peptide bond, see Scheme 1. We expect that omercapto-N-phenylalkanamides, HS(CH,),-CONH-

Distance I

Scheme 1.

Chimica Acta 307 (1995) 333-340

C,H, (1,n = 5;2, n = 10; and 3, n = 151, will form closely packed SAMs and that the distance between the phenyl group and the substrate surface will be determined by the methylene chain length. This study is significant to the understanding of the SERS mechanism. Two types of enhancement mechanisms are currently supported by experiments: chemical enhancement mechanism and electromagnetic (EM) field enhancement mechanism [37-401. The chemical enhancement mechanism is a “shortrange’ ’ effect, involving direct electronic coupling between the energy levels of an adsorbed molecule and those of the metal substrate. This mechanism is analogous to the one for resonance Raman scattering, in which the intrinsic polarizability of the adsorbed molecule is enhanced. The EM field enhancement mechanism is a “long-range” effect, involving an increase in the local EM field, or equivalently, an increase in the effective photon density for Raman excitation. It has been shown previously that SERS intensity decreases as the distance between a Raman label and the substrate surface increases [41,42]. The existence of SERS at a distance larger than 5 nm suggests that the EM mechanism is operative. However, we believe that the chemical enhancement cannot be ruled out completely because the Raman labels may penetrate the polymer spacer layer used in these experiments [41,42] and thus interact with the metal substrate surface directly. This possibility is difficult to exclude even if a relatively ordered Langmuir-Blodgett (LB) film is used as the spacer layer [43,44]. The inherently rough nature of an SERS-active surface promotes the formation of defects within the LB film. To alleviate the above problem, we designed and tested SAMs with covalently attached Raman labels for studying the distance dependence of SERS, see Scheme 1. This approach offers several advantages. First, direct electronic coupling between the phenyl Raman label and the metal surface is negligible. The strong metalthiolate interactions [45] force the phenyl group to be separated from the metal surface by the intervening methylene chain. Second, the alkanethiol moiety is known to promote the formation of closely packed solid-like layers which are structurally more ordered and contain fewer defect sites than LB films do [l-3]. Third, the surface coverage of the Raman label is expected to approach one monolayer and

M. Tsen, L. Sun /Analytica Chimica Acta 307 (1995) 333-340

remain relatively constant as the chain length is varied. A constant or known surface coverage is obviously very important for quantifying SERS as a function of distance. Finally, SAMs will significantly stabilize the morphology of SERS metal particles by preventing them from coalescence. A stable and reproducible surface morphology is critical for quantifying the dependence of SERS on the distance [46]. This study is also significant for the development of SERS-based chemical sensors. SAM modification of SERS-active metal surfaces has been shown to be an effective method for detecting non-adsorbing molecules [36]. Functionalizing SAMs with terminal groups capable of modulating surface binding properties represents a new strategy to enhance the molecular specificity of SERS-based analytical methods. If the self-assembling molecule has a shorter chain length, then the distance between the molecule to be detected and the substrate metal surface will be shorter; thus larger enhancement is expected. On the other hand, SAMs are structurally more ordered and stable when the chain is longer. Ordered SAMs, in turn, allow better control over the binding properties of the terminal functional groups. These two factors, which influence the sensitivity and the selectivity of a practical SAM-SERS sensor, will have to be balanced to achieve optimum performance. An accurate and quantitative measurement of the SERS enhancement factor (EF) as a function of distance will provide a valuable guide to the design of SAM-SERS sensors.

2. Experimental 2.1. Chemicals and materials Water of 18.2 MR cm resistivity was produced by passing deionized water through a series of purifying cartridges (Milli-Q Plus, Millipore, Marlborough, MA). Tetrahydrofuran (THF) (LC grade, Fisher Scientific, Pittsburgh, PA), aniline, 6-bromohexanoyl chloride, thiolacetic acid, 11-bromoundecanoic acid, dicyclohexylcarbodiimide (DCC), thionyl chloride, and 16-hydroxyhexadecanoic acid (Aldrich, Milwaukee, WI> were used as received. Other chemicals were reagent grade or better and used as received.

335

2.2. Synthesis of o-mercapto-N-phenylalkanamides 6-Mercapto-N-phenylhexanamide (I). To a stirred solution of 6-bromohexanoyl chloride (8.52 g, 40 mmol) in diethylether (50 ml) was added aniline (4.55 ml, 50 mmol) in diethylether (20 ml) over a 25-min period under nitrogen. The mixture was transferred to a separation funnel and washed sequentially with 5% NaOH (2 X 30 ml), 10% HCl (2 X 30 ml), and brine (2 X 30 ml). Drying over MgSO, and evaporation of the solvent gave 10.48 g (97% yield) of 6-bromo-N-phenylhexanamide (la) as a white solid. ‘H NMR (CDCI,): 6 7.52-7.10 (m, 5H), 3.41 (t, 2H), 2.37 (t, 2H); 1.9-1.5 (m, 7H). A mixture of la from the above step, sodium methylate (2.7 g, 50 mmol), and thiolacetic acid (3.6 ml, 50 mmol) in degassed CH,OH (100 ml) was refluxed under nitrogen for 5 h and then cooled to room temperature [47]. More sodium methylate (2.7 g, 50 mmol) was added, and the mixture was refluxed under nitrogen for an additional 2 h. After cooling to room temperature, the reaction mixture was quenched with half-saturated NH,Cl (75 ml) and extracted with CHCl, (2 X 40 ml). The organic layer was washed with brine (2 X 20 ml) and dried over MgSO,. Evaporation of the solvent and recrystallization from a mixture of alcohol and hexane gave 6.89 g (79% yield) of 1 as a white solid. ‘H NMR (CDCl,): 6 7.0-7.5 (m, 5H), 2.51 (t, 2H), 2.36 (t, 2H); 1.7-1.3 (m, SH). 11 Mercapto-N-phenylundecanamide (2). A mixture of 11-bromoundecanoic acid (7.96 g, 30 mmol) and thionyl chloride (2.17 ml, 30 mmol) was stirred and heated gently under constant aspiration to remove any gas evolved from the reaction. Then, triethylamine (15 ml) in diethylether (100 ml> was added, followed by dropwise addition of aniline (3.65 ml, 40 mmol) over a 30-min period under constant stirring. The reaction mixture was transferred to a separation funnel and washed successively with 5% NaOH (2 X 50 ml>, 5% HCl (2 X 50 ml), and brine (2 X 50 ml). Drying over MgSO, and evaporation of the solvent yielded 8.6 g (84% yield) of solid ll-bromo-N-phenylundecanamide (2a). ’ H NMR (CDCl,): 6 7.5-7.0 (m, 5H1, 3.39 (t, 2H1, 2.33 (t, 2H); 1.9-1.1 (m, 17H). Treating 2a according to the method for converting la to 1 afforded 4.9

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g (67% yield) of 2 as a white solid. ‘H NMR (CDCl,): 6 7.5-7.0 (m, 5H), 2.68 (t, 2H), 2.34 (t, 2H); 1.9-1.2 (m, 18H). 16-Mercapto-N-phenylhexadecanamide (3). A mixture of 16-hydroxyhexadecanoic acid (5.0 g, 18 mmol) and 48% hydrobromic acid (25 ml, 220 mmol) in glacial acetic acid (25 ml) was stirred and refluxed for 40 h [47]. After cooling to room temperature, the white solid was isolated by filtration, washed with water, and recrystallized from hexane to give 5.8 g (94% yield) of 16-bromohexadecanoic acid (3a) as a white leaf-like solid. ‘H NMR (CDCl,): 6 3.38 (t, 2H), 2.51 (t, 2H); 1.9-1.2 (m, 26H). A mixture of 3a (3.0 g, 9 mmol), dicyclohexylcarbodiimide (DCC) (2.06 ml, 10 mmol), and aniline (1.28 ml, 10 mmol) in CH,Cl, (50 ml) was stirred at room temperature for 10 h [48,49]. After the dicyclohexylurea precipitate was filtered off, the solvent was removed from the remaining solution to yield a white solid. The solid was redissolved in ethyl acetate (75 ml), washed with dilute HCl (2 X 30 ml), 5% NaHCO, (2 X 30 ml), and brine (2 X 30 ml). Drying over MgSO, and removal of the solvent gave 3.6 g (97% yield) of 16-bromo-N-phenylhexadecanamide (3b) as a white solid. rH NMR (CDCl,): 6 7.5-7.0 (m, 5H), 3.40 (t, 2H), 2.31 (t, 2H); 1.9-1.2 (m, 27H). Treating 3b according to the method for converting la to 1 gave 3.05 g (94% yield) of 3 as a white solid. ‘H NMR (CDCl,): S 7.5-7.0 (m, 5H), 2.49 (t, 2H), 2.34 (t, 2H); 1.8-1.1 (m, 28H). 2.3. Instrumentation

and measurements

The SERS measurement system consists of a krypton ion laser (Model Innova 90K, Coherent Laser Group, Santa Clara, CA), a 2-inch diameter holographic notch filter (Model Notch-Plus, Kaiser Optical Systems, Ann Arbor, MI), a 0.5-m single-grating Czerny-Turner spectrograph (Model 500M, SPEX Industries, Edison, NJ), a liquid N,-cooled 1024-by256-pixel charge-coupled device (CCD) (Model CCD-lOOOLF, SPEX Industries), and a data acquisition and analysis system (SPEX Industries). Laser power was measured by a semiconductor detector (Model 840-C and 818-SL/CM, Newport, Irvine, CA). The spectral positions of the horizontal CCD pixels were calibrated using the emission lines of known wavelengths from a Ne lamp (Model

Chimica Acta 307 (199.5) 333-340

AlA/NE-2, Chicago Miniature Lamp, Buffalo Grove, IL) [50]. Spectral analysis, theoretical modeling, and data graphics were performed using a combination of commercial software, including GRAMS/386 (Galactic Industries), Excel (Microsoft), and AutoCAD LT (Autodesk). Typical conditions for Raman scattering measurements were 50 mW 647.1 nm excitation, 200 pm slit width (equivalent to 6.7 cm- ’ band pass), and 5 s integration time. The SERS spectra were corrected for slowly varying spectral background using set points more than 200 cm-’ apart. The laser beam was focused to a point on the sample surface using a f = 500 mm spherical focusing lens. The electrochemical system for roughening Ag electrodes consisted of a bipotentiostat (Model AFRDES, Pine Instruments, Grove City, PA), an IBM-compatible 486DX2/50 computer (ZEOS International, Minneapolis, MN), and an analog-digital interface board with programmable software (Model AT-MIO-16F-5, National Instruments, Austin, TX) capable of controlling electrode potential and recording cell current. 2.4. Substrate and sample preparation Roughened Ag electrodes were prepared according to the procedure reported by Van Duyne with slight modification [51]. An Ag wire of 0.5 mm diameter (99.9998% pure, Johnson Matthey, Ward Hill, MA) was bent with a segment parallel to the surface to be polished. The wire was sealed in a glass tube with Torr Seal epoxy (Varian, Lexington, MA) which was cured at room temperature for 8 h and then at 60” C for an additional 4 h. The excess epoxy was mechanically polished away with 600-grit sand paper to expose a line-shaped electrode with defined area (ca. 0.02 cm2). The electrode was further polished successively with 9.5 and 1.0 pm alumina-water slurry (Buehler, Lake Bluff, IL) on a polishing cloth (MICROCLOTH, Buehler). After each polishing step, the electrode was sonicated in a water-ethanol mixture for 3 min and washed thoroughly with water. The Ag electrode was electrochemically roughened twice in a 0.1 M KC1 electrolyte using a double-potential-step waveform of 0 mV cathodic potential, 200 mV anodic potential (vs.

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Chimica Acta 307 (1995) 333-340

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a home-made Ag/AgCl/saturated KC1 reference electrode), and 25 mC cm-’ Faradaic charge. Immediately after being rinsed with water and THF, the roughened electrode was immersed in THF solution of 1.0 mM thiol for 10 min. After rinsing with THF and drying in a stream of N,, SERS from the monolayer-coated electrode was measured in a cell filled with pure water without potential control.

3. Results and discussion 1.0

Fig. 1 shows the SERS spectra of 1, 2, and 3 adsorbed on roughened Ag surfaces. Two major peaks located at 997 and 1597 cm-’ result from phenyl skeleton vibrations, which can be assigned to the totally symmetric ring breathing mode and a ring C&C stretch mode, respectively [52]. The 997 cm-’ peak is an excellent Raman marker for studying the distance dependence of SERS because (1) its prominent intensity favors detection with a good signal-

%

c

E al

-E -

Cd I

I

I

I

1.0

Raman

I

I,

1.2

Shift

I

I

I

1.4

I

I

I

I

I

I

I

I

1.6

( 1 O3 cm-’ )

Fig. 1. Representative SERS spectra of phenyl terminated SAMs adsorbed on Ag surfaces electrochemically roughened ex situ: (A) 6-mercapto-N-phenylhexanamide 1, HS(CH,),CONHC,H,; (B) 11-mercapto-N-phenylundecanamide 2, HS(CH2),aCONHC,Hs; and (C) 16-mercapto-N-phenylhexadecanamide 3, HS(CH,),,CONHC,Hs. The unit of the scale bar is counts per second per mW of 647.1 nm laser excitation,

1.5 Distance

2.0

2.5

(n,)

Fig. 2. Normalized SERS enhancement factor vs. distance plot. Each experimental data point is represented by a rectangle whose height is equal to the standard deviation of a data set consisting of results obtained from 5 to 9 independent SERS spectra. The solid line is the “best” fit (see text) calculated according to the Gersten and Nitzan model. The two adjustable fitting parameters, which specify the dimensions of a hemispheroid surface protrusion, are 30 nm for the semimajor axis and 7.5 nm for the semiminor axis. The aspect ratio of the hemispheroid is, therefore, 4.0.

to-noise ratio, especially at large distances and (2) its relatively constant spectral position ensures that the peak can be identified unambiguously. Fig. 2 shows a plot of normalized 997 cm-’ peak intensity as a function of phenyl-to-surface distance. We assume that the phenyl-to-surface distance in an w-mercapto-N-phenylalkanamide SAM is equal to the thickness of an w-mercapto-alkanoic acid SAM if both SAMs contain the same number of methylene units. In this study, we have used the thickness values measured with a ellipsometer by Bain et al. [47]. Fig. 2 also includes a normalized intensity vs. distance plot, calculated according to the theoretical model of Gersten and Nitzan (GN model) [53]. The bulk dielectric constants of Ag and water from literature are used in the calculations 154,551. Several assumptions have been made in order to fit the theoretical curve with the experimental data in Fig. 2. The GN model approximates a real rough surface with an isolated hemispheroid protrusion whose major axis is parallel to the macroscopic surface normal. According to this model, the decay rate of EF as a function of distance increases when the aspect ratio (ellipsoidal eccentricity) of the hemispheroid increases or when the overall size of the

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M. Tsen, L. Sun /Analytica

hemispheroid decreases. Consequently, there exist many sets of aspect ratio and size combinations, all of which lead to good fits for Fig. 2. However, some sets of these two parameters are physically less plausible than others. For example, aspect ratios of greater than 10 do not seem to represent the typical distribution of particle shapes on an electrochemitally anodized Ag surface, as seen by SEM [46]. Furthermore, the particle size cannot be too small because the dielectric constants for particles smaller than 2.5 nm differ from the bulk values, or too large because Rayleigh approximation requires that the particle size is small as compared to the wavelength of the incident radiation [56]. We have used the above restrictions, which are imposed primarily by the GN model, as guidelines for selecting the most plausible set of fitting parameters (Fig. 2). Using the parameters from the best fit to the GN model, we find that EF at 1.08 nm, which corresponds to the SAM of 1, is 4.4 X 107. This value is much larger than the measured value (vide infra). Nevertheless, the general shape of the EF vs. distance plot is not very sensitive to the absolute value of the EF 1531. We have also used another EM model, as described by Murray [56,57], to generate a normalized EF vs. distance plot. This model requires only one adjustable parameter, viz. the radius of curvature of an arbitrary surface protrusion, for comparing the plot with the experimental data. We find, from the best fit to Murray’s model, that the radius of the curvature is about 4.5 nm and that the EF is 4.7 X lo6 at 1.08 nm. In comparison, the now classic spacer experiments by Murray and Allara showed that their data best fit Murray’s model if the radius of the curvature is 18 nm [42]. Further comparison between experimental data and theoretical models requires considerable improvements in both experiments and theories. For example, SERS-active substrates with more defined size and shape distributions, such as Ag island films or Ag-coated latex particles [58], may be used. EM models that average EF over the entire spheroid surface and over all molecular orientations would generate more realistic results for experimental verification 1371. For practical analytical applications, data in Fig. 2 may be best analyzed by fitting to a decaying exponential. The most useful number is d1,2, which we

Chimica Acta 307 (1995) 333-340

define as the distance at which an SERS signal decays to half of its initial value. We find, by curve fitting, that d,,, is about 0.35 nm. This value is almost 10 times smaller than the value we estimated from the plot reported by Cotton et al. [43]. Their d 1,2 value is 3.2 nm. Using the data reported in another study by Kovacs et al. [44], we find a similar d 1,2 of 3.4 nm: again, 10 times larger than our result. Three major differences between our experimental conditions and those reported by Cotton et al. or Kovacs et al. may account for the above discrepancies in the d1,2 values. First, the Raman labels used in their studies are chromophores with a high optical extinction. The surface Raman scattering of these chromophores under the 514.5 nm excitation is enhanced not only through SERS mechanisms but also through the resonance Raman mechanism. In contrast, our Raman label, the phenyl group, does not have significant absorption at the 647.1 nm excitation so that it is enhanced only through SERS mechanisms. Second, LB films are the spacer layers in both Cotton’s and Kovacs’s studies whereas SAM is used as the spacer in this study. We believe that a SAM spacer contains less defects than does an LB spacer [2,3]. Therefore, in our study, the Raman label is less likely to be in direct contact with the SERSactive Ag surface at the defect sites. Finally, the distance range probed in Cotton’s and Kovacs’s studies is about 7-10 times larger than the range probed in this study. One may argue that since the EF vs. distance plots in both theoretical models are non-exponential, the theories may predict a larger decay rate at short distances. However, the results of our calculations using both models show that a plot that fits Cotton’s or Kovacs’s data over the long distance range does not fit our data in the short range. The difference between the plot and our data in the short range scales approximately with the same factor of 10 as discussed earlier. Therefore, the discrepancies in the d1,2 values cannot be explained within the framework of the EM models. We have also re-examined the data obtained by Murray and coworkers [41,42] and find that their d 1,2 is 1.5 f 0.5 nm, which is between the dI,z measured in this study and those in Cotton’s and Kovacs’s studies. It should be emphasized here that electrochemi-

M. Tsen, L. Sun /Analytica

Chimica Acta 307 (1995) 333-340

tally roughened silver surfaces were used in this study whereas silver island films were used in Cotton’s and Kovacs’s studies and silver films on roughened calcium fluoride were used in Murray’s study. SEM images have shown that the size and shape distributions of the roughness features on these silver surfaces are quite different [41-44,461. The difference in surface morphology, although not easy to be quantified, might be another factor that causes the observed difference in the d1,2 values. The EF of SERS can be experimentally determined. Here, we estimate the EF for a SAM by comparing the measured SERS intensity to the calculated intensity of non-enhanced Raman scattering. The intensity (photon s-l mW- ‘) of non-enhanced or normal Raman scattering from a SAM is [51] I Norm =

N,utiafiP,ToTiv,Q~

(1)

where Nsud is the surface coverage (molecules cm-‘); a is the Raman scattering cross section (cm’ sr-l molecule-‘); 0 is the solid angle of collecting optics (sr); P, is the incident photon flux expressed as number of photons per second per mW of laser power (counts s- ’ mW- ‘1; To is the transmission of the collecting optics; TM is the transmission of the monochromator; and Q, is the quantum efficiency of the detector. The enhancement factor EF is just EF=%

339

ing to Eq. 1, the value for INorm is 0.5 counts s-l mW_‘. From Eq. 2 and the measured Zs,,, of 50 counts s-l mW_’ (Fig. lA), the EF at 1.08 nm, which corresponds to the value for the phenyl group in the SAM of 1, is found to be 100. This is a rather low value compared to the most frequently cited value of lo6 for pyridine on Ag [51], even if the effect of the 1.08 nm spacer layer is considered. The cause of this difference is being investigated.

4. Conclusions

The most significant finding in this study is that the SERS enhancement factor decays as a function of molecule-surface distance at a rate about 10 times larger than those reported in two previous studies. This conclusion, however, needs to be verified with more data points in the enhancement factor vs. distance plot. In addition, detailed spectral analysis of the vibrational modes from the Raman label in conjunction with those modes from the methylene groups and structural characterization of the SAMs by other analytical techniques are also important to substantiate the conclusion. Currently, we are actively conducting research in these directions.

I I Norm

(2)

where IsEas is the measured SERS intensity for one monolayer of scatterers. Typical value ’ for Nsurf is 4.7 X 1014 molecules cm-‘. We assume that the normal Raman scattering cross-section for the phenyl pendant group is the same as that of benzene, which is 33 X 10m30 cm’ sr-l molecule- ’ [51]. Other parameters for our Raman system are 0 = 0.087 sr for a f/3 collecting lens; P, = 3.3 X 1015 counts s-l mW_’ at 647.1 nm; To = 0.85, based on reflection loss on the surfaces of the collecting optical elements; TM = 0.40 [61], and Q, = 0.35 [61]. Accord-

1We assume kanethiol SAM (43 X J3)R30° Au(ll1) lattice, (43 X d3)R30° details.

a monolayer coverage equal to that of an n-alon Au(ll1) surface. Since the thiols form a lattice that is commensurate with the underlying the thiol surface coverage is just the inverse of the unit cell area, 0.214 nm*. See Refs. [59,60] for

Acknowledgements Financial support from the University of Minnesota in the form of start-up fund is gratefully acknowledged. LS appreciates helpful discussion with R.P. Van Duyne.

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